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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  \[^{{{n}^{2}}-n}{{C}_{2}}{{=}^{{{n}^{2}}-n}}{{C}_{10}}\], then \[n=\]

    A) 12

    B) 4 only

    C) \[-3\]only

    D) 4 or \[-3\]

    Correct Answer: D

    Solution :

    \[^{{{n}^{2}}-n}{{C}_{2}}{{=}^{{{n}^{2}}-n}}{{C}_{10}}{{\Rightarrow }^{{{n}^{2}}-n}}{{C}_{{{n}^{2}}-n-2}}{{=}^{{{n}^{2}}-n}}{{C}_{10}}\] \[\Rightarrow {{n}^{2}}-n-2=10\] or \[n=4,\ -3\].


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