The number of terms in the expansion of  ${\left( {\sqrt[4]{9} + \sqrt[6]{8}} \right)^{500}}$, which are integers is

The middle term in the expansion of ${\left( {x + \frac{1}{x}} \right)^{10}}$ is

If the sum of the coefficients in the expansion of $(x - 2y + 3 z)^n,$ $n \in N$ is $128$ then the greatest coefficie nt in the exp ansion of $(1 + x)^n$ is

The sum of the coefficient of $x^{2 / 3}$ and $x^{-2 / 5}$ in the binomial expansion of $\left(x^{2 / 3}+\frac{1}{2} x^{-2 / 5}\right)^9$ is :

If in the expansion of ${(1 + x)^m}{(1 - x)^n}$, the coefficient of $x$ and ${x^2}$ are $3$ and $-6$ respectively, then m is

If the coefficient of the second, third and fourth terms in the expansion of ${(1 + x)^n}$ are in $A.P.$, then $n$ is equal to