The term independent of $x$ in ${\left( {2x - \frac{1}{{2{x^2}}}} \right)^{12}}$is
$-7930$
$-495$
$495$
$7920$
If the coefficients of ${x^7}$ and ${x^8}$ in ${\left( {2 + \frac{x}{3}} \right)^n}$ are equal, then $n$ is
The coefficient of $x ^7$ in $\left(1-x+2 x^3\right)^{10}$ is $........$.
Two middle terms in the expansion of ${\left( {x - \frac{1}{x}} \right)^{11}}$ are
Find a positive value of $m$ for which the coefficient of $x^{2}$ in the expansion $(1+x)^{m}$ is $6$
In the expansion of ${\left( {x - \frac{3}{{{x^2}}}} \right)^9},$ the term independent of $x$ is