The coefficient of $x^3$ in the expansion of $(x - \frac{1}{x})^7$ is

If the middle term in the expansion of ${\left( {x^2 + \frac{1}{x}} \right)^n}$ is $924x^6$,then $n = $

In the polynomial $(x - 1)(x - 2)(x - 3) \dots (x - 100)$,the coefficient of $x^{99}$ is

If $t_r$ is the $r^{\text{th}}$ term in the expansion of $(2^x + 4^{-x})^8$ and if $t_3 = 7t_2$,then $x =$

In the expansion of $(1 + 3x + 2x^2)^6$,the coefficient of $x^{11}$ 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 $.......$