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

  • question_answer
    Let \[{{T}_{n}}\] denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If \[{{T}_{n+1}}-{{T}_{n}}=21\], then n equals

    A) 5

    B) 7

    C) 6

    D) 4

    Correct Answer: B

    Solution :

    [b] \[^{n+1}{{C}_{3}}{{-}^{n}}{{C}_{3}}=21\] \[\because \,\,\,{{\,}^{n}}{{C}_{r}}{{+}^{n}}{{C}_{r-1}}{{=}^{n+1}}{{C}_{r}}\] \[{{\Rightarrow }^{n}}{{C}_{2}}=21\Rightarrow n=7\]

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