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

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…

Why is chlorobenzene inert towards S_(N)1 and S_(N)2 reactions?

If S_(1), S_(2), S_(3) are the sums of n natural numbers, their squares, their cubes respectively show that 9S_(2)^(2) = S_(3)(1+8S_(1)) .

In a knockout tournament, 2^(n) equally skilld players, S_(1), S_(2), …, S_(2^(n)) are participating. In each round, players are divided in pairs at random and winner from each pair moves to 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 is_______.

If S_1, S_2, S_3 are the sum of first n natural numbers, their squares and their cubes, respectively , show that 9 S_(2)^(2) = S_(3) (1+ 8S_1)

Explain the stereochemistry of S_(N)2 and S_(N)1 reaction with suitable examples.

The solubility of anhydrous AlCl_(3) and hydrous AlCl_(3) in diethyl ether are S_(1) and S_(2) respectively. Then -

If S_(1), S_(2), S_(3) be respectively the sums of n, 2n and 3n terms of a G.P., prove that, S_(1)(S_(3) - S_(2)) = (S_(2) - S_(1))^(2) .

Let the sum of n, 2n, 3n terms of an A.P. be S_1, S_2 and S_3 , respectively, show that S_3 =3(S_2-S_1)

Which one out of S_(N)1 and S_(N)2 reactions is more suceptible to steric effect and why?