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 .............

  • [JEE MAIN 2024]
  • A

    $305$

  • B

    $806$

  • C

    $604$

  • D

    $204$

Similar Questions

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

  • [JEE MAIN 2023]

Find the cocfficient of $x^{5}$ in $(x+3)^{8}$

Find the coefficient of $x^{6} y^{3}$ in the expansion of $(x+2 y)^{9}$