A) \[\frac{1}{7}\]
B) \[\frac{-1}{7}\]
C) - 7
D) 7
Correct Answer: C
Solution :
\[{{T}_{r+1}}{{=}^{8}}{{C}_{r}}{{(x)}^{8-r}}{{\left( -\frac{1}{2x} \right)}^{r}}\]\[{{=}^{8}}{{C}_{r}}{{\left( \frac{-1}{2} \right)}^{r}}{{x}^{8-r-r}}\] For coefficient of\[{{x}^{2}}\], \[8-2r=2\] Þ \[r=3\] Coefficient of \[{{x}^{2}}{{=}^{8}}{{C}_{3}}{{\left( \frac{-1}{2} \right)}^{3}}\]= \[-\frac{8!}{5!\,3!}\frac{1}{{{2}^{3}}}=-7\].
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