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

  • question_answer
    If  \[^{n}{{C}_{r-1}}=36,{{\ }^{n}}{{C}_{r}}=84\] and  \[^{n}{{C}_{r+1}}=126\], then the value of \[r\] is           [IIT 1979; Pb. CET 1993, 2003; DCE 1999, 2000; MP PET 2001]

    A) 1

    B) 2

    C) 3

    D) None of these

    Correct Answer: C

    Solution :

    Here \[\frac{^{n}{{C}_{r-1}}}{^{n}{{C}_{r}}}\] = \[\frac{36}{84}\] and \[\frac{^{n}{{C}_{r}}}{^{n}{{C}_{r+1}}}=\frac{84}{126}\]. Þ \[3n-10r=-3\] and \[4n-10r=6\] On solving, we get \[n=9\],\[r=3\].


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