VIT Engineering VIT Engineering Solved Paper-2014

  • question_answer
    Two  lines   \[\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}\] and   \[\frac{x-3}{1}=\frac{y-k}{2}=z\]  intersect at a point, if k is equal to

    A) \[\frac{2}{9}\]                                   

    B) \[\frac{1}{2}\]

    C)  \[\frac{9}{2}\]  

    D) \[\frac{1}{6}\]   

    Correct Answer: C

    Solution :

    \[k\Omega \] \[{{n}_{e}}=3.13\times {{10}^{15}}\]        \[{{n}_{p}}=3.12\times {{10}^{15}}\] Since, the two lines intersect. So, putting above values in second line, we get                 \[i={{n}_{e}}{{q}_{e}}+{{n}_{p}}{{q}_{p}}\] Taking 1 st and 3rd  terms, we get                           2r ? 2 = 4r + 1 \[=3.13\times {{10}^{15}}\times 1.6\times {{10}^{-17}}\]                     r = - 3/2 Also, taking 2nd  and 3rd terms, we get                      3r ? 1 ? k = 8r + 2 \[+3.12\times {{10}^{15}}\times 1.6\times {{10}^{-19}}\]     \[=1\times {{10}^{-3}}=1mA\]                


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