JEE Main & Advanced Mathematics Sequence & Series Question Bank Harmonic Progression

  • question_answer
    If \[H\] is the harmonic mean between \[p\] and \[q\], then the value of  \[\frac{H}{p}+\frac{H}{q}\]  is [MNR 1990; UPSEAT 2000,  01]

    A) 2

    B) \[\frac{pq}{p+q}\]

    C) \[\frac{p+q}{pq}\]

    D) None of these

    Correct Answer: A

    Solution :

    As given \[H=\frac{2pq}{p+q}\] \[\therefore \ \ \frac{H}{p}+\frac{H}{q}=\frac{2q}{p+q}+\frac{2p}{p+q}=\frac{2\,(p+q)}{p+q}=2\].


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