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1 . A shop stores x kg of rice. The first customer buys half this amount plus half a kg of rice. The second customer buys half the remaining amount plus half a kg of rice. Then the third customer also buys half the remaining amount plus half a kg of rice. Thereafter, no rice is left in the shop. Which of the following best describes the value of x? *CAT 2008*

(1) 2 ≤ x ≤ 6 (2) 5 ≤ x ≤ 8

(3) 9 ≤ x ≤ 12 (4) 11≤ x ≤ 14

(5) 13 ≤ x ≤ 18

*2. *The number of solutions of the equation 2x + y = 40 where both x and y are positive integers and x ≤ y is: *CAT 2006*

(1) 7 (2) 13

(3) 14 (4) 18

(5) 20

3. If three positive real numbers x, y, z satisfy y – x = z – y and xyz = 4, then what is the minimum possible value of y? *CAT 2004*

1. 2^{1/3} 2. 2^{2/3 }

3 .2^{1/4 } 4. 2^{3/4}

4. Extra: If p, q and r are the lengths of the sides of a triangle, then the range of the expression below is? P^{2} + q^{2} + r^{2} / (pq + rq + pr)

(1) (1,2) (2) [1,2)

(3) (1,3) (4) (-1/2,3)

5. Consider a sequence where the n^{th }term, tn = n/(n+2), n = 1, 2, ….

The value of t3 x t4 x t5 x….x t53 equals: *CAT 2006*

(1) 2/495 (2) 2/477

(3) 12/55 (4) 1/1485

(5) 1/2970

6. If a_{1} = 1 and a_{n+1} – 3a_{n} + 2 = 4n for every positive integer n, then

a_{100} equals?* CAT 2005*

1. 3^{99} – 200 2. 3^{99} + 200

3. 3^{100} – 200 4. 3^{100} + 200

7. Find the sum* CAT 2008*

(1) 2008 – 1/2008 (2) 2007 – 1/2007

(3) 2007 – 1/2008 (4)2008 – 1/2007

(5) 2008 – 1/2009

8. ABCDEF is a regular hexagon and angle AOF = 90°. FO is parallel to ED. What is the ratio of the area of the triangle AOF to that of the hexagon ABCDEF? CAT 2003

a) 1/12 b) 1/6

c) 1/24 d) 1/18

9. In the figure given below, AB is the chord of a circle with centre O.ABis extended to C such that BC =OB.The straight line CO is produced to meet the circle at D. If LACD = y degrees and LAOD = x degrees such that x = ky, then the value of k is?

a) 3 b) 2

c) 1 d) 4

10. Let f(x) be a function satisfying f(x).f(y) = f(xy) for all real x, y. If f(2) = 4, then what is the value of f(1/2)? *CAT 2008
*(1) 0 (2) 1/4

(3) 1/2 (4) 1

(5) Cannot be determined