VIT Engineering VIT Engineering Solved Paper-2014

  • question_answer
    If the line lx + my ? n = 0  will be a normal to the hyperbola, then \[\frac{{{a}^{2}}}{{{l}^{2}}}-\frac{{{b}^{2}}}{{{m}^{2}}}=\frac{{{\left( {{a}^{2}}+{{b}^{2}} \right)}^{2}}}{k},\] where k is equal to

    A) n                                            

    B) \[{{n}^{2}}\]

    C) \[{{n}^{3}}\]                                      

    D) None of these

    Correct Answer: B

    Solution :

    The equation of any normal to \[{{e}_{\max }}=0.005\times 10\times 100\pi =5\pi \] is  \[{{v}_{0}}=\frac{1}{2\pi \sqrt{LC}}\] \[=\frac{1}{2\pi \sqrt{1\times {{10}^{-3}}\times 0.1\times {{10}^{-6}}}}\]    \[=\frac{{{10}^{5}}}{2\pi }Hz\]        ...(i) The straight line lx + my ? n = 0 will be              normal to the hyperbola \[E=\frac{12375}{5000}\] then Eq. (i) and lx  + my ? n = 0  represent the same line.                 \[=2.475eV=4\times {{10}^{-19}}J\]               \[{{\text{l}}_{\text{eye}}}\text{=}\left( \text{photon flux} \right)\text{ }\!\!\times\!\!\text{ energy of a photon}\]                 \[{{\text{l}}_{\text{eye}}}\text{=}\left( 5\times {{10}^{4}} \right)\times 4\times {{10}^{-19}}\]                 \[=2\times {{10}^{-14}}\left( W/{{m}^{2}} \right)\]                 and                \[=\frac{{{l}_{ear}}}{{{l}_{eye}}}=\frac{{{10}^{-13}}}{2\times {{10}^{-14}}}=5\]                 \[\mu =\frac{\Delta {{V}_{p}}}{\Delta {{V}_{g}}}\]       \[\Rightarrow \]                 \[\Delta {{V}_{p}}=-\mu \times \Delta {{V}_{s}}\]                \[=-50\left( -20 \right)=10V\]                 \[E=\Delta m{{c}^{2}}\]      \[=0.5\times {{10}^{-3}}\times {{\left( 3\times {{10}^{8}} \right)}^{2}}\]                 \[=4.5\times {{10}^{13}}\]                    \[E=\frac{4.5\times {{10}^{13}}}{3.6\times {{10}^{6}}}\]


You need to login to perform this action.
You will be redirected in 3 sec spinner