The $6^{th}$ term in the expansion of $\left( 2x^2 - \frac{1}{3x^2} \right)^{10}$ 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 coefficients of the $r^{\text{th}}$,$(r+1)^{\text{th}}$,and $(r+2)^{\text{th}}$ terms in the expansion of $(1+x)^n$ are in the ratio $4:15:42$,then $n-r=$

Let the coefficients of $x^{-1}$ and $x^{-3}$ in the expansion of $(2x^{1/5} - x^{-1/5})^{15}$,$x > 0$,be $m$ and $n$ respectively. If $r$ is a positive integer such that $mn^2 = {}^{15}C_r \cdot 2^r$,then the value of $r$ is equal to

Write the general term in the expansion of $(x^{2}-y)^{6}$.

The interval in which $x$ must lie so that the numerically greatest term in the expansion of $(1 - x)^{21}$ has the numerically greatest coefficient is