TCS new latest placement papers of Aptitude-Analytical Questions answers 2014-2015
Latest TCS Placement Papers Fully Solved 2014-2015 batch
TCS Placement Paper 2014 -2015
1) A power unit is there by the bank of a river of 900 meters. A cable is made from power unit to power a plant opposite to that of the river of 2000mts. The cost of the cable below water is Rs. 5/- per meter and cost of cable on the bank is Rs. 4/- per meter. Then find out the amount to be invested to connect those two stations?
Explanation:
Required length of wire = 2000 mts cost of cable below water = 900 * 5 = 4500 cost of cable on the bank of river= (2000 - 900) * 4 = 4400 Total cost = 4500 + 4400 = 8900.
2) A farmer had 20 hens. All but 2 died. How many hens are still alive?
Explanation:
"All but 2" means 2. So, all but 2 died means that there are only two hens are alive and others were dead. So, the answer is 2.
3) At this series: 7, 10, 8, 11, 9, 12... What number should come next?
Explanation:
This is a simple alternating addition and subtraction series. In the first pattern, 3 are added; in the second, 2 are subtracted.
4) A college has 10 basketball players. A 5-member team and a captain will be selected out of these 10 players. How many different selections can be made?
Explanation:
We can select the 5 member team out of the 10 in 10C5 ways = 252 ways. The captain can be selected from amongst the remaining 5 players in 5 ways. Therefore, total ways the selection of 5 players and a captain can be made = 252*5 = 1260.
5) There are 3 gentlemen in a meeting: Mr. Yellow, Mr. Green and Mr. Brown. They are wearing yellow, green and brown ties. Mr. Yellow says: "Did you notice that the colors of our ties are different from our names?" The person who is wearing the green tie says, "Yes, you are right!" Do you know Brown is wearing what colour of tie?
Explanation:
We know that Mr. Yellow was not wearing a yellow tie because of his statement. He also was not wearing the green tie because the one wearing the green tie agreed to his statement. Therefore, Mr. Yellow was wearing a brown tie. Mr. Green was wearing a yellow tie. And Mr. Brown was wearing the green tie.
6) g[0]=1,g[1]=-1,g[n]=2*g[n-1]-3*g[n-2] then calculate g[4]= ?
Explanation:
From the given function g[n] =2*g [n-1]-3*g [n-2] put values of n as first 2 then 3, then 4 and you will get the answer. G[2] = 2*g[1]-3*g[0]=-2-3 =-5 , G[3]=2*g[2]-3*g[1] =2*(-5)-3*(-1)=-7, G [4] =2*g[3]-3*g[2]=2*(-7)-3*(-5) =1
7) Ten years ago X was half of Y. If the ratio of their present ages is 3:4, what will be the total of their present ages?
Explanation:
Let X's age 10 years ago = x years. Then, Y's age 10 years ago = 2x years. (x + 10)/ (2x + 10) = 3/4 => 4 (x + 10) = 3 (2x + 10) x = 5 Total of their present ages = (x + 10 + 2x + 10) = 3x + 20 = 15 + 20 = 35 years.
8) A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:
Answer: 120KMPH
9) In a circular racetrack of length 100 m, three persons A, B and C start together. A and B start in the same direction at speeds of 10 m/s and 8 m/s respectively. While C runs in the opposite at 15 m/s. When will all the three meet for the first time after the start?
Explanation:
Since the track is a circular track A and B will meet every 50 seconds. i.e. 100 / (10-8). Since it is a multiple of 50 they will be meeting at the starting point every 50 Seconds. If you multiply 15 x 50 you will get 750 and after the second 50 it will be 1500. All of them will meet at the starting point after 100s
10) A class of 100 students. 24 of them are girls and 32 are not. Which base am I using?
Explanation:
Let the base be X. Therefore (X*X + X*0 + 0) = (2*X +4) + (3*X + 2), X * X = 5 * X + 6, X * X - 5 * X -6 = 0, (X- 6) (X+1) = 0 Therefore base is 6.
11) Siva, Sathish, Amar and Praveen are playing cards. Amar is to the right of Sathish, who is to the right of Siva. Who is to the right of Amar?
Answer: Praveen
12) Ferrari is leading car manufacturer. Ferrari S.P.A. is an Italian sports car. It has enjoyed great success. If Mohan's Ferrari is 3 times faster than his old MERCEDES which gave him 35 km/ph if Mohan travelled 490 km in his Ferrari the how much time in hours he took?
Explanation:
Time = (Distance/Speed) = (490/35) Therefore the total time = time/3 = (490/35)/3 = 4.6666 Approximately 4.7
13) My flight takes off at 2 AM from a place at 18N 10E and landed 10 Hrs later at a place with coordinates 36N 70W. What is the local time when my plane landed?
Explanation:
Total change in degrees in east-west direction = 70 + 10 degrees =80 degrees, Time change due to the change in Longitude = 80*4 = 320 minutes = 5 hrs 20 min. According to the person the time would have been = 2 am + 10 hrs = 12 am. But according to the local time the time would be = 12 - 5.20 = 6 .40am
14) A class of 25 students took a science test. 10 students had an average (arithmetic mean) score of 80. The other students had an average score of 60. What is the average score of the whole class?
Explanation:
80 × 10 + 60 × 15 = 800 + 900 = 1700 Total number of students = 25 Average weight = 1700/25 The average score of the whole class is 68.
15) The cost of one pencil, two pens and four erasers is Rs.22 while the cost of five pencils, four pens and two erasers is Rs.32. How much will three pencils, three pens and three erasers cost?
Explanation:
x + 2y + 4z = 22 -------->1 5x + 4y + 2z = 32 ------->2 multiply eqn (2) by 2 and substract from eqn(1) dividing by 3 we get 3x + 2y = 14--------->3 multiplying eqn (1) by 5 and subtracting eqn (2) then divide by 6 we get y + 3z = 13---------->4 Adding eqn (3) and (4) we get 3x + 3y +3z = 27
16) A is 20 percent more efficient than B. If the two persons can complete a piece of work in 60 days. In how many days A working alone can complete the work?
Explanation:
Ratio of time taken by A and B is 1: 1.2 i.e. 5:6 Let the time taken by A be 5x and by B be 6x , 1/5x + 1/ 6x = 1/60 => x =22. Time taken by A = 5 * 22 = 110
17) On a certain island, 5% of the 10000 inhabitants are one-legged and half of the others go barefooted. What is the least number of Shoes needed in the island?
Explanation:
In any case the one legged people will all require one shoe per head. From the remaining, half will go barefooted and therefore they need no shoes. And the rest will need two shoes per head. And this works out at one shoe per person for the others. Therefore for the whole population on the average one shoe per head
18) Look at this series: 14, 28, 20, 40, 32, 64, what number should come next?
Explanation:
This is an alternating multiplication and subtracting series: First, multiply by 2 and then subtract 8.
19) Two pipes A and B can fill a tank in 24 min. and 32 min. respectively. If both the pipes are opened simultaneously, after how much time B should be closed so that the tank is full in 18 minutes?
Explanation:
Let B be closed after x minutes. Then, part filled by (A + B) in x min. + part filled by an in (18 - x) min. = 1. X {1/24 + 1/32] + (18 - x) X 1/24 = 1 or 7x/96 + (18 - x)/24 = 1 7x + 4(18 -x) = 96 or x=8 Hence, B must be closed after 8 minutes
20) At a car park there are 100 vehicles, 60 of which are cars, 30 are vans and the remaining are Lorries. If every vehicle is equally likely to leave, find the probability of car leaving second if either a lorry or van had left first :
Explanation:
Let S be the sample space and A be the event of a van leaving first. n(S) = 100 n (A) = 30 Probability of a van leaving first: P (A) = 30/100 = 3/10 Let B be the event of a lorry leaving first. n (B) = 100 - 60 - 30 = 10 Probability of a lorry leaving first: P (B) = 10/100 = 1/10 If either a lorry or van had left first, then there would be 99 vehicles remaining, 60 of which are cars. Let T be the sample space and C be the event of a car leaving. n (T) = 99 n(C) = 60 Probability of a car leaving after a lorry or van has left: P(C) = 60/99 = 20/33
21) A red house is built from red bricks. A blue house is built from blue bricks. A white house is built from white bricks. Then what is a greenhouse made from?
Explanation:
Glass i.e. Buildings are made of bricks. But a greenhouse is made of glass.
22) If Rs. 782 be divided into three parts, proportional to 1/2: 2/3: 3/4, then the first part is: www.allindiajobs.in
Explanation:
Given ratio = 1/2: 2/3:3/4 = 6: 8: 9 1st part = 782*(6/22) = 213.2727.. Approximately equals to 213 www.allindiaobs.in
23) A man decides to buy a nice horse. He pays $60 for it, and he is very content with the strong animal. After a year, the value of the horse has increased to $70 and he decides to sell the horse . But after a few days later he regrets his decision to sell the beautiful horse, and he buys it again. Unfortunately he has to pay $80 to get it back, so he loses $10. After another year of owing the horse, he finally decides to sell the horse for $90. What is the overall profit the man makes?
Explanation:
The total expenses are $60 + $80 = $140 and the total earnings are $70 +$90 = $160. The overall profit = $160 - $140 = $ 20
24) When I become as old as my father is now, I will be 5 times the age of my son. In addition, my son will be 8 yrs older than What I am now. If the sum of my father's age and my age is equal to100. How old is my son now?
Explanation:
Let us consider the ages of the man, his father & his son is m, f & s respectively. Then according to the problem F=5s............ (i) S + f-m = m+8........ (ii) F + m = 100........... (iii) Putting (i) in (iii) we get 5s+m=100........ (iv) Putting (i) in (ii) we get 6s-2m=8............ (v) Equating (iv) & (v) we get s = 13, f = 65 & m = 36
25) Nine persons went to the hostel for taking their meals, 8 of them spent Rs.12 each on their meals and ninth spend Rs. 8 more then the average expenditure of all nine. What is the total money spent by them?
Explanation:
Let average expenditure be x Then 8*12 +(x+8) = 9x i.e. 104 + x = 9x; 8x = 104 x = 13 Therefore total money spent is 9x = 9*13 =117
26) The average of a list of 6 numbers is 20. If we remove one of the numbers, the average of the remaining numbers is 15. What is the number that was removed?
Explanation:
The removed number could be obtained by difference between the sum of original 6 numbers and the sum of remaining 5 numbers i.e. sum of original 6 numbers - sum of remaining 5 numbers sum of original 6 numbers = 20 × 6 = 120 sum of remaining 5 numbers = 15 × 5 = 75 Number removed = sum of original 6 numbers - sum of remaining 5 numbers 120 - 75 = 45
27) In the word ORGANISATIONAL, if the first and second, third and fourth, fifth and sixth letters are interchanged, what would be the 12th letter from right?
Explanation:
After interchanging R O A G I N S A T I O N A L 14 13 12 11 10 9 8 7 6 5 4 3 2 1
28) What are the number of edges, number of vertices and number of faces of a planar cube among the following options?
We know cube has 6 faces, 12 edges and 8 vertices
29 How many alphabets need to be there in a language if one were to make 1 million distinct 3 digit initials using the alphabets of the language?
Explanation:
Let the number of required alphabets in the language be 'n'. Therefore, using 'n' alphabets we can form n * n * n = n3 distinct 3 digit initials. These n3 different initials = 1 million i.e. n3 = 106 (1 million = 106) => n3 = (102)3 => n = 102 = 100
30) Today's high school students spend too much time thinking about trivial and distracting matters such as fashion. Additionally, they often dress inappropriately on school grounds. Rather than spending time writing another detailed dress policy, we should make school uniforms mandatory. If students were required to wear uniforms, it would increase a sense of community and harmony in our schools and it would instill a sense of discipline in our students. Another positive effect would be that teachers and administrators would no longer have to act as clothing police, freeing them up to focus on more important issues.
This paragraph best supports the statement that
Options:
a) inappropriate clothing leads to failing grades
b) students who wear school uniforms get into better colleges
c) teachers and administrators spend at least 25% of their time enforcing the dress code.
d) school uniforms should be compulsory for high school students
Answer: Explanation:
The support for choice e is in the third sentence "we should make school uniforms mandatory". There is no evidence provided to support choices a, b, and d. And although we know that teachers and administrators are spending some of their time enforcing dress code, the paragraph does not quantify how much of their time is spent that way, so there is no support for choice c.
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TCS Previous years 2012 Technical Hr and Interview Questions
♦ What does static variable mean?
♦ What is a pointer?
♦ What is a structure?
♦ What are the differences between structures and arrays?
♦ In header files whether functions are declared or defined?
♦ What are the differences between malloc() and calloc()?
♦ What are macros? what are its advantages and disadvantages?
♦ Difference between pass by reference and pass by value?
♦ What is static identifier?
♦ Where are the auto variables stored?
♦ Where does global, static, local, register variables, free memory and C Program instructions get stored?
♦ Difference between arrays and linked list?
♦ What are enumerations?
♦ What is a class?
♦ What is an object?
♦ What is the difference between an object and a class?
♦ What is the difference between class and structure?
♦ What is public, protected, private?
♦ What are virtual functions?
♦ What is friend function?
♦ What is a scope resolution operator?
♦ What do you mean by inheritance?
♦ What is abstraction?
♦ What is a data structure?
♦ What does abstract data type means?
♦ Evaluate the following prefix expression " ++ 26 + - 1324" (Similartypes can be asked)
♦ Convert the following infix expression to post fix notation ((a+2)*(b+4)) -1 (Similar types can be asked)
♦ How is it possible to insert different type of elements in stack?
♦ Stack can be described as a pointer. Explain.
♦ Write a Binary Search program
♦ What is the difference between an Abstract class and Interface?
♦ What is user defined exception?
♦ What do you know about the garbage collector?
♦ What is the difference between java and c++?
♦ In an HTML form I have a button which makes us to open another page in 15 seconds. How will you dothat?
♦ What is the difference between process and threads?
♦ What is update method called?
♦ Have you ever used HashTable and Directory?
♦ What are statements in Java?
♦ What is RMI?
♦ Explain about RMI Architecture?
♦ What are Servelets?
♦ What is the use of servlets?
♦ Explain RMI Architecture?
♦ How will you pass values from HTML page to the servlet?
♦ How do you load an image in a Servelet?
♦ What is purpose of applet programming?
♦ How will you communicate between two applets?
♦ What are the basic functions of an operating system?
♦ Explain briefly about, processor, assembler, compiler, loader, linker and the functions executed by them.
♦ What are the difference phases of software development? Explain briefly?
♦ Differentiate between RAM and ROM?
♦ What is DRAM? In which form does it store data?
♦ What is cache memory?
♦ What is hard disk and what is its purpose?
♦ Differentiate between Complier and Interpreter?
♦ What are the different tasks of Lexical analysis?
♦ What are the different functions of Syntax phase, Sheduler?
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TCS Previous years Technical Hr and Aptitude questions with answers
TCS Placement Paper 2012:-
1. Which Is The Smallest No Divides 2880 And Gives A Perfect Square?
A.1
B.2
C.5
D.6
Ans: C
2. Two Bowls Are Taken, One Contains Water And Another Contains Tea Equal Amount . One Spoon Of Water From 1st Is Added To second Bowl And Mixed Well, And A Spoon Of Mixture Is Taken From Second Bowl And Added To The 1st Bowl. Which Statement Will Hold Good For The Above?
{
Thought Process :
Water Bowl Tea Bowl
100 100
90w (+10w= Spoon Volume) 100tea+10water
90w+ (10*10/11)Tea+ 10/11 W 100t- (10*10/11) T
+ 10w- 10/11w
(1st Bowl’s Water Volume Is Equal To 2nd Bowls Tea Volume)
3. Form 8 Digit Numbers From By Using 1, 2,3,4,5 With Repetition Is Allowed And Must Be Divisible By 4?
A.31250
B.97656
C.78125
D.97657
Ans: C
4. Rearrange And Categorize The Word ‘Rapeteka’?
Ans: Bird
5. One Problem On (785^3-235^3)/(785^2+785*235+235^2)
Ans: You Are Free To Carry A Calculator With You But You Should Not Use It To Solve This Kind Of Problem.
Because It Is Simple:
A3-b3 / A2+ab+b2
Ans Is : A-b Here 785-235= 550 That's It.
6. In School There Are Some Bicycles And 4 Wheeler Wagons. One Tuesday There Are 190 Wheels In The Campus. How Many Bicycles Are There?
Ans: 15
Thought Process : B*2+w*4=190 I.E. , B+2w=95 Now See U Can Not Solve 2 Unknowns From 1 Equation, So Just Plot Options Here To Get The Right Answer And Verify If You Are Getting Integers As Values Of B And W.
7. There Are Two Persons Paul And Jay .Paul Lies On Monday, Tuesday, Wednesday And The Remaining Days He Speaks Truth. Jay Lies On Thursday, Friday, Saturday And The Remaining Days He Speaks Truth. Once They Meet Each Other, In Their Conversation Paul Says That Yesterday Is The Day One Among Those I Lie. Jay Also Says That Yesterday I Also Lie. What Is That Day?
A) Sunday.
B) Tuesday.
C) Thursday.
D) Wednesday
[Thought Process: Now This Day Cannot Be Sunday Because In Monday Paul Speaks Truth And Sunday Everyone Tells Truth. So It Must Be Weekdays. Again, Tuesday Can Not Possible Because Monday And Tuesday Paul Speaks Truth. In Case Of Thrust Day, Paul Speaks Lie And Wednesday He Speaks True. And Joy Speaks Truth In Thursday And He Speak Lies In Wednesday. So, Thursday Is The Answer.
8. A Father Has 7 Penny’s With Him And 1 Water Melon Is For 1p, 2chickoos For 1p, 3 Grapes Foe 1p. He Has Three Sons. How Can He Share The Fruits Equally?
Ans: 1 Watermelon, 2chickoos, 1grape
9. (1/2) Of A Number Is 3 Times More Than The (1/6) Of The Same Number?
Ans: 9
10. There Are Two Pipes A And B. If A Filled 10 Liters In Hour B Can Fills 20 Liters In Same Time. Likewise B Can Fill 10, 20, 40, 80,160…. If B Filled In (1/16) Th Of A Tank In 3 Hours, How Much Time Will It Take To Fill Completely?
Ans: 7 Hours
11.A certain pump can drain a full 375-gallon tank in 15 minutes. At this rate, how many more minutes would it take to drain a full 600-gallon tank?
(A) 9
(B) 15
(C) 18
(D) 24
(E) 25
12. If n is an even integer, which of the following must be an odd integer?
(A) 3n-2
(B) 3(n+1)
(C)n-2
(D)n/3
(E)n^2
13. Cindy has a collection of 80 records. If 40 percent of her records are jazz records, and the rest are blues records, how many blues records does she have?
(A) 32
(B) 40
(C) 42
(D) 48
(E) 50
14. Express 2,750,389 in scientific notation.
(A) 27.50389 x 105
(B) 275.0389 x 103
(C) 27.50389 x 106
(D) 0.2750389 x 107
(E) 2.750389 x 106
15. A rectangle and a triangle have equal areas. The length of the rectangle is 12 inches, and its width is 8 inches. If the base of the triangle is 32 inches, what is the length, in inches, of the altitude drawn to the base?
(A) 6
(B) 8
(C) 9
(D) 12
(E) 16
16. If the area of a triangle is 24 and its base is 6, what is the length of the altitude to that base?
(A)3
(B)6
(C)8
(D)10
(E)unknown
17.Lenny's average score after 3 tests is 88. What score on the 4th test would bring Lenny's average up to exactly 90?
(A)92
(B)93
(C)94
(D)95
(E)96
18. If an integer is divisible by 6 and by 9, then the integer must be divisible by which of the following?
A. 12
B. 18
C. 24
D. 36
E. 54
19.If Jeff and Jimmy have less than 22 dollars between them, and Jeff has 8 dollars, which of the following could be the number of dollars that Jimmy has?
I.12
II. 14
III. 16
A. I only
B. III only
C. I & III.
D. I & II
E. Neither I, II, nor III are correct
20.Stephanie drove at an average rate of 50 miles per hour for two hours and then increased her average rate by 50% for the t 3 hours. Her average rate of speed for the 5 hours was t miles per hour. What is the value of t?
A. 55 mph
B. 60 mph
C. 65 mph
D. 70 mph
E. 75 mph
21. How many complete tanks of water, each with a capacity of 3 cubic meters, are needed to fill an empty cylindrical tank whose height is 3 meters and whose base has a radius of 2 meters?
A) 12
B) 13
C) 14
D) 15
E) 16
22. Any serious policy discussion about acceptable levels of risk in connection with explosions is not well served if the participants fail to use the word “explosion” and use the phrase “energetic disassembly” instead. In fact, the word“explosion” elicits desirable reactions, such as a heightened level of attention, whereas the substitute phrase does not. Therefore, of the two terms, “explosion” is the one that should be used throughout discussions of this sort. Which of the following is an assumption on which the argument above depends?
(A) In the kind of discussion at issue, the advantages of desirable reactions to the term “explosion” outweigh the drawbacks,if any, arising from undesirable reactions to that term.
(B) The phrase “energetic disassembly” has not so far been used as a substitute for the word “explosion” in the kind of discussion at issue.
(C) In any serious policy discussion, what is said by the participants is more important than how it is put into words.
(D) The only reason that people would have for using “energetic disassembly” in place of “explosion” is to render impossible any serious policy discussionconcerning explosions.
(E) The phrase “energetic disassembly” is not necessarily out of place in describing a controlled rather than an accidental
explosion
23. A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one-gallon or half- gallon cans, what is the least amount of paint, in gallons, that must be purchased in order to measure out the portions needed for the mixture?
(A) 2
(B) 2 ½
(C) 3
(D) 3 ½
(E) 4
24. To buy a computer system, a customer can choose one of 4 monitors, one of 2 keyboards, one of 4 computers and one of 3 printers. Determine the number of possible systems that a customer can choose from.
(A) 96
(B)98
(C)98.5
(D) 94
(E)100
25. A student can select one of 6 different mathematics books, one of 3 different chemistry books and one of 4different science books. In how any different ways can a student select a book of mathematics, a book of chemistry and a book of science?
A) 14
(B)12
(C)72
(D) 74
(E)76
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TCS Placement papers solved questions with detailed explnations
1. If 3y + x > 2 and x + 2y≤3, What can be said about the value of y?
A. y = -1
B. y >-1
C. y <-1
D. y = 1
Answer: B
Multiply the second equation with -1 then it will become - x - 2y≥ - 3. Add the equations. You will get y > -1.
2. If the price of an item is decreased by 10% and then increased by 10%, the net effect on the price of the item is
A. A decrease of 99%
B. No change
C. A decrease of 1%
D. An increase of 1%
Answer: C
If a certain number is increased by x% then decreased by x% or vice versa, the net change is always decrease.
This change is given by a simple formula −(x10)2= −(1010)2= −1%. Negitive sign indicates decrease.
3. If m is an odd integer and n an even integer, which of the following is definitely odd?
A. (2m+n)(m-n)
B. (m+n2)+(m−n2)
C. m2+mn+n2
D. m +n
Answer: C and D (Original Answer given as D)
You just remember the following odd ± odd = even; even ± even = even; even ± odd = odd
Also odd x odd = odd; even x even = even; even x odd = even.
4. What is the sum of all even integers between 99 and 301?
A. 40000
B. 20000
C. 40400
D. 20200
Answer: D
The first even number after 99 is 100 and last even number below 301 is 300. We have to find the sum of even numbers from 100 to 300. i.e., 100 + 102 + 104 + ............... 300.
Take 2 Common. 2 x ( 50 + 51 + ...........150)
There are total 101 terms in this series. So formula for the sum of n terms when first term and last term is known is n2(a+l)
So 50 + 51 + ...........150 = 1012(50+150)
So 2 x 1012(50+150) = 20200
5. There are 20 balls which are red, blue or green. If 7 balls are green and the sum of red balls and green balls is less than 13, at most how many red balls are there?
A. 4
B. 5
C. 6
D. 7
Answer: B
Given R + B + G = 17; G = 7; and R + G < 13. Substituting G = 7 in the last equation, We get R < 6. So maximum value of R = 6
6. If n is the sum of two consecutive odd integers and less than 100, what is greatest possibility of n?
A. 98
B. 94
C. 96
D. 99
Answer : C
We take two odd numbers as (2n + 1) and (2n - 1).
Their sum should be less than 100. So (2n + 1) + (2n - 1) < 100 ⇒ 4n < 100.
The largest 4 multiple which is less than 100 is 96
7. x2 < 1/100, and x < 0 what is the highest range in which x can lie?
A. -1/10 < x < 0
B. -1 < x < 0
C. -1/10 < x < 1/10
D. -1/10 < x
Answer: A
Remember:
(x - a)(x - b) < 0 then value of x lies in between a and b.
(x - a)(x - b) > 0 then value of x does not lie inbetween a and b. or ( −∞, a) and (b, −∞) if a < b
x2 < 1/100 ⇒
(x2−1/100)<0⇒(x2−(1/10)2)<0⇒(x−1/10)(x+1/10)<0
So x should lie in between - 1/10 and 1/10. But it was given that x is -ve. So x lies in -1/10 to 0
8. There are 4 boxes colored red, yellow, green and blue. If 2 boxes are selected, how many combinations are there for at least one green box or one red box to be selected?
A. 1
B . 6
C. 9
D. 5
Answer: 5
Total ways of selecting two boxes out of 4 is 4C2 = 6. Now, the number of ways of selecting two boxes where none of the green or red box included is only 1 way. (we select yellow and blue in only one way). If we substract this number from total ways we get 5 ways.
9. All faces of a cube with an eight - meter edge are painted red. If the cube is cut into smaller cubes with a two - meter edge, how many of the two meter cubes have paint on exactly one face?
A. 24
B. 36
C. 60
D. 48
Answer : A
If there are n cubes lie on an edge, then total number of cubes with one side painting is given by 6×(n−2)2. Here side of the bigger cube is 8, and small cube is 2. So there are 4 cubes lie on an edge. Hence answer = 24
10. Two cyclists begin training on an oval racecourse at the same time. The professional cyclist completes each lap in 4 minutes; the novice takes 6 minutes to complete each lap. How many minutes after the start will both cyclists pass at exactly the same spot where they began to cycle?
A. 10
B. 8
C. 14
D. 12
Answer: D
The faster cyclyst comes to the starting point for every 4 min so his times are 4, 8, 12, ......... The slower cyclist comes to the starting point for every 6 min so his times are 6, 12, 18, ......... So both comes at the end of the 12th min.
11. M, N, O and P are all different individuals; M is the daughter of N; N is the son of O; O is the father of P; Among the following statements, which one is true?
A. M is the daughter of P
B. If B is the daughter of N, then M and B are sisters
C. If C is the granddaughter of O, then C and M are sisters
D. P and N are bothers.
Answer: B
From the diagram it is clear that If B is the daughter of N, then M and B are sisters. Rectangle indicates Male, and Oval indicates Female.
12. In the adjoining diagram, ABCD and EFGH are squres of side 1 unit such that they intersect in a square of diagonal length (CE) = 1/2. The total area covered by the squares is
A. Cannot be found from the information
B. 1 1/2
C. 1 7/8
D. None of these
Answer: C
Let CG = x then using pythogerous theorem CG2+GE2=CE2
⇒ x2+x2=(1/2)2⇒2x2=1/4⇒x2=1/8
Total area covered by two bigger squares = ABCD + EFGE - Area of small square = 2 - 1/8 = 15/8
13. There are 10 stepping stones numbered 1 to 10 as shown at the side. A fly jumps from the first stone as follows; Every minute it jumps to the 4th stone from where it started - that is from 1st it would go to 5th and from 5th it would go to 9th and from 9th it would go to 3rd etc. Where would the fly be at the 60th minute if it starts at 1?
A. 1
B. 5
C. 4
D. 9
Answer : A
Assume these steps are in circular fashion.
Then the fly jumps are denoted in the diagram. It is clear that fly came to the 1st position after 5th minute. So again it will be at 1st position after 10th 15th .....60th. min.
So the fly will be at 1st stone after 60th min.
14. What is the remainder when 617+1176 is divided by 7?
A. 1
B. 6
C. 0
D. 3
Answer: C
617 = (7−1)17 =
17C0.717−17C1.716.11.....+17C16.71.116−17C17.117
If we divide this expansion except the last term each term gives a remainder 0. Last term gives a remainder of - 1.
Now From Fermat little theorem, [ap−1p]Rem=1
So [1767]Rem=1
Adding these two remainders we get the final remainder = 0
15. In base 7, a number is written only using the digits 0, 1, 2, .....6. The number 135 in base 7 is 1 x 72 + 3 x 7 + 5 = 75 in base 10. What is the sum of the base 7 numbers 1234 and 6543 in base 7.
A. 11101
B. 11110
C. 10111
D. 11011
Answer: B
In base 7 there is no 7. So to write 7 we use 10. for 8 we use 11...... for 13 we use 16, for 14 we use 20 and so on.
So from the column d, 4 + 3 = 7 = 10, we write 0 and 1 carried over. now 1 + 3 + 4 = 8 = 11, then we write 1 and 1 carried over. again 1 + 2 + 5 = 8 = 11 and so on
16. The sequence {An} is defined by A1 = 2 and An+1=An+2n what is the value of A100
A. 9902
B. 9900
C. 10100
D. 9904
Answer: A
We know that A1 = 2 so A2=A1+1=A1+2(1)=4
A3=A2+1=A2+2(2)=8
A4=A3+1=A3+2(3)=14
So the first few terms are 2, 4, 8, 14, 22, ......
The differences of the above terms are 2, 4, 6, 8, 10...
and the differences of differences are 2, 2, 2, 2. all are equal. so this series represents a quadratic equation.
Assume An = an2+bn+c
Now A1 = a + b + c = 2
A2 = 4a + 2b + c = 4
A3 = 9a + 3b + c = 8
Solving above equations we get a = 1, b = - 1 and C = 2
So substituting in An = n2+bn+c = n2−n+2
Substitute 100 in the above equation we get 9902.
17.Find the number of rectangles from the adjoining figure (A square is also considered a rectangle)
A. 864
B. 3276
C. 1638
D. None
Answer: C
To form a rectangle we need two horizontal lines and two vertical lines. Here there are 13 vertical lines and 7 horizontal lines. The number of ways of selecting 2 lines from 13 vertical lines is 13C2 and the number of ways of selecting 2 lines from 7 horizontals is 7C2. So total rectangles = 7C2x13C2
18. A, B, C and D go for a picnic. When A stands on a weighing machine, B also climbs on, and the weight shown was 132 kg. When B stands, C also climbs on, and the machine shows 130 kg. Similarly the weight of C and D is found as 102 kg and that of B and D is 116 kg. What is D's weight
A. 58kg
B. 78 kg
C. 44 kg
D. None
Answer : C
Given A + B = 132; B + C = 130; C + D = 102, B + D = 116
Eliminate B from 2nd and 4th equation and solving this equation and 3rd we get D value as 44.
19. Roy is now 4 years older than Erik and half of that amount older than Iris. If in 2 years, roy will be twice as old as Erik, then in 2 years what would be Roy's age multiplied by Iris's age?
A. 28
B. 48
C. 50
D. 52
Answer: 48
20. X, Y, X and W are integers. The expression X - Y - Z is even and the expression Y - Z - W is odd. If X is even what must be true?
A. W must be odd
B. Y - Z must be odd
C. W must be odd
D. Z must be odd
Answer: A or C (But go for C)
21. Mr and Mrs Smith have invited 9 of their friends and their spouses for a party at the Waikiki Beach resort. They stand for a group photograph. If Mr Smith never stands next to Mrs Smith (as he says they are always together otherwise). How many ways the group can be arranged in a row for the photograph?
A. 20!
B. 19! + 18!
C. 18 x 19!
D. 2 x 19!
Answer: C
22. In a rectanglular coordinate system, what is the area of a triangle whose vertices whose vertices have the coordinates (4,0), (6, 3) adn (6 , -3)
A. 6
B. 7
C. 7.5
D. 6.5
Answer: A
23. A drawer holds 4 red hats and 4 blue hats. What is the probability of getting exactly three red hats or exactly three blue hats when taking out 4 hats randomly out of the drawer and immediately returning every hat to the drawer before taking out the next?
A. 1/2
B. 1/8
C. 1/4
D. 3/8
Answer: B
24. In how many ways can we distribute 10 identical looking pencils to 4 students so that each student gets at least one pencil?
A. 5040
B. 210
C. 84
D. None of these
Answer: C
25. The prime factorization of intezer N is A x A x B x C, where A, B and C are all distinct prine intezers. How many factors does N have?
A. 12
B. 24
C. 4
D. 6
Answer: A
26. Tim and Elan are 90 km from each other.they start to move each other simultanously tim at speed 10 and elan 5 kmph. If every hour they double their speed what is the distance that Tim will pass until he meet Elan
A. 45
B. 60
C. 20
D. 80
Answer: B
27. A father purchases dress for his three daughter. The dresses are of same color but of different size .the dress is kept in dark room .What is the probability that all the three will not choose their own dress.
A. 2/3
B. 1/3
C. 1/6
D. 1/9
Answer: B
28. N is an integer and N>2, at most how many integers among N + 2, N + 3, N + 4, N + 5, N + 6, and N + 7 are prime integers?
A. 1
B. 3
C. 2
D. 4
Answer: C
29. A turtle is crossing a field. What is the total distance (in meters) passed by turtle? Consider the following two statements
(X) The average speed of the turtle is 2 meters per minute
(Y) Had the turtle walked 1 meter per minute faster than his average speed it would have finished 40 minutes earlier
A. Statement X alone is enough to get the answer
B. Both statements X and Y are needed to get the answer
C. Statement Y alone is enough to get the answer
D. Data inadequate
Answer: B
30. Given the following information, who is youngest?
C is younger than A; A is talled than B
C is older than B; C is younger than D
B is taller than C; A is older than D
A. D
B. B
C. C
D. A
Answer: B
31. If P(x) = ax4+bx3+cx2+dx+e has roots at x = 1, 2, 3, 4 and P(0) = 48, what is P(5)
A. 48
B. 24
C. 0
D. 50
Answer: A
32. If west is called as North-East,North-East as East, East is called as South-West,South-West is called as North, North is called as North-west,North-West as South and Soouth is called as South-East, then pole star in which direction?
a)North-East
b)North-West
c)North
d)South-West
Ans b)
Since Pole Star is always in North, and in code North is said North-West, Hence Pole Star will be in North_West
32 Re-arrange and categorize the word IARLGOTLA
a)Mobile Phone
b)animal
c) Vehicle
d)Furniture
33 A car left Canterbury at 7.12 am and arrived in Birmingham, 180 miles distant at 10.57 am. What was its average speed in miles per hour?
a)42
b)44
c)46
d)48
Time taken = 3 hours 45m = 3.75 hours (15/4 hours if you prefer fractions).
Speed = distance / time taken = 180 / 3.75 = 48 mph
34 A sheet of paper has statements numbered from 1 to 40. For each value of n from 1 to 40, statement n says "At least n of the statements on this sheet are true." Which statements are true and which are false?
a)The odd numbered statements are true and the even numbered are false
b)The even numbered statements are true and the odd numbered are false.
c)The first 13 statements are true and the rest are false.
d)The first 26 statements are false and the rest are true.
35Tom lies on Mondays, Tuesdays and Wednesdays, and tells the truth on the other days of the week. Jerry, on the other hand, lies on Thursdays, Fridays and Saturdays, but tells the truth on the other days of the week. Now they make the following statements to Mikie – Tom: Yesterday was one of those days when I lie. Jerry: Yesterday was one of those days when I lie too. What day is it?
a)Thursday -Answer
b)Tuesday
c)Sunday
d)Monday
_______________________________________________________________________________
TCS Aptitude-reasoning placement papers
1) The water from one outlet, flowing at a constant rate, can fill the swimming pool in 9 hours. The water from second outlet, flowing at a constant rate can fill up the same pool in approximately in 5 hours. If both the outlets are used at the same time, approximately what is the number of hours required to fill the pool?
ans: (1/A) + (1/B) = 1/T
So when you solved, and got 14/45, that was equal to 1/T. To find T, you need to take the reciprocal; T = 45/14,
(3.21)
u
2) If 75 % of a class answered the first question on a certain test correctly, 55 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percentage answered both correctly?
ans: n(a ^ b) =n(a)+n(b)-n(a v b)
= 0.75+0.55-0.8
= 0.5
(50%)
3) A student's average ( arithmetic mean) test score on 4 tests is 78. What must be the students score on a 5th test for the students average score on the 5th test to be 80?
ans: 4 tests sum=78*4=312
5 tests sum=80*5=400
then 5th test score=400-312=88
(88)
4) Rural households have more purchasing power than do urban households at the same income level, since some of the income urban and suburban households use for food and shelter can be used by the rural households for other needs. Which of the following inferences is best supported by the statement made above?
(A) The average rural household includes more people than does the average urban or suburban household.
(B) Rural households have lower food and housing costs than do either urban or suburban households.
(C) Suburban households generally have more purchasing power than do either rural or urban households.
(D) The median income of urban and suburban households is generally higher than that of rural households.
(E) All three types of households spend more of their income on housing than on all other purchases combined.
ans: B
5) Jose is a student of horticulture in the University of Hose. In a horticultural experiment in his final year, 200 seeds were planted in plot I and 300 were planted in plot II. If 57% of the seeds in plot I germinated and 42% of the seeds in plot II germinated, what percent of the total number of planted seeds germinated?
ans: 200 * 57 % = 114 and 300* 42% = 126.
Total = 240 out of 500.
(48%).
6) A closed cylindrical tank contains 36 pie cubic feet of water and its filled to half its capacity. When the tank is placed upright on its circular base on level ground, the height of water in the tank is 4 feet. When the tank is placed on its side on level ground, what is the height, in feet, of the surface of the water above the ground?
ans: What given Volume = 36
Height = 4ft
Volume = Pi* r2 * h
36 = Pi*r2 * 4
r2 =9
r = 3
So the radius is 3 which means the diameter is 6.
7) The present ratio of students to teachers at a certain school is 30 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of the teachers would then be 25 to 1 What is the present number of teachers?
ans: 30/1 = s/t Current student to teacher ratio
s+50/t+5 = 25/1 Future student to teacher ratio
solving the first equation first equation for s gives s = 30t.
Substitute this value of s into the second equation, and solve for t.
s+50/t+5 = 25/1
30t + 50 = 25t + 125 multiply both sides by t+5
5t = 75 simplify by subtraction
t = 15
(15)
8) College T has 1000 students. Of the 200 students majoring in one or more of the sciences,130 are majoring in Chemistry and 150 are majoring in Biology. If at least 30 of the students are not majoring in either Chemistry or Biology, then the number of students majoring in both Chemistry and Biology could be any number from
ans: total=200
neither>=30
chemistry=130
bio=130
maximum common=minimum of the two=130
if neither=30
then common=150+130+30-200=110
range is 110-130
9) Kelly and Chris are moving into a new city. Both of them love books and thus packed several boxes with books. If Chris packed 60% of the total number of boxes, what was the ratio of the number of boxes Kelly packed to the number of boxes Chris packed?
ans: 100-60=40
40:60=2:3
10) A drug that is highly effective in treating many types of infection can, at present, be obtained only from the bark of the ibora, a tree that is quite rare in the wild. It takes the bark of 5,000 trees to make one kilogram of the drug. It follows, therefore, that continued production of the drug must inevitably lead to the ibora's extinction. Which of the following, if true, most seriously weakens the argument above?
ans: The ibora can be propagated from cuttings and grown under cultivation.
11) Machine A produces bolts at a uniform rate of 120 every 40 second, and Machine B produces bolts at a uniform rate of 100 every 20 seconds. If the two machines run simultaneously, how many seconds will it take for them to produce a total of 200 bolts?
ans: Machine A produces 120/40 = 3 bolts in 1 seconds and machine B produces 100/20 = 5 bolts in one second.
Hence, both of them will produce 8 bolts per second.
Hence, they wil take 200/8 = 25 seconds to produce 200 bolts.
(25)
12) Wood smoke contains dangerous toxins that cause changes in human cells. Because wood smoke presents such a high health risk, legislation is needed to regulate the use of open-air fires and wood burning stoves
ans: In valleys where wood is used as the primary heating fuel, the concentration of smoke results in poor air quality.
13) Analysing the good returns that Halocircle Insurance Pvt Ltd was giving, Ratika bought a 1-year, Rs 10,000 certificate of deposit that paid interest at an annual rate of 8% compounded semi-annually.What was the total amount of interest paid on this certificate at maturity?
ans: @8%, for half year you get 400/- 10000x 8/100x1/2=400
for the next year there will be interest on your investment of 10000 and also on your accrue interest of Rs.400/-
that means another 400/+ interest on 400/- @8% for half year.=400+ (400x8/100x1/2)
400+400+16=816
14) Juan is a gold medalist in athletics. In the month of May, if Juan takes 11 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?
ans: 11x/y
15) A certain company retirement plan has a rule of 70 provision that allows an employee to retire when the employee's age plus years of employment with the company total at least 70. In what year could a female employee hired in 1986 on her 32nd birthday first be eligible to retire under this provision?
ans: The female employee must gain at least 70 points.
Now she has 32 and every year gives her two more points: one for age and one for additional year of employment, so 32 + 2 * (number of years) = 70
(Number of years) = 19
So, 1986 + 19 = 2005
16) Homeowners aged 40 to 50 are more likely to purchase ice cream and are more likely to purchase it in larger amounts than are members of any other demographic group. The popular belief that teenagers eat more ice-cream than adults must, therefore, be false. The argument is flawed because the author _____
ans: fails to distinguish between purchasing and consuming
17) Andalusia has been promoting the importance of health maintenance. From January 1,1991 to January 1,1993, the number of people enrolled in health maintenance organizations increased by 15 percent. The enrollment on January 1,1993 was 45 million. How many million people(to the nearest million) was enrolled in health maintenance organizations on January 1,1991?
ans: let there are 'x' population at jan1,1991
15% of x = 15/100*(x)
(x)+[15/100*(x)]=45 /* as there is 15% increase from 1991 to 1993*/
x=39.13
18) What is the lowest possible integer that is divisible by each of the integers 1 through 7, inclusive?
ans: L.C.M of(1,2,3,4,5,6,7)=2*2*3*5*7=420
19) If the area of a square region having sides of length 6 cms is equal to the area of a rectangular region having width 2.5 cms, then the length of the rectangle, in cms, is
ans: Area of a Square
s x s
6 x 6 = 36
Area of a Rectangle
lw
?(2.5)
=36 as it is equal to the area of a square
36/2.5 = 14.4 cm
20) A tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume. If 2500 gallons of water evaporate from the tank, the remaining solution will be approximately what percentage of sodium chloride?
ans: Original =10,000 ----> sodium chloride = 5% ie 500
New = 10,000-2,500 = 7500.
New % = (500/7500) * 100
= 6.67%
21) After loading a dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day of the crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by two crews did the day crew load?
ans: Number of workers
Day shift: 5 workers (this is an easy number to find 4/5 of)
Night shift: 4 workers (4/5 of 5 = 4)
Boxes loaded per worker
Day shift: 4 boxes per worker
Night shift: 3 boxes per worker (3/4 of 4 = 3)
Total boxes loaded
Day shift: 5 workers times 4 boxes per worker = 20 boxes
Night shift: 4 workers times 3 boxes per worker = 12 boxes
Combined total boxes for both shifts = 20 + 12 = 32
Of the 32 boxes, the day shift loaded 20 of them.
20/32 = 5/8
22) A bakery opened yesterday with its daily supply of 40 dozen rolls. Half of the rolls were sold by noon and 80 % of the remaining rolls were sold between noon and closing time. How many dozen rolls had not been sold when the bakery closed yesterday?
ans: 4 rolls were not sold.............half of them were sold by noon.......so 20 rolls remain....and then 20% were not sold,, so 20% of the 20 rolls is 4 then it is the answer
23) If n=4p, where p is a prime number greater than 2, how many different positive even divisors does n have including n?
ans: 4
24) A dealer originally bought 100 identical batteries at a total cost of q rupees. If each battery was sold at 50 percent above the original cost per battery, then, in terms of q, for how many rupees was each battery sold?
ans: bought for q/100 dollars per battery
each battery sold with profit 50% is
q/100 + q/100*50/100
=q/100+q/200
=3q/200
25) The price of lunch for 15 people was 207 pounds, including a 15 percent gratuity of service. What was the average price per person, EXCLUDING the gratuity?
ans: Let the net price excluding the gratuity of service = x pounds
Then, total price including 15% gratuity of service = x + 0.15 x = 1.15 x pounds
So, 1.15 x = 207 pounds
==> x = 207 / 1.15 = 180 pounds
Net price of lunch for each person = 180 / 15 = 12 pounds
26) Of the following, which is the closest approximation of (50.2*0.49)/199.8 ?
ans: For approximation
(50.2*0.49)/199.8 can be taken as
50*0.5/200 = 25/200 = 1/8 = 0.125
27) How many prime numbers between 1 and 100 are factors of 7150?
ans: 7,150 = 2 * 5 * 5 * 11 * 13
so there are 4 distinct prime numbers that are below 100
28) Guitar Strings often go dead - become less responsive and bright in tone - after a few weeks of intense use. A researcher whose son is a classical guitarist hypothesized that dirt and oil, rather than changes in the material properties of the string, were responsible. Which of the following investigations is most likely to yield significant information that would help evaluate the researcher's hypothesis?
ans: Determining whether smearing various substances on new guitar strings causes them to go dead
29) Red blood cells in which the malarial-fever parasite resides are eliminated from a person's body after 120 days. Because the parasite cannot travel to a new generation of red blood cells, any fever that develops in a person more than 120 days after that person has moved to a malaria free region is not due to malarial parasite. Which of the following, if true, most seriously weakens the conclusion above?
ans: In some cases, the parasite that causes malarial fever travels to cells of the spleen, which are less frequently eliminated from a person’s body than are red blood cells.
30) Among a group of 2500 people, 35 percent invest in municipal bonds, 18 percent invest in oil stocks, and 7 percent invest in both municipal bonds and oil stocks. If 1 person is to be randomly selected from 2500 people, what is the probability that the person selected will be one who invests in municipal bonds but not in oil stocks
ans: 7/25
31) When a polygraph test is judged inconclusive, this is no reflection on the examinee. Rather, such a judgment means that the test has failed to show whether the examinee was truthful or untruthful. Nevertheless, employers will sometime refuse to hire a job applicant because of an inconclusive polygraph test result. Which of the following conclusions can most properly be drawn from the information above?
ans: An inconclusive polygraph test result is sometimes unfairly held against the examinee
32) Country Club has an indoor swimming club. Thirty percent of the members of a swim club have passed the lifesaving test. Among the members who have not passed the test, 12 have taken the preparatory course and 30 have not taken the course. How many members are there in the swim club?
ans: Suppose there are x members, non pass members arre 7x/10 which are equal to 12 + 30 = 42
7x/10 = 42
x = 60
There are 60 members in that club
33) A necklace is made by stringing N individual beads together in the repeating pattern red bead, green bead, white bead, blue bead and yellow bead. If the necklace begins with a red bead and ends with a white bead, then N could be:
ans: R G W B Y is the bead pattern and it repeats.
Bead want to end with White.
So, the 3rd, 8th, 13th, 18th... beads will be W.
this can be expressed as 5n+3,where n is an integer.(counting no of white bead)
Test each of the answer choices to determine which is multiple of 5 plus a value of 3.Of the options ,only 68=5(13)+3 can be written in the form 5n+3.
So,the answer is 68.
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33 A dog taken four leaps for every five leaps of hare but three leaps of the dog is equal to four leaps of the hare. Compare speed?
Let the distance covered by dog in 1 leap is x and hare covered 1 leap is y.
then, 3x = 4y
=> x =(4/3) y
=> 4x =(16/3) y
Then, The ratio of speeds of dog and hare = Ratio of distances covered by them in the same time
= 4x : 5y
= (16/3)y : 5y
=(16/3) : 5
= 16:15 Ans...=16:15
34 There are two boxes,one containing 39 red balls & the other containing 26 green balls.you are allowed to move the balls b/w the boxes so that when you choose a box random & a ball at random from the chosen box,the probability of getting a red ball is maximized.this maximum probability is
a)60 b)50 c)80 d)30
the probability of getting a red ball should be maximized so we will keep 1 red ball in the first box and transfer remaining 38 red balls to other box which has green. The reason for doing this only this combination will make the probability of getting red ball is maximum (i.e) 1.
In the question its mentioned that first we have to choose a box at random.
So 2 boxes are there, probability of selecting a bag is 1/2
Probability of getting red ball from first box is 1
Probability of getting green ball from second box is 38/64
So (1/2)*1 for first box and (1/2)*(38/64) for box 2
answer is (1/2)*1 + ((1/2)*(38/64) which is approximately 0.8
Next number in the given series 1, 7, 8, 49, 50, 56, 57, 343
344 because
1*7=7
7+1-8
7*7=49
49+1=50
8*7=56
56+1=57
49*7=343
343+1=344
ans= 344
q.1 in how many ways can 3 postcards can be posted in 5 postboxes?
q.2.in how many ways can 5 postboxes hold 3 post cards?
q.1 in how many ways can 3 postcards can be posted in 5 postboxes?
first post card can be posted in any of the 5 post boxes =5c1 ways
second post card can be posted in any of the 5 post boxes =5c1 ways
third post card can be posted in any of the 5 post boxes =5c1 ways
number of ways=5c1*5c1*5c1=125=5^3
q.2.in how many ways can 5 postboxes hold 3 post cards?
first post box can hold 3 post cards in 3c1 ways
second post box can hold 3 post cards in 3c1 ways
third post box can hold 3 post cards in 3c1 ways
fourth post box can hold 3 post cards in 3c1 ways
fifth post box can hold 3 post cards in 3c1 ways
so number of ways =3c1*3c1*3c1*3c1*3c1=3^5
35 A number has exactly 3 prime factors, 125 factors of this number are perfect squares and 27 factors of this number are perfect cubes. overall how many factors does the number have???
Answer for this question is 729
The explanation goes like this
Let a,b,c be three prime no.
since the no. of perfect square as a factor is 125
which can only be if every prime no. has power in the multiple of 2 including zeros(bcoz any no. to the power of zero is a perfect square)
so power must be 0,2,4,6,8
thereby 5*5*5=125
Since no. of cube as a factor is 27
therefore power in the prime no. will be in the multiple of 3
so power are 0,3,6
hence the no. N=a^8*b^8*c^8
hence total no. of factor is (8+1)(8+1)(8+1)=729
there r three buckets..of 8,5 n 3 litres...out of which only 8 ltr bucket is fully filled...u hv to fill exact 4-4 ltr liquid in 8 and 5 litre bucket by using only these buckets in minimm num of steps......
8ltr 5ltr 3ltr
initially 8 0 0
step1 3 5 0
step2 3 2 3
step3 6 2 0
step4 6 0 2
step5 1 5 2
step 6 1 4 3
step 7 4 4 0
total 7 steps
36 The climb from foot to top of a hill 800 meters, Jack can climb at 16 meters per minute and rests for two minutes or 20meters per 2 minutes and rest for one minute. Paul can climb at 10 meters per one minute and rest for one minute or16 meters per minute and rest for 2 minutes. If take has to reach the top in exactly two hours. What is the maximum number of rests that he can take?
a) 41 b) 42 c) 40 d) 43
total=800m
16m per min means for 1m=800/16 =50min to climb
10m per min means for 1m=800/10=80min to climb for paul .....the total time is 2hours==120min....so,time taken for rest by paul is 120-80=40min
length of minute hand is 5.4 cm, area covered by this in 10 min is ?
a)50.97 b)57.23 c)55.45 d)59.14
t will be (3.14*5.4*5.4)*10/60 = 15.26 cm2.
37 Raj tossed 3 dices and there results are noted down then what is the probability that raj gets 10?
a) 1/72 b) 1/9 c) 25/216 d)1/8
ossible event.......(1,3,6)(1,4,5)(1,5,4)(1,6,3)(2,2,6)(2,3,5)(2,4,4)(2,5,3)(2,6,2)(3,1,6)(3,2,5)(3,3,4)(3,4,3)(3,5,2)(3,6,1)(4,1,5)(4,2,4)(4,3,3)(4,4,2)(4,5,1)(5,1,4)(5,2,3)(5,3,2)(5,4,1)(6,1,3)(6,2,2)(6,3,1)
total 27 possible event
so probability = 27/216 i.e 1/8
answer-------d(1/8)
Probability of a sum of 3: 1/216 = 0.5%
Probability of a sum of 4: 3/216 = 1.4%
Probability of a sum of 5: 6/216 = 2.8%
Probability of a sum of 6: 10/216 = 4.6%
Probability of a sum of 7: 15/216 = 7.0%
Probability of a sum of 8: 21/216 = 9.7%
Probability of a sum of 9: 25/216 = 11.6%
Probability of a sum of 10: 27/216 = 12.5%
Probability of a sum of 11: 27/216 = 12.5%
Probability of a sum of 12: 25/216 = 11.6%
Probability of a sum of 13: 21/216 = 9.7%
Probability of a sum of 14: 15/216 = 7.0%
Probability of a sum of 15: 10/216 = 4.6%
Probability of a sum of 16: 6/216 = 2.8%
Probability of a sum of 17: 3/216 = 1.4%
Probability of a sum of 18: 1/216 = 0.5%
38 Apple costs L rupees per kilogram for first 30kgs and Q rupees per kilogram for each additional kilogram. If the price of 33 kilograms is 11.67and for 36kgs of Apples is 12.48 then the cost of first 10 kegs of Apples is
a) 3.50 b) 10.53 c) 1.17 d)2.8
30L+3Q=11.67
30L+6Q=12.48
------------
3Q=.81 Q= .27
from that L=0.362 cost of 10 kg apple is 10*.362=3.6
The letters in the word ABUSER are permuted in all possible ways and arranged in alphabetical order then find the word at position 49 in the permuted alphabetical order?
a) ARBSEU
b) ARBESU
c) ARBSUE
d) ARBEUS
AB**** =4!= 24 ways
AE****=4!=24 ways next word is 49th so
AR**** in alphabetical order **** will be BESU
ans is B
39 A is twice efficient than B. A and B can both work together to complete a work in 7 days. Then find in how many days A alone can complete the work?
ans is 10.5
gn:
A+B=(1/7)
A=2B
=>B=1/21
A=2/21
=>A take (21/2)=10.5 days to complete the work.
In 8*8 chess board what is the total number of squares.
1^2+2^2+3^2+4^2+5^2+6^2+7^2+8^2=204....
formula=1^2+2^2+3^2+....+n^2
40 X,Y,W,Z ARE INTEGER THE EXPRESSION X-Y-Z IS EVEN&Y-W-Z ODD IF X IS EVEN THEN WHICH OF FOLLOWING IS TRUE(a)Y MUST BE ODD(b)Y-Z MUST BE ODD(c)W MUST BE ODD(d)Z MUST BE ODD
Ans.(c)W must be ODD
X-Y-Z=even and X even no.
hence (y-z) must be even because (even -even = even)
and y-w-z=y-z-w=odd and (y-z) is even so W must be odd because (even - odd=odd)
hence option (c) is correct
41 Two cyclist begin training on oval racecourse at same timethe professional cyclist complete each lap in 4 sec noves take 6 mintue how many mintue after start will both cyclist pass at exactly same spot where they begin to cycle(a)10(b)8(C)14(D)12
ans is d.
simply LCM of 4 and 6.
which of following true:A occur only B or C occur B occur D&E occurf occur if Cnot occur g occur if A and F occur option A occur whenever F occur2)F never occur3) G not occur if D not occur4)none of these
3) g nt occure i d not occure
a=>b or c
b=>d & e
f=>c not
g =>a & f
1) a occure whenevr f :- depen on c where as 'a' can occure if 'c' not ..so this is not true
2) f nevr occure => depnd on c only n c is indipendent ...if c not occure f will occure ....so this is also not true
3) g not occure if d not:-g depnd on a & f ...if d not ocuure b will not occure (as b=>d&e) a will occure if c occure...if c occure f will not occure ...hence g will not occure...this is true
House1 is older than H2, H3 is taller than H4,H4 is older than H1...(i)H1 is older than H3 (ii)H2 is taller than H4 (a)only 1 (b)both (c)neither (d)only2
c)neither, is the answer.
42 In how many ways can 20 identical pencils be distributed among three girls so that each gets at least 1 pencil? now A'+B'+C''=17,
number of non negative integers of A',B',C' are (17+3-1)C(3-1)
so total Combinations are 19c2=19*9 = 171,
simple formula for this kind of problems is
(n-1)c(r-1)
so 19c2= 171
if p(x)=ax^4+bx^3+cx^2+dx+e has roots at x=1,2,3,4 & p(0)=48.what is p(5)
if 1 is a root then x-1 is a factor of p(x)
similarly x-2 is a factor,x-3 ,x-4 are factors
but p(x) is 4th degree polynomial therefore it can be in the form
p(x) = Q(x-1)(x-2)(x-3)(x-4) , where Q is a constant
but given p(0) =48
therefore 24 Q =48
Q=2
p(x) =2(x-1)(x-2)(x-3)(x-4)
p(5)= 2*4*3*2*1 = 48
1!+2!+3!...+50! divided by 5!
remainder will be ?
1!+2!+3!...+50! divided by 5!
remainder will be whatever is obtained by dividing 1!+2!+3!+4! with 5!.
so remainder is obtained by dividing (1+2+6+24)= 33 with 5! ( 120).
so remainder is 33.
43 If there are Six periods in each working day of a school, In how many ways can one arrange 5 subjects such that each subject is allowed at least one period?
we have 5 sub and 6 periods so their arrangement is 6P5 and now we have 1 period which we can fill with any of the 5 subjects so 5C1
6P5*5C1=3600
44 An article manufactured by a company consists of two parts X and Y. In the process of manufacturing of part X, 9 out 100 parts many be defective. Similarly , 5 out of 100 are likely to be defective in the manufacturer of Y. Calculate the probability that the assembled product will not be defective?
a)0.6485
b)0.6565
c)0.8645
d)none of these
ans=c (0.8645)
probablity of nondefective of x= 91/100=.91
probablity of non defective of y= 95/100=.95
so, probablity of nondefective product=.91*.95=0.8645
45 There are six multiple choice questions in the examination. How many sequences of anwers are possible, if the first two question have 3 choices each, the next two have 4 choice each and last two have 5 choices each?
3c1*3c1*4c1*4c1*5c1*5c1=3600
for any one of first three option of Q.1 we have three options in Q.2 4 option in Q.3.....this goes on...
ind the area (in square units) of the triangle formed by 2x+3y=5, y=x and X-Axis.
the points of intersection for lines:
2x+3y=5 and x=y => 5x=5 => x=1 and y=1 =>(1,1)
x=y and y=0(x-axis) => x=0 and y=0 =>(0,0)
2x+3y=5 and y=0(x-axis) => 2x=5 => x=5/2 and y=0 =>(5/2,0)
area of triangle with vertices (x1,y1),(x2,y2),(x3,y3) is
|x1(y2-y3)+x2(y3-y1)+x3(y1-y2)|/2
=|1(0-0)+0(0-1)+5/2(1-0)|/2
=|1+5/2|/2
=7/4 sq units...
46 Arun was all bent on building a new house. He carefully got the blue print of his house designed buy his friend Ashwin, a civil engineer. He wanted to build a room of dimension 27 by 48 ft and lay tiles in this room. Each tile was of dimension 2 by 3 ft. How many tiles should Arun buy?
27*48/2*3=216
47 Roy is now 4 year older than Erik and half of that amount than Lewis.If in two years Roy will be twice as old as Erick,then in two year what would be Roy age multiplied by Lewis age??
ans is 48 firstly two equation from 1st sentence ..
suppose roy=x, erik=y, lewis=z
so x=y+4....(1)
2nd is x=z+2...(2) (Roy is now 4 year older than Erik and half of that amount than Lewis so 4/2=2)
also after 2 years erik and roy relation wil b
x+2=2(y+2).. (3)
so put this into 1st equ. u will get y=2..
and then x=6,z=4(by substituting other)
nw asking multiplication after two years of roy n lewis is (6+2)*(4+2)=48..
if there are maximum acute angles then how many convex hectagons are there there can be max 3 acute angles in a convex polygon which is a triangle.
48 The number of bacteria was growing in a city exponentially.at 4 pm yesterday , the number of bacteria was 400 and at 6 pm yesterday it was 3600.How many bacteria were there at 7pm yesterday?
The number of bacteria was growing in a city exponentially.at 4 pm yesterday , the number of bacteria was 400 and at 6 pm yesterday it was 3600.How many bacteria were there at 7pm yesterday?
.49 There are 12 children in a family .the youngest 1 is a boy.then find the probabality of finding boy in the family.
a)4096
b)2048
c)2
d)2!
Probability cannot be more than 1..it ranges from 0 to 1..
there can be two options..either a boy/girl in a family
asked is to find a boy=1/2
given 12 children but it is already mentioned that the youngest is a boy so no need to count that..
hence,1/2*1/2*1/2......(11 times)=1/2048 option b..but the option is wrong..it should be 1/2048
50 A volume of 10936 l is in a conatiner of sphere . how many semispheres of volume 4 l each will be required to transfer all the water into small semispheres?
v10936/4=2734.....is the ans
a volume of A are having in a container of sphere. how many semi hemispheres of B volume each will be required to transfer all the A in to semi hemispheres?
ans is A/B.
51 My name is PREET.But my son accidentally types the by interchanging a pair of letters in my name.What is the probability that despite this interchange, the name remains unchanged? a.5% b.20% c.25% d.12.5%
10%
Selecting any two - 5C2 = 10[ treating E AND E as distinct)
Selecting EE = 1
1/10 * 100 = 10%
TCS 2013 placement new pattern questions 02
1 Four friends namely Rahul, Ravi, Rajesh and Rohan contested for a dairy milk chocolate. To decide which friend will get the chocolate they decided to throw two dice. Every friend was asked to choose a number and if the sum of the numbers on two dice equals that number, the concerned person will get the chocolate. Rahul's choice was7, Ravi's choice was 9, Rajesh's choice was 10 and Rohan's choice was 11. Who has the maximum probability of winning the amount.
a) Rahul b) Ravi c) Rajesh d) Rohan
Rahul has chosen 7, similarly Ravi-9,Rajesh-10,Rohan-11
(1,1)(1,2)(1,3)(1,4)(1,5)(1,6) Sum of the digits are= 2,3,4,5,6,7
(2,1)(2,2)(2,3)(2,4)(2,5)(2,6) Sum of the digits are= 3,4,5,6,7,8
(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)Sum of the digits are= 4,5,6,7,8,9
(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)Sum of the digits are= 5,6,7,8,9,10
(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)Sum of the digits are= 6,7,8,9,10,11
(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)Sum of the digits are= 7,8,9,10,11,12
Among these 7 comes 6 times, 9 comes 4times, 10 comes 3times,11 comes only 2 times.
So the maximum probability goes to Rahul
2 Messrs. Siva Constructions, leading agents in Chennai prepared models of their lands in the shape of a rectangle and triangle. They made models having same area. The length and width of rectangle model are 24 inches and 8 inches respectively. The base of the triangle model is 16 inches. What is the altitude of triangle model from the base to the top?
a) 24 inches b) 8 inches c) 20 inches d) 32 inches
Area of a rectangle= Area of the Triangle
So, l*b=1/2(b*h)
24*8=1/2(16*8)
therefore 24inches will be the answer
3 There is a 12*6 grid..grid contains 1*1 squares..what is d total number of squares..(consider 1*1,2*2,3*3,4*4,5*5,6*6 size squares as well).Lady has 25 blues, 7 red,9 yellow gloves and hats.how many gloves of same colour.
(max + min + 2) = 25 + 9 +2=36
1!+2!+.....=50!=?
3.10350532 × 10^64
Anita make cube with dimension 5*5*5 using 1*1*1 cubes.find no. Of cubes to make it hollow of same shape.
To make the 5*5*5 hollow, the inner cubic part must be removed. This would constitute one cube each from front,back,top,bottom,left and right ! Since the 5*5*5 is made up of 1*1*1 cubes, 3*3*3 cubes (i.e. 5-2*5-2*5-2) would have to be removed to make it hollow with the shape retained. 27 cubes would be removed, remaining 125-27=98.
1) if 3y + x > 2 and x + 2y
let 3y+x=2
y+2y+x=2
2y+x=2-y(ans)
3y > 2 -x
2y > 4/3 - 2x/3
x+2y > 4/3 + x/3
x + 2y > 1/3(4 + x)
4 Tim and Elan are 90 km from each other, they start to move each other simultaneously, Tim at speed 10 and Elan 5kmph, if every hour they double their speed what is the distance that Tim will pass until he meet Elan?
Tim and Elan will cover the distance in ratio of 2: 1 in same time.
so out of 90 kms, Tim will travel 60 kms and Elan will travel 30 mtrs.
he length and breadth of a field is 300x400ft,if there are 3 ants on average per square inch of field,find the approximate number of ants in field
as 300 ft=3600 inch and 400 ft=4800 inch.then area in sqr inch=17280000
1 sqr inch need 3 ant hence 17280000 sqr inch need 3*17280000 ants.
.diagonal of a square is double the side of an equilateral triangle find the ratio of area of triangle to area of square
let sides of equilateral triangle be 'a', therefore area= √3/4 * a^2
now, diagonal of square is 2a therefore sides of square will be √2*a
and area of square = 2 a^2
hence, ratio = (√3/4* a^2)/(2* a^2)
answer = √3/8
5 Given a collection of points P in the plane, a 1-set is a point in P that can be separated from the rest by a line, .i.e the point lies on one side of the line while the others lie on the other side.
The number of 1-sets of P is denoted by n1(P). The minimum value of n1(P) over all configurations P of 5 points in the plane in general position(.i.e no three points in P lie on a line) is
a)3 b)5 c) 2 d)1
The meaning of this question is little complicated. In easy language the question should be:
6 There are some points in the plane. We have to make a separation between these points by forming a line in such a way that one point could be separate from the others. No 3 points are in a line. Maximum no of methods for plotting the line and minimum no of methods for plotting the line will be (arrangement of points is your choice)
Now Answer Is:
For Maximize: The number of methods, Points should be drawn in the circumference of the CIRCLE So answer would be the number of total point in the plane.
For minimize: The number of methods we should draw 3 points in a TRIANGLE and all other point inside this triangle in such a way that no 3 points could be in a line.
If it will be allowed to draw the points in a line then minimum possibilities will be 2 only, because if we take all points in a line then you can separate only the corner points from the others.
For example
If we have 10 points then maximum possibilities = 10
and minimum = 3
similarly for 5 points
Max = 5, Min = 3
for 19
max= 19 Min = 3
f(x)=f(f(x))=f(x^2)....how many such functions with degree >2 exist
does not exist....
In a sequence of integers, A(n)=A(n-1)-A(n-2),where A(n) is the nth term in the sequence, n is an integer and n>=3, A(1)=1,A(2)=1. Calculate S(1000), where S(1000) is the sum of first 1000 terms.
check it now
A(1)=1,A(2)=1.
A(3)=A(2)-A(1) acc to the given formula A(n)=A(n-1)-A(n-2)
A(3)=1-1=0.
similarliy,A(4)=A(3)-A(2)=0-1=-1.
A(5)=A(4)-A(3)=-1-0=-1.
A(6)=A(5)-A(4)=-1-(-1)=0.
after 6th term seq is repeating like...1,1,0,-1,-1,0...after every 6 terms
so the sum of these 6 terms are 1+1+0+(-1)+(-1)+0=0.
now we have to find sum of 1000 terms...
sum of first 600 terms is 0...(as consider 1,1,0,-1,-1,0 as one sequence,now consider 166 seq i.e 166*6=996 terms)
so the sum of first 996 terms is 0...after that 4 terms come i.e 1,1,0,-1
so the sum of last 4 terms = 1+1+0+(-1)=1.
7 planet four firesides in 4-dimensional space and thus the currency used by it's residentds are 3-dimensional objects. the rupee notes are cubical in shape while their conis are spherical. however the coni minting machinery lays out some stipulations on the size of the coins. the diameter of the conins should be at least 64 mm and not exceed 512 mm. given a conin the diameter of the next larger coin is at least 50% greater . the diameter of the coin must allways be an integer you are asked to disign a set of coins of different diameters with these requirements and your goal is to desing as many coins as possible. how many coins can you desing
1st coin=64cm
2nd "=64+32(50% of 64)=96cm
similarly 3rd=96+48=144
4th=144+72=216
5th=216+108=324
6th=324+112=436
7th not possible
ans is 6
8 There are 3 boys A, B, C and 2 Girls D, E. E always sit right to A. Girls never sit in extreme positions and in the middle position. C always sits in the extreme positions. Who is sitting immediate right to E?
ns is either B or C
POSSIBLE WAYS TO SIT
1) B/C D A E C/B
2) A E B D C
9 What is reminder when 6^17+17^6 is devided by 7?
(7-1)^17 + (7*2+3)^6
binomial theorem
-1+3^6=728
728%7=0
(40*40* 40-31*31*31)/(40*40+40*31+31*31)=?a simle calcutation
(a^3-b^3)/(a^2+ab+b^2)
a-b
40-31=9
10 In base 7,a number is written only using the digits 0,1,....6.the number 135 in base 7 is 1x7^2+3x7+5=75 in base 10.what is the sum of the same of the base 7 numbers 1234 and 6543 in base 7?
11110
1234
6543
-------
11110 which is 7^4+7^3+7^2+7= 2401+343 +49+7= 2800
11 There are 20 balls which are red,blue or green,If 7 balls are green and the sum of red balls and green balls is less than 13,atmost how many red balls are there
5, atmost there can be 5 red balls so that sum of green and red can be less than 13 (7+5=12)
3y+x>2 and x+2y-1
y
the ans is y>1.
explanation:
x+2y-1=0
so x+2y=1
now 3y+x>2 given
we can write in this way x+2y+y>2
then putting x+2y=1 we get 1+y>2 =>y>2-1=>y>1
12 Find the no of zeros in the product of 1^1*2^2*3^3*.....*49^49??
total zeros at the end of product 5^5 x 10^10 x 15^15 x 20^20 x 25^25 x 30^30 x 35^35 x 40^40 x 45^45 will be 5+10+15+20+50+30+35+40+45 = 250 zeros
13 n! has 13 zeros than wat is the higest and lowest value of n??
Here we have to consider only the 5,10,15,20.... these terms..
so form (5,10,15,20,30,35,40,45,55 ) we got 1 no of zero from each.
Now from 25(5*5) and 50(5*5*2) we got 2 no of zeroes form each.
so upto 55 factorial we get (9+4)= 13 zeroes.
so 55! is the smallest value and 59! is the largest value.
The sequence {A(n)} is defined by A(1)=2 and A(n+1)=A(n)+2n. What is the value of A(100).
The sequence {A(n)} is defined by A(1)=2 and A(n+1)=A(n)+2n.
The value of A(100)=A(99+1)=A(99)+2*99
=A(98)+2*98+2*99
=A(97)+2*97+2*98+2*99
A(100)=A(1)+2*1+2*2+2*3+......+2*98+2*99
= 2+(2*1+2*2+2*3+......+2*98+2*99)
= 2+2(1+2+3+.....+98+99)
= 2+2(sum of the first 99 natural numbers)
= 2+2(99*100/2) [sum of the first n natural numbers={n*(n+1)/2}]
= 2+9900
= 9902
14 A,B COMMON TO ALL THREE. THEN ATLEAST 1 ELEMNT COMMON TO 2 IE X1,X2,X2,X3,X3,X1. FINDMINIMUM ELEMENTS IN EACH GROUP. ANSWER IS 4.
15 Directions for Q. 1 to Q. 5: Refer the data:
J, K, L, M and N collected stamps. They collected a total of 100 stamps. None of them collected less than 10.
No two among them collected the same number.
(i) 3 collected the same number as K and M together.
(ii) L collected 3 more than the cube of an integer
(iii) The no. collected by J was the square of an integer.
(iv) Total no. collected by K was either the square or cube of an integer.
1. The no. collected by J was:
(1) 27 (2) 49 (3) 36 (4) 64
2. The no. collected by K was:
(1) 16 (2) 27 (3) 25 (4) 36
3. The difference of numbers collected by L & M was:
(1) 3 (2) 2 (3) 5 (4) 9
in the question the number collected by J should be cube of the integer and l should collect 3 more than square of integer.
J+L+N=K+M
so the sum of J+L+N=K+M=50
l=3^2+3=12
so J=3^3=27
n=50-27-12=11
now k is either square or cube so possibilty are 36 or 16.and m=14 or 34
so j=27
now value for k can come after solving question 3
m-l=14-12=2 or 34-12=22
so there is 2 in option so value of m is 14 and k=36.
16 Bhanu spends 30% of his income on petrol on scooter. ? of the remaining on house rent and the balance on food. If he spends Rs.300 on petrol then what is the expenditure on house rent?
let the income x,so in petrol he spends 3x/10 rs,remaining x-3x/10=7x/10 on house rent and balance on.now 3x/10=300,so x=1000,on house rent he spends rs 700-balane..
Let exp(m,n) = m to the power n. If exp(10, m) = n exp(2, 2) where to and n are integers then n = exp(m,n) = m to the power n= m^n
exp(10, m) = n exp(2, 2) = n*2^2 = 4*n
10^m =4*n
when m=2,
n=25
so min integer values of m and n are 2 and 25 respectively.
A Grocer bought 24 kg coffee beans at price X per kg. After a while one third of stock got spoiled so he sold the rest for $200 per kg and made a total profit of twice the cost. What must be the price of X?
A. $33 1/3 B. 66 2/3 C.44 4/9 D.50 1/3
ns: C. 44 4/9
cost price= 24*X $,
spoiled= 24*1/3=8 kg, now total amount= (24-8)=16 kg
selling price= 16*200$ =3200$
profit= (3200-24*X)
profit=2* cost , (3200-24*X)= 2*24*X, x=44 4/9
17 The age of two people is in the ratio 6:8. the sum of their ages is 77. after 2 years the ratio of their ages becomes 5:7. wat is their present age?
The ratio of two people be 6x and 8x
sum of their ages is 6x+8y=77
after 2 yrs,ratio is 5:7,so,
(6x+2)/(8x+2)=5/7
on cross multiplying this,
x=2
hence age of a person 6(2)=12
hence another person ages is 8(2)=16
answer is 12,16
MOTHER +DAUGHTER+INFANT AGE IS 74. MOTHER AGE IS 46 MORE THEN DAUGHTER AND INFANT.
AND INFANT AGE IS 0.4 OF DAUGHTER. FIND DAUGHTERS AGE.
M+D+I = 74 ..,.,.Equ..1
I=0.4D
M=D+0.4D+46
M=1.4D+46
put in equ 1
1.4D+46+D+0.4D=74 as I=0.4D
2.8D=74-46
D=28/2.8
D=10.,.,.
,
16 Mr and mrs smith had invited 9 of their friend and their spouses for party at wiki beachresort.the stand for group photograph if mr smith never stand next to mrs smith then how many way group arrange in row(A)20!(B)19!+18!(C)18*19!(D)2*19!
simplest... ans is 18*19!
method ..: mr and mrs smith never b together so out of 20(with both them) 19 can b any place so total = 19!
also 1 of them can stand with other so 18 places /..
so total is 18*19!..
19!*18bcoz along with mr and mrs smith can be arranged in 19!*2 (2 bcoz of mr and mrs smith arrangement) all together can be arranged in 20! ways so no mr and mrs smith can be arranged in 20!-19!*2 =19!*18
Is this solution Helpfull? Yes (8) | No (2) viresh (4 Day ago)
20!-(19!*2)
total possibility minus they will be together
A father purchases dress for his three daughter. The dresses are of same color but of different size .the dress is kept in dark room .What is the probability that all the three will not choose their own dress...
a dosesnot choose his dress 2/3
b dosesnot choose his dress 1/2
c dosesnot choose his dress 1 total 1/3
17 Leena cuts small cubes of 3 cubic cm each.She joined it to make a cuboid of length 10 cm,width 3cm, and depth 3 cm.How many more cubes does she need to make a perfect cube?
a)910 b)250 c)750 d)650
ns is a)910. To make cube we need 10*10*10=1000. now we have only 10*3*3=90.so the more cube we need are 1000-90=910.
18 Q:- A boy wants to make cuboids of dimension 5m,6m & 7m from small cubes of .03m^3.Later he realized that he can make some cuboids by making it hollow.Then it takes some cubes less.What is the number of cubes to be removed
a)2000 b)5000 c)3000 d)7000
Volume of the cuboid= 5*6*7
No of cubes needed = (5*6*7)/0.03 = 7000
Volume of hollow cube= (5-2)(6-2)(7-2)
No of cubes needed = (5-2)(6-2)(7-2)/0.03 = (3*4*5)/0.03= 2000
So, number of cubes to be removed = 7000 - 2000 = 5000
19 An empty tankbe filled with aninlet pipe 'A' in 42 minutes. after 12 minutes an outlet pipe 'B' is opened which can empty the tank in 30 minutes. After 6 minutes another inlet pipe 'C' opened into the same tank, which can fill the tank in 35 minutes and the tank is filled find the time taken to fill the tank?
he milk and water in two vessels A and B are in the ratio 4 : 3 and 2: 3 respectively. In what ratio, the liquids in both the vessels be mixed to obtain a new mixture in vessel C containing half milk and half water?
let c.p. of 1liter milk is 1RS.
now milk in 1st mixer is 4/7 and in 2nd mixure is 2/5.
milk in finle mixer is 1/2
now from mixure formula..
4/7 2/5
1/2
1/10 1/14
so ratio is 14/10 =7/5
20 How many kgs. of wheat costing Rs. 8 per kg must be mixed with 86 kg of rice costing Rs. 6.40 per kg so that 20% gain may be obtained by Belling the mixture at Rs. 7.20 per kg ?
Ex. 4. .How many kgs. of wheat costing Rs. 8 per kg must be mixed with 86 kg of rice costing Rs. 6.40 per kg so that 20% gain may be obtained by Belling the mixture at Rs. 7.20 per kg ?
Sol. S.P. of 1 kg mixture = Rs. 7.20,Gain = 20%.
? C.P. of 1 kg mixture = Rs.[(100/120)*7.20]=Rs. 6.
By the rule of alligation, we have:
C_P. of 1 kg wheat of 1st kind C.P. of 1 kg wheat of 2nd kind
(800p) . (540 p)
Mean price
( 600 p)
60 200
Wheat of 1st kind: Wheat of 2nd kind = 60 : 200 = 3 : 10.
Let x kg of wheat of 1st kind be mixed with 36 kg of wheat of 2nd kind.
Then, 3 : 10 = x : 36 or lOx = 3 * 36 or x = 10.8 kg.
21 In what ratio must water be mixed with milk to gain 20 % by selling the mixture at cost price?
let the sp op 1 l mix is =re 1
cp =(100/120)*1=5/6
cp of one let. water =0
so ratio=1-(5/6)/(5/6)-0=1/5
so required ratio =1:5
How much water must be added to 60 litres of milk at 1 ½ litres for Rs. 2
So as to have a mixture worth Rs.10 2/3 a litre ?
x=(sin nx/n)=?
x=(sin nx/n)
so,
nx=sin nx
sin is one to one function and there is only one case for φ=0 where sinφ=φ
so nx=0
so x=0 (n!=0)
ans will be 0
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2013-2014 new batch asked questions some users contributions from different campus recruitments all over India
1) The wages of 24 men and 16 women amounts to Rs.11600/day. Half the number of men and 37 women earn the same amount /day. What is the daily wage of a man
Explanations
Let the wage of a man be m and woman be w
24m+16W=11600
12m+37w=11600
24m*37-12m*16=11600*(37-16)
12m(2*37-16)=11600*(37-16)
Solving m=11600*21/(12*58) =200*7/4=350
2) The sum of three digits in a number is 17 The sum of square of the digits is 109 .If we subtract 495 from the number, the number is reversed. Find the number
Explanations
Let the digits abc
a+b+c=17-Eqn1
a^2+b^2+c^2 =109 -Eqn -2
Also 100a+10b+c-495=100c+10b+a
99(a-c)=495 Thus a-c =5 The possible combinations are (6,1)(7,2)(8,3)(9,4)
Case 1: (6,1)
From Eqn 1,b+17-7=10 which not possible as b is a single digit
Case 2:(7,2)
From eqn 1 b=17-9=8
Verifying with eqn 2,49+4+64=117and hence not valid
Case 3: (8,3)
From eqn 1,b=17-11=6
Verifying with eqn 2,64+9+36 = 109 and hence valid
Thus the number is 863
3) Find the last two0 digits of (102^3921)+(3081^3921)
Ans 02
To find out the last 2 digits of a term where the number ends with 1, multiply the tens digit of the number with the last digit of the exponent This will give you the tens digit Unit digit will always be 1
Applying this shortcut
for 102^3921,last 2 digits is (2^1) 1=21
for 3081^3921,last 2 digits is (8^1)=81
Adding both we get 102
Hence last two digits of the expression is 02
4) To find out the last 2 digits of a term where the number ends with 1, multiply the tens digit of the number with the last digit of the exponent This will give you the tens digit Unit digit will always be 1
Applying this shortcut
for 102^3921,last 2 digits is (2^1) 1=21
for 3081^3921,last 2 digits is (8^1)=81
Adding both we get 102
Hence last two digits of the expression is 02
4 A series is given as 1,6,7,13,20,33,.......and so on Find the sum of first 52 terms
1st and 2nd terms are 1,6
3rd term is 7 which is sum of first+second
4the term is 13 which is sum of second +thirds
Expanding the series further by adding a few more terms it is 1,6,7,13,20,33,53,86,139,and so on
Now if we add the terms for upto 1,2,3,4,5,6 terms it is
1,2,14,27,47,80,133,219 and so on
5)
Ans 26.25 sq units
The Radius of the circle R circumscribing a triangle is given by the formula
R-ABC /(4*Area of Triangle)
Area of Triangle - 1/2*base*height - 1/2*BC*Ad-1.5BC (As Ad -3)
A,B,C are the side which are 17.5 9 and BC respectively
Hence radius R -17 .5*9*BC/(4*1.5BC) -17.5*9/6-26.25 squints
6) A calculator has a key for squaring and another key for inverting. So if x is the displayed number, then pressing the square key will replace x by x^2 and pressing the invert key will replace x by 1/x. If initially the number displayed is 6 and one alternatively presses the invert and square key 16 times each, then the final number displayed (assuming no round off or overflow errors) will be
Ever n number of inverse key has no effect on the number.
By pressing the square key, the value got increased like 2, 4, 8, .... Which are in the format of 2n. So after the 16 pressings the power becomes 216
So the final number will be 6216=665536
7) How many two digit numbers are there which when subtracted from the number formed by reversing it's digits as well as when added to the number formed by reversing its digits,
result in a perfect square.
Let the number xy = 10x + y
Given that, 10x+y - (10y - x) = 9(x-y) is a perfect square
So x-y can be 1, 4, 9. -------- (1)
So given that 10x+y +(10y +x) = 11(x+y) is a perfect square.
So x+y be 11. Possible options are (9,2), (8,3),(7,4),(6,5) ---------(2)
From the above two conditions only (6,5) satisfies the condition
Only 1 number 56 satisfies.
8) Find the 55th word of SHUVANK in dictionary
Sol: Arranging the letters in alphabetical order we get : A H K N S U V
Now Total words start with A are 6!
Total words start with AH are 5! = 120
Now
Total words start with AHK are 4! = 24
Total words start with AHN are 4! = 24
Total words start with AHSK are 3! = 6
Now AHSNKUV will be the last word required.
9) Car A leaves city C at 5pm and is driven at a speed of 40kmph. 2 hours later another car B leaves city C and is driven in the same direction as car A. In how much time will car B be 9 kms ahead of car A if the speed of car is 60kmph
Relative speed = 60 - 40 = 20 kmph
Initial gap as car B leaves after 2 hours = 40 x 2 = 80 kms
Car B should be 9 km ahead of the A at a required time so it must be 89 km away
Time = 89 / 20 = 4.45 hrs or 267 mins
10) n is a natural number and n^3 has 16 factors. Then how many factors can n^4 have?
Total factors of a number N=ap.bq.cr... is (p+1)(q+1)(r+1)...
As n3 has 16 factors n3 can be one of the two formats given below
n3 =a15
n3 = a3.b3
If n3 =a15 then n = a5 and number of factors of n4 = 21
n3 = a3.b3 then n = ab and number of factors n4 = 25
11)Two cars start from the same point at the same time towards the same destination which is 420 km away. The first and second car travel at respective speeds of 60 kmph and 90 kmph. After traveling for sometime the speeds of the two cars get interchanged. Finally the second car reaches the destination one hour earlier than the first. Find the time after which the speeds get interchanged?
Let the total time taken by the cars be a and b
Let the time after which the speed is interchanged be t
For car A, 60t+90(a-t) = 420, 90a - 30t = 420 .......(1)
For car B, 90t + 60(b-t) = 420, 60b + 30t = 420 ....(2)
Using both (1) and (2), we get 90a + 60b = 840
But as a - b =1, 90a + 60(a-1) = 840.
Solving a = 6.
Substituting in equation 1, we get t = 4
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1. What are the total number of divisors of 600(including 1 and 600)?
a. 24
b. 40
c. 16
d. 20
Sol: Option a
If N=ap×bq×cr.... then the number of factors of N = (p+1)(q+1)(r+1) ....
600 = 23×3×52
So number of factors of 600 = (3+1)(1+1)(2+1) = 24
2. What is the sum of the squares of the first 20 natural numbers (1 to 20)?
a. 2870
b. 2000
c. 5650
d. 44100
Sol: Option a
Use formula n(n+1)(2n+1)/6
3. What is ∑K=028K2(28KC) where 28KC is the number of ways of choosing k items from 28 items?
a. 406 * 227
b. 306 * 226
c. 28 * 227
d. 56 * 227
Sol: A
Consider (1+x)n=C0+C1x+C2x2+.....+Cnxn .......(1)
Differentiating w.r.t x we get
n(1+x)n−1=C1+2C2x+3C3x2+.....+nCnxn−1
Multiplying by x on both sides,
x.n(1+x)n−1=x.C1+2C2x2+3C3x3+.....
Now again differentiating w.r.t to x
n(1+x)n−1+n(n−1)x(1+x)n−2=C0+22C1x+32C2x2+42C3x3.....
Putting x = 1, we get
n(n+1)2n−2=C1+22C2+32C3+42C4
Now substituting n = 28
28(28+1)228−2 = 812.226 = 406.227
4. What is ∑K=0283K(28KC) where 28KC is the number of ways of choosing k items from 28 items?
a. 256
b. 3* 227
c. 329
d. 3* 427
Sol: Option A
We know that C0+3C1+32C2+.....+3nCn=4n
Substitute n = 28
We get ∑K=0283K(28KC) = 428= 256
5. A call center agent has a list of 305 phone numbers of people in alphabetic order of names (but she does not have any of the names). She needs to quickly contact Deepak Sharma to convey a message to him. If each call takes 2 minutes to complete, and every call is answered, what is the minimum amount of time in which she can guarantee to deliver the message to Mr Sharma.
a. 18 minutes
b. 610 minutes
c. 206 minutes
d. 34 minutes
Sol: Option A
6. The times taken by a phone operator to complete a call are 2,9,3,1,5 minutes respectively. What is the average time per call?
a. 4 minutes
b. 7 minutes
c. 1 minutes
d. 5 minutes
Sol: Option A
7. The times taken by a phone operator to complete a call are 2,9,3,1,5 minutes respectively. What is the median time per call?
a. 5 minutes
b. 7 minutes
c. 1 minutes
d. 4 minutes
Sol: NO option is correct. Median is 3
8. Eric throws two dice, and his score is the sum of the values shown. Sandra throws one die, and her score is the square of the value shown. What is the probability that Sandra’s score will be strictly higher than Eric’s score?
a. 137/216
b. 17/36
c. 173/216
d. 5/6
Sol: A
9. What is the largest integer that divides all three numbers 23400,272304,205248 without leaving a remainder?
a. 48
b. 24
c. 96
d. 72
Sol: Option B
Find GCD
10. Of the 38 people in my office, 10 like to drink chocolate, 15 are cricket fans, and 20 neither like chocolate nor like cricket. How many people like both cricket and chocolate?
a. 7
b. 10
c. 15
d. 18
Sol: Option A
11. If f(x) = 2x+2 what is f(f(3))?
a. 18
b. 8
c. 64
d. 16
Sol: Option A
12. If f(x) = 7 x +12, what is f-1(x) (the inverse function)?
a. (x-12)/7
b. 7x+12
c. 1/(7x+12)
d. No inverse exists
Sol: Option A
13. A permutation is often represented by the cycles it has. For example, if we permute the numbers in the natural order to 2 3 1 5 4, this is represented as (1 3 2) (5 4). In this the (132) says that the first number has gone to the position 3, the third number has gone to the position 2, and the second number has gone to position 1, and (5 4) means that the fifth number has gone to position 4 and the fourth number has gone to position 5. The numbers with brackets are to be read cyclically. If a number has not changed position, it is kept as a single cycle. Thus 5 2 1 3 4 is represented as (1345)(2). We may apply permutations on itself If we apply the permutation (132)(54) once, we get 2 3 1 5 4. If we apply it again, we get 3 1 2 4 5 , or (1 2 3)(4) (5) If we consider the permutation of 7 numbers (1457)(263), what is its order (how many
times must it be applied before the numbers appear in their original order)?
a. 12
b. 7
c. 7! (factorial of 7)
d. 14
Sol: Not yet solved
14. What is the maximum value of x3y3 + 3 x*y when x+y = 8?
a. 4144
b. 256
c. 8192
d. 102
Sol: Option A
The question probably be x3.y3+3x∗y
Sustitute x = 4 and y = 4
15. Two circles of radii 5 cm and 3 cm touch each other at A and also touch a line at B and C. The distance BC in cms is?
a. √ 60
b. √ 62
c. √ 68
d. √ 64
Sol:Option A
√d2−(r1−r2)2
d = distance between centers
16. In Goa beach, there are three small picnic tables. Tables 1 and 2 each seat three people. Table 3 seats only one person, since two of its seats are broken. Akash, Babu, Chitra, David, Eesha, Farooq, and Govind all sit at seats at these picnic tables. Who sits with whom and at which table are determined by the following constraints:
a. Chitra does not sit at the same table as Govind.
b. Eesha does not sit at the same table as David.
c. Farooq does not sit at the same table as Chitra.
d. Akash does not sit at the same table as Babu.
e. Govind does not sit at the same table as Farooq.
Which of the following is a list of people who could sit together at table 2?
a. Govind, Eesha, Akash
b. Babu, Farooq, Chitra
c. Chitra, Govind, David.
d. Farooq, David, Eesha.
Sol: Option A
17. There are a number of chocolates in a bag. If they were to be equally divided among 14 children, there are 10 chocolates left. If they were to be equally divided among 15 children, there are 8 chocolates left. Obviously, this can be satisfied if any multiple of 210 chocolates are added to the bag. What is the remainder when the minimum feasible number of chocolates in the bag is divided by 9?
a. 2
b. 5
c. 4
d. 6
Sol: Option B
18. Let f(m,n) =45*m + 36*n, where m and n are integers (positive or negative) What is the minimum positive value for f(m,n) for all values of m,n (this may be achieved for various values of m and n)?
a. 9
b. 6
c. 5
d. 18
Sol: Option A
19. What is the largest number that will divide 90207, 232585 and 127986 without leaving a remainder?
a. 257
b. 905
c. 351
d. 498
Sol: Option A
20. We have an equal arms two pan balance and need to weigh objects with integral weights in the range 1 to 40 kilo grams. We have a set of standard weights and can place the weights in any pan. . (i.e) some weights can be in a pan with objects and some weights can be in the other pan. The minimum number of standard weights required is:
a. 4
b. 10
c. 5
d. 6
Sol: Option A
21. A white cube(with six faces) is painted red on two different faces. How many different ways can this be done (two paintings are considered same if on a suitable rotation of the cube one painting can be carried to the other)?
a. 2
b. 15
c. 4
d. 30
Sol: Option A
22. How many divisors (including 1, but excluding 1000) are there for the number 1000?
a. 15
b. 16
c. 31
d. 10
Sol: Option A
23. In the polynomial f(x) =2*x^4 - 49*x^2 +54, what is the product of the roots, and what is the sum of the roots (Note that x^n denotes the x raised to the power n, or x multiplied by itself n times)?
a. 27,0
b. 54,2
c. 49/2,54
d. 49,27
Sol: Option A
24. In the polynomial f(x) = x^5 + a*x^3 + b*x^4 +c*x + d, all coefficients a, b, c, d are integers. If 3 + sqrt(7) is a root, which of the following must be also a root?(Note that x^n denotes the x raised to the power n, or x multiplied by itself n times. Also sqrt(u) denotes the square root of u, or the number which when multiplied by itself, gives the number u)?
a. 3-sqrt(7)
b. 3+sqrt(21)
c. 5
d. sqrt(7) + sqrt(3)
Sol: Option A
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TCS New Questions 2013-2014 TCS New Pattern of Questions from Openseesame
1. If 3y + x > 2 and x + 2y≤3, What can be said about the value of y?
A. y = -1
B. y >-1
C. y <-1
D. y = 1
Answer: B
Multiply the second equation with -1 then it will become - x - 2y≥ - 3. Add the equations. You will get y > -1.
2. If the price of an item is decreased by 10% and then increased by 10%, the net effect on the price of the item is
A. A decrease of 99%
B. No change
C. A decrease of 1%
D. An increase of 1%
Answer: C
If a certain number is increased by x% then decreased by x% or vice versa, the net change is always decrease. This change is given by a simple formula −(x/10)2= −(10/10)2= −1%. Negitive sign indicates decrease.
3. If m is an odd integer and n an even integer, which of the following is definitely odd?
A. (2m+n)(m-n)
B. (m+n2)+(m−n2)
C. m2+mn+n2
D. m +n
Answer: C and D (Original Answer given as D)
You just remember the following odd ± odd = even; even ± even = even; even ± odd = odd
Also odd x odd = odd; even x even = even; even x odd = even.
4. What is the sum of all even integers between 99 and 301?
A. 40000
B. 20000
C. 40400
D. 20200
Answer: D
The first even number after 99 is 100 and last even number below 301 is 300. We have to find the sum of even numbers from 100 to 300. i.e., 100 + 102 + 104 + ............... 300.
Take 2 Common. 2 x ( 50 + 51 + ...........150)
There are total 101 terms in this series. So formula for the sum of n terms when first term and last term is known is n/2(a+l)
So 50 + 51 + ...........150 = 1012(50+150)
So 2 x 101/2(50+150) = 20200
5. There are 20 balls which are red, blue or green. If 7 balls are green and the sum of red balls and green balls is less than 13, at most how many red balls are there?
A. 4
B. 5
C. 6
D. 7
Answer: B
Given R + B + G = 17; G = 7; and R + G < 13. Substituting G = 7 in the last equation, We get R < 6. So maximum value of R = 6
6. If n is the sum of two consecutive odd integers and less than 100, what is greatest possibility of n?
A. 98
B. 94
C. 96
D. 99
Answer : C
We take two odd numbers as (2n + 1) and (2n - 1).
Their sum should be less than 100. So (2n + 1) + (2n - 1) < 100 ⇒ 4n < 100.
The largest 4 multiple which is less than 100 is 96
7. x2 < 1/100, and x < 0 what is the highest range in which x can lie?
A. -1/10 < x < 0
B. -1 < x < 0
C. -1/10 < x < 1/10
D. -1/10 < x
Answer: A
8. There are 4 boxes colored red, yellow, green and blue. If 2 boxes are selected, how many combinations are there for at least one green box or one red box to be selected?
A. 1
B . 6
C. 9
D. 5
Answer: 5
Total ways of selecting two boxes out of 4 is 4C2 = 6. Now, the number of ways of selecting two boxes where none of the green or red box included is only 1 way. (we select yellow and blue in only one way). If we substract this number from total ways we get 5 ways.
9. All faces of a cube with an eight - meter edge are painted red. If the cube is cut into smaller cubes with a two - meter edge, how many of the two meter cubes have paint on exactly one face?
A. 24
B. 36
C. 60
D. 48
Answer : A
If there are n cubes lie on an edge, then total number of cubes with one side painting is given by 6×(n−2)2. Here side of the bigger cube is 8, and small cube is 2. So there are 4 cubes lie on an edge. Hence answer = 24
10. Two cyclists begin training on an oval racecourse at the same time. The professional cyclist completes each lap in 4 minutes; the novice takes 6 minutes to complete each lap. How many minutes after the start will both cyclists pass at exactly the same spot where they began to cycle?
A. 10
B. 8
C. 14
D. 12
Answer: D
The faster cyclyst comes to the starting point for every 4 min so his times are 4, 8, 12, ......... The slower cyclist comes to the starting point for every 6 min so his times are 6, 12, 18, ......... So both comes at the end of the 12th min.
11 Tim and Elan are 90 km from each other.they start to move each other simultanously tim at speed 10 and elan 5 kmph. If every hour they double their speed what is the distance that Tim will pass until he meet Elan
A. 45
B. 60
C. 20
D. 80
Answer: B
12 . A father purchases dress for his three daughter. The dresses are of same color but of different size .the dress is kept in dark room .What is the probability that all the three will not choose their own dress.
A. 2/3
B. 1/3
C. 1/6
D. 1/9
Answer: B
13 . N is an integer and N>2, at most how many integers among N + 2, N + 3, N + 4, N + 5, N + 6, and N + 7 are prime integers?
A. 1
B. 3
C. 2
D. 4
Answer: C
14 A turtle is crossing a field. What is the total distance (in meters) passed by turtle? Consider the following two statements
(X) The average speed of the turtle is 2 meters per minute
(Y) Had the turtle walked 1 meter per minute faster than his average speed it would have finished 40 minutes earlier
A. Statement X alone is enough to get the answer
B. Both statements X and Y are needed to get the answer
C. Statement Y alone is enough to get the answer
D. Data inadequate
Answer: B
15 . Given the following information, who is youngest?
C is younger than A; A is talled than B
C is older than B; C is younger than D
B is taller than C; A is older than D
A. D
B. B
C. C
D. A
Answer: B
16 Find the number of rectangles from the adjoining figure (A square is also considered a rectangle)
A. 864
B. 3276
C. 1638
D. None
Answer: C
17 A, B, C and D go for a picnic. When A stands on a weighing machine, B also climbs on, and the weight shown was 132 kg. When B stands, C also climbs on, and the machine shows 130 kg. Similarly the weight of C and D is found as 102 kg and that of B and D is 116 kg. What is D's weight
A. 58kg
B. 78 kg
C. 44 kg
D. None
Answer : C
Given A + B = 132; B + C = 130; C + D = 102, B + D = 116
Eliminate B from 2nd and 4th equation and solving this equation and 3rd we get D value as 44.
18 Mr and Mrs Smith have invited 9 of their friends and their spouses for a party at the Waikiki Beach resort. They stand for a group photograph. If Mr Smith never stands next to Mrs Smith (as he says they are always together otherwise). How many ways the group can be arranged in a row for the photograph?
A. 20!
B. 19! + 18!
C. 18 x 19!
D. 2 x 19!
Answer: C
19 Roy is now 4 years older than Erik and half of that amount older than Iris. If in 2 years, roy will be twice as old as Erik, then in 2 years what would be Roy's age multiplied by Iris's age?
A. 28
B. 48
C. 50
D. 52
Answer: 48
20 X, Y, X and W are integers. The expression X - Y - Z is even and the expression Y - Z - W is odd. If X is even what must be true?
A. W must be odd
B. Y - Z must be odd
C. W must be odd
D. Z must be odd
Answer: A or C (But go for C)
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TCS Latest Placement Paper Questions With Solutions
1. A manufacturer of chocolates makes 6 different flavors of chocolates. The chocolates are sold in boxes of 10. How many “different” boxes of chocolates can be made?
Sol:
If n similar articles are to be distributed to r persons, x1+x2+x3......xr=n each person is eligible to take any number of articles then the total ways are n+r−1Cr−1
In this case x1+x2+x3......x6=10
in such a case the formula for non negative integral solutions is n+r−1Cr−1
Here n =6 and r=10. So total ways are 10+6−1C6−1 = 3003
2. In a single throw with two dice, find the probability that their sum is a multiple either of 3 or 4.
a. 1/3
b. 1/2
c. 5/9
d. 17/36
Sol: Their sum can be 3,4,6,8,9,12
For two dice, any number from 2 to 7 can be get in (n-1) ways and any number from 8 to 12 can be get in (13 - n) ways.
Then possible ways are 2 + 3 + 5 + 5 + 4 + 1 = 20 possible cases.
So probability is (20/36)=(5/9)
3. B alone can do piece of work in 10 days. A alone can do it in 15 days. If the total wages for the work is Rs 5000, how much should B be paid if they work together for the entire duration of the work?
a. 2000
b. 4000
c. 5000
d. 3000
Sol:
Time taken by A and B is in the ratio of = 3:2
Ratio of the Work = 2 : 3 (since, time and work are inversely proportional)
Total money is divided in the ratio of 2 : 3 and B gets Rs.3000
4. The letters in the word ADOPTS are permuted in all possible ways and arranged in alphabetical order then find the word at position 42 in the permuted alphabetical order?
a) AOTDSP
b) AOTPDS
c) AOTDPS
d) AOSTPD
SOL:
In alphabetical order : A D O P S T
A _ _ _ _ _ : the places filled in 5! ways = 120, But we need a rank less than 120. So the word starts with A.
A D _ _ _ _ : empty places can be filled in 4!=24
A O _ _ _ _ : the places filled with 4! ways = 24. If we add 24 + 24 this total crosses 42. So We should not consider all the words starting with AO.
A O D _ _ _ : 3!= 6
A O P _ _ _ : 3!=6
Till this 36 words are obtained, we need the 42nd word.
AOS _ _ _ : 3!= 6
Exactly we are getting the sum 42. So last 3 letters in the descending order are TPD.
So given word is AOSTPD
5. Arun makes a popular brand of ice cream in a rectangular shaped bar 6cm long, 5cm wide and 2cm thick. To cut costs, the company had decided to reduce the volume of the bar by 19%. The thickness will remain same, but the length and width will be decreased by some percentage. The new width will be,
a. 5.5
b. 4.5
c. 7.5
d. 6.5
Sol:
Volume =l×b×h = 6×5×2 = 60 cm3
Now volume is reduced by 19%.
Therefore, new volume = (100−19)100×60=48.6
Now, thickness remains same and let length and breadth be reduced to x%
so, new volume: (x100×6)(x100×5)2=48.6
Solving we get x =90
thus length and width is reduced by 10%
New width = 5-(10% of 5)=4.5
6. If all the numbers between 11 and 100 are written on a piece of paper. How many times will the number 4 be used?
Sol: We have to consider the number of 4's in two digit numbers. _ _
If we fix 4 in the 10th place, unit place be filled with 10 ways. If we fix 4 in units place, 10th place be filled with 9 ways (0 is not allowed)
So total 19 ways.
Alternatively:
There are total 9 4's in 14, 24, 34...,94
& total 10 4's in 40,41,42....49
thus, 9+10=19.
7. If twenty four men and sixteen women work on a day, the total wages to be paid is 11,600. If twelve men and thirty seven women work on a day, the total wages to be paid remains the same. What is the wages paid to a man for a day’s work?
Sol: Let man daily wages and woman daily wages be M and W respectively
24M+16W=11600
12M+37W=11600
solving the above equations gives M=350 and W=200
8. The cost price of a cow and a horse is Rs 3 lakhs. The cow is sold at 20% profit and the horse is sold at 10% loss. Overall gain is Rs 4200. What is the cost price of the cow?
Sol:
Profit = 4200
Profit =SP - CP
4200=SP - 300000 therefore SP=304200
x+y = 300000
1.2x + 0.9y = 304200
Solving for x = 114000 = CP of cow.
9. 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4......
In the above sequence what is the number of the position 2888 of the sequence.
a) 1
b) 4
c) 3
d) 2
Sol: First if we count 1223334444. they are 10
In the next term they are 20
Next they are 30 and so on
So Using n(n+1)2×10≤2888
For n = 23 we get LHS as 2760. Remaining terms 128.
Now in the 24th term, we have 24 1's, and next 48 terms are 2's. So next 72 terms are 3's.
The 2888 term will be “3”.
10. How many 4-digit numbers contain no.2?
Sol: Total number of four digit numbers =9000 (i.e 1000 to 9999 )
We try to find the number of numbers not having digit 2 in them.
Now consider the units place it can be selected in 9 ways (i.e 0,1,3,4,5,6,7,8,9)
Tens place it can be selected in 9 ways (i.e 0,1,3,4,5,6,7,8,9)
Hundreds place it can be selected in 9 ways (i.e 0,1,3,4,5,6,7,8,9)
Thousands place can be selected in 8 ways (i.e 1,3,4,5,6,7,8,9) here '0' cannot be taken
Total number of numbers not having digit 2 in it =9 x 9 x 9 x 8 =5832
Total number of numbers having digit 2 in it = 9000-5832 =3168
11. The value of diamond varies directly as the square of its weight. If a diamond falls and breaks into two pieces with weights in the ratio 2:3. what is the loss percentage in the value?
Sol: Let weight be “x”
the cost of diamond in the original state is proportional to x2
when it is fallen it breaks into two pieces 2y and the 3y
x = 5y
Original value of diamond = (5y)2 = 25y2
Value of diamond after breakage = (2y)2+(3y)2=13y2
so the percentage loss will be = 25y2−13y225y2×100=48%
12. Five college students met at a party and exchanged gossips. Uma said, “Only one of us is lying”. David said, “Exactly two of us are lying”. Thara said, “Exactly 3 of us are lying”. Querishi said, “Exactly 4 of us are lying”. Chitra said “All of us are lying”. Which one was telling the truth?
a)David
b)Querishi
c)Chitra
d)Thara
Sol: As all are contradictory statements, it is clear that ONLY one of them is telling the truth. So remaining 4 of them are lying. Querishi mentioned that exactly 4 are lying. So, he is telling the truth.
Explanation: Let us 1st assume that Uma is telling the truth. Then according to her only one is lying. But if only one is lying then all the others’ statements are contradicting the possibility. In the same way all the other statements should be checked. If we assume the Querishi is telling the truth, according to him exactly 4 members are lying. So all the others are telling lies and he is the one who is telling the truth. This case fits perfectly.
13. Cara, a blue whale participated in a weight loss program at the biggest office. At the end of every month, the decrease in weight from original weight was measured and noted as 1, 2, 6, 21, 86, 445, 2676. While Cara made a steadfast effort, the weighing machine showed an erroneous weight once. What was that.
a) 2676
b) 2
c) 445
d) 86
SOL: This is a number series problem nothing to do with the data given.
1x 1+1=2
2 x 2+2=6
6 x 3+3=21
21 x 4+4=88 and not 86
88 x 5+5 = 445
445*6+6 = 2676
14. A man who goes to work long before sunrise every morning gets dressed in the dark. In his sock drawer he has 6 black and 8 blue socks. What is the probability that his first pick was a black sock, but his second pick was a blue sock?
SOL: This is a case of without replacement. We have to multiply two probabilities. 1. Probability of picking up a black sock, and probability of picking a blue sock, given that first sock is black.
6C114C1×8C113C1=2491
15. There are 6 red balls,8 blue balls and 7 green balls in a bag. If 5 are drawn with replacement, what is the probability at least three are red?
Sol: At least 3 reds means we get either : 3 red or 4 red or 5 red. And this is a case of replacement.
case 1 : 3 red balls : 6/21 x 6/21 x 6/21 x 15/21 x 15/21
case 2 : 4 red balls : 6/21 x 6/21 x 6/21 x 6/21 x 15/21
case 3 : 5 red balls : 6/21 x 6/21 x 6/21 x 6/21 x 6/21
Total probability = = (6/21 x 6/21 x 6/21 x 15/21 x 15/21)+(6/21 x 6/21 x 6/21 x 6/21 x (15 )/21)+ (6/21 x 6/21 x 6/21 x 6/21 x 6/21)
= 312/16807
16. Total number of 4 digit number do not having the digit 3 or 6.
Sol:
consider 4 digits _ _ _ _
1st blank can be filled in 7C1 ways (0,3,6 are neglected as the first digit should not be 0)
2st blank can be filled in 8C1 ways (0 considered along with 1,2,4,5,7,8,9)
3st blank can be filled in 8C1 ways
4st blank can be filled in 8C1 ways
Therefore total 4 digit number without 3 or 6 is 7 x 8 x 8 x 8=3584
17. Find the missing in the series: 70, 54, 45, 41,____.
Sol: 40
70-54 = 16 = 42
54-45 = 9 = 32
45-41 = 4 = 22
41-40 = 1 = 12
18. A school has 120, 192 and 144 students enrolled for its science, arts and commerce courses. All students have to be seated in rooms for an exam such that each room has students of only the same course and also all rooms have equal number of students. What is the least number of rooms needed?
Sol: We have to find the maximum number which divides all the given numbers so that number of roots get minimized. HCF of 120,192 & 144 is 24. Each room have 24 students of the same course.
Then rooms needed 12024+19224+14424 = 5 +8 + 6 = 19
19. A farmer has a rose garden. Every day he picks either 7,6,24 or 23 roses. When he plucks these number of flowers the next day 37,36,9 or 18 new flowers bloom. On Monday he counts 189 roses. If he continues on his plan each day, after some days what can be the number of roses left behind? (Hint : Consider number of roses remaining every day)
a)7
b)4
c)30
d)37
Sol:
let us consider the case of 23. when he picks up 23 roses the next day there will be 18 new, so in this case., 5 flowers will be less every day. So when he counts 189, the next day 184, 179,174,169,................
finally the no. of roses left behind will be 4.
20. What is the 32nd word of "WAITING" in a dictionary?
Sol: Arranging the words of waiting in Alphabetical Order : A,G,I,I,N,T,W
Start with A_ _ _ _ _ _ This can be arranged in 6!/2! ways=720/2=360 ways
so can't be arranged starting with A alone as it is asking for 32nd word so it is out of range
AG_ _ _ _ _then the remaining letters can be arranged in 5!/2! ways so,120/2=60 ways. Out of range as it has to be within 32 words.
AGI_ _ _ _ Now the remaining letters can be arranged in 4! ways =24
AGN _ _ _ _ can be arranged in 4!/2! ways or 12 ways
so,24+12 =36th word so out of range. So we should not consider all the words start with AGN
now AGNI_ _ _can be arranged in 3! ways =6 ways
so 24+6=30 within range
Now only two word left so, arrange in alphabetical order.
AGNTIIW - 31st word
AGNTIWI - 32nd word
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TCS Aptitude Questions
1. If f(x) = (1+x+x2+x3+.......x2012)2−x2012, g(x) = 1+x+x2+x3+.......x2011.Then what is the remainder when f(x) is divided by g(x)
Let us multiply g(x) with x on the both sides
x.g(x) = x+x2+x3+.......x2012
add 1 on both sides
x. g(x) + 1 = 1+x+x2+x3+.......x2012
Substitute this value in f(x)
then f(x) = (x.g(x)+1)2−x2012
f(x) = x2.g(x)2+2.g(x)+1−x2012
Now f(x) is divisible by g(x) first two terms are exactly divisible by g(x) and we get 1 - x2012
But 1 - x2012 = (1 - x)(1+x+x2+x3+.......x2011)
if this expression is divisible by g(x) we get 0 as remainder.
2. A number has exactly 3 prime factors, 125 factors of this number are perfect squares and 27 factors of this number are perfect cubes. overall how many factors does the number have?
We know that the total factors of a number N = ap.bq.cr ....
Now the total factors which are perfect squares of a number N = ([p2]+1).([q2]+1).([r2]+1)....
where [x] is greatest intezer less than that of x.
Given ([p2]+1).([q2]+1).([r2]+1).... = 125
So [p2]+1 = 5; [q2]+1 = 5; [p2]+1 = 5
[p2] = 4 ⇒ p = 8 or 9, similarly q = 8 or 9, r = 8 or 9
Given that 27 factors of this number are perfect cubes
so ([p3]+1).([q3]+1).([r3]+1).... = 27
So [p3]+1 = 3 ⇒ = [p3] = 2
⇒ p = 6, 7, 8
By combining we know that p = q = r = 84
Number of factors of this number = (8+1).(8+1).(8+1) = 729
3. In a class there are 60% of girls of which 25% poor. What is the probability that a poor girl is selected is leader?
Assume total students in the class = 100
Then Girls = 60% (100) = 60
Poor girls = 25% (60) = 15
So probability that a poor girls is selected leader = Poor girls / Total students = 15/100 = 15%
4. A and B are running around a circular track of length 120 meters with speeds 12 m/s and 6 m/s in the same direction. When will they meet for the first time?
A meets B when A covers one round more than B.
A's relative speed = (12 - 6) m/s. So he takes 120 / 6 seconds to gain one extra round.
So after 20 seconds A meets B.
5. A completes a work in 20 days B in 60 days C in 45 days. All three persons working together on a project got a profit of Rs.26000 what is the profit of B?
We know that profits must be shared as the ratio of their efficiencies. But efficiencies are inversely proportional to the days. So efficiencies of A : B : C = 1/20 : 1/60 : 1/45 = 9 : 3 : 4
So B share in the total profit = 3 / 13 X 26000 = Rs.6000
6. A completes a piece of work in 3/4 of the time in B does, B takes 4/5 of the time in C does. They got a profit of Rs. 40000 how much B gets?
Assume C takes 20 Days. Now B takes 4/5 (20) = 16 days. A takes 3/4(16) = 12
Now their efficiencies ratio = 1/20 : 1/16 : 1/12 = 12 : 15 : 20
B's share in the profit of Rs.40000 = 15/47 (40000) = Rs.12765
7. An empty tank be filled with an inlet pipe ‘A’ in 42 minutes. After 12 minutes an outlet pipe ‘B’ is opened which can empty the tank in 30 minutes. After 6 minutes another inlet pipe ‘C’ opened into the same tank, which can fill the tank in 35 minutes and the tank is filled. Find the time taken to fill the tank?
Assume total tank capacity = 210 Liters
Now capacity of pipe A = 210/42 = 5 Liters
Capacity of B = 210 / 30 = - 7 Liters
Capacity of C = 210 / 35 = 6 min
Assume tank gets filled in x min after the third pipe got opened.
So x×5+6×(−2)+4x=210
⇒48+4x=210⇒4x=162⇒x=40.5
Total time taken to fill the tank = 40.5 + 12 + 6 = 51.5
8. Mother, daughter and an infant combined age is 74, and mother's age is 46 more than daughter and infant. If infant age is 0.4 times of daughter age, then find daughters age.
Assume M + D + I = 74; .................(1)
Also given M - D - I = 46 ⇒ M = D + I + 46
Also I = 0.4 D ⇒ I = 2/5 D
Substituting M and I values in the first equation we get D - 25D - 46 + D + 25D = 74
Solving D = 10
9. A Grocer bought 24 kg coffee beans at price X per kg. After a while one third of stock got spoiled so he sold the rest for $200 per kg and made a total profit of twice the cost. What must be the price of X?
Total Cost price = 24×X
As 1/3rd of the beans spoiled, remaining beans are 2/3 (24) = 16 kgs
Selling price = 200 × 16 = 3200
Profit = Selling price - Cost price = 3200 - 24×X
Given Profit = 2 × Cost price
3200 - 24×X = 2 × (24×X)
Solving X = 44.44
10. Bhanu spends 30% of his income on petrol on scooter 20% of the remaining on house rent and the balance on food. If he spends Rs.300 on petrol then what is the expenditure on house rent?
Given 30% (Income ) = 300 ⇒ Income = 1000
After having spent Rs.300 on petrol, he left with Rs.700.
His spending on house rent = 20% (700) = Rs.140
11. Let exp(m,n) = m to the power n. If exp(10, m) = n exp(2, 2) where to and n are integers then n =
Given 10m=n.22
⇒ 2m×5m=n.22⇒2m−2×5m=n
For m = 2 we get least value of n = 25, and for m > 2 we get infinite values are possible for n.
12. How many kgs. of wheat costing Rs. 5 per kg must be mixed with 45 kg of rice costing Rs. 6.40 per kg so that 20% gain may be obtained by selling the mixture at Rs. 7.20 per kg ?
If the selling price of the mixture is Rs.7.2 when sold at 20% profit then
CP ×120100 = 7.2 ⇒ CP = Rs.6
Now by applying weighted average formula = K×5+45×6.4K+45=6
⇒ K = 18 kgs
13. The diagonal of a square is twice the side of equilateral triangle then the ratio of Area of the Triangle to the Area of Square is?
Let the side of equilateral triangle = 1 unit.
We know that area of an equilateral triangle = 3√4a2
As side = 1 unit area of the equilateral triangle = 3√4
Now Diagonal of the square = 2 (side of the equilateral triangle) = 2
We know that area of the square = 12D2 where D = diagonal
So area of the square = 12(22)=2
Ratio of the areas of equilateral triangle and square = 3√4 : 2 ⇒ 3√:8
14. Raj tossed 3 dices and there results are noted down then what is the probability that raj gets 10?
Always remember when 3 dice are rolled the number of ways of getting n ( where n is the sum of faces on dice)
= (n−1)C2 where n = 3 to 8
= 25 where n = 9, 12
= 27 where n = 10, 11
= (20−n)C2 where n = 13 to 18
The required probability = 2763 = 27216
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TCS Model Question Paper
Aptitude Questions
1. What are the total number of divisors of 600(including 1 and 600)?
a. 24
b. 40
c. 16
d. 20 Sol: Option a
If N=ap×bq×cr.... then the number of factors of N = (p+1)(q+1)(r+1) ....
600 = 23×3×52
So number of factors of 600 = (3+1)(1+1)(2+1) = 24
2. What is the sum of the squares of the first 20 natural numbers (1 to 20)?
a. 2870
b. 2000
c. 5650
d. 44100 Sol: Option a
Use formula n(n+1)(2n+1)6
3. In the polynomial f(x) = x^5 + a*x^3 + b*x^4 +c*x + d, all coefficients a, b, c, d are integers. If 3 + sqrt(7) is a root, which of the following must be also a root?(Note that x^n denotes the x raised to the power n, or x multiplied by itself n times. Also sqrt(u) denotes the square root of u, or the number which when multiplied by itself, gives the number u)?
a. 3-sqrt(7)
b. 3+sqrt(21)
c. 5
d. sqrt(7) + sqrt(3) Sol: Option A
4. How many divisors (including 1, but excluding 1000) are there for the number 1000?
a. 15
b. 16
c. 31
d. 10 Sol: Option A
5. A call center agent has a list of 305 phone numbers of people in alphabetic order of names (but she does not have any of the names). She needs to quickly contact Deepak Sharma to convey a message to him. If each call takes 2 minutes to complete, and every call is answered, what is the minimum amount of time in which she can guarantee to deliver the message to Mr Sharma.
a. 18 minutes
b. 610 minutes
c. 206 minutes
d. 34 minutes Sol: Option A
6. The times taken by a phone operator to complete a call are 2,9,3,1,5 minutes respectively. What is the average time per call?
a. 4 minutes
b. 7 minutes
c. 1 minutes
d. 5 minutes Sol: Option A
7. The times taken by a phone operator to complete a call are 2,9,3,1,5 minutes respectively. What is the median time per call?
a. 5 minutes
b. 7 minutes
c. 1 minutes
d. 4 minutes Sol: NO option is correct. Median is 3
8. Eric throws two dice, and his score is the sum of the values shown. Sandra throws one die, and her score is the square of the value shown. What is the probability that Sandra’s score will be strictly higher than Eric’s score?
a. 137/216
b. 17/36
c. 173/216
d. 5/6 Sol: A
9. What is the largest integer that divides all three numbers 23400,272304,205248 without leaving a remainder?
a. 48
b. 24
c. 96
d. 72 Sol: Option B
10. Of the 38 people in my office, 10 like to drink chocolate, 15 are cricket fans, and 20 neither like chocolate nor like cricket. How many people like both cricket and chocolate?
a. 7
b. 10
c. 15
d. 18 Sol: Option A
11. If f(x) = 2x+2 what is f(f(3))?
a. 18
b. 8
c. 64
d. 16 Sol: Option A
12. If f(x) = 7 x +12, what is f-1(x) (the inverse function)?
a. (x-12)/7
b. 7x+12
c. 1/(7x+12)
d. No inverse exists Sol: Option A
13. A permutation is often represented by the cycles it has. For example, if we permute the numbers in the natural order to 2 3 1 5 4, this is represented as (1 3 2) (5 4). In this the (132) says that the first number has gone to the position 3, the third number has gone to the position 2, and the second number has gone to position 1, and (5 4) means that the fifth number has gone to position 4 and the fourth number has gone to position 5. The numbers with brackets are to be read cyclically. If a number has not changed position, it is kept as a single cycle. Thus 5 2 1 3 4 is represented as (1345)(2). We may apply permutations on itself If we apply the permutation (132)(54) once, we get 2 3 1 5 4. If we apply it again, we get 3 1 2 4 5 , or (1 2 3)(4) (5) If we consider the permutation of 7 numbers (1457)(263), what is its order (how many times must it be applied before the numbers appear in their original order)?
a. 12
b. 7
c. 7! (factorial of 7)
d. 14 Sol: Not yet solved
14. What is the maximum value of x3y3 + 3 x*y when x+y = 8?
a. 4144
b. 256
c. 8192
d. 102 Sol: Option A
The question probably be x3.y3+3x∗y
Sustitute x = 4 and y = 4
15. A white cube(with six faces) is painted red on two different faces. How many different ways can this be done (two paintings are considered same if on a suitable rotation of the cube one painting can be carried to the other)?
a. 2
b. 15
c. 4
d. 30 Sol: Option A
16. In Goa beach, there are three small picnic tables. Tables 1 and 2 each seat three people. Table 3 seats only one person, since two of its seats are broken. Akash, Babu, Chitra, David, Eesha, Farooq, and Govind all sit at seats at these picnic tables. Who sits with whom and at which table are determined by the following constraints:
a. Chitra does not sit at the same table as Govind.
b. Eesha does not sit at the same table as David.
c. Farooq does not sit at the same table as Chitra.
d. Akash does not sit at the same table as Babu.
e. Govind does not sit at the same table as Farooq.
Which of the following is a list of people who could sit together at table 2?
a. Govind, Eesha, Akash
b. Babu, Farooq, Chitra
c. Chitra, Govind, David.
d. Farooq, David, Eesha. Sol: Option A
17. There are a number of chocolates in a bag. If they were to be equally divided among 14 children, there are 10 chocolates left. If they were to be equally divided among 15 children, there are 8 chocolates left. Obviously, this can be satisfied if any multiple of 210 chocolates are added to the bag. What is the remainder when the minimum feasible number of chocolates in the bag is divided by 9?
a. 2
b. 5
c. 4
d. 6 Sol: Option B
18. Let f(m,n) =45*m + 36*n, where m and n are integers (positive or negative) What is the minimum positive value for f(m,n) for all values of m,n (this may be achieved for various values of m and n)?
a. 9
b. 6
c. 5
d. 18 Sol: Option A
19. What is the largest number that will divide 90207, 232585 and 127986 without leaving a remainder?
a. 257
b. 905
c. 351
d. 498 Sol: Option A
20. We have an equal arms two pan balance and need to weigh objects with integral weights in the range 1 to 40 kilo grams. We have a set of standard weights and can place the weights in any pan. . (i.e) some weights can be in a pan with objects and some weights can be in the other pan. The minimum number of standard weights required is:
a. 4
b. 10
c. 5
d. 6 Sol: Option A
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Latest TCS Placement Papers Fully Solved 2014-2015 batch
TCS Placement Paper 2014 -2015
1) A power unit is there by the bank of a river of 900 meters. A cable is made from power unit to power a plant opposite to that of the river of 2000mts. The cost of the cable below water is Rs. 5/- per meter and cost of cable on the bank is Rs. 4/- per meter. Then find out the amount to be invested to connect those two stations?
Explanation:
Required length of wire = 2000 mts cost of cable below water = 900 * 5 = 4500 cost of cable on the bank of river= (2000 - 900) * 4 = 4400 Total cost = 4500 + 4400 = 8900.
2) A farmer had 20 hens. All but 2 died. How many hens are still alive?
Explanation:
"All but 2" means 2. So, all but 2 died means that there are only two hens are alive and others were dead. So, the answer is 2.
3) At this series: 7, 10, 8, 11, 9, 12... What number should come next?
Explanation:
This is a simple alternating addition and subtraction series. In the first pattern, 3 are added; in the second, 2 are subtracted.
4) A college has 10 basketball players. A 5-member team and a captain will be selected out of these 10 players. How many different selections can be made?
Explanation:
We can select the 5 member team out of the 10 in 10C5 ways = 252 ways. The captain can be selected from amongst the remaining 5 players in 5 ways. Therefore, total ways the selection of 5 players and a captain can be made = 252*5 = 1260.
5) There are 3 gentlemen in a meeting: Mr. Yellow, Mr. Green and Mr. Brown. They are wearing yellow, green and brown ties. Mr. Yellow says: "Did you notice that the colors of our ties are different from our names?" The person who is wearing the green tie says, "Yes, you are right!" Do you know Brown is wearing what colour of tie?
Explanation:
We know that Mr. Yellow was not wearing a yellow tie because of his statement. He also was not wearing the green tie because the one wearing the green tie agreed to his statement. Therefore, Mr. Yellow was wearing a brown tie. Mr. Green was wearing a yellow tie. And Mr. Brown was wearing the green tie.
6) g[0]=1,g[1]=-1,g[n]=2*g[n-1]-3*g[n-2] then calculate g[4]= ?
Explanation:
From the given function g[n] =2*g [n-1]-3*g [n-2] put values of n as first 2 then 3, then 4 and you will get the answer. G[2] = 2*g[1]-3*g[0]=-2-3 =-5 , G[3]=2*g[2]-3*g[1] =2*(-5)-3*(-1)=-7, G [4] =2*g[3]-3*g[2]=2*(-7)-3*(-5) =1
7) Ten years ago X was half of Y. If the ratio of their present ages is 3:4, what will be the total of their present ages?
Explanation:
Let X's age 10 years ago = x years. Then, Y's age 10 years ago = 2x years. (x + 10)/ (2x + 10) = 3/4 => 4 (x + 10) = 3 (2x + 10) x = 5 Total of their present ages = (x + 10 + 2x + 10) = 3x + 20 = 15 + 20 = 35 years.
8) A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:
Answer: 120KMPH
9) In a circular racetrack of length 100 m, three persons A, B and C start together. A and B start in the same direction at speeds of 10 m/s and 8 m/s respectively. While C runs in the opposite at 15 m/s. When will all the three meet for the first time after the start?
Explanation:
Since the track is a circular track A and B will meet every 50 seconds. i.e. 100 / (10-8). Since it is a multiple of 50 they will be meeting at the starting point every 50 Seconds. If you multiply 15 x 50 you will get 750 and after the second 50 it will be 1500. All of them will meet at the starting point after 100s
10) A class of 100 students. 24 of them are girls and 32 are not. Which base am I using?
Explanation:
Let the base be X. Therefore (X*X + X*0 + 0) = (2*X +4) + (3*X + 2), X * X = 5 * X + 6, X * X - 5 * X -6 = 0, (X- 6) (X+1) = 0 Therefore base is 6.
11) Siva, Sathish, Amar and Praveen are playing cards. Amar is to the right of Sathish, who is to the right of Siva. Who is to the right of Amar?
Answer: Praveen
12) Ferrari is leading car manufacturer. Ferrari S.P.A. is an Italian sports car. It has enjoyed great success. If Mohan's Ferrari is 3 times faster than his old MERCEDES which gave him 35 km/ph if Mohan travelled 490 km in his Ferrari the how much time in hours he took?
Explanation:
Time = (Distance/Speed) = (490/35) Therefore the total time = time/3 = (490/35)/3 = 4.6666 Approximately 4.7
13) My flight takes off at 2 AM from a place at 18N 10E and landed 10 Hrs later at a place with coordinates 36N 70W. What is the local time when my plane landed?
Explanation:
Total change in degrees in east-west direction = 70 + 10 degrees =80 degrees, Time change due to the change in Longitude = 80*4 = 320 minutes = 5 hrs 20 min. According to the person the time would have been = 2 am + 10 hrs = 12 am. But according to the local time the time would be = 12 - 5.20 = 6 .40am
14) A class of 25 students took a science test. 10 students had an average (arithmetic mean) score of 80. The other students had an average score of 60. What is the average score of the whole class?
Explanation:
80 × 10 + 60 × 15 = 800 + 900 = 1700 Total number of students = 25 Average weight = 1700/25 The average score of the whole class is 68.
15) The cost of one pencil, two pens and four erasers is Rs.22 while the cost of five pencils, four pens and two erasers is Rs.32. How much will three pencils, three pens and three erasers cost?
Explanation:
x + 2y + 4z = 22 -------->1 5x + 4y + 2z = 32 ------->2 multiply eqn (2) by 2 and substract from eqn(1) dividing by 3 we get 3x + 2y = 14--------->3 multiplying eqn (1) by 5 and subtracting eqn (2) then divide by 6 we get y + 3z = 13---------->4 Adding eqn (3) and (4) we get 3x + 3y +3z = 27
16) A is 20 percent more efficient than B. If the two persons can complete a piece of work in 60 days. In how many days A working alone can complete the work?
Explanation:
Ratio of time taken by A and B is 1: 1.2 i.e. 5:6 Let the time taken by A be 5x and by B be 6x , 1/5x + 1/ 6x = 1/60 => x =22. Time taken by A = 5 * 22 = 110
17) On a certain island, 5% of the 10000 inhabitants are one-legged and half of the others go barefooted. What is the least number of Shoes needed in the island?
Explanation:
In any case the one legged people will all require one shoe per head. From the remaining, half will go barefooted and therefore they need no shoes. And the rest will need two shoes per head. And this works out at one shoe per person for the others. Therefore for the whole population on the average one shoe per head
18) Look at this series: 14, 28, 20, 40, 32, 64, what number should come next?
Explanation:
This is an alternating multiplication and subtracting series: First, multiply by 2 and then subtract 8.
19) Two pipes A and B can fill a tank in 24 min. and 32 min. respectively. If both the pipes are opened simultaneously, after how much time B should be closed so that the tank is full in 18 minutes?
Explanation:
Let B be closed after x minutes. Then, part filled by (A + B) in x min. + part filled by an in (18 - x) min. = 1. X {1/24 + 1/32] + (18 - x) X 1/24 = 1 or 7x/96 + (18 - x)/24 = 1 7x + 4(18 -x) = 96 or x=8 Hence, B must be closed after 8 minutes
20) At a car park there are 100 vehicles, 60 of which are cars, 30 are vans and the remaining are Lorries. If every vehicle is equally likely to leave, find the probability of car leaving second if either a lorry or van had left first :
Explanation:
Let S be the sample space and A be the event of a van leaving first. n(S) = 100 n (A) = 30 Probability of a van leaving first: P (A) = 30/100 = 3/10 Let B be the event of a lorry leaving first. n (B) = 100 - 60 - 30 = 10 Probability of a lorry leaving first: P (B) = 10/100 = 1/10 If either a lorry or van had left first, then there would be 99 vehicles remaining, 60 of which are cars. Let T be the sample space and C be the event of a car leaving. n (T) = 99 n(C) = 60 Probability of a car leaving after a lorry or van has left: P(C) = 60/99 = 20/33
21) A red house is built from red bricks. A blue house is built from blue bricks. A white house is built from white bricks. Then what is a greenhouse made from?
Explanation:
Glass i.e. Buildings are made of bricks. But a greenhouse is made of glass.
22) If Rs. 782 be divided into three parts, proportional to 1/2: 2/3: 3/4, then the first part is: www.allindiajobs.in
Explanation:
Given ratio = 1/2: 2/3:3/4 = 6: 8: 9 1st part = 782*(6/22) = 213.2727.. Approximately equals to 213 www.allindiaobs.in
23) A man decides to buy a nice horse. He pays $60 for it, and he is very content with the strong animal. After a year, the value of the horse has increased to $70 and he decides to sell the horse . But after a few days later he regrets his decision to sell the beautiful horse, and he buys it again. Unfortunately he has to pay $80 to get it back, so he loses $10. After another year of owing the horse, he finally decides to sell the horse for $90. What is the overall profit the man makes?
Explanation:
The total expenses are $60 + $80 = $140 and the total earnings are $70 +$90 = $160. The overall profit = $160 - $140 = $ 20
24) When I become as old as my father is now, I will be 5 times the age of my son. In addition, my son will be 8 yrs older than What I am now. If the sum of my father's age and my age is equal to100. How old is my son now?
Explanation:
Let us consider the ages of the man, his father & his son is m, f & s respectively. Then according to the problem F=5s............ (i) S + f-m = m+8........ (ii) F + m = 100........... (iii) Putting (i) in (iii) we get 5s+m=100........ (iv) Putting (i) in (ii) we get 6s-2m=8............ (v) Equating (iv) & (v) we get s = 13, f = 65 & m = 36
25) Nine persons went to the hostel for taking their meals, 8 of them spent Rs.12 each on their meals and ninth spend Rs. 8 more then the average expenditure of all nine. What is the total money spent by them?
Explanation:
Let average expenditure be x Then 8*12 +(x+8) = 9x i.e. 104 + x = 9x; 8x = 104 x = 13 Therefore total money spent is 9x = 9*13 =117
26) The average of a list of 6 numbers is 20. If we remove one of the numbers, the average of the remaining numbers is 15. What is the number that was removed?
Explanation:
The removed number could be obtained by difference between the sum of original 6 numbers and the sum of remaining 5 numbers i.e. sum of original 6 numbers - sum of remaining 5 numbers sum of original 6 numbers = 20 × 6 = 120 sum of remaining 5 numbers = 15 × 5 = 75 Number removed = sum of original 6 numbers - sum of remaining 5 numbers 120 - 75 = 45
27) In the word ORGANISATIONAL, if the first and second, third and fourth, fifth and sixth letters are interchanged, what would be the 12th letter from right?
Explanation:
After interchanging R O A G I N S A T I O N A L 14 13 12 11 10 9 8 7 6 5 4 3 2 1
28) What are the number of edges, number of vertices and number of faces of a planar cube among the following options?
We know cube has 6 faces, 12 edges and 8 vertices
29 How many alphabets need to be there in a language if one were to make 1 million distinct 3 digit initials using the alphabets of the language?
Explanation:
Let the number of required alphabets in the language be 'n'. Therefore, using 'n' alphabets we can form n * n * n = n3 distinct 3 digit initials. These n3 different initials = 1 million i.e. n3 = 106 (1 million = 106) => n3 = (102)3 => n = 102 = 100
30) Today's high school students spend too much time thinking about trivial and distracting matters such as fashion. Additionally, they often dress inappropriately on school grounds. Rather than spending time writing another detailed dress policy, we should make school uniforms mandatory. If students were required to wear uniforms, it would increase a sense of community and harmony in our schools and it would instill a sense of discipline in our students. Another positive effect would be that teachers and administrators would no longer have to act as clothing police, freeing them up to focus on more important issues.
This paragraph best supports the statement that
Options:
a) inappropriate clothing leads to failing grades
b) students who wear school uniforms get into better colleges
c) teachers and administrators spend at least 25% of their time enforcing the dress code.
d) school uniforms should be compulsory for high school students
Answer: Explanation:
The support for choice e is in the third sentence "we should make school uniforms mandatory". There is no evidence provided to support choices a, b, and d. And although we know that teachers and administrators are spending some of their time enforcing dress code, the paragraph does not quantify how much of their time is spent that way, so there is no support for choice c.
________________________________________________________________________
TCS
new and latest placement paper aptitude questions based on
TCS visited
in RVR and JC COLLEGE OF ENGINEERING,in Andhrapradesh for Btech
students.TCS this year new question papers and TCS Technical HR
Interview questions and TCS campus recruitment procedure ,TCS new
selection procedure, written test pattern shared by Jhansi campus
recruitment experience
ME WITH TCS -Me With TCS new placement paper pattern for 2014-2015 batch
Hai, I am Jhansi Yarlagadda presently doing my B.Tech final year . Recently TCS visited our campus for recruitment ….
My aptitude questions are given some which I remember
1)A beaker contains 180 liters of wine each day 60lts of wine is replaced with same amount of water what is the amount of wine after 3 days?
2) a+b=3 ,a^2+b^2=7 find a^4+b^4=?
3)Paul started from home with his bicycle traveling 6kmph at 12:00 pm and john started at 13:30 traveling 9kmph. at what time john will 3km ahead of paul?
4) Saving = income-expenditure income in the ratio 1:2;3 and expenditure in the ratio 3:2:1 let persons income and expenditures be a,b,c .. find their savings in increasing order ..
5) 1*1!+2*2!+3*3!+4*4!+.......+2012*2012!
6) A leap year it is and what is the probability of getting 53 Sundays ???
7) Jake is faster than Paul. Jake and Paul each walk 24 km. The sum of their speeds is 7 km/h and the sum of time taken by them is 14 hours. Then Jake's speed is equal to :
8) 60% of male in a town and 70% of female in a town are eligible to vote. out of which 70% of male and 60% of female who are eligible to vote voted 4 candidate A. what is the value of votes in % did A get?
9) A number( exactly not is a four digit number started with 7) is given 9393 should be added to it so that it must be divided by 12,24,32,54
10) There is a circle with 2 triangles inscribed in it. in opposite direction making a star. The triangle is equilateral of side 12. u have to tell the area of the remaining portion of the circle. 11) A man has 3 shirts, 4 pairs of trousers and 6 ties. What are the number of ways in which he can dress himself with a combination of all the three? 12) A, E, F, and G ran a race.
A said "I did not finish 1st /4th
E said "I did not finish 4th"
F said "I finished 1st"
G said "I finished 4th"
If there were no ties and exactly 3 children told the truth, when who finishes 4th?
TCS Technical interview questions asked in this years new and latest campus recruitment i RVR&JC COLLEGE OF ENGINEERING AP.TCS Asked technical questions are lnaguages C,C++,java projects,truncate etc Below I described my Technical interview in TCS and me
TCS Technical interview
First I knocked the door
Me: may I come in sir
Tr: come in Me: good evng sir,
good evening (two members in panel Tr and Mr)
Tr: good evening, good evening sir please take your seat
Me: thank you sir
Tr: give your resume
Me: gave
Tr: introduce yourself
Me: Told For 10 mins
Tr: define artificial intelligence
Me: told
Tr: diff btw c, c++, Java
Me: Told
Tr: Can you give different stages to deliver a project
Me: told
Tr: what are roll back and delete operations
Me: Told
Tr: What is truncate?
Me: I told but it's not up to the mark
Tr: Write a query using 10% salary hike only employee joined in leap year
Me: Wrote but not up to mark but I explained it how we can get that
Tr: Asked me to write a program to add N and the results should be single digit
Me: Wrote
Tr: Are you an IT candidate can't you be ashamed of not writing a code properly?
Tr: Look and ECE guy wrote it look
Me: sir it's not the program u asked he wrote code for Armstrong
Tr: can I show you result am I am I???
Me: no sir I got it. It can be coded in that way too Sorry sir
Tr: tell me ur project!!!
Me: Told
Tr: I don't know why you study by mug up all programs if I ask you fibanocii , all the listed programs u did I know u can write these but that why I asked this to write
Me: gave a smile
Tr: why u people are doing this?
Me: me sir can I try it again
Tr: yes, u can
Me: took a min and wrote but it’s not up to his mark
Tr: yah this is good than previous one. Nice try
Tr: mr: would you like ask her anything? Mr: no
Tr: any questions
Me: no
Tr: okay you can leave now
Me: Thank you sir it's pleasure to get interviewed by u!!
Tr: smiled
TCS HR Interview questions in campus recruitment in RVR&JC COLLEGE OF ENGINEERING AP
Here in our college some panels have all the three tr, mr, and hr Next....
HR After 5 mins..
Hr: okay Jhansi tell about you yourself not in CV
Me: told about the club I initiated
Hr: is that still running?
Me: yes sir
Hr: gave me water bottle tell me use if it other than filling fuels
Me: sir, if we fill it with some sand and place a rocket (Diwali cracker) we can launch it easily wit out any sort of fear I am thinking for other use
Hr: okay Jhansi why tcs?
Me: told
Hr: why u have been in Guntur since 8 years why not u have chosen other place
Me: sir , I am not a gunturian but for my studies I have been living in Guntur bacically I am from ongole and I told him that I have got seat here and I am staying in hostel since 8 years
Hr: why RVR only
Me: its best college aggregated my NBA 5 times. It's stood in top ten in Andhra and top 92 all over Indian colleges
Hr: what are u doing to improve in English?
Me: told
Hr: are willing to do night shifts
Me: yes sir
Hr: are willing to go anywhere
Me: yes sir I am and I love traveling I have been to Munnar , ooty and I visited all most all South Indian places if I get chance to join tcs I will vist north too
Hr: okay Jhansi can u talk about water bottle for one min?
Me: yes sir Hr: can u can u???
Me: yes sir I can Hr: okay start
Me: waste bottle it's I made up of plastic. Its shape depends on its maker. It has a wrapper. It has a cap which is blue in colour. We can use it to blow horn by placing a rubber to its mouth. This bottle is product of Kinley Hr: okay stop
Hr: do you know about bond?
Me: no sir
Hr: explained
Tr: why tcs why not other company
Me: TCS is the best company without boundaries for career growth
Hr: it's best so u opt tcs???
Me: no sir I can put all my skills if I work for tcs and I can get global exposure and chance to work with multiple employees across 81 nations
Hr: what are the other companies visiting your campus
Me: to my knowledge tcs is first and we have inter graph. , mahindra stayam and some other companies
Hr: why should I hire you?
Me: sir as a fresher I don't have any experience but if get chance to work in tcs I will never let your decisions down. And I am skilled, talented and I work hard too
Hr: do you wana go for higher studies?
Me: no sir, but if at all my career growth insist me to do higher studies then I will do. Moreover we have online opportunities too
Hr: do you have any back logs
Me: no sir no back logs no year gaps
Hr: can u sign bond?
Me: yes sir Hr : any questions
Me: no
Hr: okay Jhansi you can leave now.
Me: thanku sir...
Hr: see you again.
At last he smiled to me At last came out and cried because if tr scolding’s This is is my TCS Experience ..These questions based on my memory TCS Aptitude Technical and HR interview experience in my college recruitment procedure will help you guys This is my first interview. I am from RVR&JC COLLEGE OF ENGINEERING, Guntur, Andhra Pradesh. I hope this may help you …all the best guys. I have got offer letter from Tcs on November 8th 2013. Out 900 Students appeared 114 got selected and I am one among them.
ME WITH TCS -Me With TCS new placement paper pattern for 2014-2015 batch
Hai, I am Jhansi Yarlagadda presently doing my B.Tech final year . Recently TCS visited our campus for recruitment ….
My aptitude questions are given some which I remember
1)A beaker contains 180 liters of wine each day 60lts of wine is replaced with same amount of water what is the amount of wine after 3 days?
2) a+b=3 ,a^2+b^2=7 find a^4+b^4=?
3)Paul started from home with his bicycle traveling 6kmph at 12:00 pm and john started at 13:30 traveling 9kmph. at what time john will 3km ahead of paul?
4) Saving = income-expenditure income in the ratio 1:2;3 and expenditure in the ratio 3:2:1 let persons income and expenditures be a,b,c .. find their savings in increasing order ..
5) 1*1!+2*2!+3*3!+4*4!+.......+2012*2012!
6) A leap year it is and what is the probability of getting 53 Sundays ???
7) Jake is faster than Paul. Jake and Paul each walk 24 km. The sum of their speeds is 7 km/h and the sum of time taken by them is 14 hours. Then Jake's speed is equal to :
8) 60% of male in a town and 70% of female in a town are eligible to vote. out of which 70% of male and 60% of female who are eligible to vote voted 4 candidate A. what is the value of votes in % did A get?
9) A number( exactly not is a four digit number started with 7) is given 9393 should be added to it so that it must be divided by 12,24,32,54
10) There is a circle with 2 triangles inscribed in it. in opposite direction making a star. The triangle is equilateral of side 12. u have to tell the area of the remaining portion of the circle. 11) A man has 3 shirts, 4 pairs of trousers and 6 ties. What are the number of ways in which he can dress himself with a combination of all the three? 12) A, E, F, and G ran a race.
A said "I did not finish 1st /4th
E said "I did not finish 4th"
F said "I finished 1st"
G said "I finished 4th"
If there were no ties and exactly 3 children told the truth, when who finishes 4th?
TCS Technical interview questions asked in this years new and latest campus recruitment i RVR&JC COLLEGE OF ENGINEERING AP.TCS Asked technical questions are lnaguages C,C++,java projects,truncate etc Below I described my Technical interview in TCS and me
TCS Technical interview
First I knocked the door
Me: may I come in sir
Tr: come in Me: good evng sir,
good evening (two members in panel Tr and Mr)
Tr: good evening, good evening sir please take your seat
Me: thank you sir
Tr: give your resume
Me: gave
Tr: introduce yourself
Me: Told For 10 mins
Tr: define artificial intelligence
Me: told
Tr: diff btw c, c++, Java
Me: Told
Tr: Can you give different stages to deliver a project
Me: told
Tr: what are roll back and delete operations
Me: Told
Tr: What is truncate?
Me: I told but it's not up to the mark
Tr: Write a query using 10% salary hike only employee joined in leap year
Me: Wrote but not up to mark but I explained it how we can get that
Tr: Asked me to write a program to add N and the results should be single digit
Me: Wrote
Tr: Are you an IT candidate can't you be ashamed of not writing a code properly?
Tr: Look and ECE guy wrote it look
Me: sir it's not the program u asked he wrote code for Armstrong
Tr: can I show you result am I am I???
Me: no sir I got it. It can be coded in that way too Sorry sir
Tr: tell me ur project!!!
Me: Told
Tr: I don't know why you study by mug up all programs if I ask you fibanocii , all the listed programs u did I know u can write these but that why I asked this to write
Me: gave a smile
Tr: why u people are doing this?
Me: me sir can I try it again
Tr: yes, u can
Me: took a min and wrote but it’s not up to his mark
Tr: yah this is good than previous one. Nice try
Tr: mr: would you like ask her anything? Mr: no
Tr: any questions
Me: no
Tr: okay you can leave now
Me: Thank you sir it's pleasure to get interviewed by u!!
Tr: smiled
TCS HR Interview questions in campus recruitment in RVR&JC COLLEGE OF ENGINEERING AP
Here in our college some panels have all the three tr, mr, and hr Next....
HR After 5 mins..
Hr: okay Jhansi tell about you yourself not in CV
Me: told about the club I initiated
Hr: is that still running?
Me: yes sir
Hr: gave me water bottle tell me use if it other than filling fuels
Me: sir, if we fill it with some sand and place a rocket (Diwali cracker) we can launch it easily wit out any sort of fear I am thinking for other use
Hr: okay Jhansi why tcs?
Me: told
Hr: why u have been in Guntur since 8 years why not u have chosen other place
Me: sir , I am not a gunturian but for my studies I have been living in Guntur bacically I am from ongole and I told him that I have got seat here and I am staying in hostel since 8 years
Hr: why RVR only
Me: its best college aggregated my NBA 5 times. It's stood in top ten in Andhra and top 92 all over Indian colleges
Hr: what are u doing to improve in English?
Me: told
Hr: are willing to do night shifts
Me: yes sir
Hr: are willing to go anywhere
Me: yes sir I am and I love traveling I have been to Munnar , ooty and I visited all most all South Indian places if I get chance to join tcs I will vist north too
Hr: okay Jhansi can u talk about water bottle for one min?
Me: yes sir Hr: can u can u???
Me: yes sir I can Hr: okay start
Me: waste bottle it's I made up of plastic. Its shape depends on its maker. It has a wrapper. It has a cap which is blue in colour. We can use it to blow horn by placing a rubber to its mouth. This bottle is product of Kinley Hr: okay stop
Hr: do you know about bond?
Me: no sir
Hr: explained
Tr: why tcs why not other company
Me: TCS is the best company without boundaries for career growth
Hr: it's best so u opt tcs???
Me: no sir I can put all my skills if I work for tcs and I can get global exposure and chance to work with multiple employees across 81 nations
Hr: what are the other companies visiting your campus
Me: to my knowledge tcs is first and we have inter graph. , mahindra stayam and some other companies
Hr: why should I hire you?
Me: sir as a fresher I don't have any experience but if get chance to work in tcs I will never let your decisions down. And I am skilled, talented and I work hard too
Hr: do you wana go for higher studies?
Me: no sir, but if at all my career growth insist me to do higher studies then I will do. Moreover we have online opportunities too
Hr: do you have any back logs
Me: no sir no back logs no year gaps
Hr: can u sign bond?
Me: yes sir Hr : any questions
Me: no
Hr: okay Jhansi you can leave now.
Me: thanku sir...
Hr: see you again.
At last he smiled to me At last came out and cried because if tr scolding’s This is is my TCS Experience ..These questions based on my memory TCS Aptitude Technical and HR interview experience in my college recruitment procedure will help you guys This is my first interview. I am from RVR&JC COLLEGE OF ENGINEERING, Guntur, Andhra Pradesh. I hope this may help you …all the best guys. I have got offer letter from Tcs on November 8th 2013. Out 900 Students appeared 114 got selected and I am one among them.
__________________________________________________________________
TCS New Placement Paper Question Pattern 2013-2014
Question Pattern of TCS Campus Placement 2013. It is the new questions we get from different students
1. An empty tank be filled with an inlet pipe ‘A’ in 42 minutes. after 12 minutes an outlet pipe ‘B’ is opened which can empty the tank in 30 minutes.
After 6 minutes another inlet pipe ‘C’ opened into the same tank, which can fill the tank in 35 minutes and the tank is filled find the time taken to fill the tank?
Ans
Rate at which A fill is 1/42 per min
A filled for 12 min so tank filled by A will be 12/42
Similarly B empty the tank for 6 min
now the volume will be (18/42) -(6/30) = 8/35 because at the 6 min A has also filled.
Now the amount left to be filled is (1-8/35) = 27/35
Now C comes it fills 1/35 per minute.
So from now the amount will be filled is (1/42+1/35-1/30) = 2/105 per minute
So to fill the required amount it will take 105/2 * 27/35 = 40.5 min
So total time is 12+6+40.5 = 58.5 min
2. A boy wants to make cuboids of dimension 5m,6m & 7m from small cubes of .03m^3.Later he realized that he can make some cuboids by making it hollow.
Then it takes some cubes less. What is the number of cubes to be removed
a)2000
b)5000
c)3000
d)7000
Ans
Total no of cubes = 5*6*7/0.03=7000
for making it hollow we have to remove (5-2)*(6-2)*(7-2)/0.03=2000.
3. Leena cuts small cubes of 3 cubic cm each. She joined it to make a cuboids of length 10 cm,width 3cm, and depth 3 cm.How many more cubes does she need to make a perfect cube?
a)910
b)250
c)750
d)650
Ans
To make cube we need 10*10*10=1000.
Now we have only 10*3*3=90.
So the more cube we need are 1000-90=910.
4. What is the distance between the z-intercept from x-intercept in the eqn ax+by+cz+d=0
Ans
square root of (d/a)^2 + (d/c)^2
5. 10 men and 10 women are there.They dance with each other.Is there possibility that two men are dance with same girl and vice versa?
a)22
b)20
c)10
d)none of these
Ans
none of these
6. A father purchases dress for his three daughter. The dresses are of same color but of different size .The dress is kept in dark room .What is the probability that all the three will not choose their own dress…
a) 2/3
b) 1/3
c) 1/6
d) 1/9
Ans
Proper Selections:
A B C
A C B
C B A
B A C (i.e. total 4)
Improper selection:
B C A
C A B (i.e. total 2)
Probability for improper selection= 2/6 = 1/3
7. Mr and Mrs smith had invited 9 of their friend and their spouses for party at wiki beachresort.the stand for group photograph if mr smith never stand next to mrs smith then how many way group arrange in row.
(A)20!
(B)19!+18!
(C)18*19!
(D)2*19!
Ans
Mr and Mrs smith never be together so out of 20 (with both them) 19 can b any place so total = 19!
20 because their invitees are with their spouses.
Also 1 of them can stand with other so 18 places
So total is 18*19!
8. Tim and Elan are 90 km from each other, they start to move each other simultaneously, Tim at speed 10 and Elan 5kmph, if every hour they double their speed what is the distance that Tim will pass until he meet Elan?
(A)45
(B)60
(C)20
(D)80
Ans
60
9. MOTHER +DAUGHTER+INFANT AGE IS 74. MOTHER AGE IS 46 MORE THEN DAUGHTER AND INFANT. AND INFANT AGE IS 0.4 OF DAUGHTER. FIND DAUGHTERS AGE.
Ans
m+d+i=74 (1)
m=46+(d+i) (2)
i=0.4d (3)
solving we get d = 10
10. The age of two people is in the ratio 6:8. the sum of their ages is 77. after 2 years the ratio of their ages becomes 5:7. wat is their present age?
11. A Grocer bought 24 kg coffee beans at price X per kg. After a while one third of stock got spoiled so he sold the rest for $200 per kg and made a total profit of twice the cost. What must be the price of X?
A.$33 1/3
B. 66 2/3
C.44 4/9
D.50 1/3
Cost price= 24*X,
spoiled= 24*1/3=8 kg, now total amount= (24-8)=16 kg
selling price= 16*200 =3200
profit= (3200-24*X)
profit=2* cost , (3200-24*X)= 2*24*X, x=400/9 =44 4/9
12. Let exp(m,n) = m to the power n. If exp(10, m) = n exp(2, 2) where to and n are integers then n =
exp(10, m) = n * exp(2, 2) = n*(2^2) = 4*n
10^m=4*n ; where m,n integers
m=2, n=25 satisfies for the least value
13.Bhanu spends 30% of his income on petrol on scooter. ? of the remaining on house rent and the balance on food. If he spends Rs.300 on petrol then what is the expenditure on house rent?
Let the income x, so in petrol he spends 3x/10 rs,remaining x-3x/10=7x/10 on house rent and balance on.now 3x/10=300,so x=1000,
on house rent he spends rs 700-balance.
14. Directions for Q. 1 to Q. 5: Refer the data:
J, K, L, M and N collected stamps.
They collected a total of 100 stamps.
None of them collected less than 10.
No two among them collected the same number.
(i) 3 collected the same number as K and M together.
(ii) L collected 3 more than the cube of an integer
(iii) The no. collected by J was the square of an integer.
(iv) Total no. collected by K was either the square or cube of an integer.
1. The no. collected by J was:
(1) 27 (2) 49 (3) 36 (4) 64
2. The no. collected by K was:
(1) 16 (2) 27 (3) 25 (4) 36
3. The difference of numbers collected by L & M was:
(1) 3 (2) 2 (3) 5 (4) 9
L=12,N=11,J=27,M=14,K=36
Given,
K+M+J+L+N=100 ———(i)
K,M,J,L,N>10 ———(ii)
K?M?N?J?L ———(iii)
K+M=J+L+N ———(iv)
L=3 + X^3 , where X is an integer ———(v)
J= Y^3, where Y is an integer (Modify the question here it should be like that) ———(vi)
K=Z^2 or Z^3, where Z is an integer ———(vii)
Now from the ques value of J can be 27 or 64
but if we take 64 then eqn iv would not satisfy so J=27
Again considering eqn ii, iv & ii we can say that L+N = 23 & K+M=50
Now from eqn v the value of L must be 11, thus L=11
That conclude N = 12
Now from the questio part 3,
The difference of numbers collected by L & M was:
(1) 3 (2) 2 (3) 5 (4) 9
Considering the fact M-L=any of those values
Now M=L+any of those values
M=11+any of those values
Now considering each values, M= 14, value =3; K=50-14 =36 which is a square of integer, thus satisfies
again M=13, value = 2; K=37 which is neither square or cube of any integer
M=16, value = 5; K=34 which is neither square or cube of any integer
M=20, value = 9; K=30 which is neither square or cube of any integer
Thus M = 14 & K = 36.
15. How many kgs. of wheat costing Rs. 8 per kg must be mixed with 86 kg of rice costing Rs. 6.40 per kg so that 20% gain may be obtained by Belling the mixture at Rs. 7.20 per kg ?
Ans : 25.8
Question Pattern of TCS Campus Placement 2013. It is the new questions we get from different students
1. An empty tank be filled with an inlet pipe ‘A’ in 42 minutes. after 12 minutes an outlet pipe ‘B’ is opened which can empty the tank in 30 minutes.
After 6 minutes another inlet pipe ‘C’ opened into the same tank, which can fill the tank in 35 minutes and the tank is filled find the time taken to fill the tank?
Ans
Rate at which A fill is 1/42 per min
A filled for 12 min so tank filled by A will be 12/42
Similarly B empty the tank for 6 min
now the volume will be (18/42) -(6/30) = 8/35 because at the 6 min A has also filled.
Now the amount left to be filled is (1-8/35) = 27/35
Now C comes it fills 1/35 per minute.
So from now the amount will be filled is (1/42+1/35-1/30) = 2/105 per minute
So to fill the required amount it will take 105/2 * 27/35 = 40.5 min
So total time is 12+6+40.5 = 58.5 min
2. A boy wants to make cuboids of dimension 5m,6m & 7m from small cubes of .03m^3.Later he realized that he can make some cuboids by making it hollow.
Then it takes some cubes less. What is the number of cubes to be removed
a)2000
b)5000
c)3000
d)7000
Ans
Total no of cubes = 5*6*7/0.03=7000
for making it hollow we have to remove (5-2)*(6-2)*(7-2)/0.03=2000.
3. Leena cuts small cubes of 3 cubic cm each. She joined it to make a cuboids of length 10 cm,width 3cm, and depth 3 cm.How many more cubes does she need to make a perfect cube?
a)910
b)250
c)750
d)650
Ans
To make cube we need 10*10*10=1000.
Now we have only 10*3*3=90.
So the more cube we need are 1000-90=910.
4. What is the distance between the z-intercept from x-intercept in the eqn ax+by+cz+d=0
Ans
square root of (d/a)^2 + (d/c)^2
5. 10 men and 10 women are there.They dance with each other.Is there possibility that two men are dance with same girl and vice versa?
a)22
b)20
c)10
d)none of these
Ans
none of these
6. A father purchases dress for his three daughter. The dresses are of same color but of different size .The dress is kept in dark room .What is the probability that all the three will not choose their own dress…
a) 2/3
b) 1/3
c) 1/6
d) 1/9
Ans
Proper Selections:
A B C
A C B
C B A
B A C (i.e. total 4)
Improper selection:
B C A
C A B (i.e. total 2)
Probability for improper selection= 2/6 = 1/3
7. Mr and Mrs smith had invited 9 of their friend and their spouses for party at wiki beachresort.the stand for group photograph if mr smith never stand next to mrs smith then how many way group arrange in row.
(A)20!
(B)19!+18!
(C)18*19!
(D)2*19!
Ans
Mr and Mrs smith never be together so out of 20 (with both them) 19 can b any place so total = 19!
20 because their invitees are with their spouses.
Also 1 of them can stand with other so 18 places
So total is 18*19!
8. Tim and Elan are 90 km from each other, they start to move each other simultaneously, Tim at speed 10 and Elan 5kmph, if every hour they double their speed what is the distance that Tim will pass until he meet Elan?
(A)45
(B)60
(C)20
(D)80
Ans
60
9. MOTHER +DAUGHTER+INFANT AGE IS 74. MOTHER AGE IS 46 MORE THEN DAUGHTER AND INFANT. AND INFANT AGE IS 0.4 OF DAUGHTER. FIND DAUGHTERS AGE.
Ans
m+d+i=74 (1)
m=46+(d+i) (2)
i=0.4d (3)
solving we get d = 10
10. The age of two people is in the ratio 6:8. the sum of their ages is 77. after 2 years the ratio of their ages becomes 5:7. wat is their present age?
11. A Grocer bought 24 kg coffee beans at price X per kg. After a while one third of stock got spoiled so he sold the rest for $200 per kg and made a total profit of twice the cost. What must be the price of X?
A.$33 1/3
B. 66 2/3
C.44 4/9
D.50 1/3
Cost price= 24*X,
spoiled= 24*1/3=8 kg, now total amount= (24-8)=16 kg
selling price= 16*200 =3200
profit= (3200-24*X)
profit=2* cost , (3200-24*X)= 2*24*X, x=400/9 =44 4/9
12. Let exp(m,n) = m to the power n. If exp(10, m) = n exp(2, 2) where to and n are integers then n =
exp(10, m) = n * exp(2, 2) = n*(2^2) = 4*n
10^m=4*n ; where m,n integers
m=2, n=25 satisfies for the least value
13.Bhanu spends 30% of his income on petrol on scooter. ? of the remaining on house rent and the balance on food. If he spends Rs.300 on petrol then what is the expenditure on house rent?
Let the income x, so in petrol he spends 3x/10 rs,remaining x-3x/10=7x/10 on house rent and balance on.now 3x/10=300,so x=1000,
on house rent he spends rs 700-balance.
14. Directions for Q. 1 to Q. 5: Refer the data:
J, K, L, M and N collected stamps.
They collected a total of 100 stamps.
None of them collected less than 10.
No two among them collected the same number.
(i) 3 collected the same number as K and M together.
(ii) L collected 3 more than the cube of an integer
(iii) The no. collected by J was the square of an integer.
(iv) Total no. collected by K was either the square or cube of an integer.
1. The no. collected by J was:
(1) 27 (2) 49 (3) 36 (4) 64
2. The no. collected by K was:
(1) 16 (2) 27 (3) 25 (4) 36
3. The difference of numbers collected by L & M was:
(1) 3 (2) 2 (3) 5 (4) 9
L=12,N=11,J=27,M=14,K=36
Given,
K+M+J+L+N=100 ———(i)
K,M,J,L,N>10 ———(ii)
K?M?N?J?L ———(iii)
K+M=J+L+N ———(iv)
L=3 + X^3 , where X is an integer ———(v)
J= Y^3, where Y is an integer (Modify the question here it should be like that) ———(vi)
K=Z^2 or Z^3, where Z is an integer ———(vii)
Now from the ques value of J can be 27 or 64
but if we take 64 then eqn iv would not satisfy so J=27
Again considering eqn ii, iv & ii we can say that L+N = 23 & K+M=50
Now from eqn v the value of L must be 11, thus L=11
That conclude N = 12
Now from the questio part 3,
The difference of numbers collected by L & M was:
(1) 3 (2) 2 (3) 5 (4) 9
Considering the fact M-L=any of those values
Now M=L+any of those values
M=11+any of those values
Now considering each values, M= 14, value =3; K=50-14 =36 which is a square of integer, thus satisfies
again M=13, value = 2; K=37 which is neither square or cube of any integer
M=16, value = 5; K=34 which is neither square or cube of any integer
M=20, value = 9; K=30 which is neither square or cube of any integer
Thus M = 14 & K = 36.
15. How many kgs. of wheat costing Rs. 8 per kg must be mixed with 86 kg of rice costing Rs. 6.40 per kg so that 20% gain may be obtained by Belling the mixture at Rs. 7.20 per kg ?
Ans : 25.8
TCS Previous years 2012 Technical Hr and Interview Questions
♦ What does static variable mean?
♦ What is a pointer?
♦ What is a structure?
♦ What are the differences between structures and arrays?
♦ In header files whether functions are declared or defined?
♦ What are the differences between malloc() and calloc()?
♦ What are macros? what are its advantages and disadvantages?
♦ Difference between pass by reference and pass by value?
♦ What is static identifier?
♦ Where are the auto variables stored?
♦ Where does global, static, local, register variables, free memory and C Program instructions get stored?
♦ Difference between arrays and linked list?
♦ What are enumerations?
♦ What is a class?
♦ What is an object?
♦ What is the difference between an object and a class?
♦ What is the difference between class and structure?
♦ What is public, protected, private?
♦ What are virtual functions?
♦ What is friend function?
♦ What is a scope resolution operator?
♦ What do you mean by inheritance?
♦ What is abstraction?
♦ What is a data structure?
♦ What does abstract data type means?
♦ Evaluate the following prefix expression " ++ 26 + - 1324" (Similartypes can be asked)
♦ Convert the following infix expression to post fix notation ((a+2)*(b+4)) -1 (Similar types can be asked)
♦ How is it possible to insert different type of elements in stack?
♦ Stack can be described as a pointer. Explain.
♦ Write a Binary Search program
♦ What is the difference between an Abstract class and Interface?
♦ What is user defined exception?
♦ What do you know about the garbage collector?
♦ What is the difference between java and c++?
♦ In an HTML form I have a button which makes us to open another page in 15 seconds. How will you dothat?
♦ What is the difference between process and threads?
♦ What is update method called?
♦ Have you ever used HashTable and Directory?
♦ What are statements in Java?
♦ What is RMI?
♦ Explain about RMI Architecture?
♦ What are Servelets?
♦ What is the use of servlets?
♦ Explain RMI Architecture?
♦ How will you pass values from HTML page to the servlet?
♦ How do you load an image in a Servelet?
♦ What is purpose of applet programming?
♦ How will you communicate between two applets?
♦ What are the basic functions of an operating system?
♦ Explain briefly about, processor, assembler, compiler, loader, linker and the functions executed by them.
♦ What are the difference phases of software development? Explain briefly?
♦ Differentiate between RAM and ROM?
♦ What is DRAM? In which form does it store data?
♦ What is cache memory?
♦ What is hard disk and what is its purpose?
♦ Differentiate between Complier and Interpreter?
♦ What are the different tasks of Lexical analysis?
♦ What are the different functions of Syntax phase, Sheduler?
Working at TCS - Why Should I Join TCS?
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TCS Previous years Technical Hr and Aptitude questions with answers
TCS Placement Paper 2012:-
1. Which Is The Smallest No Divides 2880 And Gives A Perfect Square?
A.1
B.2
C.5
D.6
Ans: C
2. Two Bowls Are Taken, One Contains Water And Another Contains Tea Equal Amount . One Spoon Of Water From 1st Is Added To second Bowl And Mixed Well, And A Spoon Of Mixture Is Taken From Second Bowl And Added To The 1st Bowl. Which Statement Will Hold Good For The Above?
{
Thought Process :
Water Bowl Tea Bowl
100 100
90w (+10w= Spoon Volume) 100tea+10water
90w+ (10*10/11)Tea+ 10/11 W 100t- (10*10/11) T
+ 10w- 10/11w
(1st Bowl’s Water Volume Is Equal To 2nd Bowls Tea Volume)
3. Form 8 Digit Numbers From By Using 1, 2,3,4,5 With Repetition Is Allowed And Must Be Divisible By 4?
A.31250
B.97656
C.78125
D.97657
Ans: C
4. Rearrange And Categorize The Word ‘Rapeteka’?
Ans: Bird
5. One Problem On (785^3-235^3)/(785^2+785*235+235^2)
Ans: You Are Free To Carry A Calculator With You But You Should Not Use It To Solve This Kind Of Problem.
Because It Is Simple:
A3-b3 / A2+ab+b2
Ans Is : A-b Here 785-235= 550 That's It.
6. In School There Are Some Bicycles And 4 Wheeler Wagons. One Tuesday There Are 190 Wheels In The Campus. How Many Bicycles Are There?
Ans: 15
Thought Process : B*2+w*4=190 I.E. , B+2w=95 Now See U Can Not Solve 2 Unknowns From 1 Equation, So Just Plot Options Here To Get The Right Answer And Verify If You Are Getting Integers As Values Of B And W.
7. There Are Two Persons Paul And Jay .Paul Lies On Monday, Tuesday, Wednesday And The Remaining Days He Speaks Truth. Jay Lies On Thursday, Friday, Saturday And The Remaining Days He Speaks Truth. Once They Meet Each Other, In Their Conversation Paul Says That Yesterday Is The Day One Among Those I Lie. Jay Also Says That Yesterday I Also Lie. What Is That Day?
A) Sunday.
B) Tuesday.
C) Thursday.
D) Wednesday
[Thought Process: Now This Day Cannot Be Sunday Because In Monday Paul Speaks Truth And Sunday Everyone Tells Truth. So It Must Be Weekdays. Again, Tuesday Can Not Possible Because Monday And Tuesday Paul Speaks Truth. In Case Of Thrust Day, Paul Speaks Lie And Wednesday He Speaks True. And Joy Speaks Truth In Thursday And He Speak Lies In Wednesday. So, Thursday Is The Answer.
8. A Father Has 7 Penny’s With Him And 1 Water Melon Is For 1p, 2chickoos For 1p, 3 Grapes Foe 1p. He Has Three Sons. How Can He Share The Fruits Equally?
Ans: 1 Watermelon, 2chickoos, 1grape
9. (1/2) Of A Number Is 3 Times More Than The (1/6) Of The Same Number?
Ans: 9
10. There Are Two Pipes A And B. If A Filled 10 Liters In Hour B Can Fills 20 Liters In Same Time. Likewise B Can Fill 10, 20, 40, 80,160…. If B Filled In (1/16) Th Of A Tank In 3 Hours, How Much Time Will It Take To Fill Completely?
Ans: 7 Hours
11.A certain pump can drain a full 375-gallon tank in 15 minutes. At this rate, how many more minutes would it take to drain a full 600-gallon tank?
(A) 9
(B) 15
(C) 18
(D) 24
(E) 25
12. If n is an even integer, which of the following must be an odd integer?
(A) 3n-2
(B) 3(n+1)
(C)n-2
(D)n/3
(E)n^2
13. Cindy has a collection of 80 records. If 40 percent of her records are jazz records, and the rest are blues records, how many blues records does she have?
(A) 32
(B) 40
(C) 42
(D) 48
(E) 50
14. Express 2,750,389 in scientific notation.
(A) 27.50389 x 105
(B) 275.0389 x 103
(C) 27.50389 x 106
(D) 0.2750389 x 107
(E) 2.750389 x 106
15. A rectangle and a triangle have equal areas. The length of the rectangle is 12 inches, and its width is 8 inches. If the base of the triangle is 32 inches, what is the length, in inches, of the altitude drawn to the base?
(A) 6
(B) 8
(C) 9
(D) 12
(E) 16
16. If the area of a triangle is 24 and its base is 6, what is the length of the altitude to that base?
(A)3
(B)6
(C)8
(D)10
(E)unknown
17.Lenny's average score after 3 tests is 88. What score on the 4th test would bring Lenny's average up to exactly 90?
(A)92
(B)93
(C)94
(D)95
(E)96
18. If an integer is divisible by 6 and by 9, then the integer must be divisible by which of the following?
A. 12
B. 18
C. 24
D. 36
E. 54
19.If Jeff and Jimmy have less than 22 dollars between them, and Jeff has 8 dollars, which of the following could be the number of dollars that Jimmy has?
I.12
II. 14
III. 16
A. I only
B. III only
C. I & III.
D. I & II
E. Neither I, II, nor III are correct
20.Stephanie drove at an average rate of 50 miles per hour for two hours and then increased her average rate by 50% for the t 3 hours. Her average rate of speed for the 5 hours was t miles per hour. What is the value of t?
A. 55 mph
B. 60 mph
C. 65 mph
D. 70 mph
E. 75 mph
21. How many complete tanks of water, each with a capacity of 3 cubic meters, are needed to fill an empty cylindrical tank whose height is 3 meters and whose base has a radius of 2 meters?
A) 12
B) 13
C) 14
D) 15
E) 16
22. Any serious policy discussion about acceptable levels of risk in connection with explosions is not well served if the participants fail to use the word “explosion” and use the phrase “energetic disassembly” instead. In fact, the word“explosion” elicits desirable reactions, such as a heightened level of attention, whereas the substitute phrase does not. Therefore, of the two terms, “explosion” is the one that should be used throughout discussions of this sort. Which of the following is an assumption on which the argument above depends?
(A) In the kind of discussion at issue, the advantages of desirable reactions to the term “explosion” outweigh the drawbacks,if any, arising from undesirable reactions to that term.
(B) The phrase “energetic disassembly” has not so far been used as a substitute for the word “explosion” in the kind of discussion at issue.
(C) In any serious policy discussion, what is said by the participants is more important than how it is put into words.
(D) The only reason that people would have for using “energetic disassembly” in place of “explosion” is to render impossible any serious policy discussionconcerning explosions.
(E) The phrase “energetic disassembly” is not necessarily out of place in describing a controlled rather than an accidental
explosion
23. A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one-gallon or half- gallon cans, what is the least amount of paint, in gallons, that must be purchased in order to measure out the portions needed for the mixture?
(A) 2
(B) 2 ½
(C) 3
(D) 3 ½
(E) 4
24. To buy a computer system, a customer can choose one of 4 monitors, one of 2 keyboards, one of 4 computers and one of 3 printers. Determine the number of possible systems that a customer can choose from.
(A) 96
(B)98
(C)98.5
(D) 94
(E)100
25. A student can select one of 6 different mathematics books, one of 3 different chemistry books and one of 4different science books. In how any different ways can a student select a book of mathematics, a book of chemistry and a book of science?
A) 14
(B)12
(C)72
(D) 74
(E)76
__________________________________________________________________________________________________________
TCS Placement papers solved questions with detailed explnations
1. If 3y + x > 2 and x + 2y≤3, What can be said about the value of y?
A. y = -1
B. y >-1
C. y <-1
D. y = 1
Answer: B
Multiply the second equation with -1 then it will become - x - 2y≥ - 3. Add the equations. You will get y > -1.
2. If the price of an item is decreased by 10% and then increased by 10%, the net effect on the price of the item is
A. A decrease of 99%
B. No change
C. A decrease of 1%
D. An increase of 1%
Answer: C
If a certain number is increased by x% then decreased by x% or vice versa, the net change is always decrease.
This change is given by a simple formula −(x10)2= −(1010)2= −1%. Negitive sign indicates decrease.
3. If m is an odd integer and n an even integer, which of the following is definitely odd?
A. (2m+n)(m-n)
B. (m+n2)+(m−n2)
C. m2+mn+n2
D. m +n
Answer: C and D (Original Answer given as D)
You just remember the following odd ± odd = even; even ± even = even; even ± odd = odd
Also odd x odd = odd; even x even = even; even x odd = even.
4. What is the sum of all even integers between 99 and 301?
A. 40000
B. 20000
C. 40400
D. 20200
Answer: D
The first even number after 99 is 100 and last even number below 301 is 300. We have to find the sum of even numbers from 100 to 300. i.e., 100 + 102 + 104 + ............... 300.
Take 2 Common. 2 x ( 50 + 51 + ...........150)
There are total 101 terms in this series. So formula for the sum of n terms when first term and last term is known is n2(a+l)
So 50 + 51 + ...........150 = 1012(50+150)
So 2 x 1012(50+150) = 20200
5. There are 20 balls which are red, blue or green. If 7 balls are green and the sum of red balls and green balls is less than 13, at most how many red balls are there?
A. 4
B. 5
C. 6
D. 7
Answer: B
Given R + B + G = 17; G = 7; and R + G < 13. Substituting G = 7 in the last equation, We get R < 6. So maximum value of R = 6
6. If n is the sum of two consecutive odd integers and less than 100, what is greatest possibility of n?
A. 98
B. 94
C. 96
D. 99
Answer : C
We take two odd numbers as (2n + 1) and (2n - 1).
Their sum should be less than 100. So (2n + 1) + (2n - 1) < 100 ⇒ 4n < 100.
The largest 4 multiple which is less than 100 is 96
7. x2 < 1/100, and x < 0 what is the highest range in which x can lie?
A. -1/10 < x < 0
B. -1 < x < 0
C. -1/10 < x < 1/10
D. -1/10 < x
Answer: A
Remember:
(x - a)(x - b) < 0 then value of x lies in between a and b.
(x - a)(x - b) > 0 then value of x does not lie inbetween a and b. or ( −∞, a) and (b, −∞) if a < b
x2 < 1/100 ⇒
(x2−1/100)<0⇒(x2−(1/10)2)<0⇒(x−1/10)(x+1/10)<0
So x should lie in between - 1/10 and 1/10. But it was given that x is -ve. So x lies in -1/10 to 0
8. There are 4 boxes colored red, yellow, green and blue. If 2 boxes are selected, how many combinations are there for at least one green box or one red box to be selected?
A. 1
B . 6
C. 9
D. 5
Answer: 5
Total ways of selecting two boxes out of 4 is 4C2 = 6. Now, the number of ways of selecting two boxes where none of the green or red box included is only 1 way. (we select yellow and blue in only one way). If we substract this number from total ways we get 5 ways.
9. All faces of a cube with an eight - meter edge are painted red. If the cube is cut into smaller cubes with a two - meter edge, how many of the two meter cubes have paint on exactly one face?
A. 24
B. 36
C. 60
D. 48
Answer : A
If there are n cubes lie on an edge, then total number of cubes with one side painting is given by 6×(n−2)2. Here side of the bigger cube is 8, and small cube is 2. So there are 4 cubes lie on an edge. Hence answer = 24
10. Two cyclists begin training on an oval racecourse at the same time. The professional cyclist completes each lap in 4 minutes; the novice takes 6 minutes to complete each lap. How many minutes after the start will both cyclists pass at exactly the same spot where they began to cycle?
A. 10
B. 8
C. 14
D. 12
Answer: D
The faster cyclyst comes to the starting point for every 4 min so his times are 4, 8, 12, ......... The slower cyclist comes to the starting point for every 6 min so his times are 6, 12, 18, ......... So both comes at the end of the 12th min.
11. M, N, O and P are all different individuals; M is the daughter of N; N is the son of O; O is the father of P; Among the following statements, which one is true?
A. M is the daughter of P
B. If B is the daughter of N, then M and B are sisters
C. If C is the granddaughter of O, then C and M are sisters
D. P and N are bothers.
Answer: B
From the diagram it is clear that If B is the daughter of N, then M and B are sisters. Rectangle indicates Male, and Oval indicates Female.
12. In the adjoining diagram, ABCD and EFGH are squres of side 1 unit such that they intersect in a square of diagonal length (CE) = 1/2. The total area covered by the squares is
A. Cannot be found from the information
B. 1 1/2
C. 1 7/8
D. None of these
Answer: C
Let CG = x then using pythogerous theorem CG2+GE2=CE2
⇒ x2+x2=(1/2)2⇒2x2=1/4⇒x2=1/8
Total area covered by two bigger squares = ABCD + EFGE - Area of small square = 2 - 1/8 = 15/8
13. There are 10 stepping stones numbered 1 to 10 as shown at the side. A fly jumps from the first stone as follows; Every minute it jumps to the 4th stone from where it started - that is from 1st it would go to 5th and from 5th it would go to 9th and from 9th it would go to 3rd etc. Where would the fly be at the 60th minute if it starts at 1?
A. 1
B. 5
C. 4
D. 9
Answer : A
Assume these steps are in circular fashion.
Then the fly jumps are denoted in the diagram. It is clear that fly came to the 1st position after 5th minute. So again it will be at 1st position after 10th 15th .....60th. min.
So the fly will be at 1st stone after 60th min.
14. What is the remainder when 617+1176 is divided by 7?
A. 1
B. 6
C. 0
D. 3
Answer: C
617 = (7−1)17 =
17C0.717−17C1.716.11.....+17C16.71.116−17C17.117
If we divide this expansion except the last term each term gives a remainder 0. Last term gives a remainder of - 1.
Now From Fermat little theorem, [ap−1p]Rem=1
So [1767]Rem=1
Adding these two remainders we get the final remainder = 0
15. In base 7, a number is written only using the digits 0, 1, 2, .....6. The number 135 in base 7 is 1 x 72 + 3 x 7 + 5 = 75 in base 10. What is the sum of the base 7 numbers 1234 and 6543 in base 7.
A. 11101
B. 11110
C. 10111
D. 11011
Answer: B
In base 7 there is no 7. So to write 7 we use 10. for 8 we use 11...... for 13 we use 16, for 14 we use 20 and so on.
So from the column d, 4 + 3 = 7 = 10, we write 0 and 1 carried over. now 1 + 3 + 4 = 8 = 11, then we write 1 and 1 carried over. again 1 + 2 + 5 = 8 = 11 and so on
16. The sequence {An} is defined by A1 = 2 and An+1=An+2n what is the value of A100
A. 9902
B. 9900
C. 10100
D. 9904
Answer: A
We know that A1 = 2 so A2=A1+1=A1+2(1)=4
A3=A2+1=A2+2(2)=8
A4=A3+1=A3+2(3)=14
So the first few terms are 2, 4, 8, 14, 22, ......
The differences of the above terms are 2, 4, 6, 8, 10...
and the differences of differences are 2, 2, 2, 2. all are equal. so this series represents a quadratic equation.
Assume An = an2+bn+c
Now A1 = a + b + c = 2
A2 = 4a + 2b + c = 4
A3 = 9a + 3b + c = 8
Solving above equations we get a = 1, b = - 1 and C = 2
So substituting in An = n2+bn+c = n2−n+2
Substitute 100 in the above equation we get 9902.
17.Find the number of rectangles from the adjoining figure (A square is also considered a rectangle)
A. 864
B. 3276
C. 1638
D. None
Answer: C
To form a rectangle we need two horizontal lines and two vertical lines. Here there are 13 vertical lines and 7 horizontal lines. The number of ways of selecting 2 lines from 13 vertical lines is 13C2 and the number of ways of selecting 2 lines from 7 horizontals is 7C2. So total rectangles = 7C2x13C2
18. A, B, C and D go for a picnic. When A stands on a weighing machine, B also climbs on, and the weight shown was 132 kg. When B stands, C also climbs on, and the machine shows 130 kg. Similarly the weight of C and D is found as 102 kg and that of B and D is 116 kg. What is D's weight
A. 58kg
B. 78 kg
C. 44 kg
D. None
Answer : C
Given A + B = 132; B + C = 130; C + D = 102, B + D = 116
Eliminate B from 2nd and 4th equation and solving this equation and 3rd we get D value as 44.
19. Roy is now 4 years older than Erik and half of that amount older than Iris. If in 2 years, roy will be twice as old as Erik, then in 2 years what would be Roy's age multiplied by Iris's age?
A. 28
B. 48
C. 50
D. 52
Answer: 48
20. X, Y, X and W are integers. The expression X - Y - Z is even and the expression Y - Z - W is odd. If X is even what must be true?
A. W must be odd
B. Y - Z must be odd
C. W must be odd
D. Z must be odd
Answer: A or C (But go for C)
21. Mr and Mrs Smith have invited 9 of their friends and their spouses for a party at the Waikiki Beach resort. They stand for a group photograph. If Mr Smith never stands next to Mrs Smith (as he says they are always together otherwise). How many ways the group can be arranged in a row for the photograph?
A. 20!
B. 19! + 18!
C. 18 x 19!
D. 2 x 19!
Answer: C
22. In a rectanglular coordinate system, what is the area of a triangle whose vertices whose vertices have the coordinates (4,0), (6, 3) adn (6 , -3)
A. 6
B. 7
C. 7.5
D. 6.5
Answer: A
23. A drawer holds 4 red hats and 4 blue hats. What is the probability of getting exactly three red hats or exactly three blue hats when taking out 4 hats randomly out of the drawer and immediately returning every hat to the drawer before taking out the next?
A. 1/2
B. 1/8
C. 1/4
D. 3/8
Answer: B
24. In how many ways can we distribute 10 identical looking pencils to 4 students so that each student gets at least one pencil?
A. 5040
B. 210
C. 84
D. None of these
Answer: C
25. The prime factorization of intezer N is A x A x B x C, where A, B and C are all distinct prine intezers. How many factors does N have?
A. 12
B. 24
C. 4
D. 6
Answer: A
26. Tim and Elan are 90 km from each other.they start to move each other simultanously tim at speed 10 and elan 5 kmph. If every hour they double their speed what is the distance that Tim will pass until he meet Elan
A. 45
B. 60
C. 20
D. 80
Answer: B
27. A father purchases dress for his three daughter. The dresses are of same color but of different size .the dress is kept in dark room .What is the probability that all the three will not choose their own dress.
A. 2/3
B. 1/3
C. 1/6
D. 1/9
Answer: B
28. N is an integer and N>2, at most how many integers among N + 2, N + 3, N + 4, N + 5, N + 6, and N + 7 are prime integers?
A. 1
B. 3
C. 2
D. 4
Answer: C
29. A turtle is crossing a field. What is the total distance (in meters) passed by turtle? Consider the following two statements
(X) The average speed of the turtle is 2 meters per minute
(Y) Had the turtle walked 1 meter per minute faster than his average speed it would have finished 40 minutes earlier
A. Statement X alone is enough to get the answer
B. Both statements X and Y are needed to get the answer
C. Statement Y alone is enough to get the answer
D. Data inadequate
Answer: B
30. Given the following information, who is youngest?
C is younger than A; A is talled than B
C is older than B; C is younger than D
B is taller than C; A is older than D
A. D
B. B
C. C
D. A
Answer: B
31. If P(x) = ax4+bx3+cx2+dx+e has roots at x = 1, 2, 3, 4 and P(0) = 48, what is P(5)
A. 48
B. 24
C. 0
D. 50
Answer: A
32. If west is called as North-East,North-East as East, East is called as South-West,South-West is called as North, North is called as North-west,North-West as South and Soouth is called as South-East, then pole star in which direction?
a)North-East
b)North-West
c)North
d)South-West
Ans b)
Since Pole Star is always in North, and in code North is said North-West, Hence Pole Star will be in North_West
32 Re-arrange and categorize the word IARLGOTLA
a)Mobile Phone
b)animal
c) Vehicle
d)Furniture
33 A car left Canterbury at 7.12 am and arrived in Birmingham, 180 miles distant at 10.57 am. What was its average speed in miles per hour?
a)42
b)44
c)46
d)48
Time taken = 3 hours 45m = 3.75 hours (15/4 hours if you prefer fractions).
Speed = distance / time taken = 180 / 3.75 = 48 mph
34 A sheet of paper has statements numbered from 1 to 40. For each value of n from 1 to 40, statement n says "At least n of the statements on this sheet are true." Which statements are true and which are false?
a)The odd numbered statements are true and the even numbered are false
b)The even numbered statements are true and the odd numbered are false.
c)The first 13 statements are true and the rest are false.
d)The first 26 statements are false and the rest are true.
35Tom lies on Mondays, Tuesdays and Wednesdays, and tells the truth on the other days of the week. Jerry, on the other hand, lies on Thursdays, Fridays and Saturdays, but tells the truth on the other days of the week. Now they make the following statements to Mikie – Tom: Yesterday was one of those days when I lie. Jerry: Yesterday was one of those days when I lie too. What day is it?
a)Thursday -Answer
b)Tuesday
c)Sunday
d)Monday
_______________________________________________________________________________
TCS Aptitude-reasoning placement papers
1) The water from one outlet, flowing at a constant rate, can fill the swimming pool in 9 hours. The water from second outlet, flowing at a constant rate can fill up the same pool in approximately in 5 hours. If both the outlets are used at the same time, approximately what is the number of hours required to fill the pool?
ans: (1/A) + (1/B) = 1/T
So when you solved, and got 14/45, that was equal to 1/T. To find T, you need to take the reciprocal; T = 45/14,
(3.21)
u
2) If 75 % of a class answered the first question on a certain test correctly, 55 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percentage answered both correctly?
ans: n(a ^ b) =n(a)+n(b)-n(a v b)
= 0.75+0.55-0.8
= 0.5
(50%)
3) A student's average ( arithmetic mean) test score on 4 tests is 78. What must be the students score on a 5th test for the students average score on the 5th test to be 80?
ans: 4 tests sum=78*4=312
5 tests sum=80*5=400
then 5th test score=400-312=88
(88)
4) Rural households have more purchasing power than do urban households at the same income level, since some of the income urban and suburban households use for food and shelter can be used by the rural households for other needs. Which of the following inferences is best supported by the statement made above?
(A) The average rural household includes more people than does the average urban or suburban household.
(B) Rural households have lower food and housing costs than do either urban or suburban households.
(C) Suburban households generally have more purchasing power than do either rural or urban households.
(D) The median income of urban and suburban households is generally higher than that of rural households.
(E) All three types of households spend more of their income on housing than on all other purchases combined.
ans: B
5) Jose is a student of horticulture in the University of Hose. In a horticultural experiment in his final year, 200 seeds were planted in plot I and 300 were planted in plot II. If 57% of the seeds in plot I germinated and 42% of the seeds in plot II germinated, what percent of the total number of planted seeds germinated?
ans: 200 * 57 % = 114 and 300* 42% = 126.
Total = 240 out of 500.
(48%).
6) A closed cylindrical tank contains 36 pie cubic feet of water and its filled to half its capacity. When the tank is placed upright on its circular base on level ground, the height of water in the tank is 4 feet. When the tank is placed on its side on level ground, what is the height, in feet, of the surface of the water above the ground?
ans: What given Volume = 36
Height = 4ft
Volume = Pi* r2 * h
36 = Pi*r2 * 4
r2 =9
r = 3
So the radius is 3 which means the diameter is 6.
7) The present ratio of students to teachers at a certain school is 30 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of the teachers would then be 25 to 1 What is the present number of teachers?
ans: 30/1 = s/t Current student to teacher ratio
s+50/t+5 = 25/1 Future student to teacher ratio
solving the first equation first equation for s gives s = 30t.
Substitute this value of s into the second equation, and solve for t.
s+50/t+5 = 25/1
30t + 50 = 25t + 125 multiply both sides by t+5
5t = 75 simplify by subtraction
t = 15
(15)
8) College T has 1000 students. Of the 200 students majoring in one or more of the sciences,130 are majoring in Chemistry and 150 are majoring in Biology. If at least 30 of the students are not majoring in either Chemistry or Biology, then the number of students majoring in both Chemistry and Biology could be any number from
ans: total=200
neither>=30
chemistry=130
bio=130
maximum common=minimum of the two=130
if neither=30
then common=150+130+30-200=110
range is 110-130
9) Kelly and Chris are moving into a new city. Both of them love books and thus packed several boxes with books. If Chris packed 60% of the total number of boxes, what was the ratio of the number of boxes Kelly packed to the number of boxes Chris packed?
ans: 100-60=40
40:60=2:3
10) A drug that is highly effective in treating many types of infection can, at present, be obtained only from the bark of the ibora, a tree that is quite rare in the wild. It takes the bark of 5,000 trees to make one kilogram of the drug. It follows, therefore, that continued production of the drug must inevitably lead to the ibora's extinction. Which of the following, if true, most seriously weakens the argument above?
ans: The ibora can be propagated from cuttings and grown under cultivation.
11) Machine A produces bolts at a uniform rate of 120 every 40 second, and Machine B produces bolts at a uniform rate of 100 every 20 seconds. If the two machines run simultaneously, how many seconds will it take for them to produce a total of 200 bolts?
ans: Machine A produces 120/40 = 3 bolts in 1 seconds and machine B produces 100/20 = 5 bolts in one second.
Hence, both of them will produce 8 bolts per second.
Hence, they wil take 200/8 = 25 seconds to produce 200 bolts.
(25)
12) Wood smoke contains dangerous toxins that cause changes in human cells. Because wood smoke presents such a high health risk, legislation is needed to regulate the use of open-air fires and wood burning stoves
ans: In valleys where wood is used as the primary heating fuel, the concentration of smoke results in poor air quality.
13) Analysing the good returns that Halocircle Insurance Pvt Ltd was giving, Ratika bought a 1-year, Rs 10,000 certificate of deposit that paid interest at an annual rate of 8% compounded semi-annually.What was the total amount of interest paid on this certificate at maturity?
ans: @8%, for half year you get 400/- 10000x 8/100x1/2=400
for the next year there will be interest on your investment of 10000 and also on your accrue interest of Rs.400/-
that means another 400/+ interest on 400/- @8% for half year.=400+ (400x8/100x1/2)
400+400+16=816
14) Juan is a gold medalist in athletics. In the month of May, if Juan takes 11 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?
ans: 11x/y
15) A certain company retirement plan has a rule of 70 provision that allows an employee to retire when the employee's age plus years of employment with the company total at least 70. In what year could a female employee hired in 1986 on her 32nd birthday first be eligible to retire under this provision?
ans: The female employee must gain at least 70 points.
Now she has 32 and every year gives her two more points: one for age and one for additional year of employment, so 32 + 2 * (number of years) = 70
(Number of years) = 19
So, 1986 + 19 = 2005
16) Homeowners aged 40 to 50 are more likely to purchase ice cream and are more likely to purchase it in larger amounts than are members of any other demographic group. The popular belief that teenagers eat more ice-cream than adults must, therefore, be false. The argument is flawed because the author _____
ans: fails to distinguish between purchasing and consuming
17) Andalusia has been promoting the importance of health maintenance. From January 1,1991 to January 1,1993, the number of people enrolled in health maintenance organizations increased by 15 percent. The enrollment on January 1,1993 was 45 million. How many million people(to the nearest million) was enrolled in health maintenance organizations on January 1,1991?
ans: let there are 'x' population at jan1,1991
15% of x = 15/100*(x)
(x)+[15/100*(x)]=45 /* as there is 15% increase from 1991 to 1993*/
x=39.13
18) What is the lowest possible integer that is divisible by each of the integers 1 through 7, inclusive?
ans: L.C.M of(1,2,3,4,5,6,7)=2*2*3*5*7=420
19) If the area of a square region having sides of length 6 cms is equal to the area of a rectangular region having width 2.5 cms, then the length of the rectangle, in cms, is
ans: Area of a Square
s x s
6 x 6 = 36
Area of a Rectangle
lw
?(2.5)
=36 as it is equal to the area of a square
36/2.5 = 14.4 cm
20) A tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume. If 2500 gallons of water evaporate from the tank, the remaining solution will be approximately what percentage of sodium chloride?
ans: Original =10,000 ----> sodium chloride = 5% ie 500
New = 10,000-2,500 = 7500.
New % = (500/7500) * 100
= 6.67%
21) After loading a dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day of the crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by two crews did the day crew load?
ans: Number of workers
Day shift: 5 workers (this is an easy number to find 4/5 of)
Night shift: 4 workers (4/5 of 5 = 4)
Boxes loaded per worker
Day shift: 4 boxes per worker
Night shift: 3 boxes per worker (3/4 of 4 = 3)
Total boxes loaded
Day shift: 5 workers times 4 boxes per worker = 20 boxes
Night shift: 4 workers times 3 boxes per worker = 12 boxes
Combined total boxes for both shifts = 20 + 12 = 32
Of the 32 boxes, the day shift loaded 20 of them.
20/32 = 5/8
22) A bakery opened yesterday with its daily supply of 40 dozen rolls. Half of the rolls were sold by noon and 80 % of the remaining rolls were sold between noon and closing time. How many dozen rolls had not been sold when the bakery closed yesterday?
ans: 4 rolls were not sold.............half of them were sold by noon.......so 20 rolls remain....and then 20% were not sold,, so 20% of the 20 rolls is 4 then it is the answer
23) If n=4p, where p is a prime number greater than 2, how many different positive even divisors does n have including n?
ans: 4
24) A dealer originally bought 100 identical batteries at a total cost of q rupees. If each battery was sold at 50 percent above the original cost per battery, then, in terms of q, for how many rupees was each battery sold?
ans: bought for q/100 dollars per battery
each battery sold with profit 50% is
q/100 + q/100*50/100
=q/100+q/200
=3q/200
25) The price of lunch for 15 people was 207 pounds, including a 15 percent gratuity of service. What was the average price per person, EXCLUDING the gratuity?
ans: Let the net price excluding the gratuity of service = x pounds
Then, total price including 15% gratuity of service = x + 0.15 x = 1.15 x pounds
So, 1.15 x = 207 pounds
==> x = 207 / 1.15 = 180 pounds
Net price of lunch for each person = 180 / 15 = 12 pounds
26) Of the following, which is the closest approximation of (50.2*0.49)/199.8 ?
ans: For approximation
(50.2*0.49)/199.8 can be taken as
50*0.5/200 = 25/200 = 1/8 = 0.125
27) How many prime numbers between 1 and 100 are factors of 7150?
ans: 7,150 = 2 * 5 * 5 * 11 * 13
so there are 4 distinct prime numbers that are below 100
28) Guitar Strings often go dead - become less responsive and bright in tone - after a few weeks of intense use. A researcher whose son is a classical guitarist hypothesized that dirt and oil, rather than changes in the material properties of the string, were responsible. Which of the following investigations is most likely to yield significant information that would help evaluate the researcher's hypothesis?
ans: Determining whether smearing various substances on new guitar strings causes them to go dead
29) Red blood cells in which the malarial-fever parasite resides are eliminated from a person's body after 120 days. Because the parasite cannot travel to a new generation of red blood cells, any fever that develops in a person more than 120 days after that person has moved to a malaria free region is not due to malarial parasite. Which of the following, if true, most seriously weakens the conclusion above?
ans: In some cases, the parasite that causes malarial fever travels to cells of the spleen, which are less frequently eliminated from a person’s body than are red blood cells.
30) Among a group of 2500 people, 35 percent invest in municipal bonds, 18 percent invest in oil stocks, and 7 percent invest in both municipal bonds and oil stocks. If 1 person is to be randomly selected from 2500 people, what is the probability that the person selected will be one who invests in municipal bonds but not in oil stocks
ans: 7/25
31) When a polygraph test is judged inconclusive, this is no reflection on the examinee. Rather, such a judgment means that the test has failed to show whether the examinee was truthful or untruthful. Nevertheless, employers will sometime refuse to hire a job applicant because of an inconclusive polygraph test result. Which of the following conclusions can most properly be drawn from the information above?
ans: An inconclusive polygraph test result is sometimes unfairly held against the examinee
32) Country Club has an indoor swimming club. Thirty percent of the members of a swim club have passed the lifesaving test. Among the members who have not passed the test, 12 have taken the preparatory course and 30 have not taken the course. How many members are there in the swim club?
ans: Suppose there are x members, non pass members arre 7x/10 which are equal to 12 + 30 = 42
7x/10 = 42
x = 60
There are 60 members in that club
33) A necklace is made by stringing N individual beads together in the repeating pattern red bead, green bead, white bead, blue bead and yellow bead. If the necklace begins with a red bead and ends with a white bead, then N could be:
ans: R G W B Y is the bead pattern and it repeats.
Bead want to end with White.
So, the 3rd, 8th, 13th, 18th... beads will be W.
this can be expressed as 5n+3,where n is an integer.(counting no of white bead)
Test each of the answer choices to determine which is multiple of 5 plus a value of 3.Of the options ,only 68=5(13)+3 can be written in the form 5n+3.
So,the answer is 68.
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33 A dog taken four leaps for every five leaps of hare but three leaps of the dog is equal to four leaps of the hare. Compare speed?
Let the distance covered by dog in 1 leap is x and hare covered 1 leap is y.
then, 3x = 4y
=> x =(4/3) y
=> 4x =(16/3) y
Then, The ratio of speeds of dog and hare = Ratio of distances covered by them in the same time
= 4x : 5y
= (16/3)y : 5y
=(16/3) : 5
= 16:15 Ans...=16:15
34 There are two boxes,one containing 39 red balls & the other containing 26 green balls.you are allowed to move the balls b/w the boxes so that when you choose a box random & a ball at random from the chosen box,the probability of getting a red ball is maximized.this maximum probability is
a)60 b)50 c)80 d)30
the probability of getting a red ball should be maximized so we will keep 1 red ball in the first box and transfer remaining 38 red balls to other box which has green. The reason for doing this only this combination will make the probability of getting red ball is maximum (i.e) 1.
In the question its mentioned that first we have to choose a box at random.
So 2 boxes are there, probability of selecting a bag is 1/2
Probability of getting red ball from first box is 1
Probability of getting green ball from second box is 38/64
So (1/2)*1 for first box and (1/2)*(38/64) for box 2
answer is (1/2)*1 + ((1/2)*(38/64) which is approximately 0.8
Next number in the given series 1, 7, 8, 49, 50, 56, 57, 343
344 because
1*7=7
7+1-8
7*7=49
49+1=50
8*7=56
56+1=57
49*7=343
343+1=344
ans= 344
q.1 in how many ways can 3 postcards can be posted in 5 postboxes?
q.2.in how many ways can 5 postboxes hold 3 post cards?
q.1 in how many ways can 3 postcards can be posted in 5 postboxes?
first post card can be posted in any of the 5 post boxes =5c1 ways
second post card can be posted in any of the 5 post boxes =5c1 ways
third post card can be posted in any of the 5 post boxes =5c1 ways
number of ways=5c1*5c1*5c1=125=5^3
q.2.in how many ways can 5 postboxes hold 3 post cards?
first post box can hold 3 post cards in 3c1 ways
second post box can hold 3 post cards in 3c1 ways
third post box can hold 3 post cards in 3c1 ways
fourth post box can hold 3 post cards in 3c1 ways
fifth post box can hold 3 post cards in 3c1 ways
so number of ways =3c1*3c1*3c1*3c1*3c1=3^5
35 A number has exactly 3 prime factors, 125 factors of this number are perfect squares and 27 factors of this number are perfect cubes. overall how many factors does the number have???
Answer for this question is 729
The explanation goes like this
Let a,b,c be three prime no.
since the no. of perfect square as a factor is 125
which can only be if every prime no. has power in the multiple of 2 including zeros(bcoz any no. to the power of zero is a perfect square)
so power must be 0,2,4,6,8
thereby 5*5*5=125
Since no. of cube as a factor is 27
therefore power in the prime no. will be in the multiple of 3
so power are 0,3,6
hence the no. N=a^8*b^8*c^8
hence total no. of factor is (8+1)(8+1)(8+1)=729
there r three buckets..of 8,5 n 3 litres...out of which only 8 ltr bucket is fully filled...u hv to fill exact 4-4 ltr liquid in 8 and 5 litre bucket by using only these buckets in minimm num of steps......
8ltr 5ltr 3ltr
initially 8 0 0
step1 3 5 0
step2 3 2 3
step3 6 2 0
step4 6 0 2
step5 1 5 2
step 6 1 4 3
step 7 4 4 0
total 7 steps
36 The climb from foot to top of a hill 800 meters, Jack can climb at 16 meters per minute and rests for two minutes or 20meters per 2 minutes and rest for one minute. Paul can climb at 10 meters per one minute and rest for one minute or16 meters per minute and rest for 2 minutes. If take has to reach the top in exactly two hours. What is the maximum number of rests that he can take?
a) 41 b) 42 c) 40 d) 43
total=800m
16m per min means for 1m=800/16 =50min to climb
10m per min means for 1m=800/10=80min to climb for paul .....the total time is 2hours==120min....so,time taken for rest by paul is 120-80=40min
length of minute hand is 5.4 cm, area covered by this in 10 min is ?
a)50.97 b)57.23 c)55.45 d)59.14
t will be (3.14*5.4*5.4)*10/60 = 15.26 cm2.
37 Raj tossed 3 dices and there results are noted down then what is the probability that raj gets 10?
a) 1/72 b) 1/9 c) 25/216 d)1/8
ossible event.......(1,3,6)(1,4,5)(1,5,4)(1,6,3)(2,2,6)(2,3,5)(2,4,4)(2,5,3)(2,6,2)(3,1,6)(3,2,5)(3,3,4)(3,4,3)(3,5,2)(3,6,1)(4,1,5)(4,2,4)(4,3,3)(4,4,2)(4,5,1)(5,1,4)(5,2,3)(5,3,2)(5,4,1)(6,1,3)(6,2,2)(6,3,1)
total 27 possible event
so probability = 27/216 i.e 1/8
answer-------d(1/8)
Probability of a sum of 3: 1/216 = 0.5%
Probability of a sum of 4: 3/216 = 1.4%
Probability of a sum of 5: 6/216 = 2.8%
Probability of a sum of 6: 10/216 = 4.6%
Probability of a sum of 7: 15/216 = 7.0%
Probability of a sum of 8: 21/216 = 9.7%
Probability of a sum of 9: 25/216 = 11.6%
Probability of a sum of 10: 27/216 = 12.5%
Probability of a sum of 11: 27/216 = 12.5%
Probability of a sum of 12: 25/216 = 11.6%
Probability of a sum of 13: 21/216 = 9.7%
Probability of a sum of 14: 15/216 = 7.0%
Probability of a sum of 15: 10/216 = 4.6%
Probability of a sum of 16: 6/216 = 2.8%
Probability of a sum of 17: 3/216 = 1.4%
Probability of a sum of 18: 1/216 = 0.5%
38 Apple costs L rupees per kilogram for first 30kgs and Q rupees per kilogram for each additional kilogram. If the price of 33 kilograms is 11.67and for 36kgs of Apples is 12.48 then the cost of first 10 kegs of Apples is
a) 3.50 b) 10.53 c) 1.17 d)2.8
30L+3Q=11.67
30L+6Q=12.48
------------
3Q=.81 Q= .27
from that L=0.362 cost of 10 kg apple is 10*.362=3.6
The letters in the word ABUSER are permuted in all possible ways and arranged in alphabetical order then find the word at position 49 in the permuted alphabetical order?
a) ARBSEU
b) ARBESU
c) ARBSUE
d) ARBEUS
AB**** =4!= 24 ways
AE****=4!=24 ways next word is 49th so
AR**** in alphabetical order **** will be BESU
ans is B
39 A is twice efficient than B. A and B can both work together to complete a work in 7 days. Then find in how many days A alone can complete the work?
ans is 10.5
gn:
A+B=(1/7)
A=2B
=>B=1/21
A=2/21
=>A take (21/2)=10.5 days to complete the work.
In 8*8 chess board what is the total number of squares.
1^2+2^2+3^2+4^2+5^2+6^2+7^2+8^2=204....
formula=1^2+2^2+3^2+....+n^2
40 X,Y,W,Z ARE INTEGER THE EXPRESSION X-Y-Z IS EVEN&Y-W-Z ODD IF X IS EVEN THEN WHICH OF FOLLOWING IS TRUE(a)Y MUST BE ODD(b)Y-Z MUST BE ODD(c)W MUST BE ODD(d)Z MUST BE ODD
Ans.(c)W must be ODD
X-Y-Z=even and X even no.
hence (y-z) must be even because (even -even = even)
and y-w-z=y-z-w=odd and (y-z) is even so W must be odd because (even - odd=odd)
hence option (c) is correct
41 Two cyclist begin training on oval racecourse at same timethe professional cyclist complete each lap in 4 sec noves take 6 mintue how many mintue after start will both cyclist pass at exactly same spot where they begin to cycle(a)10(b)8(C)14(D)12
ans is d.
simply LCM of 4 and 6.
which of following true:A occur only B or C occur B occur D&E occurf occur if Cnot occur g occur if A and F occur option A occur whenever F occur2)F never occur3) G not occur if D not occur4)none of these
3) g nt occure i d not occure
a=>b or c
b=>d & e
f=>c not
g =>a & f
1) a occure whenevr f :- depen on c where as 'a' can occure if 'c' not ..so this is not true
2) f nevr occure => depnd on c only n c is indipendent ...if c not occure f will occure ....so this is also not true
3) g not occure if d not:-g depnd on a & f ...if d not ocuure b will not occure (as b=>d&e) a will occure if c occure...if c occure f will not occure ...hence g will not occure...this is true
House1 is older than H2, H3 is taller than H4,H4 is older than H1...(i)H1 is older than H3 (ii)H2 is taller than H4 (a)only 1 (b)both (c)neither (d)only2
c)neither, is the answer.
42 In how many ways can 20 identical pencils be distributed among three girls so that each gets at least 1 pencil? now A'+B'+C''=17,
number of non negative integers of A',B',C' are (17+3-1)C(3-1)
so total Combinations are 19c2=19*9 = 171,
simple formula for this kind of problems is
(n-1)c(r-1)
so 19c2= 171
if p(x)=ax^4+bx^3+cx^2+dx+e has roots at x=1,2,3,4 & p(0)=48.what is p(5)
if 1 is a root then x-1 is a factor of p(x)
similarly x-2 is a factor,x-3 ,x-4 are factors
but p(x) is 4th degree polynomial therefore it can be in the form
p(x) = Q(x-1)(x-2)(x-3)(x-4) , where Q is a constant
but given p(0) =48
therefore 24 Q =48
Q=2
p(x) =2(x-1)(x-2)(x-3)(x-4)
p(5)= 2*4*3*2*1 = 48
1!+2!+3!...+50! divided by 5!
remainder will be ?
1!+2!+3!...+50! divided by 5!
remainder will be whatever is obtained by dividing 1!+2!+3!+4! with 5!.
so remainder is obtained by dividing (1+2+6+24)= 33 with 5! ( 120).
so remainder is 33.
43 If there are Six periods in each working day of a school, In how many ways can one arrange 5 subjects such that each subject is allowed at least one period?
we have 5 sub and 6 periods so their arrangement is 6P5 and now we have 1 period which we can fill with any of the 5 subjects so 5C1
6P5*5C1=3600
44 An article manufactured by a company consists of two parts X and Y. In the process of manufacturing of part X, 9 out 100 parts many be defective. Similarly , 5 out of 100 are likely to be defective in the manufacturer of Y. Calculate the probability that the assembled product will not be defective?
a)0.6485
b)0.6565
c)0.8645
d)none of these
ans=c (0.8645)
probablity of nondefective of x= 91/100=.91
probablity of non defective of y= 95/100=.95
so, probablity of nondefective product=.91*.95=0.8645
45 There are six multiple choice questions in the examination. How many sequences of anwers are possible, if the first two question have 3 choices each, the next two have 4 choice each and last two have 5 choices each?
3c1*3c1*4c1*4c1*5c1*5c1=3600
for any one of first three option of Q.1 we have three options in Q.2 4 option in Q.3.....this goes on...
ind the area (in square units) of the triangle formed by 2x+3y=5, y=x and X-Axis.
the points of intersection for lines:
2x+3y=5 and x=y => 5x=5 => x=1 and y=1 =>(1,1)
x=y and y=0(x-axis) => x=0 and y=0 =>(0,0)
2x+3y=5 and y=0(x-axis) => 2x=5 => x=5/2 and y=0 =>(5/2,0)
area of triangle with vertices (x1,y1),(x2,y2),(x3,y3) is
|x1(y2-y3)+x2(y3-y1)+x3(y1-y2)|/2
=|1(0-0)+0(0-1)+5/2(1-0)|/2
=|1+5/2|/2
=7/4 sq units...
46 Arun was all bent on building a new house. He carefully got the blue print of his house designed buy his friend Ashwin, a civil engineer. He wanted to build a room of dimension 27 by 48 ft and lay tiles in this room. Each tile was of dimension 2 by 3 ft. How many tiles should Arun buy?
27*48/2*3=216
47 Roy is now 4 year older than Erik and half of that amount than Lewis.If in two years Roy will be twice as old as Erick,then in two year what would be Roy age multiplied by Lewis age??
ans is 48 firstly two equation from 1st sentence ..
suppose roy=x, erik=y, lewis=z
so x=y+4....(1)
2nd is x=z+2...(2) (Roy is now 4 year older than Erik and half of that amount than Lewis so 4/2=2)
also after 2 years erik and roy relation wil b
x+2=2(y+2).. (3)
so put this into 1st equ. u will get y=2..
and then x=6,z=4(by substituting other)
nw asking multiplication after two years of roy n lewis is (6+2)*(4+2)=48..
if there are maximum acute angles then how many convex hectagons are there there can be max 3 acute angles in a convex polygon which is a triangle.
48 The number of bacteria was growing in a city exponentially.at 4 pm yesterday , the number of bacteria was 400 and at 6 pm yesterday it was 3600.How many bacteria were there at 7pm yesterday?
The number of bacteria was growing in a city exponentially.at 4 pm yesterday , the number of bacteria was 400 and at 6 pm yesterday it was 3600.How many bacteria were there at 7pm yesterday?
.49 There are 12 children in a family .the youngest 1 is a boy.then find the probabality of finding boy in the family.
a)4096
b)2048
c)2
d)2!
Probability cannot be more than 1..it ranges from 0 to 1..
there can be two options..either a boy/girl in a family
asked is to find a boy=1/2
given 12 children but it is already mentioned that the youngest is a boy so no need to count that..
hence,1/2*1/2*1/2......(11 times)=1/2048 option b..but the option is wrong..it should be 1/2048
50 A volume of 10936 l is in a conatiner of sphere . how many semispheres of volume 4 l each will be required to transfer all the water into small semispheres?
v10936/4=2734.....is the ans
a volume of A are having in a container of sphere. how many semi hemispheres of B volume each will be required to transfer all the A in to semi hemispheres?
ans is A/B.
51 My name is PREET.But my son accidentally types the by interchanging a pair of letters in my name.What is the probability that despite this interchange, the name remains unchanged? a.5% b.20% c.25% d.12.5%
10%
Selecting any two - 5C2 = 10[ treating E AND E as distinct)
Selecting EE = 1
1/10 * 100 = 10%
TCS 2013 placement new pattern questions 02
1 Four friends namely Rahul, Ravi, Rajesh and Rohan contested for a dairy milk chocolate. To decide which friend will get the chocolate they decided to throw two dice. Every friend was asked to choose a number and if the sum of the numbers on two dice equals that number, the concerned person will get the chocolate. Rahul's choice was7, Ravi's choice was 9, Rajesh's choice was 10 and Rohan's choice was 11. Who has the maximum probability of winning the amount.
a) Rahul b) Ravi c) Rajesh d) Rohan
Rahul has chosen 7, similarly Ravi-9,Rajesh-10,Rohan-11
(1,1)(1,2)(1,3)(1,4)(1,5)(1,6) Sum of the digits are= 2,3,4,5,6,7
(2,1)(2,2)(2,3)(2,4)(2,5)(2,6) Sum of the digits are= 3,4,5,6,7,8
(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)Sum of the digits are= 4,5,6,7,8,9
(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)Sum of the digits are= 5,6,7,8,9,10
(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)Sum of the digits are= 6,7,8,9,10,11
(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)Sum of the digits are= 7,8,9,10,11,12
Among these 7 comes 6 times, 9 comes 4times, 10 comes 3times,11 comes only 2 times.
So the maximum probability goes to Rahul
2 Messrs. Siva Constructions, leading agents in Chennai prepared models of their lands in the shape of a rectangle and triangle. They made models having same area. The length and width of rectangle model are 24 inches and 8 inches respectively. The base of the triangle model is 16 inches. What is the altitude of triangle model from the base to the top?
a) 24 inches b) 8 inches c) 20 inches d) 32 inches
Area of a rectangle= Area of the Triangle
So, l*b=1/2(b*h)
24*8=1/2(16*8)
therefore 24inches will be the answer
3 There is a 12*6 grid..grid contains 1*1 squares..what is d total number of squares..(consider 1*1,2*2,3*3,4*4,5*5,6*6 size squares as well).Lady has 25 blues, 7 red,9 yellow gloves and hats.how many gloves of same colour.
(max + min + 2) = 25 + 9 +2=36
1!+2!+.....=50!=?
3.10350532 × 10^64
Anita make cube with dimension 5*5*5 using 1*1*1 cubes.find no. Of cubes to make it hollow of same shape.
To make the 5*5*5 hollow, the inner cubic part must be removed. This would constitute one cube each from front,back,top,bottom,left and right ! Since the 5*5*5 is made up of 1*1*1 cubes, 3*3*3 cubes (i.e. 5-2*5-2*5-2) would have to be removed to make it hollow with the shape retained. 27 cubes would be removed, remaining 125-27=98.
1) if 3y + x > 2 and x + 2y
let 3y+x=2
y+2y+x=2
2y+x=2-y(ans)
3y > 2 -x
2y > 4/3 - 2x/3
x+2y > 4/3 + x/3
x + 2y > 1/3(4 + x)
4 Tim and Elan are 90 km from each other, they start to move each other simultaneously, Tim at speed 10 and Elan 5kmph, if every hour they double their speed what is the distance that Tim will pass until he meet Elan?
Tim and Elan will cover the distance in ratio of 2: 1 in same time.
so out of 90 kms, Tim will travel 60 kms and Elan will travel 30 mtrs.
he length and breadth of a field is 300x400ft,if there are 3 ants on average per square inch of field,find the approximate number of ants in field
as 300 ft=3600 inch and 400 ft=4800 inch.then area in sqr inch=17280000
1 sqr inch need 3 ant hence 17280000 sqr inch need 3*17280000 ants.
.diagonal of a square is double the side of an equilateral triangle find the ratio of area of triangle to area of square
let sides of equilateral triangle be 'a', therefore area= √3/4 * a^2
now, diagonal of square is 2a therefore sides of square will be √2*a
and area of square = 2 a^2
hence, ratio = (√3/4* a^2)/(2* a^2)
answer = √3/8
5 Given a collection of points P in the plane, a 1-set is a point in P that can be separated from the rest by a line, .i.e the point lies on one side of the line while the others lie on the other side.
The number of 1-sets of P is denoted by n1(P). The minimum value of n1(P) over all configurations P of 5 points in the plane in general position(.i.e no three points in P lie on a line) is
a)3 b)5 c) 2 d)1
The meaning of this question is little complicated. In easy language the question should be:
6 There are some points in the plane. We have to make a separation between these points by forming a line in such a way that one point could be separate from the others. No 3 points are in a line. Maximum no of methods for plotting the line and minimum no of methods for plotting the line will be (arrangement of points is your choice)
Now Answer Is:
For Maximize: The number of methods, Points should be drawn in the circumference of the CIRCLE So answer would be the number of total point in the plane.
For minimize: The number of methods we should draw 3 points in a TRIANGLE and all other point inside this triangle in such a way that no 3 points could be in a line.
If it will be allowed to draw the points in a line then minimum possibilities will be 2 only, because if we take all points in a line then you can separate only the corner points from the others.
For example
If we have 10 points then maximum possibilities = 10
and minimum = 3
similarly for 5 points
Max = 5, Min = 3
for 19
max= 19 Min = 3
f(x)=f(f(x))=f(x^2)....how many such functions with degree >2 exist
does not exist....
In a sequence of integers, A(n)=A(n-1)-A(n-2),where A(n) is the nth term in the sequence, n is an integer and n>=3, A(1)=1,A(2)=1. Calculate S(1000), where S(1000) is the sum of first 1000 terms.
check it now
A(1)=1,A(2)=1.
A(3)=A(2)-A(1) acc to the given formula A(n)=A(n-1)-A(n-2)
A(3)=1-1=0.
similarliy,A(4)=A(3)-A(2)=0-1=-1.
A(5)=A(4)-A(3)=-1-0=-1.
A(6)=A(5)-A(4)=-1-(-1)=0.
after 6th term seq is repeating like...1,1,0,-1,-1,0...after every 6 terms
so the sum of these 6 terms are 1+1+0+(-1)+(-1)+0=0.
now we have to find sum of 1000 terms...
sum of first 600 terms is 0...(as consider 1,1,0,-1,-1,0 as one sequence,now consider 166 seq i.e 166*6=996 terms)
so the sum of first 996 terms is 0...after that 4 terms come i.e 1,1,0,-1
so the sum of last 4 terms = 1+1+0+(-1)=1.
7 planet four firesides in 4-dimensional space and thus the currency used by it's residentds are 3-dimensional objects. the rupee notes are cubical in shape while their conis are spherical. however the coni minting machinery lays out some stipulations on the size of the coins. the diameter of the conins should be at least 64 mm and not exceed 512 mm. given a conin the diameter of the next larger coin is at least 50% greater . the diameter of the coin must allways be an integer you are asked to disign a set of coins of different diameters with these requirements and your goal is to desing as many coins as possible. how many coins can you desing
1st coin=64cm
2nd "=64+32(50% of 64)=96cm
similarly 3rd=96+48=144
4th=144+72=216
5th=216+108=324
6th=324+112=436
7th not possible
ans is 6
8 There are 3 boys A, B, C and 2 Girls D, E. E always sit right to A. Girls never sit in extreme positions and in the middle position. C always sits in the extreme positions. Who is sitting immediate right to E?
ns is either B or C
POSSIBLE WAYS TO SIT
1) B/C D A E C/B
2) A E B D C
9 What is reminder when 6^17+17^6 is devided by 7?
(7-1)^17 + (7*2+3)^6
binomial theorem
-1+3^6=728
728%7=0
(40*40* 40-31*31*31)/(40*40+40*31+31*31)=?a simle calcutation
(a^3-b^3)/(a^2+ab+b^2)
a-b
40-31=9
10 In base 7,a number is written only using the digits 0,1,....6.the number 135 in base 7 is 1x7^2+3x7+5=75 in base 10.what is the sum of the same of the base 7 numbers 1234 and 6543 in base 7?
11110
1234
6543
-------
11110 which is 7^4+7^3+7^2+7= 2401+343 +49+7= 2800
11 There are 20 balls which are red,blue or green,If 7 balls are green and the sum of red balls and green balls is less than 13,atmost how many red balls are there
5, atmost there can be 5 red balls so that sum of green and red can be less than 13 (7+5=12)
3y+x>2 and x+2y-1
y
the ans is y>1.
explanation:
x+2y-1=0
so x+2y=1
now 3y+x>2 given
we can write in this way x+2y+y>2
then putting x+2y=1 we get 1+y>2 =>y>2-1=>y>1
12 Find the no of zeros in the product of 1^1*2^2*3^3*.....*49^49??
total zeros at the end of product 5^5 x 10^10 x 15^15 x 20^20 x 25^25 x 30^30 x 35^35 x 40^40 x 45^45 will be 5+10+15+20+50+30+35+40+45 = 250 zeros
13 n! has 13 zeros than wat is the higest and lowest value of n??
Here we have to consider only the 5,10,15,20.... these terms..
so form (5,10,15,20,30,35,40,45,55 ) we got 1 no of zero from each.
Now from 25(5*5) and 50(5*5*2) we got 2 no of zeroes form each.
so upto 55 factorial we get (9+4)= 13 zeroes.
so 55! is the smallest value and 59! is the largest value.
The sequence {A(n)} is defined by A(1)=2 and A(n+1)=A(n)+2n. What is the value of A(100).
The sequence {A(n)} is defined by A(1)=2 and A(n+1)=A(n)+2n.
The value of A(100)=A(99+1)=A(99)+2*99
=A(98)+2*98+2*99
=A(97)+2*97+2*98+2*99
A(100)=A(1)+2*1+2*2+2*3+......+2*98+2*99
= 2+(2*1+2*2+2*3+......+2*98+2*99)
= 2+2(1+2+3+.....+98+99)
= 2+2(sum of the first 99 natural numbers)
= 2+2(99*100/2) [sum of the first n natural numbers={n*(n+1)/2}]
= 2+9900
= 9902
14 A,B COMMON TO ALL THREE. THEN ATLEAST 1 ELEMNT COMMON TO 2 IE X1,X2,X2,X3,X3,X1. FINDMINIMUM ELEMENTS IN EACH GROUP. ANSWER IS 4.
15 Directions for Q. 1 to Q. 5: Refer the data:
J, K, L, M and N collected stamps. They collected a total of 100 stamps. None of them collected less than 10.
No two among them collected the same number.
(i) 3 collected the same number as K and M together.
(ii) L collected 3 more than the cube of an integer
(iii) The no. collected by J was the square of an integer.
(iv) Total no. collected by K was either the square or cube of an integer.
1. The no. collected by J was:
(1) 27 (2) 49 (3) 36 (4) 64
2. The no. collected by K was:
(1) 16 (2) 27 (3) 25 (4) 36
3. The difference of numbers collected by L & M was:
(1) 3 (2) 2 (3) 5 (4) 9
in the question the number collected by J should be cube of the integer and l should collect 3 more than square of integer.
J+L+N=K+M
so the sum of J+L+N=K+M=50
l=3^2+3=12
so J=3^3=27
n=50-27-12=11
now k is either square or cube so possibilty are 36 or 16.and m=14 or 34
so j=27
now value for k can come after solving question 3
m-l=14-12=2 or 34-12=22
so there is 2 in option so value of m is 14 and k=36.
16 Bhanu spends 30% of his income on petrol on scooter. ? of the remaining on house rent and the balance on food. If he spends Rs.300 on petrol then what is the expenditure on house rent?
let the income x,so in petrol he spends 3x/10 rs,remaining x-3x/10=7x/10 on house rent and balance on.now 3x/10=300,so x=1000,on house rent he spends rs 700-balane..
Let exp(m,n) = m to the power n. If exp(10, m) = n exp(2, 2) where to and n are integers then n = exp(m,n) = m to the power n= m^n
exp(10, m) = n exp(2, 2) = n*2^2 = 4*n
10^m =4*n
when m=2,
n=25
so min integer values of m and n are 2 and 25 respectively.
A Grocer bought 24 kg coffee beans at price X per kg. After a while one third of stock got spoiled so he sold the rest for $200 per kg and made a total profit of twice the cost. What must be the price of X?
A. $33 1/3 B. 66 2/3 C.44 4/9 D.50 1/3
ns: C. 44 4/9
cost price= 24*X $,
spoiled= 24*1/3=8 kg, now total amount= (24-8)=16 kg
selling price= 16*200$ =3200$
profit= (3200-24*X)
profit=2* cost , (3200-24*X)= 2*24*X, x=44 4/9
17 The age of two people is in the ratio 6:8. the sum of their ages is 77. after 2 years the ratio of their ages becomes 5:7. wat is their present age?
The ratio of two people be 6x and 8x
sum of their ages is 6x+8y=77
after 2 yrs,ratio is 5:7,so,
(6x+2)/(8x+2)=5/7
on cross multiplying this,
x=2
hence age of a person 6(2)=12
hence another person ages is 8(2)=16
answer is 12,16
MOTHER +DAUGHTER+INFANT AGE IS 74. MOTHER AGE IS 46 MORE THEN DAUGHTER AND INFANT.
AND INFANT AGE IS 0.4 OF DAUGHTER. FIND DAUGHTERS AGE.
M+D+I = 74 ..,.,.Equ..1
I=0.4D
M=D+0.4D+46
M=1.4D+46
put in equ 1
1.4D+46+D+0.4D=74 as I=0.4D
2.8D=74-46
D=28/2.8
D=10.,.,.
,
16 Mr and mrs smith had invited 9 of their friend and their spouses for party at wiki beachresort.the stand for group photograph if mr smith never stand next to mrs smith then how many way group arrange in row(A)20!(B)19!+18!(C)18*19!(D)2*19!
simplest... ans is 18*19!
method ..: mr and mrs smith never b together so out of 20(with both them) 19 can b any place so total = 19!
also 1 of them can stand with other so 18 places /..
so total is 18*19!..
19!*18bcoz along with mr and mrs smith can be arranged in 19!*2 (2 bcoz of mr and mrs smith arrangement) all together can be arranged in 20! ways so no mr and mrs smith can be arranged in 20!-19!*2 =19!*18
Is this solution Helpfull? Yes (8) | No (2) viresh (4 Day ago)
20!-(19!*2)
total possibility minus they will be together
A father purchases dress for his three daughter. The dresses are of same color but of different size .the dress is kept in dark room .What is the probability that all the three will not choose their own dress...
a dosesnot choose his dress 2/3
b dosesnot choose his dress 1/2
c dosesnot choose his dress 1 total 1/3
17 Leena cuts small cubes of 3 cubic cm each.She joined it to make a cuboid of length 10 cm,width 3cm, and depth 3 cm.How many more cubes does she need to make a perfect cube?
a)910 b)250 c)750 d)650
ns is a)910. To make cube we need 10*10*10=1000. now we have only 10*3*3=90.so the more cube we need are 1000-90=910.
18 Q:- A boy wants to make cuboids of dimension 5m,6m & 7m from small cubes of .03m^3.Later he realized that he can make some cuboids by making it hollow.Then it takes some cubes less.What is the number of cubes to be removed
a)2000 b)5000 c)3000 d)7000
Volume of the cuboid= 5*6*7
No of cubes needed = (5*6*7)/0.03 = 7000
Volume of hollow cube= (5-2)(6-2)(7-2)
No of cubes needed = (5-2)(6-2)(7-2)/0.03 = (3*4*5)/0.03= 2000
So, number of cubes to be removed = 7000 - 2000 = 5000
19 An empty tankbe filled with aninlet pipe 'A' in 42 minutes. after 12 minutes an outlet pipe 'B' is opened which can empty the tank in 30 minutes. After 6 minutes another inlet pipe 'C' opened into the same tank, which can fill the tank in 35 minutes and the tank is filled find the time taken to fill the tank?
he milk and water in two vessels A and B are in the ratio 4 : 3 and 2: 3 respectively. In what ratio, the liquids in both the vessels be mixed to obtain a new mixture in vessel C containing half milk and half water?
let c.p. of 1liter milk is 1RS.
now milk in 1st mixer is 4/7 and in 2nd mixure is 2/5.
milk in finle mixer is 1/2
now from mixure formula..
4/7 2/5
1/2
1/10 1/14
so ratio is 14/10 =7/5
20 How many kgs. of wheat costing Rs. 8 per kg must be mixed with 86 kg of rice costing Rs. 6.40 per kg so that 20% gain may be obtained by Belling the mixture at Rs. 7.20 per kg ?
Ex. 4. .How many kgs. of wheat costing Rs. 8 per kg must be mixed with 86 kg of rice costing Rs. 6.40 per kg so that 20% gain may be obtained by Belling the mixture at Rs. 7.20 per kg ?
Sol. S.P. of 1 kg mixture = Rs. 7.20,Gain = 20%.
? C.P. of 1 kg mixture = Rs.[(100/120)*7.20]=Rs. 6.
By the rule of alligation, we have:
C_P. of 1 kg wheat of 1st kind C.P. of 1 kg wheat of 2nd kind
(800p) . (540 p)
Mean price
( 600 p)
60 200
Wheat of 1st kind: Wheat of 2nd kind = 60 : 200 = 3 : 10.
Let x kg of wheat of 1st kind be mixed with 36 kg of wheat of 2nd kind.
Then, 3 : 10 = x : 36 or lOx = 3 * 36 or x = 10.8 kg.
21 In what ratio must water be mixed with milk to gain 20 % by selling the mixture at cost price?
let the sp op 1 l mix is =re 1
cp =(100/120)*1=5/6
cp of one let. water =0
so ratio=1-(5/6)/(5/6)-0=1/5
so required ratio =1:5
How much water must be added to 60 litres of milk at 1 ½ litres for Rs. 2
So as to have a mixture worth Rs.10 2/3 a litre ?
x=(sin nx/n)=?
x=(sin nx/n)
so,
nx=sin nx
sin is one to one function and there is only one case for φ=0 where sinφ=φ
so nx=0
so x=0 (n!=0)
ans will be 0
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2013-2014 new batch asked questions some users contributions from different campus recruitments all over India
1) The wages of 24 men and 16 women amounts to Rs.11600/day. Half the number of men and 37 women earn the same amount /day. What is the daily wage of a man
Explanations
Let the wage of a man be m and woman be w
24m+16W=11600
12m+37w=11600
24m*37-12m*16=11600*(37-16)
12m(2*37-16)=11600*(37-16)
Solving m=11600*21/(12*58) =200*7/4=350
2) The sum of three digits in a number is 17 The sum of square of the digits is 109 .If we subtract 495 from the number, the number is reversed. Find the number
Explanations
Let the digits abc
a+b+c=17-Eqn1
a^2+b^2+c^2 =109 -Eqn -2
Also 100a+10b+c-495=100c+10b+a
99(a-c)=495 Thus a-c =5 The possible combinations are (6,1)(7,2)(8,3)(9,4)
Case 1: (6,1)
From Eqn 1,b+17-7=10 which not possible as b is a single digit
Case 2:(7,2)
From eqn 1 b=17-9=8
Verifying with eqn 2,49+4+64=117and hence not valid
Case 3: (8,3)
From eqn 1,b=17-11=6
Verifying with eqn 2,64+9+36 = 109 and hence valid
Thus the number is 863
3) Find the last two0 digits of (102^3921)+(3081^3921)
Ans 02
To find out the last 2 digits of a term where the number ends with 1, multiply the tens digit of the number with the last digit of the exponent This will give you the tens digit Unit digit will always be 1
Applying this shortcut
for 102^3921,last 2 digits is (2^1) 1=21
for 3081^3921,last 2 digits is (8^1)=81
Adding both we get 102
Hence last two digits of the expression is 02
4) To find out the last 2 digits of a term where the number ends with 1, multiply the tens digit of the number with the last digit of the exponent This will give you the tens digit Unit digit will always be 1
Applying this shortcut
for 102^3921,last 2 digits is (2^1) 1=21
for 3081^3921,last 2 digits is (8^1)=81
Adding both we get 102
Hence last two digits of the expression is 02
4 A series is given as 1,6,7,13,20,33,.......and so on Find the sum of first 52 terms
1st and 2nd terms are 1,6
3rd term is 7 which is sum of first+second
4the term is 13 which is sum of second +thirds
Expanding the series further by adding a few more terms it is 1,6,7,13,20,33,53,86,139,and so on
Now if we add the terms for upto 1,2,3,4,5,6 terms it is
1,2,14,27,47,80,133,219 and so on
5)
Ans 26.25 sq units
The Radius of the circle R circumscribing a triangle is given by the formula
R-ABC /(4*Area of Triangle)
Area of Triangle - 1/2*base*height - 1/2*BC*Ad-1.5BC (As Ad -3)
A,B,C are the side which are 17.5 9 and BC respectively
Hence radius R -17 .5*9*BC/(4*1.5BC) -17.5*9/6-26.25 squints
6) A calculator has a key for squaring and another key for inverting. So if x is the displayed number, then pressing the square key will replace x by x^2 and pressing the invert key will replace x by 1/x. If initially the number displayed is 6 and one alternatively presses the invert and square key 16 times each, then the final number displayed (assuming no round off or overflow errors) will be
Ever n number of inverse key has no effect on the number.
By pressing the square key, the value got increased like 2, 4, 8, .... Which are in the format of 2n. So after the 16 pressings the power becomes 216
So the final number will be 6216=665536
7) How many two digit numbers are there which when subtracted from the number formed by reversing it's digits as well as when added to the number formed by reversing its digits,
result in a perfect square.
Let the number xy = 10x + y
Given that, 10x+y - (10y - x) = 9(x-y) is a perfect square
So x-y can be 1, 4, 9. -------- (1)
So given that 10x+y +(10y +x) = 11(x+y) is a perfect square.
So x+y be 11. Possible options are (9,2), (8,3),(7,4),(6,5) ---------(2)
From the above two conditions only (6,5) satisfies the condition
Only 1 number 56 satisfies.
8) Find the 55th word of SHUVANK in dictionary
Sol: Arranging the letters in alphabetical order we get : A H K N S U V
Now Total words start with A are 6!
Total words start with AH are 5! = 120
Now
Total words start with AHK are 4! = 24
Total words start with AHN are 4! = 24
Total words start with AHSK are 3! = 6
Now AHSNKUV will be the last word required.
9) Car A leaves city C at 5pm and is driven at a speed of 40kmph. 2 hours later another car B leaves city C and is driven in the same direction as car A. In how much time will car B be 9 kms ahead of car A if the speed of car is 60kmph
Relative speed = 60 - 40 = 20 kmph
Initial gap as car B leaves after 2 hours = 40 x 2 = 80 kms
Car B should be 9 km ahead of the A at a required time so it must be 89 km away
Time = 89 / 20 = 4.45 hrs or 267 mins
10) n is a natural number and n^3 has 16 factors. Then how many factors can n^4 have?
Total factors of a number N=ap.bq.cr... is (p+1)(q+1)(r+1)...
As n3 has 16 factors n3 can be one of the two formats given below
n3 =a15
n3 = a3.b3
If n3 =a15 then n = a5 and number of factors of n4 = 21
n3 = a3.b3 then n = ab and number of factors n4 = 25
11)Two cars start from the same point at the same time towards the same destination which is 420 km away. The first and second car travel at respective speeds of 60 kmph and 90 kmph. After traveling for sometime the speeds of the two cars get interchanged. Finally the second car reaches the destination one hour earlier than the first. Find the time after which the speeds get interchanged?
Let the total time taken by the cars be a and b
Let the time after which the speed is interchanged be t
For car A, 60t+90(a-t) = 420, 90a - 30t = 420 .......(1)
For car B, 90t + 60(b-t) = 420, 60b + 30t = 420 ....(2)
Using both (1) and (2), we get 90a + 60b = 840
But as a - b =1, 90a + 60(a-1) = 840.
Solving a = 6.
Substituting in equation 1, we get t = 4
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1. What are the total number of divisors of 600(including 1 and 600)?
a. 24
b. 40
c. 16
d. 20
Sol: Option a
If N=ap×bq×cr.... then the number of factors of N = (p+1)(q+1)(r+1) ....
600 = 23×3×52
So number of factors of 600 = (3+1)(1+1)(2+1) = 24
2. What is the sum of the squares of the first 20 natural numbers (1 to 20)?
a. 2870
b. 2000
c. 5650
d. 44100
Sol: Option a
Use formula n(n+1)(2n+1)/6
3. What is ∑K=028K2(28KC) where 28KC is the number of ways of choosing k items from 28 items?
a. 406 * 227
b. 306 * 226
c. 28 * 227
d. 56 * 227
Sol: A
Consider (1+x)n=C0+C1x+C2x2+.....+Cnxn .......(1)
Differentiating w.r.t x we get
n(1+x)n−1=C1+2C2x+3C3x2+.....+nCnxn−1
Multiplying by x on both sides,
x.n(1+x)n−1=x.C1+2C2x2+3C3x3+.....
Now again differentiating w.r.t to x
n(1+x)n−1+n(n−1)x(1+x)n−2=C0+22C1x+32C2x2+42C3x3.....
Putting x = 1, we get
n(n+1)2n−2=C1+22C2+32C3+42C4
Now substituting n = 28
28(28+1)228−2 = 812.226 = 406.227
4. What is ∑K=0283K(28KC) where 28KC is the number of ways of choosing k items from 28 items?
a. 256
b. 3* 227
c. 329
d. 3* 427
Sol: Option A
We know that C0+3C1+32C2+.....+3nCn=4n
Substitute n = 28
We get ∑K=0283K(28KC) = 428= 256
5. A call center agent has a list of 305 phone numbers of people in alphabetic order of names (but she does not have any of the names). She needs to quickly contact Deepak Sharma to convey a message to him. If each call takes 2 minutes to complete, and every call is answered, what is the minimum amount of time in which she can guarantee to deliver the message to Mr Sharma.
a. 18 minutes
b. 610 minutes
c. 206 minutes
d. 34 minutes
Sol: Option A
6. The times taken by a phone operator to complete a call are 2,9,3,1,5 minutes respectively. What is the average time per call?
a. 4 minutes
b. 7 minutes
c. 1 minutes
d. 5 minutes
Sol: Option A
7. The times taken by a phone operator to complete a call are 2,9,3,1,5 minutes respectively. What is the median time per call?
a. 5 minutes
b. 7 minutes
c. 1 minutes
d. 4 minutes
Sol: NO option is correct. Median is 3
8. Eric throws two dice, and his score is the sum of the values shown. Sandra throws one die, and her score is the square of the value shown. What is the probability that Sandra’s score will be strictly higher than Eric’s score?
a. 137/216
b. 17/36
c. 173/216
d. 5/6
Sol: A
9. What is the largest integer that divides all three numbers 23400,272304,205248 without leaving a remainder?
a. 48
b. 24
c. 96
d. 72
Sol: Option B
Find GCD
10. Of the 38 people in my office, 10 like to drink chocolate, 15 are cricket fans, and 20 neither like chocolate nor like cricket. How many people like both cricket and chocolate?
a. 7
b. 10
c. 15
d. 18
Sol: Option A
11. If f(x) = 2x+2 what is f(f(3))?
a. 18
b. 8
c. 64
d. 16
Sol: Option A
12. If f(x) = 7 x +12, what is f-1(x) (the inverse function)?
a. (x-12)/7
b. 7x+12
c. 1/(7x+12)
d. No inverse exists
Sol: Option A
13. A permutation is often represented by the cycles it has. For example, if we permute the numbers in the natural order to 2 3 1 5 4, this is represented as (1 3 2) (5 4). In this the (132) says that the first number has gone to the position 3, the third number has gone to the position 2, and the second number has gone to position 1, and (5 4) means that the fifth number has gone to position 4 and the fourth number has gone to position 5. The numbers with brackets are to be read cyclically. If a number has not changed position, it is kept as a single cycle. Thus 5 2 1 3 4 is represented as (1345)(2). We may apply permutations on itself If we apply the permutation (132)(54) once, we get 2 3 1 5 4. If we apply it again, we get 3 1 2 4 5 , or (1 2 3)(4) (5) If we consider the permutation of 7 numbers (1457)(263), what is its order (how many
times must it be applied before the numbers appear in their original order)?
a. 12
b. 7
c. 7! (factorial of 7)
d. 14
Sol: Not yet solved
14. What is the maximum value of x3y3 + 3 x*y when x+y = 8?
a. 4144
b. 256
c. 8192
d. 102
Sol: Option A
The question probably be x3.y3+3x∗y
Sustitute x = 4 and y = 4
15. Two circles of radii 5 cm and 3 cm touch each other at A and also touch a line at B and C. The distance BC in cms is?
a. √ 60
b. √ 62
c. √ 68
d. √ 64
Sol:Option A
√d2−(r1−r2)2
d = distance between centers
16. In Goa beach, there are three small picnic tables. Tables 1 and 2 each seat three people. Table 3 seats only one person, since two of its seats are broken. Akash, Babu, Chitra, David, Eesha, Farooq, and Govind all sit at seats at these picnic tables. Who sits with whom and at which table are determined by the following constraints:
a. Chitra does not sit at the same table as Govind.
b. Eesha does not sit at the same table as David.
c. Farooq does not sit at the same table as Chitra.
d. Akash does not sit at the same table as Babu.
e. Govind does not sit at the same table as Farooq.
Which of the following is a list of people who could sit together at table 2?
a. Govind, Eesha, Akash
b. Babu, Farooq, Chitra
c. Chitra, Govind, David.
d. Farooq, David, Eesha.
Sol: Option A
17. There are a number of chocolates in a bag. If they were to be equally divided among 14 children, there are 10 chocolates left. If they were to be equally divided among 15 children, there are 8 chocolates left. Obviously, this can be satisfied if any multiple of 210 chocolates are added to the bag. What is the remainder when the minimum feasible number of chocolates in the bag is divided by 9?
a. 2
b. 5
c. 4
d. 6
Sol: Option B
18. Let f(m,n) =45*m + 36*n, where m and n are integers (positive or negative) What is the minimum positive value for f(m,n) for all values of m,n (this may be achieved for various values of m and n)?
a. 9
b. 6
c. 5
d. 18
Sol: Option A
19. What is the largest number that will divide 90207, 232585 and 127986 without leaving a remainder?
a. 257
b. 905
c. 351
d. 498
Sol: Option A
20. We have an equal arms two pan balance and need to weigh objects with integral weights in the range 1 to 40 kilo grams. We have a set of standard weights and can place the weights in any pan. . (i.e) some weights can be in a pan with objects and some weights can be in the other pan. The minimum number of standard weights required is:
a. 4
b. 10
c. 5
d. 6
Sol: Option A
21. A white cube(with six faces) is painted red on two different faces. How many different ways can this be done (two paintings are considered same if on a suitable rotation of the cube one painting can be carried to the other)?
a. 2
b. 15
c. 4
d. 30
Sol: Option A
22. How many divisors (including 1, but excluding 1000) are there for the number 1000?
a. 15
b. 16
c. 31
d. 10
Sol: Option A
23. In the polynomial f(x) =2*x^4 - 49*x^2 +54, what is the product of the roots, and what is the sum of the roots (Note that x^n denotes the x raised to the power n, or x multiplied by itself n times)?
a. 27,0
b. 54,2
c. 49/2,54
d. 49,27
Sol: Option A
24. In the polynomial f(x) = x^5 + a*x^3 + b*x^4 +c*x + d, all coefficients a, b, c, d are integers. If 3 + sqrt(7) is a root, which of the following must be also a root?(Note that x^n denotes the x raised to the power n, or x multiplied by itself n times. Also sqrt(u) denotes the square root of u, or the number which when multiplied by itself, gives the number u)?
a. 3-sqrt(7)
b. 3+sqrt(21)
c. 5
d. sqrt(7) + sqrt(3)
Sol: Option A
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TCS New Questions 2013-2014 TCS New Pattern of Questions from Openseesame
1. If 3y + x > 2 and x + 2y≤3, What can be said about the value of y?
A. y = -1
B. y >-1
C. y <-1
D. y = 1
Answer: B
Multiply the second equation with -1 then it will become - x - 2y≥ - 3. Add the equations. You will get y > -1.
2. If the price of an item is decreased by 10% and then increased by 10%, the net effect on the price of the item is
A. A decrease of 99%
B. No change
C. A decrease of 1%
D. An increase of 1%
Answer: C
If a certain number is increased by x% then decreased by x% or vice versa, the net change is always decrease. This change is given by a simple formula −(x/10)2= −(10/10)2= −1%. Negitive sign indicates decrease.
3. If m is an odd integer and n an even integer, which of the following is definitely odd?
A. (2m+n)(m-n)
B. (m+n2)+(m−n2)
C. m2+mn+n2
D. m +n
Answer: C and D (Original Answer given as D)
You just remember the following odd ± odd = even; even ± even = even; even ± odd = odd
Also odd x odd = odd; even x even = even; even x odd = even.
4. What is the sum of all even integers between 99 and 301?
A. 40000
B. 20000
C. 40400
D. 20200
Answer: D
The first even number after 99 is 100 and last even number below 301 is 300. We have to find the sum of even numbers from 100 to 300. i.e., 100 + 102 + 104 + ............... 300.
Take 2 Common. 2 x ( 50 + 51 + ...........150)
There are total 101 terms in this series. So formula for the sum of n terms when first term and last term is known is n/2(a+l)
So 50 + 51 + ...........150 = 1012(50+150)
So 2 x 101/2(50+150) = 20200
5. There are 20 balls which are red, blue or green. If 7 balls are green and the sum of red balls and green balls is less than 13, at most how many red balls are there?
A. 4
B. 5
C. 6
D. 7
Answer: B
Given R + B + G = 17; G = 7; and R + G < 13. Substituting G = 7 in the last equation, We get R < 6. So maximum value of R = 6
6. If n is the sum of two consecutive odd integers and less than 100, what is greatest possibility of n?
A. 98
B. 94
C. 96
D. 99
Answer : C
We take two odd numbers as (2n + 1) and (2n - 1).
Their sum should be less than 100. So (2n + 1) + (2n - 1) < 100 ⇒ 4n < 100.
The largest 4 multiple which is less than 100 is 96
7. x2 < 1/100, and x < 0 what is the highest range in which x can lie?
A. -1/10 < x < 0
B. -1 < x < 0
C. -1/10 < x < 1/10
D. -1/10 < x
Answer: A
8. There are 4 boxes colored red, yellow, green and blue. If 2 boxes are selected, how many combinations are there for at least one green box or one red box to be selected?
A. 1
B . 6
C. 9
D. 5
Answer: 5
Total ways of selecting two boxes out of 4 is 4C2 = 6. Now, the number of ways of selecting two boxes where none of the green or red box included is only 1 way. (we select yellow and blue in only one way). If we substract this number from total ways we get 5 ways.
9. All faces of a cube with an eight - meter edge are painted red. If the cube is cut into smaller cubes with a two - meter edge, how many of the two meter cubes have paint on exactly one face?
A. 24
B. 36
C. 60
D. 48
Answer : A
If there are n cubes lie on an edge, then total number of cubes with one side painting is given by 6×(n−2)2. Here side of the bigger cube is 8, and small cube is 2. So there are 4 cubes lie on an edge. Hence answer = 24
10. Two cyclists begin training on an oval racecourse at the same time. The professional cyclist completes each lap in 4 minutes; the novice takes 6 minutes to complete each lap. How many minutes after the start will both cyclists pass at exactly the same spot where they began to cycle?
A. 10
B. 8
C. 14
D. 12
Answer: D
The faster cyclyst comes to the starting point for every 4 min so his times are 4, 8, 12, ......... The slower cyclist comes to the starting point for every 6 min so his times are 6, 12, 18, ......... So both comes at the end of the 12th min.
11 Tim and Elan are 90 km from each other.they start to move each other simultanously tim at speed 10 and elan 5 kmph. If every hour they double their speed what is the distance that Tim will pass until he meet Elan
A. 45
B. 60
C. 20
D. 80
Answer: B
12 . A father purchases dress for his three daughter. The dresses are of same color but of different size .the dress is kept in dark room .What is the probability that all the three will not choose their own dress.
A. 2/3
B. 1/3
C. 1/6
D. 1/9
Answer: B
13 . N is an integer and N>2, at most how many integers among N + 2, N + 3, N + 4, N + 5, N + 6, and N + 7 are prime integers?
A. 1
B. 3
C. 2
D. 4
Answer: C
14 A turtle is crossing a field. What is the total distance (in meters) passed by turtle? Consider the following two statements
(X) The average speed of the turtle is 2 meters per minute
(Y) Had the turtle walked 1 meter per minute faster than his average speed it would have finished 40 minutes earlier
A. Statement X alone is enough to get the answer
B. Both statements X and Y are needed to get the answer
C. Statement Y alone is enough to get the answer
D. Data inadequate
Answer: B
15 . Given the following information, who is youngest?
C is younger than A; A is talled than B
C is older than B; C is younger than D
B is taller than C; A is older than D
A. D
B. B
C. C
D. A
Answer: B
16 Find the number of rectangles from the adjoining figure (A square is also considered a rectangle)
A. 864
B. 3276
C. 1638
D. None
Answer: C
17 A, B, C and D go for a picnic. When A stands on a weighing machine, B also climbs on, and the weight shown was 132 kg. When B stands, C also climbs on, and the machine shows 130 kg. Similarly the weight of C and D is found as 102 kg and that of B and D is 116 kg. What is D's weight
A. 58kg
B. 78 kg
C. 44 kg
D. None
Answer : C
Given A + B = 132; B + C = 130; C + D = 102, B + D = 116
Eliminate B from 2nd and 4th equation and solving this equation and 3rd we get D value as 44.
18 Mr and Mrs Smith have invited 9 of their friends and their spouses for a party at the Waikiki Beach resort. They stand for a group photograph. If Mr Smith never stands next to Mrs Smith (as he says they are always together otherwise). How many ways the group can be arranged in a row for the photograph?
A. 20!
B. 19! + 18!
C. 18 x 19!
D. 2 x 19!
Answer: C
19 Roy is now 4 years older than Erik and half of that amount older than Iris. If in 2 years, roy will be twice as old as Erik, then in 2 years what would be Roy's age multiplied by Iris's age?
A. 28
B. 48
C. 50
D. 52
Answer: 48
20 X, Y, X and W are integers. The expression X - Y - Z is even and the expression Y - Z - W is odd. If X is even what must be true?
A. W must be odd
B. Y - Z must be odd
C. W must be odd
D. Z must be odd
Answer: A or C (But go for C)
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TCS Latest Placement Paper Questions With Solutions
1. A manufacturer of chocolates makes 6 different flavors of chocolates. The chocolates are sold in boxes of 10. How many “different” boxes of chocolates can be made?
Sol:
If n similar articles are to be distributed to r persons, x1+x2+x3......xr=n each person is eligible to take any number of articles then the total ways are n+r−1Cr−1
In this case x1+x2+x3......x6=10
in such a case the formula for non negative integral solutions is n+r−1Cr−1
Here n =6 and r=10. So total ways are 10+6−1C6−1 = 3003
2. In a single throw with two dice, find the probability that their sum is a multiple either of 3 or 4.
a. 1/3
b. 1/2
c. 5/9
d. 17/36
Sol: Their sum can be 3,4,6,8,9,12
For two dice, any number from 2 to 7 can be get in (n-1) ways and any number from 8 to 12 can be get in (13 - n) ways.
Then possible ways are 2 + 3 + 5 + 5 + 4 + 1 = 20 possible cases.
So probability is (20/36)=(5/9)
3. B alone can do piece of work in 10 days. A alone can do it in 15 days. If the total wages for the work is Rs 5000, how much should B be paid if they work together for the entire duration of the work?
a. 2000
b. 4000
c. 5000
d. 3000
Sol:
Time taken by A and B is in the ratio of = 3:2
Ratio of the Work = 2 : 3 (since, time and work are inversely proportional)
Total money is divided in the ratio of 2 : 3 and B gets Rs.3000
4. The letters in the word ADOPTS are permuted in all possible ways and arranged in alphabetical order then find the word at position 42 in the permuted alphabetical order?
a) AOTDSP
b) AOTPDS
c) AOTDPS
d) AOSTPD
SOL:
In alphabetical order : A D O P S T
A _ _ _ _ _ : the places filled in 5! ways = 120, But we need a rank less than 120. So the word starts with A.
A D _ _ _ _ : empty places can be filled in 4!=24
A O _ _ _ _ : the places filled with 4! ways = 24. If we add 24 + 24 this total crosses 42. So We should not consider all the words starting with AO.
A O D _ _ _ : 3!= 6
A O P _ _ _ : 3!=6
Till this 36 words are obtained, we need the 42nd word.
AOS _ _ _ : 3!= 6
Exactly we are getting the sum 42. So last 3 letters in the descending order are TPD.
So given word is AOSTPD
5. Arun makes a popular brand of ice cream in a rectangular shaped bar 6cm long, 5cm wide and 2cm thick. To cut costs, the company had decided to reduce the volume of the bar by 19%. The thickness will remain same, but the length and width will be decreased by some percentage. The new width will be,
a. 5.5
b. 4.5
c. 7.5
d. 6.5
Sol:
Volume =l×b×h = 6×5×2 = 60 cm3
Now volume is reduced by 19%.
Therefore, new volume = (100−19)100×60=48.6
Now, thickness remains same and let length and breadth be reduced to x%
so, new volume: (x100×6)(x100×5)2=48.6
Solving we get x =90
thus length and width is reduced by 10%
New width = 5-(10% of 5)=4.5
6. If all the numbers between 11 and 100 are written on a piece of paper. How many times will the number 4 be used?
Sol: We have to consider the number of 4's in two digit numbers. _ _
If we fix 4 in the 10th place, unit place be filled with 10 ways. If we fix 4 in units place, 10th place be filled with 9 ways (0 is not allowed)
So total 19 ways.
Alternatively:
There are total 9 4's in 14, 24, 34...,94
& total 10 4's in 40,41,42....49
thus, 9+10=19.
7. If twenty four men and sixteen women work on a day, the total wages to be paid is 11,600. If twelve men and thirty seven women work on a day, the total wages to be paid remains the same. What is the wages paid to a man for a day’s work?
Sol: Let man daily wages and woman daily wages be M and W respectively
24M+16W=11600
12M+37W=11600
solving the above equations gives M=350 and W=200
8. The cost price of a cow and a horse is Rs 3 lakhs. The cow is sold at 20% profit and the horse is sold at 10% loss. Overall gain is Rs 4200. What is the cost price of the cow?
Sol:
Profit = 4200
Profit =SP - CP
4200=SP - 300000 therefore SP=304200
x+y = 300000
1.2x + 0.9y = 304200
Solving for x = 114000 = CP of cow.
9. 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4......
In the above sequence what is the number of the position 2888 of the sequence.
a) 1
b) 4
c) 3
d) 2
Sol: First if we count 1223334444. they are 10
In the next term they are 20
Next they are 30 and so on
So Using n(n+1)2×10≤2888
For n = 23 we get LHS as 2760. Remaining terms 128.
Now in the 24th term, we have 24 1's, and next 48 terms are 2's. So next 72 terms are 3's.
The 2888 term will be “3”.
10. How many 4-digit numbers contain no.2?
Sol: Total number of four digit numbers =9000 (i.e 1000 to 9999 )
We try to find the number of numbers not having digit 2 in them.
Now consider the units place it can be selected in 9 ways (i.e 0,1,3,4,5,6,7,8,9)
Tens place it can be selected in 9 ways (i.e 0,1,3,4,5,6,7,8,9)
Hundreds place it can be selected in 9 ways (i.e 0,1,3,4,5,6,7,8,9)
Thousands place can be selected in 8 ways (i.e 1,3,4,5,6,7,8,9) here '0' cannot be taken
Total number of numbers not having digit 2 in it =9 x 9 x 9 x 8 =5832
Total number of numbers having digit 2 in it = 9000-5832 =3168
11. The value of diamond varies directly as the square of its weight. If a diamond falls and breaks into two pieces with weights in the ratio 2:3. what is the loss percentage in the value?
Sol: Let weight be “x”
the cost of diamond in the original state is proportional to x2
when it is fallen it breaks into two pieces 2y and the 3y
x = 5y
Original value of diamond = (5y)2 = 25y2
Value of diamond after breakage = (2y)2+(3y)2=13y2
so the percentage loss will be = 25y2−13y225y2×100=48%
12. Five college students met at a party and exchanged gossips. Uma said, “Only one of us is lying”. David said, “Exactly two of us are lying”. Thara said, “Exactly 3 of us are lying”. Querishi said, “Exactly 4 of us are lying”. Chitra said “All of us are lying”. Which one was telling the truth?
a)David
b)Querishi
c)Chitra
d)Thara
Sol: As all are contradictory statements, it is clear that ONLY one of them is telling the truth. So remaining 4 of them are lying. Querishi mentioned that exactly 4 are lying. So, he is telling the truth.
Explanation: Let us 1st assume that Uma is telling the truth. Then according to her only one is lying. But if only one is lying then all the others’ statements are contradicting the possibility. In the same way all the other statements should be checked. If we assume the Querishi is telling the truth, according to him exactly 4 members are lying. So all the others are telling lies and he is the one who is telling the truth. This case fits perfectly.
13. Cara, a blue whale participated in a weight loss program at the biggest office. At the end of every month, the decrease in weight from original weight was measured and noted as 1, 2, 6, 21, 86, 445, 2676. While Cara made a steadfast effort, the weighing machine showed an erroneous weight once. What was that.
a) 2676
b) 2
c) 445
d) 86
SOL: This is a number series problem nothing to do with the data given.
1x 1+1=2
2 x 2+2=6
6 x 3+3=21
21 x 4+4=88 and not 86
88 x 5+5 = 445
445*6+6 = 2676
14. A man who goes to work long before sunrise every morning gets dressed in the dark. In his sock drawer he has 6 black and 8 blue socks. What is the probability that his first pick was a black sock, but his second pick was a blue sock?
SOL: This is a case of without replacement. We have to multiply two probabilities. 1. Probability of picking up a black sock, and probability of picking a blue sock, given that first sock is black.
6C114C1×8C113C1=2491
15. There are 6 red balls,8 blue balls and 7 green balls in a bag. If 5 are drawn with replacement, what is the probability at least three are red?
Sol: At least 3 reds means we get either : 3 red or 4 red or 5 red. And this is a case of replacement.
case 1 : 3 red balls : 6/21 x 6/21 x 6/21 x 15/21 x 15/21
case 2 : 4 red balls : 6/21 x 6/21 x 6/21 x 6/21 x 15/21
case 3 : 5 red balls : 6/21 x 6/21 x 6/21 x 6/21 x 6/21
Total probability = = (6/21 x 6/21 x 6/21 x 15/21 x 15/21)+(6/21 x 6/21 x 6/21 x 6/21 x (15 )/21)+ (6/21 x 6/21 x 6/21 x 6/21 x 6/21)
= 312/16807
16. Total number of 4 digit number do not having the digit 3 or 6.
Sol:
consider 4 digits _ _ _ _
1st blank can be filled in 7C1 ways (0,3,6 are neglected as the first digit should not be 0)
2st blank can be filled in 8C1 ways (0 considered along with 1,2,4,5,7,8,9)
3st blank can be filled in 8C1 ways
4st blank can be filled in 8C1 ways
Therefore total 4 digit number without 3 or 6 is 7 x 8 x 8 x 8=3584
17. Find the missing in the series: 70, 54, 45, 41,____.
Sol: 40
70-54 = 16 = 42
54-45 = 9 = 32
45-41 = 4 = 22
41-40 = 1 = 12
18. A school has 120, 192 and 144 students enrolled for its science, arts and commerce courses. All students have to be seated in rooms for an exam such that each room has students of only the same course and also all rooms have equal number of students. What is the least number of rooms needed?
Sol: We have to find the maximum number which divides all the given numbers so that number of roots get minimized. HCF of 120,192 & 144 is 24. Each room have 24 students of the same course.
Then rooms needed 12024+19224+14424 = 5 +8 + 6 = 19
19. A farmer has a rose garden. Every day he picks either 7,6,24 or 23 roses. When he plucks these number of flowers the next day 37,36,9 or 18 new flowers bloom. On Monday he counts 189 roses. If he continues on his plan each day, after some days what can be the number of roses left behind? (Hint : Consider number of roses remaining every day)
a)7
b)4
c)30
d)37
Sol:
let us consider the case of 23. when he picks up 23 roses the next day there will be 18 new, so in this case., 5 flowers will be less every day. So when he counts 189, the next day 184, 179,174,169,................
finally the no. of roses left behind will be 4.
20. What is the 32nd word of "WAITING" in a dictionary?
Sol: Arranging the words of waiting in Alphabetical Order : A,G,I,I,N,T,W
Start with A_ _ _ _ _ _ This can be arranged in 6!/2! ways=720/2=360 ways
so can't be arranged starting with A alone as it is asking for 32nd word so it is out of range
AG_ _ _ _ _then the remaining letters can be arranged in 5!/2! ways so,120/2=60 ways. Out of range as it has to be within 32 words.
AGI_ _ _ _ Now the remaining letters can be arranged in 4! ways =24
AGN _ _ _ _ can be arranged in 4!/2! ways or 12 ways
so,24+12 =36th word so out of range. So we should not consider all the words start with AGN
now AGNI_ _ _can be arranged in 3! ways =6 ways
so 24+6=30 within range
Now only two word left so, arrange in alphabetical order.
AGNTIIW - 31st word
AGNTIWI - 32nd word
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TCS Aptitude Questions
1. If f(x) = (1+x+x2+x3+.......x2012)2−x2012, g(x) = 1+x+x2+x3+.......x2011.Then what is the remainder when f(x) is divided by g(x)
Let us multiply g(x) with x on the both sides
x.g(x) = x+x2+x3+.......x2012
add 1 on both sides
x. g(x) + 1 = 1+x+x2+x3+.......x2012
Substitute this value in f(x)
then f(x) = (x.g(x)+1)2−x2012
f(x) = x2.g(x)2+2.g(x)+1−x2012
Now f(x) is divisible by g(x) first two terms are exactly divisible by g(x) and we get 1 - x2012
But 1 - x2012 = (1 - x)(1+x+x2+x3+.......x2011)
if this expression is divisible by g(x) we get 0 as remainder.
2. A number has exactly 3 prime factors, 125 factors of this number are perfect squares and 27 factors of this number are perfect cubes. overall how many factors does the number have?
We know that the total factors of a number N = ap.bq.cr ....
Now the total factors which are perfect squares of a number N = ([p2]+1).([q2]+1).([r2]+1)....
where [x] is greatest intezer less than that of x.
Given ([p2]+1).([q2]+1).([r2]+1).... = 125
So [p2]+1 = 5; [q2]+1 = 5; [p2]+1 = 5
[p2] = 4 ⇒ p = 8 or 9, similarly q = 8 or 9, r = 8 or 9
Given that 27 factors of this number are perfect cubes
so ([p3]+1).([q3]+1).([r3]+1).... = 27
So [p3]+1 = 3 ⇒ = [p3] = 2
⇒ p = 6, 7, 8
By combining we know that p = q = r = 84
Number of factors of this number = (8+1).(8+1).(8+1) = 729
3. In a class there are 60% of girls of which 25% poor. What is the probability that a poor girl is selected is leader?
Assume total students in the class = 100
Then Girls = 60% (100) = 60
Poor girls = 25% (60) = 15
So probability that a poor girls is selected leader = Poor girls / Total students = 15/100 = 15%
4. A and B are running around a circular track of length 120 meters with speeds 12 m/s and 6 m/s in the same direction. When will they meet for the first time?
A meets B when A covers one round more than B.
A's relative speed = (12 - 6) m/s. So he takes 120 / 6 seconds to gain one extra round.
So after 20 seconds A meets B.
5. A completes a work in 20 days B in 60 days C in 45 days. All three persons working together on a project got a profit of Rs.26000 what is the profit of B?
We know that profits must be shared as the ratio of their efficiencies. But efficiencies are inversely proportional to the days. So efficiencies of A : B : C = 1/20 : 1/60 : 1/45 = 9 : 3 : 4
So B share in the total profit = 3 / 13 X 26000 = Rs.6000
6. A completes a piece of work in 3/4 of the time in B does, B takes 4/5 of the time in C does. They got a profit of Rs. 40000 how much B gets?
Assume C takes 20 Days. Now B takes 4/5 (20) = 16 days. A takes 3/4(16) = 12
Now their efficiencies ratio = 1/20 : 1/16 : 1/12 = 12 : 15 : 20
B's share in the profit of Rs.40000 = 15/47 (40000) = Rs.12765
7. An empty tank be filled with an inlet pipe ‘A’ in 42 minutes. After 12 minutes an outlet pipe ‘B’ is opened which can empty the tank in 30 minutes. After 6 minutes another inlet pipe ‘C’ opened into the same tank, which can fill the tank in 35 minutes and the tank is filled. Find the time taken to fill the tank?
Assume total tank capacity = 210 Liters
Now capacity of pipe A = 210/42 = 5 Liters
Capacity of B = 210 / 30 = - 7 Liters
Capacity of C = 210 / 35 = 6 min
Assume tank gets filled in x min after the third pipe got opened.
So x×5+6×(−2)+4x=210
⇒48+4x=210⇒4x=162⇒x=40.5
Total time taken to fill the tank = 40.5 + 12 + 6 = 51.5
8. Mother, daughter and an infant combined age is 74, and mother's age is 46 more than daughter and infant. If infant age is 0.4 times of daughter age, then find daughters age.
Assume M + D + I = 74; .................(1)
Also given M - D - I = 46 ⇒ M = D + I + 46
Also I = 0.4 D ⇒ I = 2/5 D
Substituting M and I values in the first equation we get D - 25D - 46 + D + 25D = 74
Solving D = 10
9. A Grocer bought 24 kg coffee beans at price X per kg. After a while one third of stock got spoiled so he sold the rest for $200 per kg and made a total profit of twice the cost. What must be the price of X?
Total Cost price = 24×X
As 1/3rd of the beans spoiled, remaining beans are 2/3 (24) = 16 kgs
Selling price = 200 × 16 = 3200
Profit = Selling price - Cost price = 3200 - 24×X
Given Profit = 2 × Cost price
3200 - 24×X = 2 × (24×X)
Solving X = 44.44
10. Bhanu spends 30% of his income on petrol on scooter 20% of the remaining on house rent and the balance on food. If he spends Rs.300 on petrol then what is the expenditure on house rent?
Given 30% (Income ) = 300 ⇒ Income = 1000
After having spent Rs.300 on petrol, he left with Rs.700.
His spending on house rent = 20% (700) = Rs.140
11. Let exp(m,n) = m to the power n. If exp(10, m) = n exp(2, 2) where to and n are integers then n =
Given 10m=n.22
⇒ 2m×5m=n.22⇒2m−2×5m=n
For m = 2 we get least value of n = 25, and for m > 2 we get infinite values are possible for n.
12. How many kgs. of wheat costing Rs. 5 per kg must be mixed with 45 kg of rice costing Rs. 6.40 per kg so that 20% gain may be obtained by selling the mixture at Rs. 7.20 per kg ?
If the selling price of the mixture is Rs.7.2 when sold at 20% profit then
CP ×120100 = 7.2 ⇒ CP = Rs.6
Now by applying weighted average formula = K×5+45×6.4K+45=6
⇒ K = 18 kgs
13. The diagonal of a square is twice the side of equilateral triangle then the ratio of Area of the Triangle to the Area of Square is?
Let the side of equilateral triangle = 1 unit.
We know that area of an equilateral triangle = 3√4a2
As side = 1 unit area of the equilateral triangle = 3√4
Now Diagonal of the square = 2 (side of the equilateral triangle) = 2
We know that area of the square = 12D2 where D = diagonal
So area of the square = 12(22)=2
Ratio of the areas of equilateral triangle and square = 3√4 : 2 ⇒ 3√:8
14. Raj tossed 3 dices and there results are noted down then what is the probability that raj gets 10?
Always remember when 3 dice are rolled the number of ways of getting n ( where n is the sum of faces on dice)
= (n−1)C2 where n = 3 to 8
= 25 where n = 9, 12
= 27 where n = 10, 11
= (20−n)C2 where n = 13 to 18
The required probability = 2763 = 27216
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TCS Model Question Paper
Aptitude Questions
1. What are the total number of divisors of 600(including 1 and 600)?
a. 24
b. 40
c. 16
d. 20 Sol: Option a
If N=ap×bq×cr.... then the number of factors of N = (p+1)(q+1)(r+1) ....
600 = 23×3×52
So number of factors of 600 = (3+1)(1+1)(2+1) = 24
2. What is the sum of the squares of the first 20 natural numbers (1 to 20)?
a. 2870
b. 2000
c. 5650
d. 44100 Sol: Option a
Use formula n(n+1)(2n+1)6
3. In the polynomial f(x) = x^5 + a*x^3 + b*x^4 +c*x + d, all coefficients a, b, c, d are integers. If 3 + sqrt(7) is a root, which of the following must be also a root?(Note that x^n denotes the x raised to the power n, or x multiplied by itself n times. Also sqrt(u) denotes the square root of u, or the number which when multiplied by itself, gives the number u)?
a. 3-sqrt(7)
b. 3+sqrt(21)
c. 5
d. sqrt(7) + sqrt(3) Sol: Option A
4. How many divisors (including 1, but excluding 1000) are there for the number 1000?
a. 15
b. 16
c. 31
d. 10 Sol: Option A
5. A call center agent has a list of 305 phone numbers of people in alphabetic order of names (but she does not have any of the names). She needs to quickly contact Deepak Sharma to convey a message to him. If each call takes 2 minutes to complete, and every call is answered, what is the minimum amount of time in which she can guarantee to deliver the message to Mr Sharma.
a. 18 minutes
b. 610 minutes
c. 206 minutes
d. 34 minutes Sol: Option A
6. The times taken by a phone operator to complete a call are 2,9,3,1,5 minutes respectively. What is the average time per call?
a. 4 minutes
b. 7 minutes
c. 1 minutes
d. 5 minutes Sol: Option A
7. The times taken by a phone operator to complete a call are 2,9,3,1,5 minutes respectively. What is the median time per call?
a. 5 minutes
b. 7 minutes
c. 1 minutes
d. 4 minutes Sol: NO option is correct. Median is 3
8. Eric throws two dice, and his score is the sum of the values shown. Sandra throws one die, and her score is the square of the value shown. What is the probability that Sandra’s score will be strictly higher than Eric’s score?
a. 137/216
b. 17/36
c. 173/216
d. 5/6 Sol: A
9. What is the largest integer that divides all three numbers 23400,272304,205248 without leaving a remainder?
a. 48
b. 24
c. 96
d. 72 Sol: Option B
10. Of the 38 people in my office, 10 like to drink chocolate, 15 are cricket fans, and 20 neither like chocolate nor like cricket. How many people like both cricket and chocolate?
a. 7
b. 10
c. 15
d. 18 Sol: Option A
11. If f(x) = 2x+2 what is f(f(3))?
a. 18
b. 8
c. 64
d. 16 Sol: Option A
12. If f(x) = 7 x +12, what is f-1(x) (the inverse function)?
a. (x-12)/7
b. 7x+12
c. 1/(7x+12)
d. No inverse exists Sol: Option A
13. A permutation is often represented by the cycles it has. For example, if we permute the numbers in the natural order to 2 3 1 5 4, this is represented as (1 3 2) (5 4). In this the (132) says that the first number has gone to the position 3, the third number has gone to the position 2, and the second number has gone to position 1, and (5 4) means that the fifth number has gone to position 4 and the fourth number has gone to position 5. The numbers with brackets are to be read cyclically. If a number has not changed position, it is kept as a single cycle. Thus 5 2 1 3 4 is represented as (1345)(2). We may apply permutations on itself If we apply the permutation (132)(54) once, we get 2 3 1 5 4. If we apply it again, we get 3 1 2 4 5 , or (1 2 3)(4) (5) If we consider the permutation of 7 numbers (1457)(263), what is its order (how many times must it be applied before the numbers appear in their original order)?
a. 12
b. 7
c. 7! (factorial of 7)
d. 14 Sol: Not yet solved
14. What is the maximum value of x3y3 + 3 x*y when x+y = 8?
a. 4144
b. 256
c. 8192
d. 102 Sol: Option A
The question probably be x3.y3+3x∗y
Sustitute x = 4 and y = 4
15. A white cube(with six faces) is painted red on two different faces. How many different ways can this be done (two paintings are considered same if on a suitable rotation of the cube one painting can be carried to the other)?
a. 2
b. 15
c. 4
d. 30 Sol: Option A
16. In Goa beach, there are three small picnic tables. Tables 1 and 2 each seat three people. Table 3 seats only one person, since two of its seats are broken. Akash, Babu, Chitra, David, Eesha, Farooq, and Govind all sit at seats at these picnic tables. Who sits with whom and at which table are determined by the following constraints:
a. Chitra does not sit at the same table as Govind.
b. Eesha does not sit at the same table as David.
c. Farooq does not sit at the same table as Chitra.
d. Akash does not sit at the same table as Babu.
e. Govind does not sit at the same table as Farooq.
Which of the following is a list of people who could sit together at table 2?
a. Govind, Eesha, Akash
b. Babu, Farooq, Chitra
c. Chitra, Govind, David.
d. Farooq, David, Eesha. Sol: Option A
17. There are a number of chocolates in a bag. If they were to be equally divided among 14 children, there are 10 chocolates left. If they were to be equally divided among 15 children, there are 8 chocolates left. Obviously, this can be satisfied if any multiple of 210 chocolates are added to the bag. What is the remainder when the minimum feasible number of chocolates in the bag is divided by 9?
a. 2
b. 5
c. 4
d. 6 Sol: Option B
18. Let f(m,n) =45*m + 36*n, where m and n are integers (positive or negative) What is the minimum positive value for f(m,n) for all values of m,n (this may be achieved for various values of m and n)?
a. 9
b. 6
c. 5
d. 18 Sol: Option A
19. What is the largest number that will divide 90207, 232585 and 127986 without leaving a remainder?
a. 257
b. 905
c. 351
d. 498 Sol: Option A
20. We have an equal arms two pan balance and need to weigh objects with integral weights in the range 1 to 40 kilo grams. We have a set of standard weights and can place the weights in any pan. . (i.e) some weights can be in a pan with objects and some weights can be in the other pan. The minimum number of standard weights required is:
a. 4
b. 10
c. 5
d. 6 Sol: Option A
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