The term independent of $x$ in the expansion of $\left[\frac{x+1}{x^{2 / 3}-x^{1 / 3}+1}-\frac{x-1}{x-x^{1 / 2}}\right]^{10}, x \neq 1,$ is equal to ....... .
$240$
$225$
$210$
$196$
Number of integral tems in the expansion of $\left\{7^{\left(\frac{1}{2}\right)}+11^{\left(\frac{1}{6}\right)}\right\}^{824}$ is equal to..................
The middle term in the expansion of ${(1 + x)^{2n}}$ is
The coefficient of ${t^{24}}$ in the expansion of ${(1 + {t^2})^{12}}(1 + {t^{12}})\,(1 + {t^{24}})$ is
The constant term in the expansion of $\left(2 x+\frac{1}{x^7}+3 x^2\right)^5 \text { is }........$.
If $n$ is the degree of the polynomial,
${\left[ {\frac{1}{{\sqrt {5{x^3} + 1} - \sqrt {5{x^3} - 1} }}} \right]^8} $$+ {\left[ {\frac{1}{{\sqrt {5{x^3} + 1} + \sqrt {5{x^3} - 1} }}} \right]^8}$ and $m$ is the coefficient of $x^{12}$ in it, then the ordered pair $(n, m)$ is equal to