JEE Main & Advanced Sample Paper JEE Main - Mock Test - 6

  • question_answer
    The least value of natural number n satisfying \[C(n,5)+C(n,6)>C(n+1,5)\]is

    A) 11

    B) 10

    C) 12

    D) 13

    Correct Answer: A

    Solution :

    [a] : \[^{n}{{C}_{5}}{{+}^{n}}{{C}_{6}}{{>}^{n+1}}{{C}_{5}}{{\Rightarrow }^{n+1}}{{C}_{6}}{{>}^{n+1}}{{C}_{5}}\] \[\Rightarrow \]\[\frac{(n+1)!}{6!(n-5)!}.\frac{5!(n-4)!}{(n+1)!}>1\Rightarrow \frac{(n-4)}{6}>1\] \[\Rightarrow \]\[n-4>6\Rightarrow n>10\] Hence, least value of n = 11.

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