If the expansion of ${\left( {{y^2} + \frac{c}{y}} \right)^5}$, the coefficient of $y$ will be

The coefficient of $\frac{1}{x}$ in the expansion of ${(1 + x)^n}{\left( {1 + \frac{1}{x}} \right)^n}$ is

The term independent of $x$ in the expression of $\left(1-x^{2}+3 x^{3}\right)\left(\frac{5}{2} x^{3}-\frac{1}{5 x^{2}}\right)^{11}, x \neq 0$ is

Find the coefficient of $x^{6} y^{3}$ in the expansion of $(x+2 y)^{9}$

Find the cocfficient of $x^{5}$ in $(x+3)^{8}$

If the coefficient of the second, third and fourth terms in the expansion of ${(1 + x)^n}$ are in $A.P.$, then $n$ is equal to