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

TCS Logo


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

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?

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.

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

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?

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?

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?

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:

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

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.

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?

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

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?

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?

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?

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

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?

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

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

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?

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.

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).

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?

Company Name: TCS
No of Rounds:
Aptitude Test
Exam/Interview Date: 14-Aug-2011