Q. The term independent of $x$ in the expansion of $\left( x^{3} + \frac{2}{x^{2}} \right)^{15}is$
A) $T_{7}$
B) $T_{8}$
C) $T_{9}$
D) $T_{10}$
Explanation
(d)
$General\ term,\ T_{r + 1} = \ ^{15}C_{r}{(x}^{3})^{15 - r}\left( \frac{2}{x^{2}} \right)^{r}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \ ^{15}C_{r}x^{45 - 5r}(2)^{r}$
For term independent of $x,$ put $45 - 5r = 0 \Longrightarrow r = 9$
$\therefore$ Independent term $= T_{9 + 1} = T_{10}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.