The interval in which $x$ must lie so that the greatest term in the expansion of ${(1 + x)^{2n}}$ has the greatest coefficient, is
$\left( {\frac{{n - 1}}{n},\frac{n}{{n - 1}}} \right)$
$\left( {\frac{n}{{n + 1}},\frac{{n + 1}}{n}} \right)$
$\left( {\frac{n}{{n + 2}},\frac{{n + 2}}{n}} \right)$
None of these
${r^{th}}$ term in the expansion of ${(a + 2x)^n}$ is
If $\alpha$ and $\beta$ be the coefficients of $x^{4}$ and $x^{2}$ respectively in the expansion of
$(\mathrm{x}+\sqrt{\mathrm{x}^{2}-1})^{6}+(\mathrm{x}-\sqrt{\mathrm{x}^{2}-1})^{6}$, then
The coefficient of ${t^{24}}$ in the expansion of ${(1 + {t^2})^{12}}(1 + {t^{12}})\,(1 + {t^{24}})$ is
The coefficient of $x^4$ in ${\left[ {\frac{x}{2}\,\, - \,\,\frac{3}{{{x^2}}}} \right]^{10}}$ is :
The coefficient of $x^{1012}$ in the expansion of ${\left( {1 + {x^n} + {x^{253}}} \right)^{10}}$ , (where $n \leq 22$ is any positive integer), is