Question

In the expansion of $\frac{3-x}{(1-x{)}^2}$ coefficient of $x^r$ is $10$ then $r=$

• A. $3$
• B. $4$
• C. $3.5$
• D. $4.5$

Answer 1

The correct option is A $3$

Given, $\frac{3-x}{(1-x{)}^2}$
$=(3-x)(1-x{)}^{-2}$
$=(3-x)(1+2x+3x^2+4x^3+.....r{x}^{r-1}+(r+1)x^r+....)$
So, the $x^r$ term for the given expansion is sum of two terms.
Coefficient of $x^r$ is $3(r+1)-r$
$\Rightarrow 3r+3-r=10$
$\Rightarrow r=\frac{7}{2}$
$r$ cannot be fractional. It should be a whole number.
So $r=3$