The coefficient of $\frac{1}{x}$ in the expansion of ${(1 + x)^n}{\left( {1 + \frac{1}{x}} \right)^n}$ is
$\frac{{n!}}{{(n - 1)!(n + 1)!}}$
$\frac{{(2n)\,!}}{{(n - 1)!(n + 1)!}}$
$\frac{{n!}}{{(n - 1)!(n + 1)!}}$
None of these
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 ....... .
The coefficient of $t^{50}$ in $(1 + t^2)^{25}(1 + t^{25})(1 + t^{40})(1 + t^{45})(1 + t^{47})$ is -
If the non zero coefficient of $(2r + 4)th$ term is greater than non zero coefficient of $(r - 2)th$ term in expansion of $(1 + x)^{18}$, then number of possible integral values of $r$ is
The term independent of $x$ in the expansion of ${\left( {\frac{1}{2}{x^{1/3}} + {x^{ - 1/5}}} \right)^8}$ will be
If the fourth term in the expansion of $\left(x+x^{\log _{2} x}\right)^{7}$ is $4480,$ then the value of $x$ where $x \in N$ is equal to