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JEE Main & Advanced Sample Paper JEE Main Sample Paper-7

  • question_answer
    If \[a,\,b,\,c\] are positive number such that \[{{a}^{{{\log }_{3}}7}}=27,\,{{b}^{{{\log }_{7}}11}}=49,\,{{c}^{{{\log }_{11}}25}}=\sqrt{11}\], then sum of digits of

    A)  19                                         

    B)  17

    C)  15                                         

    D)  21

    Correct Answer: A

    Solution :

    The given expression can be written as \[S={{\left( {{\alpha }^{{{\log }_{3}}7}} \right)}^{{{\log }_{3}}7}}+{{\left( {{b}^{{{\log }_{7}}11}} \right)}^{{{\log }_{7}}11}}+{{\left( {{c}^{{{\log }_{11}}25}} \right)}^{{{\log }_{11}}25}}\] \[={{27}^{{{\log }_{3}}7}}+{{49}^{{{\log }_{7}}11}}+{{\left( \sqrt{11} \right)}^{{{\log }_{11}}25}}\] \[={{7}^{3}}+{{11}^{2}}+5\] \[=469\] \[\therefore \] Sum of digits = 19.


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