The coefficient of ${x^5}$ in the expansion of ${({x^2} - x - 2)^5}$ is
$-83$
$-82$
$-81$
$0$
The coefficient of $x^{10}$ in the expansion of $(1 + x)^2 (1 + x^2)^3 ( 1 + x^3)^4$ is euqal to
If the number of integral terms in the expansion of $\left(3^{\frac{1}{2}}+5^{\frac{1}{8}}\right)^{\text {n }}$ is exactly $33,$ then the least value of $n$ is
The coefficient of the term independent of $x$ in the expansion of $(1 + x + 2{x^3}){\left( {\frac{3}{2}{x^2} - \frac{1}{{3x}}} \right)^9}$ is
Find the term independent of $x$ in the expansion of $\left(\frac{3}{2} x^{2}-\frac{1}{3 x}\right)^{6}$
The coefficients of three successive terms in the expansion of ${(1 + x)^n}$ are $165, 330$ and $462$ respectively, then the value of n will be