If the coefficient of the middle term in the expansion of ${(1 + x)^{2n + 2}}$ is $p$ and the coefficients of middle terms in the expansion of ${(1 + x)^{2n + 1}}$ are $q$ and $r$, then

The sum of the binomial coefficients of ${\left[ {2\,x\,\, + \,\,\frac{1}{x}} \right]^n}$ is equal to $256$ . The constant term in the expansion is

The coefficient of $x^{2012}$ in the expansion of $(1-x)^{2008}\left(1+x+x^2\right)^{2007}$ is equal to

If the term without $x$ in the expansion of $\left( x ^{\frac{2}{3}}+\frac{\alpha}{ x ^3}\right)^{22}$ is $7315$ , then $|\alpha|$ is equal to $...........$.

In the expansion of ${\left( {{x^2} - 2x} \right)^{10}}$, the coefficient of ${x^{16}}$ is

The coefficient of $x^{18}$ in the expansion of $\left(x^4-\frac{1}{x^3}\right)^{15}$ is $...........$.