### TCS Placement Paper - M.I.E.T. MEERUT, SEP 10&11, 2011

2. Technical Round

3. Managerial Round

4. HR Round.

1. For the king's revelry 30 barrels of beer have b een ordered . howerver, it was found that one of them is

poisoned. The poison takes effect even if consumed in the tiniest amount after 14 hours. Yhou need to find

within 24 hours the poisoned barrel and have at your disposal some beer guzzling mice. The smallest number of

mice required to find the poisoned barrel is

1) 2

2) 1

3) 4

4) 3

hint: 2^n> no of barrels ans:4

2. 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 pint 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 maximum value of n1(P) over all configurations P of 15 points in the plane is

1) 5

2) 10

3) 15

4) 9

Ans: 15(Same as given number of points)

3. The pacelength P is the distance between the rear of two consecutive footprints for men the formula n/P=190

gives an approximate relationship between n and P where n= number os steps per minute and P= CX in meters.

Bernard knows his Pace Length is 104cm the formula applies to Bernards walking. Calculate Bernards walking speed

in kmph.

4. A hare and a tortoise have a race along a circle of 100 yards diameter. The tortoise goes in one direction

and the hare I the other. The hare starts after the tortoise had coveredc 1/7 of its distance and that tooo

leisurely. The hare and tortoise meet when the hare has covered only 1/8 of the distance. By what factor shoul

the hare increase its speed so as to ties the reace?

8

41.00

56

7

Ans: 1/7, 1/8

7*8=56

56-7=49

49-8=41

49*41/7^2=41.00

5. Mr bean visited a magic shop and bought some magical marbles of different colours along with other magical

items. While returning home whenever he saw a coloured light he took out marbles of similar colours and counted

them. So he counted the pink coloured marbles and found that he has bought 25 of them . then he counted 10 green

marbles and then 32 yellow marbles. He later counted 30 purple coloured marbles with him. But when he reached a

crossing, he looked at a red light and started counting red marbles and found that he had bought 34 red marbles.

As soon as he finished counting, it started raining heavily and by the time he reached home he was drenched.

After reaching home he found that the red, green, and yellow marbles had magically changed colours and became

white, while other marbles were unchanged . it will take 1 day to regain its colo9urs, but he needs to give

atleast one pair of marbles to his wife so as to ensure that there is atleast one pair of red, yellow and green

marbles?

70

42

68

40

Ans: 34+32+2=68

6. There are two water tanks A and B, A is much smaller than B. While water fills at the rate of 1 liter every

hour in A, it gets filled up like, 10, 20, 40,80, 160…..in tank B. 1/16 th of the tank B is filled in 21 hours.

What is the time to fill the tank fully?

a) 26

(b) 25

(c) 5

(d) 27

7. A sheet of paper has statements numbered from 1 to 20. For all values of n from 1 to 20. Statement n says 'At

least n of the statements on this sheet are false.' Which statements are true and which are false?

(a) The even numbered statements are true and the odd numbered are false.

(b) The odd numbered statements are true and the even numbered are false.

(c) The first 6 statements are true and the last 6 are false.

(d) The first 13 statements are false and the last 13 are false.

Ans. c

Note: For this type of Questions, follow this:

--At least- I'st half are true, Last half are false

--Exactly- Last second one is true or (N-1)th Statement is true

--Almost- All are true.

8. The IT giant Tirnop has recently crossed a head count of 150000 and earnings of $7 billion. As one of the

forerunners in the technology front, Tirnop continues to lead the way in products and services in India. At

Tirnop, all programmers are equal in every respect. They receive identical salaries and also write code at the

same rate. Suppose 12 such programmers take 12 minutes to write 12 lines of code in total. How long will it take

72 programmers to write 72 lines of code in total?

Hint: m1*h1/w1=m2*h2/w2

9. 45 people {a1, a2, …, a12} meet and shake hands in a circular fashion. In the pairs, {a1, a2}, {a2, a3}, …,

{a11, a12}, {a12, a1}. Then size of the smallest set of people such that the rest have shaken hands with at

least one person in the set is

(a) 12

(b) 10

(c) 18

(d) 15

Ans. d

hint: ceiling[N/3]

10. 10 suspects are rounded by the police and questioned about a bank robbery. Only one of them is guilty. The

suspects are made to stand in a line and each person declares that the person next to him on his right is

guilty. The rightmost person is not questioned. Which of the following possibilities are true?

A. All suspects are lying.

B. leftmost suspect is guilty.

C. leftmost suspect is guilty

(a) A only

(b) A and C

(c) A and B

(d) B only

ans: b

11. Alok and Bhanu play the following min-max game. Given the expression N = 15 + X*(Y - Z) Where X, Y and Z are

variables representing single digits (0 to 9), Alok would like to maximize N while Bhanu would like to minimize

it. Towards this end, Alok chooses a single digit number and Bhanu substitutes this for a variable of her choice

(X, Y or Z). Alok then chooses the next value and Bhanu, the variable to substitute the value. Finally Alok

proposes the value for the remaining variable. Assuming both play to their optimal strategies, the value of N at

the end of the game would be?

Ans. 15+18 =33

Note: For this type of questions:

x+y-z=11

x-y-z=2

x*(y+z)=18

12. How many four digit numbers can be formed using the digits 1, 2, 3, 4, 5 (but with repetition) that are

divisible by 4? Can you help Alok find the answer?

(a) 100

(b) 125

(c) 75

(d) 85

Ans:. 5^n-1= 5^4-1=125, n= no of digits

13. On planet korba, a solar blast has melted the ice caps on its equator. 9 years after the ice melts, tiny

planetoids called echina start growing on the rocks. Echina grows in the form of circle, and the relationship

between the diameter of this circle and the age of echina is given by the formula d = 4*v (t-9) for t = 9 where

d represents the diameter in mm and t the number of years since the solar blast.Jagan recorded the radius of

some echina at a particular spot as 7mm. How many years back did the solar blast occur?

a) 17 b)21.25 c)12.25 d)14.05

Ans: b

14. Ferrari S.P.A is an Italian sports car manufacturer based in Maranello, Italy. Founded by Enzo Ferrari in

1928 as Scuderia Ferrari, the company sponsored drivers and manufactured race cars before moving into production

of street-legal vehicles in 1947 as Ferrari S.P.A. Throughout its history, the company has been noted for its

continued participation in racing, especially in Formula One where it has employed great success .Rohit once

bought a Ferrari. It could go 4 times as fast as Mohan's old Mercedes. If the speed of Mohan's Mercedes is 35

km/hr and the distance traveled by the Ferrari is 490 km, find the total time taken for Rohit to drive that

distance.

20.72 b) 5.18 c) 238.25 d) 6.18

Ans: b

15. John buys a cycle for 31 dollars and given a cheque of amount 35 dollars. Shop Keeper exchanged the cheque

with his neighbor and gave change to John. After 2 days, it is known that cheque is bounced. Shop keeper paid

the amount to his neighbor. The cost price of cycle is 19 dollars. What is the profit/loss for shop keeper?

a)loss 23 b)gain 23 c)gain 54 d)Loss 54

Ans: a hint: 19+4=23

16. Middle- earth is a fictional land inhabited by hobbits, elves, dwarves and men. The hobbits and elves are

peaceful creatures that prefer slow, silent lives and appreciate nature and art. The dwarves and the men engage

in physical games. The game is as follows. A tournament is one where out of the two teams that play a match, the

one that loses get eliminated. The matches are played in different rounds, where in every round; half of the

teams get eliminated from the tournament. If there are 8 rounds played in knock out tournament, how many matches

were played?

a)257 b)256 c)72 d)255

And: d

17. (1/2) of a number is 3 more than the (1/6) of the same number?

a) 6

b) 7

c) 8

d) 9

Ans: d

18. Alice and Bob play the following coins-on-a-stack game. 100 coins are stacked one above the other. One of

them is a special (gold) coin and the rest are ordinary coins. The goal is to bring the gold coin to the top by

repeatedly moving the topmost coin to another position in the stack.

Alice starts and the players take turns. A turn consists of moving the coin on the top to a position i below the

top coin (0 = i = 100). We will call this an i-move (thus a 0-move implies doing nothing). The proviso is that

an i-move cannot be repeated; for example once a player makes a 2-move, on subsequent turns neither player can

make a 2-move.

If the gold coin happens to be on top when it's a player's turn then the player wins the game.

A. Alice has no winning strategy.

B. Initially, the gold coins the third coin from the top. Then

C. In order to win, Alice's first move should be a 0-move.

D. In order to win, Alice's first move should be a 1-move.

Ans. D

19. After the typist writes 12 letters and addresses 12 envelopes, she inserts the letters randomly into the

envelopes (1 letter per envelope). What is the probability that exactly 1 letter is inserted in an improper

envelope?

(a) 0

(b) 12/212

(c) 11/12

(d) 1/12

Ans. a

20. The IT giant Tirnop has recently crossed a head count of 150000 and earnings of $7 billion. As one of the

forerunners in the technology front, Tirnop continues to lead the way in products and services in India. At

Tirnop, all programmers are equal in every respect. They receive identical salaries ans also write code at the

same rate. Suppose 12 such programmers take 12 minutes to write 12 lines of code in total. How many lines of

code can be written by 72 programmers in 72 minutes?

(a) 72

(b) 432

(c) 12

(d) 144

Ans. b

(This question is two times repeated in my question paper)

21. A circular dartboard of radius 2 foot is at a distance of 20 feet from you. You throw a dart at it and it

hits the dartboard at some point Q in the circle. What is the probability that Q is closer to the center of the

circle than the periphery?

a) 0.75 b) 1 c) 0.25 d) 0.5

Ans: 0.25

22. Planet Fourfe resides in 4-dimensional space and thus the currency used by its residents are 3- dimensional

objects. The rupee notes are cubical in shape shile their coins are spherical. However the coin minting

machinery lays out some stipulations on the size of the coins. A. The diamere of the coins should be at least 4

mm and not exceed 16mm. B. given a coin the diameter of the next larger coin is at least 50% greater. C. the

diameter of the coin must always be na integer. You are asked to design a set of coins of different diameters

with thers requirements and your goal is to desigh as many coins as possible. How many coins can you design?

1

2

4

3

Ans: 1

23. There are two boxes, one containing 24 red balls and the other containing 38 green balls. You are allowed to

move the balls between the boxes so that when you choose a box at random and a ball at random from the chosen

box the probability of getting a red ball is maximized. This maximum probability is

.50

.39

.69

.19

24. Subha patel is an olfactory scientist working for internation flavors and fragrances. She specializes in

finding new scents recorded and reconstituted from nature thanks to living flower technology she has extracted

fragraned ingredients from different flowering plants into bottles labeled citrus lilac, woody, anisic and casis

. she has learned that a formula for a perfume is acceptable if and only if it does not violate any of the rules

listed: if the perfume contains citrus, it must also contain anisic, and the amount of anisic must equal the

amount of lilac. Woody cannot be used in combination with anisic. Anisic cannot be used in combination with

casis. If the perfume contains casis, the amount of casis must be greater than the total amount of the other

essence or essence used. Which of the following could be added to and unacceptable perfume consisting of two

parts woody and one part casis to make it acceptable?

1. Two parts woody

2. One part lilac

3. One part citrus

4. Two parts casis

Ans: Two parts casis

25. exp(m,n)= m to the power of n, if exp(10,m) = n exp(2,4),what is the value of n?

(i dont remember the options)

26. The citizens of planet Oz are 6 fingered and thus have developed a number system in base 6. A certain street

in Oz contains 1000 buildings numbered from 1 to 1000. How many 3's are used in numbering these buildings?

Express your answer in base 10.

Ans: 3 * n2=108 (n=6,....if n= number system given)

27. The dynamics of crowd behaviour are hard to study because usually people are not reliable witness of their

own behaviour. Now consider 4 people standing in the queue of a supermarket. You want to predict their behaviour

based on their age group. You get to know fro the supermarket records that their average age 3 years ago was 48

years. After a while, another person joins the queue and the present average of all the 5 is 46 years. The

present age of the last person in the queue is:

Ans: 26 years

28. A man jogs at 6 mph over a certain journey and walks over the same route at 4 mph. What is his average speed

for the journey?

a) 2.4 mph

b) 4.8 mph

c) 4 mph

d) 5 mph

Solution: Average speed=(2*x*y)/(x+y)

29. A scientist was researching on animal behavior in his lab. He was very interested in analyzing the behavior

of bear. For some reason he travelled 1mile in north direction & reached at North Pole. There he saw a bear.

He then followed the bear around 1 hr with a speed of 2km/hr in east direction. After that he travelled in south

direction & reached at his lab in2 hrs. Then what is the color of the bear?

a) White

b) Black

c) Gray

d) Brown

Solution is: White. above all the matter is nonsense

30. In a school, for a student out of 100 he got 74 of average for 7 subjects and he got 79 marks in the 8th

subject. what is the average of all the subject?

a) 76.251

b) 80.25

c) 74.265

d) 74.625

Solution: Total marks=74*7=518, then average=(518+79)/8=74.625

31. A boy got 224 points out of 300, but he had to score atleast 79%. Now he has one more exam left with him how

much he have to score in remaining exam to score atleast 79% if it is of 100 points.

Ans: 92 marks

32. The bacteria grows in exponential manner, the bacteria proportion at 3.00 P.M is 300 then at 7.00 P. M it

raise to 153600. By how much will be the proportion of bacteria at 10.00 P.M?

Ans: 39321600 (just solve it).

33. Six friends decide to share a big cake. Since all of them like the cake, they begin quarreling who gets to

first cut and have a piece of the cake. One friend suggests that they have a blindfold friend choose from well

shuffled set of cards numbered one to six. You check and find that this method works as it should simulating a

fair throw of a die. You check by performing multiple simultaneous trials of picking the cards blindfold and

throwing a die. You note that the number shown by the method of picking up a card and throwing a real world die,

sums to a number between 2 and 12. Which total would be likely to appear more often - 8,9 or 10?

a) 8

b) All are equally likely

c) 9

d) 10

Solution: Calculate how many times 8,9,10 will come when we throw 2 dice, and answer

34. 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?

a) Rs.525

b) Rs.1000

c) Rs.675

d) Rs.175

(ans 175)

35. Anoop managed to draw 7 circles of equal radii with their centres on the diagonal of a square such that the

two extreme circles touch two sides of the square and each middle circle touches two circles on either side.

Find the ratio of the side of the square to radius to the circles. You may assume that squate toot of 2 is 1.4

(a) 13.90 :1 (b) 10.40 :1 (c) 11.80 :1 (d) 15.90 :1

Ans: b

Explanation: (2+6root(2)) : 1.

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