A) 512
B) - 512
C) 521
D) 251
Correct Answer: B
Solution :
Here \[{{T}_{r+1}}={}^{\text{9}}{{C}_{r}}{{\left( \frac{{{x}^{2}}}{2} \right)}^{9-r}}{{\left( \frac{-2}{x} \right)}^{r}}\] = \[{}^{9}{{C}_{r}}\frac{{{x}^{18-3r}}{{(-2)}^{r}}}{{{2}^{9-r}}},\] this contains \[{{x}^{-9}}\] if 18 - 3r = - 9 i.e. if r = 9. Coefficient of \[{{x}^{-9}}\] = \[{}^{9}{{C}_{9}}\frac{{{(-2)}^{9}}}{{{2}^{0}}}=-{{2}^{9}}=-512\].You need to login to perform this action.
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