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 `alpha` equals

Options

A. `(3)/(5)`
B. `(10)/(3)`
C. `- (3)/(10)`
D. `- (5)/(3)`

Answer

c

Explanation

We have,
In the expansion of `(1 + alpha x)^(4)` ,
Middle term = `""^(4)C_(2) (alpha x)^(2) = 6alpha^(2) x^(2)`
In the expansion of `( 1 - ax)^(6)` ,
Middle term = `""^(6) C_(3) (-alpha x)^(3) = - 20 alpha^(3) x^(3)`
`therefore ` = Coefficient of the middle term in `(1+ alpha x)^(4)`
= Coefficient of the middle term in `(1 - alpha x )^(6)`
`rArr 6 alpha^(2) = - 20 alpha^(3) rArr alpha = 0, alpha = - (3)/(10)` .