CAT 2005 EXAM

SOLVED PAPER

SECTION—I

Sub-section I-A Number of Questions: 10 Note: Questions 1 to 10 carry one mark each. Directions for questions 1 to 8: Answer the questions independently of each other. 1. If R = jogging simultaneously from the point where one of the circular tracks touches the smaller side of the rectangular track. A jogs along the rectangular track, while B jogs along the two circular tracks in a figure of eight. Approximately, how much faster than A does B have to run, so that they take the same time to return to their starting point? (1) 3.88% (2) 4.22% (3) 4.44% (4) 4.72% 8. In a chess competition involving some boys and girls of a school, every student had to play exactly one game with every other student. It was found that in 45 games both the players were girls, and in 190 games both were boys. The number of games in which one player was a boy and the other was a girl is: (1) 200 (2) 216 (3) 235 (4) 256 Directions for questions 9 and 10: Answer the questions on the basis of the information given below. Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9 a.m. from A at a speed of 5 km/hr, reaches B, and returns to A at the same speed. Shyam starts at 9 : 45 a.m. from A at a speed of 10 km/hr, reaches B and comes back to A at the same speed. 9. At what time do Ram and Shyam first meet each other? (1) 10 a.m. (2) 10 : 10 a.m. (3) 10 : 20 a.m. (4) 10 : 30 a.m. 10. At what time does Shyam overtake Ram? (1) 10 : 20 a.m. (2) 10 : 30 a.m. (3) 10 : 40 a.m. (4) 10 : 50 a.m. Sub-section I-B Number of Questions: 20 Note: Questions 11 to 30 carry two marks each. Directions for questions 11 to 30: Answer the questions independently of each other. 11. Let x =

3065 – 2965 3064 + 2964

, then (2) 0.1 < R ≤ 0.5 (4) R > 1.0

(1) 0 < R ≤ 0.1 (3) 0.5 < R ≤ 10 .

2. What is the distance in cm between two parallel chords of lengths 32 cm and 24 cm in a circle of radius 20 cm? (1) 1 or 7 (2) 2 or 14 (3) 3 or 21 (4) 4 or 28 3. For which value of k does the following pair of equations yield a unique solution for x such that the solution is positive? x2 – y2 = 0 (x – k)2 + y2 = 1 (1) 2 (2) 0 (3) 2 (4) – 2 4. If x = (16 3 + 173 + 183 + 193), then x divided by 70 leaves a remainder of: (1) 0 (2) 1 (3) 69 (4) 35 5. A chemical plant has four tanks (A, B, C and D), each containing 1000 litres of a chemical. The chemical is being pumped from one tank to another as follows: From A to B @ 20 litres/minute From C to A @ 90 litres/minute From A to D @ 10 litres/minute From C to D @ 50 litres/minute From B to C @ 100 litres/minute From D to B @ 110 litres/minute Which tank gets emptied first, and how long does it take (in minutes) to get empty after pumping starts? (1) A, 16.66 (2) C, 20 (3) D, 20 (4) D, 25 6. Two identical circles intersect so that their centres, and the points at which they intersect, form a square of side 1 cm. The area in sq cm of the portion that is common to the two circles is: π π (1) (2) – 1 4 2 (3)

4 + 4 – 4 + 4 – ... to inf inity . Then x equals:

(2) (

(1) 3

13 – 1 ) 2

13

(3) (

13 + 1 ) 2

(4)

π 5

(4)

2 –1

7. A jogging park has two identical circular tracks touching each other, and a rectangular track enclosing the two circles. The edges of the rectangles are tangential to the circles. Two friends, A and B, start 754 APRIL 2006

12. Let g(x) be a function such that g(x+1) + g(x–1) = g(x) for every real x. Then for what value of p is the relation g(x+p) = g(x) necessarily true for every real x? (1) 5 (2) 3 (3) 2 (4) 6 13. A telecom service provider engages male and female operators for answering 1000 calls per day. A male operator can handle 40 calls per day whereas a female operator can handle 50 calls per day. The male and the female operators get a fixed wage of Rs 250 and Rs 300 THE COMPETITION MASTER

MANAGEMENT

per day respectively. In addition, a male operator gets Rs 15 per call he answers and a female operator...