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  • If the middle term in the expansion of <img alt="\left(x^2+\frac{1}{x}\right)^n" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cleft%28x%5E2&plus;%5Cfrac%7B1%7D%7Bx%7D%5Cright%29%

If the middle term in the expansion of \left(x^2+\frac{1}{x}\right)^n is 924 x^6,  then n = 

Option: 1

10


Option: 2

12


Option: 3

14


Option: 4

None of these


Answers (1)

best_answer

Since n is even therefore \left(\frac{n}{2}+1\right)^{t h} term is middle term, hence { }^n C_{n / 2}\left(x^2\right)^{n / 2}\left(\frac{1}{x}\right)^{n / 2}=924 x^6

\Rightarrow \quad x^{n / 2}=x^6 \Rightarrow n=12

Posted by

rishi.raj

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