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JEE Main & Advanced Sample Paper JEE Main Sample Paper-29

  • question_answer
    If a curve passes through the point \[(1,0)\] and has slope \[\left( 1+\frac{1}{{{x}^{2}}} \right)\] at any point \[(x,y)\] on it, then the ordinate of point on the curve whose abscissa is \[-3\], is

    A) \[\frac{3}{8}\]                                   

    B) \[\frac{-8}{3}\]

    C) \[\frac{-3}{8}\]                                                 

    D) \[\frac{8}{3}\]

    Correct Answer: B

    Solution :

    \[\frac{dy}{dx}=1+\frac{1}{{{x}^{2}}}\Rightarrow f(x)=x-\frac{1}{x}+\lambda \] \[\Rightarrow \]               \[0=1-\frac{1}{1}+\lambda \Rightarrow \lambda =0\]                 So, \[f(x)=x-\frac{1}{x}\] \[\Rightarrow \]\[f(-3)=-3-\frac{1}{(-3)}=\frac{-3+1}{3}=\frac{-8}{3}\]


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