Question

The term independent of x in the expansion of ${(x^3-\frac{1}{x^2})}^{10}$ is

• A. ${}^{10}{C}_6$
• B. ${}^{10}{C}_7$
• C. ${}^{10}{C}_9$
• D. ${}^{10}{C}_5$

Answer 1

The correct option is A ${}^{10}{C}_6$

Given,

${(x^3-\frac{1}{x^2})}^{10}$

General term

$T_{r+1}={}^n{C}_r{x}^{n-r}{y}^r$

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

$T_{r+1}={}^{10}{C}_r(x{)}^{30-3r}\frac{(-1{)}^r}{x^{2r}}$

$T_{r+1}={}^{10}{C}_r\left(x{)}^{30-5r}\right(-1{)}^r$

To find the term independent of x.

$30-5r=0$

$5r=30$

$r=6$

$T_7={}^{10}{C}_6(-1{)}^6={}^{10}{C}_6$

Hence correct option is A.