VIT Engineering VIT Engineering Solved Paper-2014

  • question_answer
    The minimum value of \[\frac{x}{\log x}\] is

    A) e            

    B) \[\frac{1}{e}\]

    C) \[{{e}^{2}}\]                                      

    D) \[{{e}^{3}}\]

    Correct Answer: A

    Solution :

    Let \[=q\times {{n}^{2/3}}\] On differentiating w.r.t. x, we get                   \[R=1k\Omega \] For maxima and minima, put f?(x) = 0.                    Log x ? 1 = 0 \[{{i}_{1}}=\frac{15}{1}mA=15mA\]           x = e Now, \[R=250\Omega \] \[{{i}_{250}}=\frac{20-15}{250}=\frac{5}{250}\]           \[=\frac{20}{1000}=20mA\] \[{{i}_{Zener}}=20-15\]  f(x) is minimum at x = e. Hence,  minimum value of f(x) at x = e is                  \[\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{n}}={{\left( \frac{1}{2} \right)}^{t/7}}\]


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