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
$\left( {12,{{\left( {20} \right)}^4}} \right)$
$\left( {8,5{{\left( {10} \right)}^4}} \right)$
$\left( {24,{{\left( {10} \right)}^8}} \right)$
$\left( {12,8{{\left( {10} \right)}^4}} \right)$
In the expansion of ${\left( {2{x^2} - \frac{1}{x}} \right)^{12}}$, the term independent of x is
The number of rational terms in the binomial expansion of $\left(4^{\frac{1}{4}}+5^{\frac{1}{6}}\right)^{120}$ is $....$
The coefficient of ${x^{100}}$ in the expansion of $\sum\limits_{j = 0}^{200} {{{(1 + x)}^j}} $ is
If the coefficients of ${x^7}$ and ${x^8}$ in ${\left( {2 + \frac{x}{3}} \right)^n}$ are equal, then $n$ is
If the coefficients of $x^{7}$ in $\left(x^{2}+\frac{1}{b x}\right)^{11}$ and $x^{-7}$ in $\left(x-\frac{1}{b x^{2}}\right)^{11}, b \neq 0$, are equal, then the value of $b$ is equal to: