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JCECE Engineering JCECE Engineering Solved Paper-2013

  • question_answer
    If\[{{(1+x-2{{x}^{2}})}^{6}}=1+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+...+{{a}_{12}}{{x}^{12}}\], then the expression\[{{a}_{2}}+{{a}_{4}}+{{a}_{6}}+...+{{a}_{12}}\]has the value

    A) \[32\]                                   

    B) \[63\]

    C) \[64\]                                   

    D) \[31\]

    Correct Answer: D

    Solution :

    \[{{(1+x-2{{x}^{2}})}^{6}}=1+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+...+{{a}_{12}}{{x}^{12}}\] On putting \[x=1\] and \[x=-1\] and adding the results,                 \[64=2(1+{{a}_{2}}+{{a}_{4}}+...)\] \[\Rightarrow \]               \[{{a}_{2}}+{{a}_{4}}+{{a}_{6}}+...+{{a}_{12}}=31\]


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