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J & K CET Engineering J and K - CET Engineering Solved Paper-2010

  • question_answer
    The coefficient of \[{{x}^{4}}\]in the expansion of \[{{(1+x)}^{-2}},\]where \[|x|<1,\] is

    A)  \[-5\]

    B)  \[5\]

    C)  \[4\]

    D)  \[-3\]

    Correct Answer: B

    Solution :

    \[{{(1+x)}^{-2}}=1-2x+3{{x}^{2}}-4{{x}^{3}}+5{{x}^{4}}\] \[-....{{(-1)}^{r}}\,(r+1)\,{{x}^{r}}+....\] Clearly, coefficient of \[{{x}^{4}}\] is 5.


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