The middle term in the expansion of ${\left( {3x - \frac{{{x^3}}}{6}} \right)^9}$ are :-

In the expansion of ${({5^{1/2}} + {7^{1/8}})^{1024}}$, the number of integral terms is

The term independent of $x$ in expansion of ${\left( {\frac{{x + 1}}{{{x^{2/3}} - {x^{\frac{1}{3}}} + 1\;}}--\frac{{x - 1}}{{x - {x^{1/2}}}}} \right)^{10}}$ is

The coefficient of $x^{7}$ in the expression $(1+x)^{10}+x(1+x)^{9}+x^{2}(1+x)^{8}+\ldots+x^{10}$ is

If $p$ and $q$ be positive, then the coefficients of ${x^p}$ and ${x^q}$ in the expansion of ${(1 + x)^{p + q}}$will be

The coefficient of ${x^4}$ in the expansion of ${(1 + x + {x^2} + {x^3})^n}$ is