Coefficient of $x^6$ in the binomial expansion ${\left( {\frac{{4{x^2}}}{3}\; - \;\frac{3}{{2x}}} \right)^9}$ is
$2438$
$2688$
$2868$
none
Coefficient of $x^{11}$ in the expansion of $\left(1+x^2\right)^4\left(1+x^3\right)^7\left(1+x^4\right)^{12}$ is
If the constant term in the expansion of $\left(\frac{\sqrt[5]{3}}{x}+\frac{2 x}{\sqrt[3]{5}}\right)^{12}, x \neq 0$, is $\alpha \times 2^8 \times \sqrt[5]{3}$, then $25 \alpha$ is equal to :
The coefficient of middle term in the expansion of ${(1 + x)^{10}}$ is
Find the coefficient of $x^{5}$ in the product $(1+2 x)^{6}(1-x)^{7}$ using binomial theorem.
The second, third and fourth terms in the binomial expansion $(x+a)^n$ are $240,720$ and $1080,$ respectively. Find $x, a$ and $n$