sample ques TCS

1. Alok and Bhanu play the following min-max game. Given the expression N=40+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) 49
(b) 51
© 31
(d) 58

7. The Barnes Foundation in Philadelphia has one of the most extra-ordinary and idiosyncratic collections in French impressionist art. Dr. Barnes who put together this collection has insisted that the paintings be hung in a particular manner specified by him at a museum designed by the French architect Paul Philippe Cret who also designed the Rodin Museum. The museum has, say, seven galleries – Eugene Boudin, Cassatt, Boudin, Forain, Gonzales, Manet and Monet. Visitors reach the main Eugene Boudin by an elevator, and they can enter and leave the exhibition only through Eugene Boudin gallery. Once inside, visitors are free to move as they choose. The following list includes all of the doorways that connect the seven galleries: There is a doorway between Eugene Boudin and Cassatt, a doorway between Eugene BoudinandBoudin, and a doorway between Eugene Boudin and Gonzales galleries. There is a doorway between Cassatt and Boudin galleries. There is a doorway between Gonzales and Forain and a doorway between Gonzales and Manet galleries. There is a doorway between Manet and Monet galleries. Which of the following rooms CANNOT be the third gallery that any visitor enters ?
(a) Monet
(b) Boudin
© Forain
(d) Cassatt

8. Mr. Beans 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 14 green marbles and then 21 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 23 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 colours, but he needs to give atleast one pair of marbles to his wife now. So how many white marbles must be choose and give to his wife so as to ensure that there is atleast one pair of red, yellow and green marbles ?
(a) 46
(b) 35
© 29
(d) 48

11. 33 people {a1, a2,…,a33} meet and shake hands in a circular fashion. In other words, there are totally 33 handshakes involving the pairs, {a1,a2}, {a2,a3},…,{a32, a33}, {a33, 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
(a) 10
(b) 11
© 16
(d) 12

12. Consider two vessels, the first containing on liter of water and the second containing one liter of pepsi. Suppose you take one glass of water out of the first vessel and pour it into the second vessel. After mixing you take one glass of the mixture from the second vessel and pour it back into the first vessel. Which one of the following statements holds now?
(a) None of the statements holds true.
(b) There is less Pepsi in the first vessel than water in the second vessel.
© There is more Pepsi in the first vessel than water in the second vessel.
(d) There is as much Pepsi in the first vessel as there is water in the second vessel.

14. 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 wining. 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 11/12 of winning the game. What is the probability that Paul with correctly pick the winner of the Ghana-Bolivia game?
(a) .92
(b) .01
© .85
(d) .15
15. There are two boxes, one containing 39 red balls and the other containing 26 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) .60
(b) .50
© .80
(d) .30

16. After the typist writes 40 letters and addresses 40 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 improver envelope?
(a) 1 – 1/40
(b) 1/40
© 1/401
(d) 0

17. 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 1/3 of its distance and that too leisurely. The hare and tortoise meet when the hare has covered only 1/4 of the distance. By what factor should be hare increase its speed so as the win the race?
(a) 4
(b) 3
© 12
(d) 5.00

19. The question is followed by two statements, A and B. Answer the question using the following instructions: Choose 1: if the question can be answered by using one of the statements alone but not by using the other statement alone. Choose 2: if the question can be answered by using either of the statements alone. Choose 3: if the question can be answered by using both statements together but not by either statement alone. Choose 4: if the question cannot be answered on the basis of the two statements. Zaheer spends 30% of his income on his children’s education, 20% on recreation and 10 % on healthcare. The corresponding percentages for Sandeep are 40%, 25% and 13%. Who spends more on children’s education? A” Zaheer spends more on recreation that Sandeep B: Sandeep spends more on healthcare than Zaheer.
(a) 3
(b) 2
© 1
(d) 4

20. Subha Patel is an olfactory scientist working for International Flavors and Fragrances. She specializes in finding new scents recorded and reconstituted from nature thanks to Living Flower Technology. She has extracted fragrance ingredients from different flowering plants into bottles labeled herbal, sweet, honey, anisic and rose. 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 herbal, it must also contain honey and there must be twice as much honey as herbal. If the perfume contains sweet, it must also contain anisic, and the amount of anisic must equal the amount of sweet. honey cannot be used in combination with anisic. anisic cannot be used in combination with rose. If the perfume contains rose, the amount of rose must be greater than the total amount of the other essence or essences used. Which of the following could be added to an unacceptable perfume consisting of two parts honey and one part rose to make it acceptable?
(a) Two parts rose
(b) One part herbal
© Two parts honey
(d) One part sweet

4. A sheet of paper has statements numbered from 1 to 20. For all values of n from 1 to 20, 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) All the statements are false.
© The odd numbered statements are true and the even numbered statements are false.
(d) The second last statement is true and the rest are false.

26. 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?
(a) 900
(b) 488
© 500
(d) 800

27. 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 (for some I between 0 and 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. Initially, the gold coin is 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.
© Alice has no winning strategy.
(d) In order to win, Alice’s first move can be a 0-move or a 1-move.

29. A circular dashboard 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 in the circle. What is the probability that Q is closer to the center of the circle than the periphery?
(a) 1.00
(b) .75
© .25
(d) .50

30. 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=10*(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, 45 years after the ice has disappeared.
(a) 450
(b) 437
© 13
(d) 320

34. A sheet of paper has statements numbered from 1 to 20. For each value of n from 1 to 20, statement n says ‘At least n 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 13 statements are false and the rest are true.
© The fist 6 statements are true and the rest are false.
(d) The odd numbered statements are true and the even numbered are false.

38. Recent report have suggested that sportsmen with decreased metabolic rates perform better in certain sports. After reading one such report, Jordon, a sportsperson from Arlington decides to undergo a rigorous physical training program for 3 months, where he performs Yoga for 3 hours, walks for 2 hours and swims for 1 hour each day. He says: I began my training on a Wednesday in a prime number month of 2008. I lost 1% of my original weight within the first 30 days. In the next two months combined, I lost 1 Kg. If he walks at 5 mph over a certain journey and walks back the same route at 8 mph at an altitude of 200 meters, what is his average speed for the journey?
(a) 6.15
(b) 3.08
© 6.50
(d) 26.67

39. The result of global warming is the ice of some glaciers is melting. 19 years after the ice disappears, tiny planets, called lichens, start to grow on the rock. Each lichen grows approximately in the shape of a circle. The relationship between the diameter of the circle and the age of the lichen can be approximated with the formula: d =12* (t-19) for t>19, 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, 32 years after the ice has disappeared.
(a) 384
(b) 156
© 19
(d) 365

40. There are two boxes, one contains 12 red balls and the other containing 47 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) .59
(b) .20
© .10
(d) .50

42. The question is followed by two statements, A and B. Answer the question using the following instructions: Choose1: if the question can be answered by using one of the statements alone but not by using the other statement alone. Choose2: if the question can be answered by using either of the statements alone. Choose3: if the question can be answered by using both statements together but not by either statement alone. Choose4: if the question cannot be answered on the basis of the two statements. Zayed spends 30% of his income on his children’s education, 20% on recreation and 10% on healthcare. The corresponding percentage for Sandeep are 40%, 25% and 13%. Who spends more on children’s education? A: Zayed spends more on recreation than Sandeep B: Sandeep spends more on healthcare than Zayed.
(a) 4
(b) 3
© 2
(d) 1

43. The question is followed by two statements, A and B. Answer the question using the following instructions: Choose1: if the question can be answered by using one of the statements alone but not by using the other statement alone. Choose2: if the question can be answered by using either of the statements alone. Choose3: if the question can be answered by using both statements together but not by either statement alone. Choose4: if the question cannot be answered on the basis of two statements. Tarun is standing 2 steps to the left of a green mark and 3 steps to the right of a black mark. He tosses a coin. If it comes up heads, he moved one step to the right, otherwise he moves one step to the left. He keeps doing this until he reaches one of the two marks, and then he stops. At which mark does he stops? A: he stops at 21 coin tosses. B: he obtains three more tails than heads.
(a) 1
(b) 3
© 4
(d) 2

45. A sheet of paper has statements numbered from 1 to 10. For all values of n from 1 to 10, 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 second last statement is true and the rest are false.
© The odd numbered statements are true and the even numbered statements are false.
(d) All the statements are false.

48. 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 of the 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 100). We will call this as 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 happen to be on the top when it’s a player’s turn then the player wins the game. Initially, the gold coin is the third coin from the top. Then
(a) In order to win, Alice’s first move should be a 1-move.
(b) Alice has no winning strategy.
© In order to win, Alice’s first move can be a 0-moveor a 1-move.
(d) In order to win, Alice’s first move should be a 0-move.
50. Consider two tumblers, the first containing one litre of milk ad the second containing one litre of coffee. Suppose you take one glass of milt out of the first tumbler and pour it into the second tumbler. After mixing you take one glass of the mixture from the second tumbler and pour it back into the first tumbler. Which one of the following statements holds now?
(a) None of the statements holds true.
(b) There is less coffee in the first tumbler than milk in the second tumbler.
© There is as much coffee in the first tumbler as there is milk in the second tumbler.
(d) There is more coffee in the first tumbler than milk in the second tumbler.

51. 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 periphery?
(a) .75
(b) 1.00
© .25
(d) .50

52. A sheet of paper has statements numbered from 1 to 10. For all values of n from 1 to 10, statement n says: ‘Exactly n of the statements on this sheet are false.’ Which statements are true and which are false?
(a) All the statements are false.
(b) The second last statement is true and the rest are false.
© The even numbered statements are true and the odd numbered statements are false.
(d) The odd numbered statements are true and the even numbered statements are false.

53. Consider two vessels, the first containing one litre of oil and the second containing one litre of coffee. Suppose you take one spoon of oil out of the first vessel and pour it into the second vessel. After mixing you take one spoon of mixture from the second vessel and pour it back into the first vessel. Which one of the following statements holds now?
(a) None of the statements holds true.
(b) There is less coffee in the first vessel than oil in the second vessel.
© There is more coffee in the first vessel than oil in the second vessel.
(d) There is as much coffee in the first vessel as there is oil in the second vessel.

55. The question is followed by two statements, A and B. Answer the question using the following instructions: Choose1: if the question can be answered by using one of the statements alone but not by using the other statement alone. Choose2: if the question can be answered by using either of the statements alone. Choose3: if the question can be answered by using both statements together but not by either statement alone. Choose4: if the question cannot be answered on the basis of two statements. Zayed spends 30% of his income on his children’s education, 20% on recreation and 10% on healthcare. The corresponding percentage for Sandeep are 40%, 25% and 13%. Who spends more on children’s education? A: Zayed spends more on recreation than Sandeep B: Sandeep spends more on healthcare than Zayed.

(a) 1
(b) 3
© 4
(d) 2

56. The question is followed by two statements, A and B. Answer the question using the following instructions: Choose1: if the question can be answered by using one of the statements alone but not by using the other statement alone. Choose2: if the question can be answered by using either of the statements alone. Choose3: if the question can be answered by using both statements together but not by either statement alone. Choose4: if the question cannot be answered on the basis of two statements. Tarak is standing 2 steps to the left of a yellow mark and 3 steps to the right of a grey mark. He tosses a coin. If it comes up heads, he moves one step to the right, otherwise he moves one step to the left. He keeps doing this until he reaches one of the two marks, and then he stops. At which mark does he stops? A: he stops at 21 coin tosses. B: he obtains three more tails than heads.
(a) 2
(b) 3
© 4
(d) 1

58. There are two boxes, one contains 47 red balls and the other containing 46 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).75
(b) .50
© .25
(d) .51

59. Consider two vessels, the first containing one liter of ink and the second containing one liter of cola. Suppose you take one glass of ink out of the first vessel and pour it into the second vessel. After mixing you take one glass of mixture from the second vessel and pour it back into the first vessel. Which one of the following statements holds now?
(a) There is as much cola in the first vessel as there is ink in the second vessel.
(b) None of the statements holds true.
© There is more cola in the first vessel than ink in the second vessel.
(d) There is less cola in the first vessel than ink in the second vessel.

1) 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

2) Paul the octopus who has been forecasting the outcome of FIFA world cup matches with tremendous accuracy has now been invited to predict ICC world cup matches in 2011. We will assume that the world cup contenders have been divided into 2 groups of 9 teams each. Each team in a group plays the other teams in the group. The top two teams from each group enter the semi finals (after which the winner is decided by knockout).

However, Paul has a soft spot for India and when India plays any team, Paul always backs India. Alas, his predictions on matches involving India are right only 2 out of 3 times. In order to qualify for the semi finals, it is sufficient for India to win 7 of its group matches. What is the probability that India will win the ICC world cup?
a) (2/3)^10 b) (2/3)^9 + 8/3 * (2/3)^9 c) 8/3 * (2/3)^9 d) (2/3)^10 + 8/3*(2/3)^9


4) A number when divided by D leaves a remainder of 8 and when divided by 3D leaves a remainder of 21 . What is the remainder left, when twice the number is divided by 3D?

a) 13 b) cannot be determined c) 3 d) 42
Ans: c


10) 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*√ (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) 12.06
Ans: b


13) 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.

Ans: b
21) Spores of a fungus, called late blight, grow and spread infection rapidly. These pathogens were responsible for the Irish potato famine of the mid-19th century. These seem to have attacked the tomato crops in England this year. The tomato crops have reduced and the price of the crop has risen up . The price has already gone up to $45 a box from $27 a box a month ago. How much more would a vegetable vendor need to pay to buy 27 boxes this month over what he would have paid last month?
a) $27 b) $ 18 c) $45 d) $ 486
22) Given a collection of 36 points P in the plane and a point equidistant from all points in P, which of the following are necessarily true?
A. The points in P lie on a circle.
B. The distance between any pair of points in P is larger than the distance between X and a point in P
a) A and B b) Neither A nor B c) B only d) A only


25) Alok and Bhanu play the following coins in a circle game. 99 coins are arranged in a circle with each coin touching two other coin. Two of the coins are special and the rest are ordinary. Alok starts and the players take turns removing an ordinary coin of their choice from the circle and bringing the other coins closer until they again form a (smaller) circle. The goal is to bring the special coins adjacent to each other and the first player to do so wins the game. Initially the special coins are separated by two ordinary coins O1 and O2. Which of the following is true?

a) In order to win, Alok should remove O1 on his first turn.
b) In order to win, Alok should remove one of the coins different from O1 and O2 on his first turn.
c) In order to win, Alok should remove O2 on his first turn.
d) Alok has no winning strategy.