A) \[-80\]
B) 320
C) 72
D) 0
Correct Answer: D
Solution :
\[{{(x-2)}^{5}}{{(1+x)}^{5}}=-{{(2-x)}^{5}}{{(1+x)}^{5}}\] \[=-{{[}^{5}}{{C}_{0}}\,{{2}^{5}}{{-}^{5}}{{C}_{1}}\,{{2}^{4}}x{{+}^{5}}{{C}_{2}}{{2}^{3}}{{x}^{2}}+...]\] \[{{[}^{5}}{{C}_{0}}\,{{+}^{5}}{{C}_{1}}\,x{{+}^{5}}{{C}_{2}}\,{{x}^{2}}+...]\] \[\therefore \] Coefficient of \[{{x}^{2}}\] is \[={{-}^{5}}{{C}_{0}}{{2}^{5}}{{.}^{5}}{{C}_{2}}{{+}^{5}}{{C}_{1}}{{.2}^{4}}.{{\,}^{5}}{{C}_{1}}{{-}^{5}}{{C}_{2}}{{2}^{3}}=0\]
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