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Harmonic mean of two numbers, 2pq/(p+q): write a relation or expression

This type of question, asked 3 times: CDS 2 2018, CDS 1 2020, CDS 2 2022. All 3 questions below, oldest first.

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  1. Question 1

    CDS 2 2018

    22
    If H is the harmonic mean of P and Q, then the value of HP+HQ\frac{H}{P} + \frac{H}{Q} is

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  2. Question 2

    CDS 1 2020

    45
    For two observations, the sum is SS and product is PP. What is the harmonic mean of these two observations?

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  3. Question 3

    CDS 2 2022

    61
    If xx is the harmonic mean between yy and zz, then which one of the following is correct ?

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