The coefficient of $x^{18}$ in the expansion of $\left(x^4-\frac{1}{x^3}\right)^{15}$ is $...........$.

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

The greatest term in the expansion of $\sqrt 3 {\left( {1 + \frac{1}{{\sqrt 3 }}} \right)^{20}}$ is

Find the coefficient of $x^{5}$ in the product $(1+2 x)^{6}(1-x)^{7}$ using binomial theorem.

The coefficient of $t^4$ in the expansion of ${\left( {\frac{{1 - {t^6}}}{{1 - t}}} \right)^3}$ is

The coefficients of three consecutive terms of $(1+x)^{n+5}$ are in the ratio $5: 10: 14$. Then $n=$