The middle term in the expansion of ${\left( {x - \frac{1}{x}} \right)^{18}}$ is

In the expansion of ${\left( {3x - \frac{1}{{{x^2}}}} \right)^{10}}$,the $5^{th}$ term from the end is:

If the coefficients of the $(2r+6)^{\text{th}}$ and $(r-1)^{\text{th}}$ terms in the expansion of $(1+x)^{21}$ are equal,then the value of $r$ is:

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

Let $n$ be a positive even integer. If the ratio of the largest coefficient and the $2^{nd}$ largest coefficient in the expansion of $(1+x)^{n}$ is $11:10$, then the number of terms in the expansion of $(1+x)^{n}$ is:

Let $\alpha$ be the constant term in the binomial expansion of $\left(\sqrt{x} - \frac{6}{x^{3/2}}\right)^n$,$n \leq 15$. If the sum of the coefficients of the remaining terms in the expansion is $649$ and the coefficient of $x^{-n}$ is $\lambda \alpha$,then $\lambda$ is equal to $..........$.