If the middle term of x2+1xn is 924 x6 , then value of n is

As there is just one middle term, $n$ must be even and

middle term is $(\frac{n}{2} + 1)$ th term, and it is given by

$\begin{array}{l} T_{n / 2 + 1} =^{n} C_{n / 2} {(x^{2})}^{n - n / 2} {(\frac{1}{x})}^{n / 2} \\ =^{n} C_{n / 2} x^{n / 2} \end{array}$

Now, $^{n} C_{n / 2} x^{n / 2} = 924 x^{6}$

$\to n / 2 = 6 \to n = 12$

[Also, note that $^{12} C_{6} = 924]$

If the middle term of ${(x^{2} + \frac{1}{x})}^{n}$ is $924 x^{6},$ then value of $n$ is