KVPY Sample Paper KVPY Stream-SX Model Paper-22

  • question_answer
    The limiting position of the point of intersection of the straight lines, \[3x+5y=1\] and \[(2+c)\,x+5{{c}^{2}}y=1\] as c tends to one is:

    A) \[\left( \frac{2}{5},\,\,-\frac{1}{25} \right)\]

    B) \[\left( \frac{1}{2},\,\,-\frac{1}{10} \right)\]

    C) \[\left( \frac{3}{8},\,\,-\frac{1}{40} \right)\]

    D) none of these

    Correct Answer: A

    Solution :

    \[x=\underset{c\,\to \,1}{\mathop{Limit}}\,\frac{5\,(c-1)\,\,(c+1)}{5\,(c-1)\,\,(3c-2)}=\frac{2}{5};\]
    \[y=\underset{c\,\to \,1}{\mathop{Limit}}\,\frac{1-c}{5\,(c-1)\,\,(3c+2)}=-\frac{1}{25}\]

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