KVPY Sample Paper KVPY Stream-SX Model Paper-10

  • question_answer
    Let the number of positive and negative solutions of \[{{x}^{2}}-6x-|5x-15|-\,5=0\] be \[\ell \] and m respectively, then

    A) \[\ell +m=2\]                

    B) \[3\ell +m=4\]

    C) \[3\ell -m=2\]                

    D) AII of these

    Correct Answer: D

    Solution :

    If \[5x\ge 15\] i.e. \[x\ge 3,\] then \[{{x}^{2}}-6x-5x+15-5=0\] i.e. \[{{x}^{2}}-11x+10=0\] i.e. \[x=1,\]10
    \[\therefore \]      \[x=10\] is a solution
    If \[5x<15\]       i.e.        \[x>3,\] then
    \[{{x}^{2}}-6x+5x-15-5=0\]
    i.e.        \[{{x}^{2}}-x-20=0\]
    i.e.        \[x=5,\,\,-\,4\]
    \[\therefore \]      \[x=-\,4\]is a solution
    Thus \[\ell =1,\] \[m=1\]


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