The Coefficient of $x ^{-6}$, in the expansion of $\left(\frac{4 x}{5}+\frac{5}{2 x^2}\right)^9$, is $........$.

If $^n{C_{r - 2}} = 36$ , $^n{C_{r - 1}} = 84$   and    $^n{C_r} = 126$ , then value of $^n{C_{2r}}$ is

Let for the $9^{\text {th }}$ term in the binomial expansion of $(3+6 x)^{n}$, in the increasing powers of $6 x$, to be the greatest for $x=\frac{3}{2}$, the least value of $n$ is $n_{0}$. If $k$ is the ratio of the coefficient of $x ^{6}$ to the coefficient of $x ^{3}$, then $k + n _{0}$ is equal to.

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

Find the middle terms in the expansion of $\left(\frac{x}{3}+9 y\right)^{10}$

If the second, third and fourth term in the expansion of ${(x + a)^n}$ are $240, 720$ and $1080$ respectively, then the value of $n$ is