A) -83
B) -82
C) -86
D) -81
Correct Answer: D
Solution :
[d] \[{{(x-2)}^{5}}{{(x+1)}^{5}}\] \[={{[}^{5}}{{C}_{0}}{{x}^{5-5}}{{C}_{1}}{{x}^{4}}\times 2+...]\]\[{{[}^{5}}{{C}_{0}}{{+}^{5}}{{C}_{1}}x+...]\] \[\Rightarrow \]Coefficient of \[{{x}^{5}}\] \[{{=}^{5}}{{C}_{0}}^{5}{{C}_{5}}{{-}^{5}}{{C}_{1}}\times 2{{\times }^{5}}{{C}_{4}}{{+}^{5}}{{C}_{2}}\times {{2}^{2}}{{\times }^{5}}{{C}_{3}}{{-}^{5}}{{C}_{3}}\times {{2}^{3}}{{\times }^{5}}{{C}_{2}}\] \[{{+}^{5}}{{C}_{4}}\times {{2}^{4}}{{\times }^{5}}{{C}_{1}}{{-}^{5}}{{C}_{5}}\times {{2}^{5}}{{\times }^{5}}{{C}_{0}}\] \[=1-5\times 5\times 2+10\times 10\times 4-10\times 10\times 8+5\times 5\times 16-32\] \[=-81\]
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