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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 45

  • question_answer
    If an integer p is chosen at random in the interval\[0\le p\le 5\], then the probability that the roots of the equation \[{{x}^{2}}+px+\frac{p}{4}+\frac{1}{2}=0\] are real is-

    A) \[\frac{4}{5}\]              

    B)        \[\frac{2}{3}\]

    C) \[\frac{3}{5}\]              

    D)        None of these

    Correct Answer: B

    Solution :

    [b] \[D\Rightarrow {{p}^{2}}-4\left( \frac{p}{4}+\frac{1}{2} \right)\ge 0\] \[\left( p-2 \right)\text{.}\left( p+1 \right)\ge 0\] \[p\le -1\,or\,p\ge 2\] In 0 ^ p ^ 5, possible values of p are 2,3,4,5 Thus, probability \[=\frac{4}{6}=\frac{2}{3}\]


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