# CAT - 2000

1

Let D be a recurring decimal of the form D = 0. a1 a2 a1 a2 a1 a2 ..., where digits a1 and a2 lie between 0 and 9. Further, at most one of them is zero. Which of the following numbers necessarily produces an integer, when multiplied by D?

2
 x 1 2 3 4 5 6 y 4 8 14 22 32 44

In the above table, for suitably chosen constants a, b and c, which one of the following best describes the relation between y and x?

3

If a1 = 1 and an+1 = 2an + 5, n = 1, 2 ..., then a100 is equal to

4

What is the value of the following expression?

$$({1\over (2^2-1)}) + ({1\over (4^2-1)}) + ({1\over (6^2-1)}) + ....+ ({1\over (20^2-1)})$$

5

A truck travelling at 70 km/hr uses 30% more diesel to travel a certain distance than it does when it travels at a speed of 50 km/hr. If the truck can travel 19.5 km/L of diesel at 50 km/hr, how far can the truck travel on 10 L of diesel at a speed of 70 km/hr?