In the expansion of ${({5^{1/2}} + {7^{1/8}})^{1024}}$, the number of integral terms is
$128$
$129$
$130$
$131$
The coefficient of $x^9$ in the expansion of $(1+x)\left(1+x^2\right)\left(1+x^3\right) \ldots . .\left(1+x^{100}\right)$ is
Find the coefficient of $x^{5}$ in the product $(1+2 x)^{6}(1-x)^{7}$ using binomial theorem.
The coefficient of $x^4$ in ${\left[ {\frac{x}{2}\,\, - \,\,\frac{3}{{{x^2}}}} \right]^{10}}$ is :
Find the $r^{\text {th }}$ term from the end in the expansion of $(x+a)^{n}$
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 :