The number of integral terms in the expansion of $(7^{1/3} + 11^{1/9})^{6561}$ 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 the coefficient of the middle term in the expansion of $(1 + x)^{2n + 2}$ is $p$ and the coefficients of the two middle terms in the expansion of $(1 + x)^{2n + 1}$ are $q$ and $r$,then:

The term independent of $x(x>0, x \neq 1)$ in the expansion of $\left[\frac{(x+1)}{\left(x^{2 / 3}-x^{1 / 3}+1\right)}-\frac{(x-1)}{(x-\sqrt{x})}\right]^{10}$ is:

If the coefficients of $x^{7}$ in $(x^{2}+\frac{1}{bx})^{11}$ and $x^{-7}$ in $(x-\frac{1}{bx^{2}})^{11}$,$b \neq 0$,are equal,then the value of $b$ is equal to:

The absolute difference of the coefficients of $x^{10}$ and $x^7$ in the expansion of $\left(2x^2+\frac{1}{2x}\right)^{11}$ is equal to