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

# Find the Middle Term in the Expansion Of: (Ii) ( a X + B X ) 12 - Mathematics

Find the middle term in the expansion of:

(ii)  $\left( \frac{a}{x} + bx \right)^{12}$

#### Solution

(ii) Here,
n = 12 (Even number)
Therefore, the middle term is the

$\left( \frac{n}{2} + 1 \right)th$   i.e. 7th term

$Now,$
$T_7 = T_{6 + 1}$
$=^{12}{}{C}_6 \left( \frac{a}{x} \right)^{12 - 6} (bx )^6$
$= ^{12}{}{C}_6 a^6 b^6$
$= \frac{12 \times 11 \times 10 \times 9 \times 8 \times 7}{6 \times 5 \times 4 \times 3 \times 2} a^6 b^6$
$= 924 a^6 b^6$

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 18 Binomial Theorem
Exercise 18.2 | Q 13.2 | Page 38