The coefficient of the term independent of $x$ in the expansion of $(1 + x + 2x^3) \left( \frac{3}{2}x^2 - \frac{1}{3x} \right)^9$ is

If the $6^{th}$ term in $\left(\frac{2p}{3} + \frac{3q}{2}\right)^9$ is $ap^bq^c$,then $a, b$ and $c$ respectively are

If $n$ is even and the middle term in the expansion of $\left(x^2+\frac{1}{x}\right)^n$ is $924 x^6$,then $n$ is equal to

The sixth term in the expansion of $\left(3-\sqrt{\frac{17}{4}+3 \sqrt{2}}\right)^{10}$ is a

The coefficient of $t^{12}$ in the expansion of $(1 + t^2)^6(1 + t^6)(1 + t^{12})$ is:

Let the ratio of the fifth term from the beginning to the fifth term from the end in the binomial expansion of $(\sqrt[4]{2}+\frac{1}{\sqrt[4]{3}})^{n}$,in the increasing powers of $\frac{1}{\sqrt[4]{3}}$ be $\sqrt[4]{6}: 1$. If the sixth term from the beginning is $\frac{\alpha}{\sqrt[4]{3}}$,then $\alpha$ is equal to $.......$