A) \[5/4\]
B) 7/4
C) \[9/4\]
D) \[3/4\]
Correct Answer: A
Solution :
Given \[{{\left( \sqrt{\frac{x}{3}}+\frac{3}{2{{x}^{2}}} \right)}^{10}}\]The standard equation is \[{{\left( a{{x}^{p}}+\frac{b}{{{x}^{q}}} \right)}^{10}}\] \[\Rightarrow \]\[n=10,p=1/2,q=2\] where \[r=\frac{np}{p+q}=\frac{10\times 1/2}{1/2+2}=2\] There, \[(r+1)th\]term in the expansion \[{{T}_{3}}={{\,}^{10}}{{C}_{2}}{{\left( \frac{1}{\sqrt{3}} \right)}^{10-2}}{{\left( \frac{3}{2} \right)}^{2}}\] \[=45\times \frac{1}{81}\times \frac{9}{4}=5/4\]
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