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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 35

  • question_answer
    If \[1+{{x}^{4}}+{{x}^{5}}=\sum\limits_{i=0}^{5}{{{a}_{i}}{{(1+x)}^{i}}}\]for all \[x\in R,\] then \[{{a}_{2}}\] is equal to

    A) \[-4\]       

    B)        \[-8\]                      

    C) \[6\]                     

    D)        \[10\]

    Correct Answer: A

    Solution :

      [a] Put \[1+x=y,\] we get \[1+{{(y-1)}^{4}}+{{(y-1)}^{5}}=\sum\limits_{i=0}^{5}{{{a}_{i}}{{y}^{i}}}\] Equating coefficients of \[{{y}^{2}}\] on both sides, we get             \[{{a}_{2}}{{=}^{4}}{{c}_{2}}{{-}^{5}}{{c}_{3}}=6-10=-4\]          


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