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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2006

  • question_answer
        If H is harmonic mean between P and Q, then the value of\[\frac{H}{P}+\frac{H}{Q}\]is

    A)  2                                            

    B)  \[\frac{PQ}{(P+Q)}\]

    C)  \[\frac{(P+Q)}{PQ}\]                                    

    D)  none of these

    Correct Answer: A

    Solution :

                    Key Idea: If H is harmonic mean between a and b, then\[H=\frac{2ab}{a+b}\] Given H is harmonic mean between P and Q. \[\therefore \]  \[H=\frac{2PQ}{P+Q}\] \[\Rightarrow \]               \[\frac{H}{P}=\frac{2Q}{P+Q}\]                 ?.. (i) Also,      \[\frac{H}{Q}=\frac{2P}{P+Q}\]                 ?. (ii) \[\therefore \]  \[\frac{H}{P}+\frac{H}{Q}=\frac{2(P+Q)}{P+Q}=2\]


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