Median of `2nC_0,2nC_1,2nC_2,.....,2nC_n` ,(when n is even) is

the A.M. of nC_(0),nC_(1),nC_(2),.........,nC_(n) is

If .^nC_0,^nC_1,^nC_2,.....^nC_n are frequencies of n+1 observations 1,2,2^2,.....2^n such that mean is 729/2^n then value of n is:

Suppose a variable assumes the values 0, 1, 2………….n with frequencies proportional to binomial coefficeints ^nC_0, ^nC_1, ^nC_2,………..^nC_n respectively. Find the mean of variable.

If ^nC_8=^nC_2 find ^nC_2

If nC_6=nC_2 , find ^nC_2 .

The value of ""^0C_0-^nC_1+^nC_2-....+ -1^(n^n)C_n is

Prove that (2nC_0)^2-(2nC_1)^2+(2nC_2)^2+.....+(2nC_2n)^2=(-1)^n2nC_n