1 A certain positive integer N has exactly 12 distinct (positive ) divisors , including itself and 1 but has only 3 distinct prime factors . If sum of these prime factors is 20 , compute the smallest possible value of N.a. 360b. 260c. 308d. 154

2 4 people A, B, C, and D are practicing target shooting at 60 glass bottles kept in a row on a table. Whenever a bullet hits a bottle, it is shattered to bits, and does not remain standing any longer. A person is awarded 1 point for every bottle he hits, and 0 points for every missed shot. Assume that all four persons fire simultaneously, and that no two hits the same bottle at the same time. What should their individual total scores be, after all bottles have been hit, such that the product of their scores is maximum?a.16, 14, 20, 10b. 12, 15, 16, 1c. 20, 21, 10, 9d. none of these

3 How many ordered pairs of integers (a, b), are there such that their product is a positive integer less than 1000?a. 99b. 545c. 635d. 1090

4 In the above question, if (a ,b ) is not different from (b , a) , then how many such pairs are possible?a. 49b. 277c. 554d. None

5 Chris and his wife invited a total of 10 families on their marriage anniversary. While the host family had just the two members, each family invited consisted of four members. If every person in the party shook hands with every other person belonging to a different family exactly once, then find the number of handshakes that took in the party.a. 800b. 801c. 740d. None

6 How many numbers are there in between 1 and 30 including both the numbers such that n! is divisible by (n + 1) ?a. 30b. 18c. 17d. 19

7 wer the question 27 & 28 based on the following information. In a game, 60 balls of V different colors are kept inside a sealed box. You are told only the value of V, but not the numbers of balls of each color. Based on this, you have to guess whether it is possible to split the balls into 20 groups of 3 each, such that in each group the 3 balls are of different colors. Your answer is to be a simple yes or no. You win a point if your guess is right otherwise you lose. 27. The minimum values of V for which you can say YES and be sure of winning?a. 3b. 40c. 41d. 6

8 The maximum value of V for which you can say No and be sure of winning?a. 2b. 1c. 4d. 3

9 A trader marked a watch 40% above the cost price and then gave a discount of 10%. If he made a net profit of Rs. 468 after paying a tax of 10% on the gross profit, find the cost price of the watch.a. Rs. 1,800b. Rs. 1,200c. Rs. 2,000d. None

10 A man invest Rs. 3000 at a rate of 5% per annum. How much more should he invest at a rate of 8%, so that he can earn a total of 6% per annum?a.Rs. 1200b.Rs. 1300c.Rs. 1500d.Rs. 2000

11 Direction for question 1 to 4 After getting a new job, Tupai Dada visits his friends & relatives in his village. He buys a cake from Flury's for Rs.624 after getting a 17% discount. His friends Rudra & Arup together have 1/6th of the cake. His cousin brother & sister had the largest portion of the cake – both together had 75% of the entire cake. Tupai Dada's father's lucky number is 13 so he had only 1/13th portion of the cake. Rest of the cake was for Tupai dada to enjoy. 1. If Tupai Dada had distributed the cake equally between his relatives & friends , what would be each one's share ?a. 1/5b. 1/6c. 5/156d. 5/6

12 If the cake was of the form pf a square and you can cut the cake only in square pieces, how many minimum square pieces need to be cut so that every body has the exact share of cake as stated above in second paragraph?a. 3042b. 156c. 6084d. 624

13 If Tupai dada has 40% share of the cake which has 3 cherries in it what is the probability that he finds only 1 cherry in his portion of cake?a. 4b. 432c. 9/40d. 0.044

14 What was the approximate worth of Tupai Dada's piece of cake?a.400b.40c.4d.16

15 A shopkeeper purchases a lamp for some amount & sells it for Rs. 412 , making a profit of p%. If his cost price and selling price of the lamp get interchanged , he would be at a loss of p2 % . what is the approximate value of p?a. 1b. 6c. 13d. 25

16 f(x) = (x+2) / (3-x) 6. Find the value of f(-1) + f(1/2)a. 1.25b. 1.5c. -1.2d. 0.8

17 A piece of spring is joined along three point ( a, a ) , (a + 28, a) , (a + 4 , a + 11) to form a triangle . A circle of same area as the triangle is rotated to form a sphere. Find the volume of the sphere in cu cm.a. 4312/3b. 616/3c. 560/3d. 3080/3

18 P(x) is a polynomial in x. when p(x) is divided by ( x - 1), the remainder is 5 and when p(x) is divided by (x + 1) , the remainder is 7. what would the remainder be when p(x) is divided by (x+1) , the remainder is 7. What would the remainder be when p(x) is divided by (x - 1)(x + 1 )?a. 3 + 2xb. 6 - xc. 6 + xd. 3 - 4x

19 To err is human. Instead of mixing 2 protons with 2 neutrons, you mix 4 protons with 3 neutrons. Each proton makes 5 plutons and each pluton makes 0.5 gluttons. Each neutron makes 2 zutons and each zuton makes 3 plutons. How many more glutton would you find?a.5b.6c.7d.8

20 A man stand at a point A on the bank of a river and looks at the top of a tree which is exactly opposite to him on the other bank. The angle of elevation is 45 degree. He walks 200 meters away from the tree and looks at the top of the tree and finds the angle of elevation to be 30 degree. Calculate the height of the tree and the width of the river?a.100(v3 + 1) , 100(v3 + 1)b.50(1/v3) , 25v3c.100 / (v3 + 1) , 100(v3 + 1)d.none

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