CAT - 2002

1

If there are 10 positive real numbers n1 < n2 < n3... < n10 , how many triplets of these numbers (n1, n2,n3), (n2, n3,n4) , ... can be generated such that in each triplet the first number is always less than the second number, and the second number is always less than the third number?

2

In $$\bigtriangleup$$ ABC, the internal bisector of angle A meets BC at D. If AB = 4, AC = 3 and angle A = 60° , then the length of AD is

3

The length of the common chord of two circles of radii 15 cm and 20 cm, whose centres are 25 cm apart, is

4

If f(x) = $$log ({(1+x) \over (1-x)})$$ then f(x) + f(y) is

5

Four horses are tethered at four corners of a square plot of side 14 m so that the adjacent horses can just reach one another. There is a small circular pond of area 20 2 m at the centre. Find the ungrazed area.