A) 252
B) 352
C) 452
D) 250
Correct Answer: A
Solution :
[a] Here, \[n=10=\]even number Here, no. of terms in the expresion be \[n+1\,i.e.11\] i.e. It has single middle terms. So, 6th be the middle terms \[\therefore \] Middle term in the expansion \[{{\left( \frac{2{{x}^{2}}}{3}+\frac{3}{2{{x}^{2}}} \right)}^{10}}{{=}^{10}}{{C}_{5}}.\left( \frac{2{{x}^{3}}}{3} \right).{{\left( \frac{3}{2{{x}^{2}}} \right)}^{5}}\] \[{{=}^{10}}{{C}_{5}}=\frac{10\times 9\times 8\times 7\times 6}{5\times 4\times 3\times 2}\] \[=9\times 4\times 7=252\] Hence option [a] is correct.
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