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J & K CET Engineering J and K - CET Engineering Solved Paper-2003

  • 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 :

    Given that,  \[{{T}_{n+1}}-{{T}_{n}}=21\] \[\therefore \] \[^{n+1}{{C}_{3}}{{-}^{n=21}}{{C}_{3}}\] \[\Rightarrow \] \[n(n-1)\,\left( \frac{3}{6} \right)=21\] \[\Rightarrow \] \[n(n-1)=42\,\,\Rightarrow \,\,n=7\]


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