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JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Definition of combinations, Conditional combinations, Division into groups, Derangements

  • question_answer
    Value of r for which \[^{15}{{C}_{r+3}}={{\,}^{15}}{{C}_{2r-6}}\] is [Pb. CET 1999]

    A) 2

    B) 4

    C) 6

    D) - 9

    Correct Answer: C

    Solution :

    Either \[r+3=2r-6\] or \[r+3+2r-6=15,\,\,(\because {{\,}^{n}}{{C}_{r}}={{\,}^{n}}{{C}_{n-r}})\] Þ \[r=9\] or\[r=6\].


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