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JEE Main & Advanced Mathematics Sequence & Series Question Bank Self Evaluation Test - Sequences and Series

  • question_answer
    The harmonic mean H of two numbers is 4 and the arithmetic mean A and geometric mean G satisfy the equation \[2A+{{G}^{2}}=27\]. The two numbers are

    A) 6, 3

    B) 9, 5

    C) 12, 7

    D) 3, 1

    Correct Answer: A

    Solution :

    [a] Let two numbers be a and b. Given \[\frac{2ab}{a+b}=4\Rightarrow ab=2\left( a+b \right)\] \[2A+{{G}^{2}}=27\] \[\Rightarrow \,\,\,\,2\left( \frac{a+b}{2} \right)+ab=27\] \[\Rightarrow \,\,\,\,ab=18\] and \[a+b=9\Rightarrow ab=9\] On solving these we get \[a=3\] & \[b=6\] or \[a=6\] & \[b=3.\]


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