The ninth term of the expansion $\left(3x - \frac{1}{2x}\right)^{8}$ is

If $n$ is the number of irrational terms in the expansion of $(3^{1/4} + 5^{1/8})^{60}$,then $(n - 1)$ is divisible by

The $13^{th}$ term in the expansion of $\left(x^{2}+\frac{2}{x}\right)^{n}$ is independent of $x$. Then the sum of the divisors of $n$ is:

In the expansion of $(1+x)^n$,the coefficients of the $p^{th}$ and $(p+1)^{th}$ terms are respectively $p$ and $q$. Then $p+q$ is equal to:

If the fourth term in the expansion of $(x+x^{\log _{2} x})^{7}$ is $4480$,then the value of $x$ where $x \in N$ is equal to

If the coefficient of $x^{15}$ in the expansion of $(ax^3 + \frac{1}{bx^{1/3}})^{15}$ is equal to the coefficient of $x^{-15}$ in the expansion of $(ax^{1/3} - \frac{1}{bx^3})^{15}$,where $a$ and $b$ are positive real numbers,then for each such ordered pair $(a, b):$