Question

Find n If the middle term in the expansion of ${(x^2+\frac{1}{x})}^{n}is924x^6,$

• A. 4
• B. 12
• C. 14
• D. None of these

Answer 1

Answer: (A)

4

We have, ${(x^2+\frac{1}{x})}^n$

Given that, Middle term$=924x^6$

${}^n{C}_2{\left(x^2\right)}^2{\left(\frac{1}{x}\right)}^{n-2}=924x^6$

${}^n{C}_2\frac{x^4}{x^2}{x}^n=924x^6$

${}^n{C}_2{x}^{n+2}=924x^6$

$n+2=6$

$\therefore n=4$