The sum of coefficients in $(1 + x - 3x^2)^{2134}$ is

For $|x| < \frac{1}{5}$,the coefficient of $x^3$ in the expansion of $\frac{1}{(1-5 x)(1-4 x)}$ is

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

Expand the expression $\left(\frac{2}{x}-\frac{x}{2}\right)^{5}$

For $x \in R, x \neq -1,$ if $(1 + x)^{2016} + x(1 + x)^{2015} + x^2(1 + x)^{2014} + \dots + x^{2016} = \sum_{i = 0}^{2016} a_i x^i,$ then $a_{17}$ is equal to

For $|x| < \frac{1}{\sqrt{2}}$, the coefficient of $x$ in the expansion of $\frac{(1 - 4x)^2 (1 - 2x^2)^{1/2}}{(4 - x)^{3/2}}$ is