Question

The $6^{th}$ coefficient in the expansion of ${(2x^2-\frac{1}{3x^2})}^{10}$

• A. $-\frac{986}{27}$
• B. $\frac{986}{27}$
• C. $\frac{896}{27}$
• D. $-\frac{896}{27}$

Answer 1

The correct option is D $-\frac{896}{27}$

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

$6^{th}$ coefficient $\to$ $5^{th}$ term

$={{}^{10}C}_5{\left(2x^2\right)}^5{\left(\frac{-1}{{3x}^2}\right)}^5$

$={{}^{10}C}_5\times 2^5\times \frac{-1}{3^5}$

$=-\frac{252\times 32}{243}$

$=-\frac{896}{27}.$

Hence, the answer is $-\frac{896}{27}.$