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JEE Main & Advanced Sample Paper JEE Main Sample Paper-27

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

    A)  \[-4\]                                       

    B)  \[-8\]

    C)  6                                

    D)  10

    Correct Answer: A

    Solution :

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


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