If the coefficients of 3 consecutive terms in the expansion of $(1+x)^{23}$ are in arithmetic progression, then those terms are

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 $S-k=$

If the term independent of $x$ in the expansion of $\left(\sqrt{x}-\frac{k}{x^2}\right)^{10}$ is 405 , then $k=$