Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# The coefficient of x4 in ( x 2 − 3 x 2 ) 10 is - Mathematics

MCQ

The coefficient of x4 in $\left( \frac{x}{2} - \frac{3}{x^2} \right)^{10}$ is

#### Options

•  $\frac{405}{256}$

•  $\frac{504}{259}$

•  $\frac{450}{263}$

• none of these

#### Solution

$\frac{405}{256}$

$\text{ Suppose } x^4 \text{ occurs at the (r + 1)th term in the given expansion } .$

$\text{ Then, we have }$

$T_{r + 1} = ^{10}{}{C}_r (\frac{x}{2} )^{10 - r} \left( \frac{- 3}{2 x^2} \right)^r$

= ( - 1 )^r " ^10C _r \frac{3^r}{2^{10 - r}} x^{10 - r - 2r}

$\text{ For this term to contain } x^4 , \text{ we must have: }$

$10 - 3r = 4$

$\Rightarrow r = 2$

$\therefore \text{ Required coefficient } = ^{10}{}{C}_2 \frac{3^2}{2^8} = \frac{10 \times 9 \times 9}{2 \times 2^8} = \frac{405}{256}$

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 18 Binomial Theorem
Q 17 | Page 47