In the expansion of ${\left( \frac{1 + x}{1 - x} \right)^2}$,the coefficient of ${x^n}$ is:

If $n$ is the degree of the polynomial,$\left[ {\frac{1}{{\sqrt {5{x^3} + 1} - \sqrt {5{x^3} - 1} }}} \right]^8 + \left[ {\frac{1}{{\sqrt {5{x^3} + 1} + \sqrt {5{x^3} - 1} }}} \right]^8$ and $m$ is the coefficient of $x^{12}$ in it,then the ordered pair $(n, m)$ is equal to

If $\lim _{x \rightarrow 1} \frac{\sqrt[4]{x^{-3}}+a \sqrt[4]{x^5}}{x-1}=-2$,then the coefficient of $x$ in the expansion of $(\sqrt[4]{x^{-3}}+a \sqrt[4]{x^5})^4$ is

If in the expansion of $(1 + x)^{21}$,the coefficients of $x^r$ and $x^{r + 1}$ are equal,then $r$ is equal to

If the coefficients of $(r-5)^{th}$ and $(2r-1)^{th}$ terms in the expansion of $(1+x)^{34}$ are equal,find $r$.

If the fourth term in the Binomial expansion of ${\left( {\frac{2}{x} + {x^{\log_8 x}}} \right)^6}$ for $x > 0$ is $20 \times 8^7$,then a value of $x$ is