KVPY Sample Paper KVPY Stream-SX Model Paper-29

  • question_answer
    The tangent to the curve, \[y=x{{e}^{{{x}^{2}}}}\] passing, through the point \[(1,e)\] also passes through the point:

    A) \[(2,3e)\]

    B) \[\left( \frac{4}{3},2e \right)\]

    C) \[\left( \frac{5}{3},2e \right)\]

    D) \[(3,6e)\]

    Correct Answer: B

    Solution :

    \[(1,e)\]lies on this
    Now, \[\frac{dy}{dx}=x{{e}^{{{x}^{2}}}}.2x+{{e}^{{{x}^{2}}}}.1\]
    Put \[x=1\]
    Equation of tangent at \[(1,e)\]
    \[\left( \frac{4}{3},2e \right)\]satisfies it
    \[\therefore \]Answer is B.

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