KVPY Sample Paper KVPY Stream-SX Model Paper-24

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

    A) \[\ell +m=2\]

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

    C) \[3\ell -m=2\]

    D) All 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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