Question

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

• A. 36
• B. -108
• C. -72
• D. -36

Answer 1

Answer: (D)

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