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JEE Main & Advanced Sample Paper JEE Main Sample Paper-44

  • question_answer
    Let \[{{A}_{1}},\,{{A}_{2}},\,{{A}_{3}},....,{{A}_{2009}}\] and \[{{H}_{1}},\,{{H}_{2}},\,{{H}_{3}},\,...{{H}_{2009}}\] are arithmetic and harmonic means inserted between two numbers ?a? and ?b?, respectively. If \[{{A}_{1005}}\,{{H}_{1005}}\] is 20011, then \[\frac{{{A}_{1006}}{{H}_{1004}}}{{{A}_{1004}}{{H}_{1006}}}\] is

    A)  1                                

    B)  2

    C)  3                                

    D)  4

    Correct Answer: A

    Solution :

     \[{{A}_{1}},\,{{A}_{2}},\,{{A}_{3,}}...,\,{{A}_{2009}}\] and \[{{H}_{1}},\,{{H}_{2}},...,{{H}_{2009}}\] are AM and HM between a and b. Hence, \[{{A}_{1}}{{H}_{2009}}={{A}_{2}}{{H}_{2008}}=...={{A}_{1005}}{{H}_{1005}}=....\] \[={{A}_{2009}}{{H}_{1}}\] \[\therefore \]    \[\frac{{{A}_{1006}}{{H}_{1004}}}{{{A}_{1004}}{{H}_{1006}}}=1\]


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