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Details of Manipal Institute Of Technology ,10 September 2011 by TCS conducted by TCS for job interview.

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5.64 hours

6 h

248h

22h

a circular dashboard of radius 2.0 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 perphery?

.75

.25

1.00

.50

A hare and a tortoise have a race along a circle of 100 yards diameter. The tortoise goes in one direction and the hare in the other. The hare starts after the tortoise has covered 1/5 of its distance and that too leisurely. the hare and tortoise meet when the hare has covered only 1/6 of the distance. by what factor should the hare increase its speed so as to tie the race?

6

30

19.00

5

Given 3 lines in the plane such that the points of intersection form a triangle with sides of lengh 20, 20, and 8 the number of points equidistant from all the 3 lines is

3

1

4

A sheet of paper has statements numbered from 1 to 20. for all values of n from 1 to 20, statement n says At most n of the statements on this sheet are false. which statements are true and which are false?the odd numbered statements are true and the even numbered are false.

all statements are false.

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

All statements are true.

The teacher is testing a students proficiency in arithmetic and poses the following question: 1/3 of a number is 3 more than 1/6 of the same number. what is the number ? can you help the student find the answer?

19

6

17

18

For the king,s revelry 62 barrels of beer have been ordered. however, it was found that one of them is poisoned. the poison takes effect even if consumed in the tiniest amount after 14 hours. you nheed to find, within 24hours, the poisoned barrel and have at your disposal some beer guzzling mice. the smallest number of mice required to find the poisoned barrel is

62

6

5

7

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 13 such programmers take 13 minutes to write 13 lines of code in total . how many lines of code can be written by 91 programmers in 91 minutes?

13

637

7

91

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 while their coins are spherical. however the coin minting machinery lays out some stipulations on the size of the coins. A. The diameter of the coins should be at least 4mm and not exceed 8mm. B. Given a coin, the diameter of the next larger coin is at least 50% greater. C. The diameter of th coin must always be an integer. you are asked to design a set of coins of different diameters with these requirements and your goal is to design as many coins as possible. How many coins can you design?

1

2

3

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-set of P is denoted by n1(p). The maximum value of n1(P) over all configurations P of 5 points in the plane is

2

5

4

6

A result of global warming is that the ice of some glaciers is melting. 16 years after the ice disappears, tiny plants, called lichens, start to grow on the rocks. ecach lichen grows approximately in the shape of a circle. The relationship between the diameter of this circle and the age of the lichen can be approximated with the formula: d=18*(t-16) for t > 16, where d represents the diameter of the lichen in millimeters, and t represents the muber of years after the ice has disappeared. Using the above formula, calculate the diameter of the lichen, 33 years after the ice has disappeared.

306

594

578

16

There are two water tank A and B, A is much smaller than B. WHile water fills at the rate of one letre every hour in A, it gets filled like 10, 20, 40, 80, 160..in Tank B. (at the end of first hour, B has 10litres, second hoiur it has 20, and so on). If tank B is 1/4 filled after 20hrs, what is the total duration required to fil it completely.

23hrs

21hrs

2hrs

22hrs

Alice and Bob play the follwoing coins oin a stack game. 100coins 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 up 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 (for some I between 0 and 100). We will call this an i-move )thus a 0-move impklies doing nothing). The proviso is that an i move canot be repeated. for example once a player makes 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 turn then the player wins the game. Initially, the gold coin is the thiurd coin from the top.

In order to win, alice,s first move should be a 0-move

in order to win, alice,s first move can be a 0-move or a 1-move

in order to win, alice,s first move should be a 1-move

alice has no winning strategy

A sheet of Paper has statements numbered from 1 to 10. For all values of n from 1 to 10. statement n says: Exactky n of the statements on this sheet are false. Which statements are true and which are false?

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

The odd numbered starements are true and the even numbered statements are false.

the second last statement is true and the rest are false.

al the statements are false.

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, Pul picks A with the same probability as A,s chances of winning. Let,s assume such rumors are to be true and that in a match Ghana and Bolivia, Ghana the stronger team has a probability of 6/7 of winning the game. What si the probability that paul will correctly pick the winner of the Ghana Boliovia game?

02

.24

.86

.76

Alok and Bhanu play the following min max game. Given the expression N= 39+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 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

57

48

30

50

24 people {a1, a2, ...a24} meet and shake hands in a circular fashion. In other words, there are totally 24 handshakes involving the pairs, {a1, a2} {a2, a3}, ..., {a23, a24}, {a24, a1}. Then the size of the smallest set of people such that the rest have shaken hands with at least one person in the set is

8

7

9

12

45 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 possibilities are true? A. All the sustpects are lying. B. The lefmost suspect is guilty. C. The righmost suspect is guilty.

A and B

A and C

B only

A only

Anoop managed to draw 5 cricle 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 of the circles. you may assume that square root of 2 is 1.4

7.60:1

12.50:1

10.50:1

9.00:1

Alok is attending a workshop ,How to do more with less, and today,s them is Working with fewer digits. The speakers discuss how a lot of miraculous mathematics can be achived if mankind (as well as womankind) had only worked with fewer digits. The problem posed at the end of the workshop is ,How many 4 digits mumbers 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?

156

50

157

125

After the typist writes 10 letters and addresses 10 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?

1- 1/10

1/10

1/10!

There are tow boxes, one containing 19 red balls and the other containing 23 green balls. you are allowed to move the balls between the boxes so that when hyou choose a box at random and a ball at random from the chosen box, the probabilty of getting a red ball is maximized, This maximu probabilty is

.45

.50

.23

.72

A hollow cube of size 5 cm is taken. with a thickness of 1 cm. it is made of smaller cubes of size 1 cm. if 4 faces of the outer surface of the cube are painted, totally how many faces of the smaller cubes remain unpainted?

900

500

488

800

The citizens of planet Oz are 7 fingered and thus have developed an umber system in base 7 . A certain street in Oz contains 100 bvuildings numbered from 1 to 100. how many 3,s are used in numbering thers buildings?

15

14

7

21

The pacelentht P is the distance between the rear of two consectutive foot prints. For men the formuls, n/P= 158 gives an appproximate relationship between n and P where, n= number of steps per minute and P=pacelentht in meters. Bernard knows his pacelength is 132cm. The formula applies to Bernard,s walking. calculate Bernard,s walking speed in kmph

8.35

208.56

16.52

11.97

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