Instructions

For the following questions answer them individually

Question 11

If a man cycles at 10 km/hr, then he arrives at a certain place at 1 p.m. If he cycles at 15 km/hr, he will arrive at the same place at 11 a.m. At what sped must he cycle to get there at noon?

Question 12

On January 1, 2004 two new societies S1 and S2 are formed, each n numbers. On the first day of each subsequent month, S1 adds b members while S2 multiples its current numbers by a constant factor r. Both the societies have the same number of members on July 2, 2004. If b = 10.5n, what is the value of r?

Question 13

If $$f(x)=x^3-4x+p$$ , and f(0) and f(1) are of opposite signs, then which of the following is necessarily true

[CAT 2004]

Question 14

Suppose n is an integer such that the sum of digits on n is 2, and $$10^{10} < n < 10^{11}$$. The number of different values of n is

Question 15

A milkman mixes 20 litres of water with 80 litres of milk. After selling one-fourth of this mixture, he adds water to replenish the quantity that he had sold. What is the current proportion of water to milk?

[CAT 2004]

Question 17

N persons stand on the circumference of a circle at distinct points. Each possible pair of persons, not standing next to each other, sings a two-minute song one pair after the other. If the total time taken for singing is 28 minutes, what is N?

[CAT 2004]

Question 18

A father and his son are waiting at a bus stop in the evening. There is a lamp post behind them. The lamp post, the father and his son stand on the same straight line. The father observes that the shadows of his head and his son's head are incident at the same point on the ground. If the heights of the lamp post, the father and his son are 6 metres, 1.8 metres and 0.9 metres respectively, and the father is standing 2.1 metres away from the post then how far (in metres) is son standing form his father?

Question 19

Let $$f(x) = ax^2 - b|x|$$ , where a and b are constants. Then at x = 0, f(x) is

[CAT 2004]

Question 20

Each family in a locality has at most two adults, and no family has fewer than 3 children.

Considering all the families together, there are adults than boys, more boys than girls, and more girls than families.

Then the minimum possible number of families in the locality is