### TCS Placement Paper & Interview On 2010 @ Karakul

#### Aptitude Paper:

1. Adam sat with his friends in the Chinnaswamy stadium at Madurai to watch the 100 metres running race organized by the Asian Athletics Association. Five rounds were run. After every round half the teams were eliminated. Finally, one team wins the game. How many teams participated in the race?

(a) 30 (b) 32 (c) 41 (d) 54

(a) 30 (b) 32 (c) 41 (d) 54

2. (1/3) of a number is 5 more than the (1/6) of the same number?

a) 6 b)36 c)30 d)72

a) 6 b)36 c)30 d)72

3. There are two pipes A and B. If A filled 10 liters in an hour, B can fill 20 liters in same time. Likewise B can fill 10, 20, 40, 80, 160. If B filled in 1/16 of a tank in 3 hours, how much time will it take to fill the tank completely?

a) 9 B) 8 c) 7 d) 6

a) 9 B) 8 c) 7 d) 6

4. Leena cut small cubes of 3 cubic cm each. She joined it to make a cuboid of length 10 cm, width 3 cm and depth 3 cm. How many more cubes oes she need to make a perfect cube?

a) 910 b) 250 c) 750 d) 650

a) 910 b) 250 c) 750 d) 650

5. A lady has fine gloves and hats in her closet- 26 blue, 30 red, and 56 yellow. The lights are out and it is totally dark. In spite of the darkness, she can make out the difference between a hat and a glove. She takes out an item out of the closet only if she is sure that if it is a glove. How many gloves must she take out to make sure she has a pair of each color?

6. 10 men and 10 women are there, they dance with each other, is there possibility that 2 men are dancing with same women and vice versa?

a) 22 b) 20 c) 10 d) none

a) 22 b) 20 c) 10 d) none

7. A game is played between 2 players and one player is declared as winner. All the winnersfrom first round are played in second round. All the winners from second round are played in third round and so on. If 8 rounds are played to declare only one player as winner, how many players are played in first round?

a) 256 b) 512 c) 64 d) 128

a) 256 b) 512 c) 64 d) 128

8. 49 members attended the party. In that 22 are males, 17 are females. The shake hands between males, females, male and female. Total 12 people given shake hands. How many such kinds of such shake hands are possible?

a) 122 b) 66 c) 48 d)1 28

a) 122 b) 66 c) 48 d)1 28

9. There is 7 friends (A1, A2, A3….A7).If A1 have to have shake with all without repeat. How many handshakes possible?

a) 6 b) 21 c) 28 d) 7

a) 6 b) 21 c) 28 d) 7

10. 20 men handshake with each other without repetition. What is the total number of handshakes made?

a) 190 b) 210 c) 150 d) 250

a) 190 b) 210 c) 150 d) 250

11. 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

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

12. A man goes 50Km north , then turned left walked 40Km, then turned right ? In which direction he is?

a) North b) South c) East d) West

a) North b) South c) East d) West

13. In T.Nagar the building were numbered from 1 to 100.Then how many 4’s will be present in the numbers?

a) 18 b) 19 c) 20 d) 21.

a) 18 b) 19 c) 20 d) 21.

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.

a) 20.72 b) 3.5 c) 238.25 d) 6.18

a) 20.72 b) 3.5 c) 238.25 d) 6.18

15. A sheet of paper has statements numbered from 1 to 70. For all values of n from 1 to 70. 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 35 statements are true and the last 35 are false.

d) The first 35 statements are false and the last 35 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 35 statements are true and the last 35 are false.

d) The first 35 statements are false and the last 35 are false.

16. If there are 30 cans out of them one is poisoned if a person tastes very little he will die within 14 hours so if there are mice to test and 24 hours to test, how many mices are required to find the poisoned can?

a) 3 b) 2 c) 6 d) 1

a) 3 b) 2 c) 6 d) 1

17. It is dark in my bedroom and I want to get two socks of the same color from my drawer, which contains 24 red and 24 blue socks. How many socks do I have to take from the drawer to get at least two socks of the same color?

a) 2 b) 3 c) 48 d) 25

a) 2 b) 3 c) 48 d) 25

18. How many 9 digit numbers are possible by using the digits 1,2,3,4,5 which are divisible by 4 if the repetition is allowed?

a) 57 b) 56 c) 59 d) 58

a) 57 b) 56 c) 59 d) 58

19. 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

Ans: 5

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

Ans: 5

20. The citizens of planet nigiet are 8 fingered and have thus developed their decimal system in base 8. A certain street in nigiet contains 1000 (in base buildings numbered 1 to 1000. How many 3s are used in numbering these buildings?

a) 54 b) 64 c) 265 d) 192

Ans: 192

a) 54 b) 64 c) 265 d) 192

Ans: 192

21. Given 3 lines in the plane such that the points of intersection form a triangle with sides of length 20, 20 and 30, the number of points equidistant from all the 3 lines is

a) 1 b) 3 c) 4 d) 0

a) 1 b) 3 c) 4 d) 0

22. Hare in the other. The hare starts after the tortoise has covered 1/5 of its distance and that too leisurely3. A hare and a tortoise have a race along a circle of 100 yards diameter. The tortoise goes in one direction and the. The hare and tortoise meet when the hare has covered only 1/8 of the distance. By what factor should the hare increase its speed so as to tie the race?

a) 37.80 b)8 c) 40 d) 5

Ans: 37.80

a) 37.80 b)8 c) 40 d) 5

Ans: 37.80

23. Here 10 programers, type 10 lines with in 10 minutes then 60lines can type within 60 minutes. How many programmers are needed?

a) 16 b) 6 c) 10 d) 60

a) 16 b) 6 c) 10 d) 60

24. Alok and Bhanu play the following min-max game. Given the expression

N = 9 + 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

a) 0 b) 27 c) 18 d) 20

N = 9 + 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

a) 0 b) 27 c) 18 d) 20

25. Alice nd Bob play the following coins-on-a-stack game. 20 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 = 20). 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 coinhappens to be on top when it’s a player’s turn then the player wins the game. Initially, the gold coinis the third coin from the top. Then

a) In order to win, Alice’s first move should be a 1-move.

b) In order to win, Alice’s first move should be a 0-move.

c) In order to win, Alice’s first move can be a 0-move or a 1-move.

d) Alice has no winning strategy.

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 = 20). 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 coinhappens to be on top when it’s a player’s turn then the player wins the game. Initially, the gold coinis the third coin from the top. Then

a) In order to win, Alice’s first move should be a 1-move.

b) In order to win, Alice’s first move should be a 0-move.

c) In order to win, Alice’s first move can be a 0-move or a 1-move.

d) Alice has no winning strategy.

26. For the FIFA world cup, Paul the octopus has been predicting the winner of each match with amazing success. It is rumored that in a match between 2 teams A and B, Paul picks A with the same probability as A’s chances of winning. Let’s assume such rumors to be true and that in a match between Ghana and Bolivia, Ghana the stronger team has a probability of 2/3 of winning the game. What is the probability that Paul will correctly pick the winner of the Ghana-Bolivia game?

a)1/9 b)4/9 c)5/9 d)2/3

Ans: 5/9

a)1/9 b)4/9 c)5/9 d)2/3

Ans: 5/9

27. 36 people {a1, a2, …, a36} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, …, {a35, a36}, {a36, 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)11 c)13 d)18

Ans: 18

a)12 b)11 c)13 d)18

Ans: 18

28. 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 and of the statements on this sheet are true.” Which statements are true and which are false?

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

b)The first 26 statements are false and the rest are true.

c)The first 13 statements are true and the rest are false.

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

statement n says “At least and of the statements on this sheet are true.” Which statements are true and which are false?

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

b)The first 26 statements are false and the rest are true.

c)The first 13 statements are true and the rest are false.

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

29. There are two boxes, one containing 10 red balls and the other containing 10 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

a)1/2 b)14/19 c)37/38 d)3/4

a)1/2 b)14/19 c)37/38 d)3/4

30. A circular dartboard of radius 1 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) 0.5 d) 0.25

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) 0.5 d) 0.25

31. A sheet of paper has statements numbered from 1 to 40. For all values of n from 1 to 40, statement n says: ‘Exactly 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 statements are false.

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

c) All the statements are false.

d) The 39th statement is true and the rest are false.

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

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

c) All the statements are false.

d) The 39th statement is true and the rest are false.

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