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KVPY Sample Paper KVPY Stream-SX Model Paper-19

  • question_answer
    If the ellipse \[\frac{{{x}^{2}}}{4}+\frac{{{y}^{2}}}{1}=1\] meet the ellipse \[\frac{{{x}^{2}}}{1}+\frac{{{y}^{2}}}{{{a}^{2}}}=1\] in four distinct points and \[a={{b}^{2}}-10\,b+25\] then the value of b does not satisfy -

    A) \[(-\infty ,\,\,2)\]

    B) (2, 3)

    C) \[(6,\,\,\infty )\]

    D) (4, 6)

    Correct Answer: D

    Solution :

    Clearly a >1
    \[{{b}^{2}}-10b+25>1\]
    \[{{b}^{2}}-10b+24>0\]
    \[b\in (-\,\infty ,\,\,4)\cup (6,\,\,\infty )\]


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