Find the coefficient of $x^{5}$ in the expansion of $(x+3)^{8}$.

Suppose $l, m, n$ respectively represent the coefficient of $x^{10}$,the constant term,and the coefficient of $x^{-10}$ in the expansion of $\left(a x^2+\frac{b}{x^3}\right)^{15}$. If $\frac{l}{m}+\frac{m}{n}=\frac{26}{11}$,then $a^2: b^2=$

Find the $r^{\text{th}}$ term from the end in the expansion of $(x+a)^{n}$.

If the $2^{\text{nd}}$,$3^{\text{rd}}$,and $4^{\text{th}}$ terms in the expansion of $(x+a)^{n}$ are $96, 216$,and $216$ respectively,and $n$ is a positive integer,then $a+x=$

If the sum of the coefficients of $x^r$ $(r=0, 1, 2, \ldots, 2n)$ in the expansion of $(1+3x-2x^2)^n$ is $128$,then $\sum_{r=1}^{2n} r \frac{^{2n}C_r}{^{2n}C_{r-1}} = $

If the coefficients of $x^{10}$ and $x^{11}$ in the expansion of $(1+\alpha x+\beta x^2)(1+x)^{11}$ are $396$ and $144$ respectively,then $\alpha^2+\beta^2=$