JEE Main & Advanced Mathematics Sequence & Series Question Bank Relation between AP., GP. and HP.

  • question_answer
    If the ratio of two numbers be \[9:1\], then the ratio of geometric and harmonic means between them will be

    A) \[1:9\]

    B) \[5:3\]

    C) \[3:5\]

    D) \[2:5\]

    Correct Answer: B

    Solution :

    Given that  \[\frac{a}{b}=\frac{9}{1}\] or \[a=9b\] Here \[H=\frac{2ab}{a+b}\] and \[G=\sqrt{ab}\] \[\Rightarrow \] \[H:G=\frac{2ab}{a+b}:\sqrt{ab}=\frac{2.9{{b}^{2}}}{10b}:3b=\frac{3}{5}\] Hence \[G:H=5:3\]


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