# (Paper) TCS Fresher Job Placement Paper : 14 Aug 2011

## TCS

## Job Interview, Question Pattern Paper

**1. Alok and Bhanu play the following min-max game. Given
the expression N=46+X+Y-Z, where X,Y and Z are variables representing single
digits (0 to 9) Alok woul like to maximize N while Bhanu would like to minimize
it. Towards this end, Alok chooses a single digit number and Bhanu substitues
this for a variable of her choice (X, Y or Z) Alok then chooses the next value
and Bhanu the Variab le to substitute the value. Finallyu 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**37

57

64

55

**2. 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 Awith the same probability as A’s
chances of winning Lets assume such rumors to b e true and that in a match b
Etween Ghana and Bolivia Ghana the stronger team has a probability of 10/11 of
winning the game. What is the probability that Paul will correctly pick the
winner of Ghana-Bolivia game?**17

01

91

83

**3. The pacelength P is the distance between the rear of
two consecutive footprints for men the formula n/P=110 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 97cm the formula applies to Bernards
walking. Calculate Bernards walking speed in kmph.**106.70

8.82

6.21

11.34

**4. 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**13.90 :1

10.40 :1

11.80 :1

15.90 :1

**5. Given 3 lines in the plane such that the points of
intersection from a triangle with sides of length 20, 20 and 11 the number of
points equidistant from all the 3 lines is**0

3

1

4

**6. Alok is attending a workshop how to do more with less
and todays theme 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 lthe end of the workshop is how
many 6 digit numbers can be formed using the digits 1, 2,3,4,5 (but with
repetition) that are divible by 4? Can you help Alok find the answer?**3125

3906

1250

3907

**7. After the typist writes 100 letters and addresses 100
envelopes she inserts the letters randomly in to the envelopes(1 letter per
envelope). What is the probability that exactly 1 letter is inserted in an
improper envelop?**0

1-1/100

1/100!

1/100

**8. 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

**9. The IT giant tirnop has recently crossed a head count
of 150000 and earnings of $7billion. 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 104 programmers in 104 minutes:**104

832

13

8

**10. A sheet of paper has statements numbered from 1 to 16 for all values of n
from 1 to 16 statement n says: ‘Exactly n of the statements on this sheet are
false’.
Which statements arte true and which are false?**The second last statement is true and the rest are false.

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

All the statements are false

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

**11. 45 suspects are rounde 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. Shich of the following possibilities are
ture? A. all the suspectrs are lying. B. the leftmost suspect is guilty. C. the
rightmost suspect is guilty.**A and C

A and B

B only

A only

**12. 45 people {a1, a2, ……a45} meet and shake hands in a circular fashion. In
other words, there are totally 45 handshakes involving the pairs, {a1, a2},
{a2,a3},…..{a44,a45},{a45,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**16

22

15

14

**13. The citizzens of planet oz are 8 fingered and thus habve developed a number
system in base 8. A certain street in Oz contains 1000 buildings nubered from 1
to 1000. How many 4s are used in numbering these buildings ? Express your answer
in base 10.**64

96

192

256

**14. Middle earth is fictional land inhabited by hobbits elves dwarves and men.
The hobbits and the elves are peaceful creatures who prefer slow silent lives
and appreciate nature and art. The dwarves and the men engage in physical games.
The game is as follows. A tournoi 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 6 rounds played in a knock out tournoi how many matches
were played?**42

64

63

65

**15. Ferrari S. p.A is an italian sports car manufacturer based in Maranello,
Italy. Founded by Enzo Ferrari in 1928 as Scuderia Ferrari, the compay sponsored
drivers and manufactured race cars bvefore moving into production of
street-legal vehicles in 1947 as Ferrari S.p.A through out is history the compay
has been noted for its continued participation in racing, especially in Formula
One, where it has enjoyed great success. Rohit once bought a Ferrari. It could
go 4 times as fast as Mohit’s old Mercedes. If the speed of Mohit’s Mercedes is
32 km/hr and the sistance traveelled by the Ferrari is 991 km, find the total
time taken for Rohit to drive that distance**7.74 Hours

247 Housr

8 Housr

30 Hours

**16. Given 3 lines in the plane such that the points on intersection form a
triangle with sides of length 20, 20 and 22 the number of points equidistant
from all the 3 lines is**4

1

0

3

**17. A circular dart board of radius 1.0 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 I th circle. What is the probability that Q is closer to the
center of circle than the periphery?**.25

.75

.50

1.00

**18. 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

**19. On the planet Oz there are 8 days in a week – Sunday to Saturday and another
day called Oz day. There are 36 hours in a day and each hour has 90 minutes
while each minute has 60 seconds. As on earth the hour hand covers the dial
twice every day. Find the approximate angle between the hands of a clock on Oz
when the time is 15:40 am**186 degrees

311 degrees

131 degdrees

146 degrees

**20. Ahollow cube of size 5 cm is taken with a thickness of 1 cm. it is made of
smaller cubes of size 1 cm. if 3 faces of the outer surface of the cube are
painted totally how many faces of the smaller cubes remain unpainted?**525

900

825

513

**21. For the king’s revelry 254 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 **9

8

254

7

**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 16 mm and not exceed 64mm. 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?**6

2

4

3

**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. 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 4 points in the
plane is**3

2

4

5

**25. There are two water tanks A and B , A is much smaller than B. While water
fills at the rate of one litre every hour in A, it gets filled up like
10,20,40,80,160 .. in tank B. (At the end of first hour, B has 10 litres, second
hour it has 20, and so on). If tank B is 1/8 filled after 23 hours, what is the
total duration required to fill it completely?**27 hours

25 hours

26 hours

3 hours

**26. A man has some socks in his drawere – 14 identical blue, 20 identical red,
and 28 identical black. The lights are out and it is totally dark. How many
socks must he take out to make sure he has a pair of each colour?**34

50

30

28

**27. A result of global warming is that the ice of some glaciers is melting . 13
years after the ice disappears, tiny plants, called lichens, start to grow on
the rocks. Each 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-13)for t>13, where d represents the
diameter of the lichen in millimeters, and t represents the number of years
after the ice has disappeared. Using the above formula calculate the diameter of
the lichen , 39 years after the ice has disappeared.**702

468

13

689

**28. Alice and bob play the following coins-on-a-track game. 50 coins are stacked
one above the other. One of them is a special (gold) coin and the reset 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 (for some I between 0 and 50). 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-moves on subsequent turns neither
player can make a 2-move. If the gold coin happens to be on top when it’s a
players turn ther the player wins the game. Initially the gold coin is the third
coin from the top then**In order to win, Alice’s first move should be a 1-move.

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

Alice has no winning strategy.

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

**29. 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?**Two parts woody

One part lilac

One part citrus

Two parts casis

**30. 5 people meet and shake hands. The maximum numbersof handshake possible if
there is to be no cycle of handshake is ( A cycle of handshake is a wequence of
people a1, a2….ak, k>2 such that the pairs {a1,a2} {a2,a3} {a(k-1),ak}, {ak,a1}
shake hands).**1

4

3

2

**31. 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

**Company Name:**TCS

**Aptitude Test**

No of Rounds:

No of Rounds:

**Exam/Interview Date:**14-Aug-2011