The value of `C(n+1,n)` is

If C(n,8)=C(n,2) , then value of n is:

If .^(n+1)C_(r+1):^(n)C_(r):^(n-1)C_(r-1)=11:6:3 , find the values of n and r.

If .^(n)C_(r-1): .^(n)C_(r): .^(n)C_(r+1)=3:4:5 , find the values of n and r.

If ^(n+1)C_(r+1): ^nC_r: ^(n-1)C_(r-1)=11:6:2 find the values of n and r.

The value of ^n C_1+^(n+1)C_2+^(n+2)C_3++^(n+m-1)C_m is equal to (a)^m+n C_(n-1) (b)^m+n C_(n-1) (c)^mC_(1)+^(m+1)C_2+^(m+2)C_3++^(m+n-1) (d)^m+1C_(m-1)

If n is a positvie integers, the value of E=(2n+1).^(n)C_(0)+(2n-1).^(n)C_(1)+(2n-3)^(n)C_(2)+………+1. ^(n)C_(n)2 is

If the value of (n + 2) . ""^(n)C_(0) *2^(n+1) - (n+1) * ""^(n)C_(1)*2^(n) + n* ""^(n)C_(2) * 2^(n-1) -... is equal to k(n +1) , the value of k is .

The value of ""(n)C_(1). X(1 - x )^(n-1) + 2 . ""^(n)C_(2) x^(2) (1 - x)^(n-2) + 3. ""^(n)C_(3) x^(3) (1 - x)^(n-3) + ….+ n ""^(n)C_(n) x^(n) , n in N is