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J & K CET Engineering J and K - CET Engineering Solved Paper-2012

  • question_answer
    If \[f'(x)=g(x)\] and \[g'(x)=-f(x)\] for all x and  \[f(1)=5,\,\,f'(1)=4,\]then the value of \[{{f}^{2}}(1)+{{g}^{2}}(1)\]is equal to

    A)  \[25\]            

    B)  \[16\]

    C)  \[41\]              

    D)  \[9\]

    Correct Answer: C

    Solution :

    Given,  \[f(1)=5\] and \[g(x)=f'(x)\] and \[f'(1)=4\] \[\therefore \] \[{{f}^{2}}(1)+{{g}^{2}}(1)={{(5)}^{2}}+{{[f'(1)]}^{2}}\] \[=25+{{(4)}^{2}}\] \[=25+16\] \[=41\]


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