Sum of co-efficients of terms of degree $m$  in the expansion of $(1 + x)^n(1 + y)^n(1 + z)^n$ is

If the coefficients of ${p^{th}}$, ${(p + 1)^{th}}$ and ${(p + 2)^{th}}$ terms in the expansion of ${(1 + x)^n}$ are in $A.P.$, then

If the constant term in the expansion of $\left(1+2 x-3 x^3\right)\left(\frac{3}{2} x^2-\frac{1}{3 x}\right)^9$ is $p$, then $108$ p is equal to....................

Prove that $\sum\limits_{r = 0}^n {{3^r}{\,^n}{C_r} = {4^n}} $

If the coefficients of $x^{7}$ and $x^{8}$ in the expansion of $\left(2+\frac{x}{3}\right)^{n}$ are equal, then the value of $n$ is equal to $.....$

The number of integral terms in the expansion of $(7^{1/3} + 11^{1/9})^{6561}$ is :-