If the term independent of $x$ in the expansion of $\left( x^{\frac{2}{3}} + \frac{\alpha}{x^3} \right)^{22}$ is $7315$,then $|\alpha|$ is equal to $...........$.

If $ab \neq 0$ and the sum of the coefficients of $x^7$ and $x^4$ in the expansion of $\left(\frac{x^2}{a}-\frac{b}{x}\right)^{11}$ is $0$,then

The $11^{th}$ term in the expansion of $\left(x+\frac{1}{\sqrt{x}}\right)^{14}$ is

Let the ratio of the fifth term from the beginning to the fifth term from the end in the binomial expansion of $(\sqrt[4]{2}+\frac{1}{\sqrt[4]{3}})^{n}$,in the increasing powers of $\frac{1}{\sqrt[4]{3}}$ be $\sqrt[4]{6}: 1$. If the sixth term from the beginning is $\frac{\alpha}{\sqrt[4]{3}}$,then $\alpha$ is equal to $.......$

If $f(n)$ is the coefficient of $x^n$ in the expansion of $(1+x)(1-x)^n$,then $f(2021)=$

$p, q$ are two prime numbers. For $n=pq$,if the expansion $\left(x^{-5/4} + 2x^{4/5}\right)^n$ contains non-zero coefficients of $x^{-n}$ and $x^0$,then the least value of such $n$ is