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JEE Main & Advanced Sample Paper JEE Main Sample Paper-32

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

    A) \[\frac{5}{2}\]          

    B)                                    \[\frac{7}{2}\]

    C) \[\frac{9}{2}\]             

    D)                   \[\frac{11}{2}\]

    Correct Answer: C

    Solution :

    \[\frac{dy}{dx}=2x-\frac{1}{{{x}^{2}}}\Rightarrow \,y={{x}^{2}}+\frac{1}{x}+c\] As, \[M(-1,\,1)\Rightarrow \,1=1-1+c\Rightarrow \,c=1\] \[\Rightarrow \,y={{x}^{2}}+\frac{1}{x}+1;\]So, \[y(-2)=\frac{9}{2}\]   


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