Question

The term independent of $x$ in the expansion of ${(3x^2-\frac{1}{3x})}^9$ is

• A. ${10}^{th}term$
• B. $7^{th}term$
• C. ${11}^{th}term$
• D. None of these

Answer 1

The correct option is B $7^{th}term$

$\text{Term independent of}x\text{in}$

${(3x^2-\frac{1}{3x})}^9$

$\text{Tr+1}=9Cr{\left(3x^2\right)}^r{(-\frac{1}{3x})}^{9-r}$

$\text{Power of}x\text{should be}0$

$2r-9+r=0$

$3r=9,r=3$

$\therefore \text{T4 (4th term) will be independent of}x$