• # question_answer The coefficient of ${{x}^{5}}$ in the expansion of ${{({{x}^{2}}-x-2)}^{5}}$ is A) -83        B) -82   C) -81        D) 0

[c]:${{({{x}^{2}}-x-2)}^{5}}={{(x-2)}^{5}}{{(1+x)}^{5}}$ $={{[}^{5}}{{C}_{0}}{{x}^{5}}{{-}^{5}}{{C}_{1}}{{x}^{4}}\times 2+...]{{[}^{5}}{{C}_{0}}{{+}^{5}}{{C}_{1}}x+...]$ $\therefore$Coefficient of ${{x}^{5}}$: $1-5.5.2+10.10.4-10.10.8+5.5.16-32$ $=1-50+400-800+400-32\text{ }=-81$