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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 23

  • 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

    Correct Answer: C

    Solution :

    [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 \[{{x}^{5}}\]: \[1-5.5.2+10.10.4-10.10.8+5.5.16-32\] \[=1-50+400-800+400-32\text{ }=-81\]


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