If the coefficients of the three consecutive terms in the expansion of $(1+x)^n$ are in the ratio $1:5:20$,then the coefficient of the fourth term is $............$.

The ninth term of the expansion $\left(3x - \frac{1}{2x}\right)^{8}$ is

Number of rational terms in the expansion of $( \sqrt{2} + \sqrt[4]{3} )^{100}$ is:

If the constant term in the binomial expansion of $\left(2x^{r} + \frac{1}{x^{2}}\right)^{10}$ is $180$,then $r$ is equal to $......$

Let the ratio of the fifth term from the beginning to the fifth term from the end in the binomial expansion of $(\sqrt[4]{2}+\frac{1}{\sqrt[4]{3}})^{n}$,in the increasing powers of $\frac{1}{\sqrt[4]{3}}$ be $\sqrt[4]{6}: 1$. If the sixth term from the beginning is $\frac{\alpha}{\sqrt[4]{3}}$,then $\alpha$ is equal to $.......$

If the ratio of the terms equidistant from the middle term in the expansion of $(1+x)^{12}$ is $\frac{1}{256}$ $(x \in N)$,then the sum of all the terms of the expansion $(1+x)^{12}$ is: