If $n$ is even positive integer, then the condition that the greatest term in the expansion of ${(1 + x)^n}$ may have the greatest coefficient also, is
$\frac{n}{{n + 2}} < x < \frac{{n + 2}}{n}$
$\frac{{n + 1}}{n} < x < \frac{n}{{n + 1}}$
$\frac{n}{{n + 4}} < x < \frac{{n + 4}}{4}$
None of these
The coefficient of $x ^7$ in $\left(1-x+2 x^3\right)^{10}$ is $........$.
Find the term independent of $x$ in the expansion of $\left(\frac{3}{2} x^{2}-\frac{1}{3 x}\right)^{6}$
Find the value of $\left(a^{2}+\sqrt{a^{2}-1}\right)^{4}+\left(a^{2}-\sqrt{a^{2}-1}\right)^{4}$
The coefficient of the term independent of $x$ in the expansion of $(1 + x + 2{x^3}){\left( {\frac{3}{2}{x^2} - \frac{1}{{3x}}} \right)^9}$ is
The number of integral terms in the expansion of ${({5^{1/2}} + {7^{1/6}})^{642}}$ is