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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2008

  • question_answer
    Let\[g(x)=\left\{ \begin{matrix}    2e, & if\,x\le 1  \\    \log (x-1), & if\,x>1  \\ \end{matrix} \right..\]The equation of the normal to\[y=g(x)\]at the point ( 3, log 2), is

    A)  \[y-2x=6+log\text{ }2\]

    B)  \[y+2x=6+log2\]

    C)  \[y+2x=6-log\text{ }2\]

    D)  \[y+2x=-6+log\text{ }2\]

    E)  \[y-2x=-6+log\text{ }2\]

    Correct Answer: B

    Solution :

    Given, \[g(x)=\left\{ \begin{matrix}    2e, & if\,x\le 1  \\    \log (x-1), & if\,x>1  \\ \end{matrix} \right.\] For the point\[(3,\text{ }log2),\]we take \[y=g(x)=\log (x-1)\]                 \[\frac{dy}{dx}=\frac{1}{(x-1)}\] \[\Rightarrow \] \[{{\left( \frac{dy}{dx} \right)}_{(3,\log 2)}}=\frac{1}{3-1}=\frac{1}{2}\] \[\therefore \]Equation of normal is \[y-log2=-2(x-3)\] \[\Rightarrow \]               \[y+2x=6+log2\]


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