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JEE Main & Advanced Sample Paper JEE Main Sample Paper-16

  • question_answer
    A function 'g' is defined for \[\forall x>0\] such that \[g(1)=1\] and \[g'({{x}^{2}})={{x}^{3}}\forall x>0\], then the value of g(4) equals

    A) \[\frac{13}{3}\]                                

    B)  3

    C) \[\frac{67}{5}\]                                

    D)  None of these

    Correct Answer: C

    Solution :

    Let\[{{x}^{2}}=t\Rightarrow g'(t)={{t}^{3/2}}\] or\[g(t)=\frac{{{t}^{5/2}}}{5/2}+C=\frac{2}{5}{{t}^{5/2}}+c\]\[g(1)=1\Rightarrow C=\frac{3}{5}\] \[\Rightarrow \]\[g(t)=\frac{2}{5}{{t}^{5/2}}+\frac{3}{5}\Rightarrow g(g)=\frac{67}{5}\]


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