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

If the coefficients of ${p^{th}}$, ${(p + 1)^{th}}$ and ${(p + 2)^{th}}$ terms in the expansion of ${(1 + x)^n}$ are in $A.P.$, then

For a positive integer $n,\left(1+\frac{1}{x}\right)^{n}$ is expanded in increasing powers of $x$. If three consecutive coefficients in this expansion are in the ratio, $2: 5: 12,$ then $n$ is equal to

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

The coefficient of $t^4$ in the expansion of ${\left( {\frac{{1 - {t^6}}}{{1 - t}}} \right)^3}$ is

If the coefficient of $x ^{10}$ in the binomial expansion of $\left(\frac{\sqrt{x}}{5^{\frac{1}{4}}}+\frac{\sqrt{5}}{x^{\frac{1}{3}}}\right)^{60}$ is $5^{ k } l$, where $l, k \in N$ and $l$ is coprime to $5$ , then $k$ is equal to