If the term independent of $x$ in the exapansion of $\left(\frac{3}{2} x^{2}-\frac{1}{3 x}\right)^{9}$ is $k,$ then $18 k$ is equal to

If $p$ and $q$ be positive, then the coefficients of ${x^p}$ and ${x^q}$ in the expansion of ${(1 + x)^{p + q}}$will be

The sum of all rational terms in the expansion of $\left(2^{\frac{1}{5}}+5^{\frac{1}{3}}\right)^{15}$ is equal to :

The coefficient of $x ^7$ in $\left(1-x+2 x^3\right)^{10}$ is $........$.

Write the general term in the expansion of $\left(x^{2}-y x\right)^{12}, x \neq 0$

Let the coefficients of third, fourth and fifth terms in the expansion of $\left(x+\frac{a}{x^{2}}\right)^{n}, x \neq 0,$ be in the ratio $12: 8: 3 .$ Then the term independent of $x$ in the expansion, is equal to ...... .