When n is a positive integer, then `(n^2)!` is

If n is a positive integer, then n^(3)+2n is divisible

If n is a positive integer then .^(n)P_(n) =

If 1;w;w^(2) are cube root of unity and n is a positive integer; then 1+w^(n)+w^(2n)={3; When n is multiple of 3;0; when n is not a multiple of 3

If 'n' is a positive integer, then n.1+ (n-1) . 2+ (n-2). 3+….. + 1.n=

If n is a positive integer, then ((n+4)!)/((n+7)!)=

If 1;w;w^2 are cube root of unity and n is a positive integer;then 1+w^n+w^(2n) = {3; When n is multiple of 3; 0; when n is not a multiple of 3

If f'(x)=(x-a)^(2n)(x-b)^(2p+1) , when n and p are positive integers, then :

If n is a positive integer then 2^(4n) - 15n - 1 is divisible by