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JEE Main & Advanced Mathematics Probability Question Bank Self Evaluation Test - Probability-I

  • question_answer
    If an integer q be chosen at random in the interval \[-10\le q\le 10,\] then the probability that the roots of the equation \[{{x}^{2}}+qx+\frac{3q}{4}+1=0\] are real is

    A) \[\frac{2}{3}\]

    B) \[\frac{15}{21}\]

    C) \[\frac{16}{21}\]

    D) \[\frac{17}{21}\]

    Correct Answer: D

    Solution :

    [d] q is an integer, then number of possible outcomes in \[[-10,10]=21\] Now, for real roots, discriminant \[\ge 0\] \[\Rightarrow (q-4)(q+1)\ge 0\Rightarrow q\ge 4,q\le -1\] Then, number of favourable outcomes \[=7+10=17\] Hence required probability\[=\frac{17}{21}\]


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