The numerically greatest term in the expansion of $(3 x-16 y)^{15}$, when $x=\frac{2}{3}$ and $y=\frac{3}{2}$, is

For $n \in N$ the largest positive integer that divides $81^n+20 n-1$ is $k$. If $S$ is the sum of all positive divisors of $k$, then $S-k=$

The term independent of $x$ in the expansion of $\left(1-3 x+2 x^3\right)\left(\frac{3 x^2}{2}-\frac{1}{3 x}\right)^9$ is

If $\sum_{r=0}^{20}{ }^{20+r} C_r=\frac{p}{q}{ }^{40} C_{20}$ and GCD of $(p, q)=1$, then $p^2-q^2=$