2. Sample Papers
  3. JEE Main & Advanced

JEE Main & Advanced Sample Paper JEE Main Sample Paper-33

  • question_answer
    If \[x\frac{{{d}^{2}}y}{d{{x}^{2}}}+\frac{dy}{dx}=\ln x,\,y(l)=\text{l }\]and \[y'(\text{l})=-\text{l}\] then \[y''\left( \frac{1}{3} \right)\], equals

    A)  1         

    B)                                     2

    C)  3    

    D)                                     4

    Correct Answer: C

    Solution :

    Given \[\frac{d}{dx}\,\left( x\frac{dy}{dx} \right)=\,\ln \,x\]             \[\Rightarrow \,x\frac{dy}{dx}=x\,\ln \,\,x-x+C\]             Now \[y'(1)=-1,\] so             \[-1=0-1+C\,\Rightarrow \,C=0\]              \[\therefore \,\frac{dy}{dx}\,=\ln \,x-1\]             Hence \[{{\left. \frac{{{d}^{2}}y}{d{{x}^{2}}} \right]}_{x=\frac{1}{3}}}=\frac{1}{x}=3\]    


You need to login to perform this action.
You will be redirected in 3 sec spinner