The middle term in the expansion of ${\left( {3x - \frac{{{x^3}}}{6}} \right)^9}$ are :-

The middle term in the expression of ${\left( {x - \frac{1}{x}} \right)^{18}}$ is

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 ...... .

The coefficient of the middle term in the binomial expansion in powers of $x$ of ${(1 + \alpha x)^4}$ and of ${(1 - \alpha x)^6}$ is the same if $\alpha $ equals

The coefficient of ${x^{32}}$ in the expansion of ${\left( {{x^4} - \frac{1}{{{x^3}}}} \right)^{15}}$ is

Middle term in the expansion of ${(1 + 3x + 3{x^2} + {x^3})^6}$ is