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JEE Main & Advanced Sample Paper JEE Main Sample Paper-36

  • question_answer
    The two curves \[y={{x}^{2}}+ax-1\] and \[y=6{{x}^{2}}+b\] touch each other at a point having \[\text{abscissca}\,\,1\] 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\[{{\left. \frac{dy}{dx} \right|}_{curve\,\,1}}={{\left. \frac{dy}{dx} \right|}_{curve\,\,2}}\]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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