The coefficient of $\frac{1}{x}$ in the expansion of ${\left( {1 + x} \right)^n}{\left( {1 + \frac{1}{x}} \right)^n}$ is :-
The coefficient of $\frac{1}{x}$ in the expansion of ${\left( {1 + x} \right)^n}{\left( {1 + \frac{1}{x}} \right)^n}$ is :-
- A
$\frac{{n!}}{{(n - 1)!\left( {n + 1} \right)!}}$
- B
$\frac{{2n!}}{{(n - 1)!\left( {n + 1} \right)!}}$
- C
$\frac{{(2n)!}}{{(2n - 1)!\left( {2n + 1} \right)!}}$
- D
None of these
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- [JEE MAIN 2023]