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 $............$.

Write the general term in the expansion of $\left(x^{2}-y\right)^{6}$

The sum of the binomial coefficients of ${\left[ {2\,x\,\, + \,\,\frac{1}{x}} \right]^n}$ is equal to $256$ . The constant term in the expansion is

If $\left(\frac{3^{6}}{4^{4}}\right) \mathrm{k}$ is the term, independent of $\mathrm{x}$, in the binomial expansion of $\left(\frac{\mathrm{x}}{4}-\frac{12}{\mathrm{x}^{2}}\right)^{12}$, then $\mathrm{k}$ is equal to ...... .

If the coefficient of $x$ in the expansion of ${\left( {{x^2} + \frac{k}{x}} \right)^5}$ is $270$, then $k =$

Find the term independent of $x$ in the expansion of $\left(\sqrt[3]{x}+\frac{1}{2 \sqrt[3]{x}}\right)^{18}, x\,>\,0$