A) \[\frac{405}{256}\]
B) \[\frac{504}{259}\]
C) \[\frac{450}{263}\]
D) None of these
Correct Answer: A
Solution :
\[term\,\,of{{\left( \frac{x}{2}-\frac{3}{{{x}^{2}}} \right)}^{10}}is\,{{\,}^{10}}{{C}_{t}}{{\left( \frac{x}{2} \right)}^{10-t}}{{\left( \frac{-3}{{{x}^{2}}} \right)}^{t}}\] Here, \[{{\operatorname{x}}^{-t+10-2t}}=\,\,{{x}^{4}}\Rightarrow \,\,-3t\,+10=\,\,4\,\,\Rightarrow \,\,t=2\] Hence coefficient of \[{{x}^{4}}\] is \[^{10}{{C}_{2}}{{\left( \frac{1}{2} \right)}^{8}}\,{{(3)}^{2}}=\frac{405}{256}\]
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