Question

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 same,if $\alpha$ =

• A. $\frac{3}{5}$
• B. $\frac{10}{3}$
• C. $-\frac{3}{10}$
• D. $-\frac{5}{3}$

Answer 1

The correct option is C $-\frac{3}{10}$

The middle terms of the above given binomial expressions will be
${}^4{C}_2(\alpha {)}^2{x}^2$ and $-{}^6{C}_3(\alpha {)}^3{x}^3$
since the coefficients are equal.
${}^4{C}_2(\alpha {)}^2=-{}^6{C}_3(\alpha {)}^3$
$\Rightarrow 6(\alpha {)}^2=-20(\alpha {)}^3$
$\Rightarrow \frac{-3}{10}=\alpha$