Q. $In\ the\ expansion\ of\ \left( {2x}^{2} - \frac{1}{x} \right)^{12},\ the\ term\ independent\ of\ x\ is$

A) 8th
B) 7th
C) 9th
D) 10th
Explanation

(c)
$The\ general\ term\ in\ the\ expansion\ of\ \left( {2x}^{2} - \frac{1}{x} \right)^{12}is$
$T_{r + 1} = ( - 1)^{r}\ ^{12}C_{r} \bullet 2^{12 - r} \bullet x^{24 - 3r}$
The term independent of $x$, put $24 - 3r = 0$
$\Longrightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ r = 8$
$\therefore In\ the\ expansion\ of\ \left( {2x}^{2} - \frac{1}{x} \right)^{12},\ the\ term\ independent\ of\ x\ is\ 9th\ term.$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.