JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Self Evaluation Test - Permutations and Combinatioins

  • question_answer
    The least positive integral values of n which satisfies the inequality \[^{10}{{C}_{n-1}}>{{2.}^{10}}{{C}_{n}}\]

    A) 7

    B) 8

    C) 9

    D) 10

    Correct Answer: B

    Solution :

    [b] We have \[^{10}{{C}_{n-1}}>{{2.}^{10}}{{C}_{n}}\] \[\Rightarrow \frac{10!}{(n-1)!(11-n)!}>2.\frac{10!}{n!(10-n)!}\] \[\Rightarrow \frac{n!}{(n-1)!}>2\frac{(11-n)!}{(10-n)!}\] i.e, \[n>22-2n\] \[\Rightarrow 3n>22\Rightarrow n>\frac{22}{3}=7\frac{1}{3}\] \[\therefore \] Least + ve integral value of n=8.

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