Question

The term independent of x in the expansion of $\bigg(\frac{1}{60} - \frac{x^8}{81}\bigg). \bigg(2x^2 - \frac{3}{x^2}\bigg)^6$ is equal to:

• A. 36
• B. -108
• C. -72
• D. -36

Answer 1

Answer: (D)

$\frac{1}{60} \bigg(2x^2 - \frac{3}{x^2}\bigg)^6 \, \, - \frac{1}{81}. x^8 \bigg(2x^2 - \frac{3}{x^2}\bigg)^6$
its general term
$\frac{1}{60} ^{6}C_{r} 2^{6-r} (-3)^r \, x^{12-r} \, - \frac{1}{81} ^6C _{r} 2^{6-r} (-3)^r 12^{20-4r}$
for term independent of $x, r$ for $I^{st}$ expression is $3$ and $r$ for second expression is $5$
$\therefore $ term independent of $x = - 36$