If the $6^{th}$ term in $\left(\frac{2p}{3} + \frac{3q}{2}\right)^9$ is $ap^bq^c$,then $a, b$ and $c$ respectively are

If the coefficients of $x^7$ and $x^8$ in $(2 + \frac{x}{3})^n$ are equal,then $n$ is

Let $a$ and $b$ be two nonzero real numbers. If the coefficient of $x^5$ in the expansion of $(ax^2 + \frac{70}{27bx})^4$ is equal to the coefficient of $x^{-5}$ in the expansion of $(ax - \frac{1}{bx^2})^7$,then the value of $2b$ is

The number of rational terms in the expansion of $(3^{1/8} + 5^{1/3})^{400}$ is

The term independent of $x(x>0, x \neq 1)$ in the expansion of $\left[\frac{(x+1)}{\left(x^{2 / 3}-x^{1 / 3}+1\right)}-\frac{(x-1)}{(x-\sqrt{x})}\right]^{10}$ is:

If the coefficients of the three successive terms in the binomial expansion of $(1 + x)^n$ are in the ratio $1 : 7 : 42,$ then the first of these terms in the expansion is (in $^{th}$)