VIT Engineering VIT Engineering Solved Paper-2014

  • question_answer
    The equation of normal to the curve \[y={{\left( 1+x \right)}^{y}}+{{\sin }^{-1}}\left( {{\sin }^{2}}x \right)\] at x = 0 is

    A)  x + y = 1

    B)  x ? y = 1

    C)  x + y = - 1                           

    D)  x ? y = - 1

    Correct Answer: A

    Solution :

    Given  curve is  \[=\frac{{{10}^{5}}}{2\pi }Hz\] On differentiating w. R. t. X, we get \[E=\frac{12375}{5000}\]                                               \[=2.475eV=4\times {{10}^{-19}}J\] \[{{\text{l}}_{\text{eye}}}\text{=}\left( \text{photon flux} \right)\text{ }\!\!\times\!\!\text{ energy of a photon}\]  \[{{\text{l}}_{\text{eye}}}\text{=}\left( 5\times {{10}^{4}} \right)\times 4\times {{10}^{-19}}\]                  [ \[=2\times {{10}^{-14}}\left( W/{{m}^{2}} \right)\] at x = 0, y = 1] Slope of normal at (x = 0) = - 1 \[=\frac{{{l}_{ear}}}{{{l}_{eye}}}=\frac{{{10}^{-13}}}{2\times {{10}^{-14}}}=5\] Equation of normal at x = 0 and y = 1 is                        Y ? 1 = - 1 (x ? 0) \[\mu =\frac{\Delta {{V}_{p}}}{\Delta {{V}_{g}}}\]           y ? 1 = - x     \[\Rightarrow \]  x + y = 1


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