Question

The term independent of $x$ in the expansion of $(x-\frac{3}{x^2}{)}^{18}$

• A. ${}^{18}{C}_6$
• B. ${}^{18}{C}_6{3}^6$
• C. ${}^{18}{C}_{12}{3}^{-6}$
• D. $3^6$

Answer 1

Answer: (B)

$T_{r+1}={}^{18}{c}_r{x}^{18-r}{\left(-\frac{3}{x^2}\right)}^r$
$={}^{18}{c}_r{x}^{18-r-2r}{\left(-3\right)}^r$
$\therefore 18-3r=0$
$\Rightarrow r=6$
$\therefore$ reqd. term $={}^{18}{c}_6{\left(-3\right)}^6={}^{18}{c}_6{\left(3\right)}^6$.