Indian Institue of Management 2008 COMMON APTITUDE TEST (CAT ) - Question Paper

part – 1

This part contains 25 questions:

1. How many integers, greater than 999 but not greater than 4000 can be formed with the digitys 0,1,2,3 and 4, if repetition of digits is allowed?
(1) 499 (2) 500 (3) 375 (4) 376 (5) 501

2. What is the number of distinct terms in the expansion of (a+b+c)20?
(1) 231 (2) 253 (3) 242 (4) 210 (5) 228

Directions for ques. three and 4:

The figure beneath indicates the plan of a town. The streets are at right angles to every other. A rectangular park (p) is situated inside the town with a diagonal road running through it. There is also a prohibited region (d) in the town.




D
P







3. Neelam rides her bicycle from her house at A to her office at B, taking the shortest path. Then the number of possible shortest paths that she can select is
(1) 60 (2) 75 (3) 45 (4) 90 (5) 72

4. Neelam rides her bicycle from her house at A to her club at C, via B taking the shortest path. Then the number of possible shortest paths that she can select is

(1) 1170 (2) 630 (3) 792 (4) 1200 (5) 936

5. Consider a right circular cone of base radius four cm and height 10 cm. A cylinder is to be placed inside the cone with 1 of the flat surfaces resting on the base of the cone. obtain the largest possible total surface area (in sq cm) of the cylinder.
(1) 100A/3 (2) 80A/3 (3) 120A/7 (4) 130A/9 (5) 110A/7

6. What are the last 2 digits of 72008 ?
(1) 21 (2) 61 (3) 01 (4) 41 (5) 81

7. In a triangle ABC, the lengths of the sides AB and AC equal 17.5cm and nine cm respectively. Let D be a point on the line segment BC such that AD is perpendicular to BC. If AD = three cm, then what is the radius (in cm) of the circle circumscribing the triangle ABC?
(1) 17.05 (2) 27.85 (3) 22.45 (4) 32.25 (5) 26.25

8. find the sum H1+1/12+1/22 + H1+1/22+1/32 ………..+ H1+1/20072 + 1/20082
(1) 2008 – 1/2008 (2) 2007 – 1/2007 (3) 2007 – 1/2008
(4) 2008 -1/2007 (5) 2008 – 1/2009

9. A shop stores x kg of rice. The 1st customer buys half this amount plus half of kg of rice. The 2nd customer buys half the remaining amount plus half a kg of rice. Then the 3rd customer also buys half the remaining amount plus half a kg of rice. Thereafter, no rice is left in the shop. Which of the subsequent best defines the value of x?

Earning:   Approval pending.