1. 20 people meet and shake hands. The maximum number of handshakes possible if there is to be no “cycle” of handshakes is (A cycle of handshakes is a sequence of k people a1, a2, ……, ak (k > 2) such that the pairs {a1, a2}, {a2, a3}, ……, {ak-1, ak}, {ak, a1} shake hands).

(a) 19 (b) 190 (c)20 (d)21

2. The pace length P is the distance between the rear of two consecutive footprints. For men, the formula, n/P = 144 gives an approximate relationship between n and P where, n = number of steps per minute and P = pace length in meters. Bernard knows his pace length is 164 cm. The formula applies to Bernard’s walking. Calculate Bernard’s walking speed kmph.

(a) 236.16 (b) 11.39 (c) 8.78 (d) 23.24

3. 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 5/6 of winning the game. What is the probability that Paul will correctly pick the winner of the Ghana- Bolivia game?

(a) 0.72 (b)0.5 (c)0.64 (d)0.83

4. 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 in1947 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 enjoyed great success. Rohit once bought a Ferrari. It could go 3 times as fast as Mohit’s old Mercedes. If the speed of Mohit’s Mercedes is 33 km/hr and the distance travelled by the Ferrari is 909 km, find the total time taken in hours for Rohit to drive that distance.

(a) 9.18 (b) 10.18 (c) 9 (d) 99

5. Anoop managed to draw 6 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 radius of the circles to the sides of the square. Assume √2 is 1.4.

(a) 9 : 1 (b) 6.2 : 1 (c) 1 : 9 (d)7.6 : 1

6. Given 3 lines in the plane such that the points of intersection form a triangle with sides of length 19, 19 and 19, the number of points equidistant from all the 3 lines is (a) 1 (b) 0 (c) 4 (d) 2

7. Planet Fourfi resides in 4-dimensional space and thus the currency used by its residents is 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.

•The diameter of the coins should be at least 64mm and not exceed 512mm.

•Given a coin, the diameter of the next larger coin is at least 50% greater.

•The diameter of the 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?

a) 6 b) 8 c) 5 d)9

8. 10 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 following possibilities are true? A) All suspects are lying B) the leftmost suspect is guilty C) rightmost suspect is guilty

(a) A only (b) A and B (c) B only (d) A and C

9. 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 min while each minute has 60 sec. 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 12:40 am.

a) 251 b) 89 c) 111 d) 71

10. A hare and tortoise 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 tortoise has covered 1/5 its distance and that leisurely. The hare and tortoise meet when the hare has covered only 1/4 of the distance. By what factor should the hare increase its speed so as to tie the race?(a) 8 (b)37 (c)45 (d)6.6

11. There are two boxes, one containing 21 red balls and the other containing 25 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 is maximized. This maximum probability is (a) 0.5 (b) 0.63 (c) 0.72 (d) 0.48

12. 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) 438 b) 500 c) 900 d) 800

13. Susan made a block with small cubes of 8 cubic cm volume to make block 3 small cubes long, 9 small cubes wide and 5 small cubes deep. She realizes that she has used more small cubes than she really needed. She realized that she could have glued a fewer number of cubes together to lock like a block with same dimensions, if it were made hollow. What is the minimum number of cubes that she needs to make the block?

a) 114 b) 135 c) 21 d) 71

14. A school yard contains only bicycles and 4 wheeled wagons. On Tuesday, the total number of wheels in the schoolyard was 114. What would be the possible number of bicycles?

a) 18 b) 17 c) 16 d) 8

15. Determine the distance between x-intercept and Z-intercept of the plane where equation is 6x+8y-3Z=72.

a) 3 b) 26.83 c) 9 d) 25.63

16. Bob, Peter, Oliver and 2 girls – Raven and Chelsey are to be seated in a row. Raven sits to left of Bob. No girl sits at extreme positions and middle positions. Peter always sits at the extreme position. Who sits to the right of Chelsey?

a) Oliver b) Bob c) Peter/Oliver d) Peter

17. A taxi driver commenced his journey from a point and he drove 10 km towards north and turned to his left and drove another 20 km. After waiting to meet a friend here, he turned to his right and continued to drive another 10 km. In which direction is he now?

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

18. 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) 4

19. A research lab in Chennai requires 100 mice and 75 sterilized cages for a certain set of laboratory experiments. To identify the mice, the lab has prepared labels with numbers 1 to 100, by combining tags numbered 0 to 9. The SPCA requires that the tags be made of toxin-free material and that the temperature of the cages be maintained at 27 degree Celsius. Also, not more than 2 mice can be caged together and each cage must be at least 2 sq. ft in area. The 5 experiments to be conducted by lab are to be thoroughly documented and performed only after a round of approval by authorities. The approval procedure takes around 48 hours. How many times is the tag numbered '4' used by the lab in numbering these mice?

a) 9 b) 19 c) 20 d) 21

20. 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 12 such programmers take 12 minutes to write 12 lines of code in total. How many lines of code can be written by 48 programmers in 48 minutes?

a) 48 b) 12 c) 192 d) 216

21. A sheet of paper has statements numbered from 1 to 30. For all values of n from 1 to 30, statement n says "At most n of the statements on this sheet are false". Which statements are true and which are false?

a) All statements are true.

b) All statements are false.

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

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

22. 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.

23. In the year 2002, Britain was reported to have had 4.3m closed – circuit television (CCTV) cameras – one for every 14 people in the country. This scrutiny is supposed to deter and detect crime. In one criminal case, the police interrogate two suspects. The ratio between the ages of the two suspects is 6:5 and the sum of their ages is 55 years. After how many years will the ratio be 8:7?

a) 11 b) 6 c) 10 d) 5

24. Alok is attending a workshop "How to do more with less" and today's theme is

*working with fewer digits.*The speakers discuss how a lot of miraculous mathematics can be achieved if mankind (as well as womankind) had only worked with fewer digits. The problem posed at the end of the workshop is- How many 6 digit numbers can be formed using the digits 1, 2, 3, 4, 5 that are divisible by 4? Can you help Alok find the answer?a) 500 b) 375 c) 3125 d) 625

25. An athlete decides to run the same distance in 1/2 less time that she usually took. By how much percent will she have to increase her average speed?

a) 40 b) 100 c) 200 d) 50

a) 40 b) 100 c) 200 d) 50

26. What is the value of (3X+8Y)/(X-2Y), if X/2Y=2

a) 8 b) none c) 10 d) 13

a) 8 b) none c) 10 d) 13

27. A lady builds 9cm length, 10cm width, 3cm height box using 1 cubic cm cubes. What is the minimum number of cubes required to build the box?

a) 730 b) 270 c) 720 d) 310

a) 730 b) 270 c) 720 d) 310

28. Alok and Bhanu play the following min-max game. Given the expression (N = 12 + 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) 30 b) 93 c) -69 d) 12

29. On planet zorba, a solar blast has melted the ice caps on its equator. 8 years after the ice melts, tiny planetoids called echina start growing on the rocks. echina grows in the form of a circle and the relationship between the diameter of this circle and the age of echina is given by the formula

d = 2 * √ (t - 8) for t ≥ 8 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 4 mm. How many years back did the solar blast occur?

(a) 18 (b)12 (c)16 (d)24

30. After the typist writes 25 letters and addresses 25 envelopes, she inserts the letters randomly into the envelopes (1 letter per envelope). What is the probability that 2 letters are inserted in to improper envelope? (a) 23/25 (b) 0 (c) 2/25 (d) 1

31. 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 8) buildings numbered 1 to 1000. How many 3s are used in numbering these buildings?

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

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

32. A and B play a game of dice between them. The dice consist of colors on their faces (instead of numbers). When the dice are thrown, A wins if both show the same color; otherwise B wins. One die has 4 red face and 2 blue faces. How many red and blue faces should the other die have if the both players have the same chances of winning?

a) 3 red and 3 blue faces b) 2 red and remaining blue

c) 6 red and 0 blue d) 4 red and remaining blue

a) 3 red and 3 blue faces b) 2 red and remaining blue

c) 6 red and 0 blue d) 4 red and remaining blue

33. Six friends decide to share a big cake. Since all of them like the cake, they begin quarreling who gets to first cut and have a piece of the cake. One friend suggests that they have a blindfold friend choose from well shuffled set of cards numbered one to six. You check and find that this method works as it should simulating a fair throw of a die. You check by performing multiple simultaneous trials of picking the cards blindfold and throwing a die. You note that the number shown by the method of picking up a card and throwing a real world die, sums to a number between 2 and 12. Which total would be likely to appear less

a) 8 b) 12 c) 9 d) 10

a) 8 b) 12 c) 9 d) 10

34. The difference between two no is 9 and the product of the two is 14.What is the square of their sum?

a) 120 b) 130 c) 137 d) 145

a) 120 b) 130 c) 137 d) 145

35. A sheet of paper has statements numbered from 1 to 40. For each value of n from 1 to 40 statement n says "At most n of the statements on this sheet are false." Which statements are true and which are false? (a) All statements are true

(b) The odd numbered statements are true the even numbered are false

(c) The first half of the statements are true and the remaining statements are false

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

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