If the second, third and fourth terms in the expansion of $(x+y)^{\mathrm{n}}$ are $135$,$30$ and $\frac{10}{3}$, respectively, then $6\left(n^3+x^2+y\right)$ is equal to .............
$305$
$806$
$604$
$204$
If in the expansion of ${(1 + x)^{21}}$, the coefficients of ${x^r}$ and ${x^{r + 1}}$ be equal, then $r$ is equal to
If the coefficient of $4^{th}$ term in the expansion of ${(a + b)^n}$ is $56$, then $n$ is
Let $[t]$ denotes the greatest integer $\leq t$. If the constant term in the expansion of $\left(3 x^2-\frac{1}{2 x^5}\right)^7$ is $\alpha$, then $[\alpha]$ is equal to $............$.
Find the cocfficient of $x^{5}$ in $(x+3)^{8}$
Find the coefficient of $x^{6} y^{3}$ in the expansion of $(x+2 y)^{9}$