Question

The middle term in the expansin of ${(\frac{2x^2}{3}+\frac{3}{2x^2})}^{th}$ is

• A. 251
• B. 252
• C. 250
• D. None of these

Answer 1

The correct option is B

252

252

Here, n,i.e., 10, is an even number

$\therefore$ Middle term $=(\frac{10}{2}+1)$th term =6th term Thus, we have:

$T_6=T_{5+1}$

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

$=\frac{10\times 9\times 8\times 7\times 6}{5\times 4\times 3\times 2}\times \frac{2^5}{3^5}\times \frac{3^5}{2^5}$

=252