In the expansion of ${\left( {2{x^2} - \frac{1}{x}} \right)^{12}}$, the term independent of x is
$10^{th}$
$9^{th}$
$8^{th}$
$7^{th}$
If $\frac{{{T_2}}}{{{T_3}}}$ in the expansion of ${(a + b)^n}$ and $\frac{{{T_3}}}{{{T_4}}}$ in the expansion of ${(a + b)^{n + 3}}$ are equal, then $n=$
The middle term in the expansion of ${(1 + x)^{2n}}$ is
In the expansion of ${({5^{1/2}} + {7^{1/8}})^{1024}}$, the number of integral terms is
If the coefficient of $x ^7$ in $\left(a x-\frac{1}{b x^2}\right)^{13}$ and the coefficient of $x^{-5}$ in $\left(a x+\frac{1}{b x^2}\right)^{13}$ are equal, then $a^4 b^4$ is equal to :
Coefficient of $x^6$ in the binomial expansion ${\left( {\frac{{4{x^2}}}{3}\; - \;\frac{3}{{2x}}} \right)^9}$ is