Q. The coefficient of the middle term in the binomial expansion in powers of $x$ of $(1 + \alpha x)^{4}$ and of $(1 - \alpha x)^{6}$ is the same, if α equals
A) $- \frac{5}{3}$
B) $\frac{10}{3}$
C) $- \frac{3}{10}$
D) $\frac{3}{5}$
Explanation
(c)
The coefficient of $x$ in the middle term of expansion of
$(1 + \alpha x)^{4} = \ ^{4}C_{2}\alpha\ ^{2}$
The coefficient of $x$ in the middle term of expansion of
$(1 - \alpha x)^{6} = \ ^{6}C_{3}( - \alpha)^{3}$
Given, $\ ^{4}C_{2}\alpha^{2} = \ ^{6}C_{3}( - \alpha)^{3}$
$\Longrightarrow \ \ \ \ \ {6\alpha}^{2} = - {20\alpha}^{3}$
$\Longrightarrow \ \ \ \ \ \ \ \ \ \alpha = \frac{- 6}{20} = \frac{- 3}{10}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.