JEE Main 2025 · Mathematics · Binomial Theorem · easy

The coefficient of x^7 in the expansion of (x^2-1/x)^11 is

Single correct option

The coefficient of

x^{7}

in the expansion of

\left(x^{2}-\dfrac{1}{x}\right)^{11}

Show answer and solution

Answer: (D) $-462$

The general term is

T_{r+1}=\binom{11}{r}(x^2)^{11-r}\left(-\tfrac1x\right)^r=(-1)^r\binom{11}{r}x^{22-3r}

. Setting

22-3r=7

gives

r=5

. The coefficient is

(-1)^5\binom{11}{5}=-462

. The sign is the usual trap.

Original question written in the JEE Main 2025 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake