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

  • question_answer
    If \[^{43}{{C}_{r-6}}={{\,}^{43}}{{C}_{3r+1}},\] then the value of r is [Kerala (Engg.) 2002]

    A) 12

    B) 8

    C) 6

    D) 10

    Correct Answer: A

    Solution :

      Given, \[^{43}{{C}_{r-6}}\,={{\,}^{43}}{{C}_{3r+1}}\] Þ \[r-6=3r+1\] or \[r-6+3r+1=43\] Þ \[r=-\frac{7}{2}\] (impossible) or \[r=12\].


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