Sixteen players `S_(1)`, `S_(2)`, `S_(3)`,…,`S_(16)` play in a tournament. Number of ways in which they can be grouped into eight pairs so that `S_(1)` and `S_(2)` are in different groups, is equal to

Sixteen players P_(1),P_(2),P_(3)….., P_(16) play in tournament. If they grouped into eight pair then the probability that P_(4) and P_(9) are in different groups, is equal to

S_(1) and S_(2) are two equipotential surfaces on which the potentials are not equal

If S_(0),S_(1),S_(2),… are areas bounded by the x-axis and half-wave of the curve y=sin pi sqrt(x)," then prove that "S_(0),S_(1),S_(2),… are in A.P…

The number of hydroxyl group(s) in N is

In a knockout tournament 2^(n) equally skilled players, S_(1),S_(2),….S_(2n), are participatingl. In each round, players are divided in pair at random and winner from each pair moves in the next round. If S_(2) reaches the semi-final, then the probability that S_(1) wins the tournament is 1/84. The value of n equals _______.

Let S_(n) denote the sum of the first n terms of an A.P.. If S_(4)=16 and S_(6)=-48 , then S_(10) is equal to :

Two SHMs s_(1) = a sin omega t and s_(2) = b sin omega t are superimposed on a particle. The s_(1) and s_(2) are along the direction which makes 37^(@) to each other

If S_1,S_2,S_3 are the sum of first n natural numbers, their squares and their cubes, respectively, show that 9S_2^2=S_3(1+8S_1) .