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JEE Main & Advanced Sample Paper JEE Main Sample Paper-3

  • question_answer
    The two curves \[y={{x}^{3}}+ax-1\]and \[y=6{{x}^{2}}+b\]touch each other at a point having abscissca 1 when

    A)  \[a=3,b=-3\]                     

    B)  \[a=9,b=3\]

    C)  \[a=0,b=-6\]                     

    D)  \[a=3,b=9\]

    Correct Answer: B

    Solution :

     Both the curves satisfied by the point \[(1,{{y}_{1}})\] So, \[1+a-1=6+b\Rightarrow a-b=6\]     ...(1) Also\[\frac{dy}{dx}{{\left| _{\text{curve1}}=\frac{dy}{dx} \right|}_{\text{curve2}}}\]at x = 1 \[{{[3{{x}^{2}}+a]}_{x=1}}={{[12x]}_{x=1}}\Rightarrow a=9\]                       ?(2) From (1) & (2) \[a=9\]and b = 3.


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