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JEE Main & Advanced Mathematics Sequence & Series Question Bank Exponential series

  • question_answer
    In  the expansion of \[(1+x+{{x}^{2}}){{e}^{-x}}\],  the coefficient of  \[{{x}^{2}}\] is

    A) 1

    B) \[-1\]

    C) 1/2

    D) -1/2

    Correct Answer: C

    Solution :

    \[(1+x+{{x}^{2}}){{e}^{-x}}=(1+x+{{x}^{2}})\] \[\left\{ 1-\frac{x}{1\ !}+\frac{{{x}^{2}}}{2\ !}-\frac{{{x}^{3}}}{3\ !}+....... \right\}\] Coefficient of \[{{x}^{2}}=1.\frac{1}{2\ !}+1.\left( -\frac{1}{1\ !} \right)+1.1=\frac{1}{2\ !}=\frac{1}{2}\].


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