Question

One value of $\alpha$ for which the coefficients of the middle terms in the expansion of $(1+\alpha x)^{4}$ and $(1-\alpha x)^{6}$ are equal, is $\frac{-3}{10} .$ Other value of ' $\alpha$ ' is

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

Answer: (A)

In the expansion of $(1+\alpha x)^{4}$
Middle term $={ }^{4} C _{2}(\alpha x )^{2}=6 \alpha^{2} x ^{2}$
In the expansion of $(1-\alpha x)^{6}$
Middle term $={ }^{6} C _{3}(-\alpha x )^{3}=-20 \alpha^{3} x ^{3}$
It is given that
Coefficient of the middle term in $(1+\alpha x)^{4}$
$=$ Coefficient of the middle term in $(1-\alpha x)^{6}$
$\Rightarrow 6 \alpha^{2}=-20 \alpha^{3} $
$\Rightarrow \alpha=0, \alpha=-\frac{3}{10}$