Coefficient of $x$ in the expansion of ${\left( {{x^2} + \frac{a}{x}} \right)^5}$ is

The total number of terms in the expansion of $(x + a)^{100} + (x - a)^{100}$ after simplification will be

Let the coefficients of the middle terms in the expansion of $\left(\frac{1}{\sqrt{6}}+\beta x\right)^{4}$,$(1-3 \beta x)^{2}$ and $\left(1-\frac{\beta}{2} x\right)^{6}$,where $\beta > 0$,respectively form the first three terms of an $A.P.$ If $d$ is the common difference of this $A.P.$,then $50-\frac{2 d}{\beta^{2}}$ is equal to.

The numerically greatest term in the expansion of $(5+3x)^6$ when $x=1$ is:

The numerically greatest term in the expansion of $(2x - 3y)^{13}$ when $x = \frac{7}{2}$ and $y = \frac{3}{7}$ is:

The $6^{th}$ term in the expansion of $\left( 2x^2 - \frac{1}{3x^2} \right)^{10}$ is