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  3. CEE Kerala Engineering

CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2006

  • question_answer
    The number of triangles which can be formed by using the vertices of a regular polygon of \[(n+3)\]sides is 220. Then n is equal to:

    A)  8                                            

    B)  9

    C)  10                         

    D)         11

    E)  12

    Correct Answer: B

    Solution :

    Number of triangle\[{{=}^{n+3}}{{C}_{3}}=220\] \[\Rightarrow \]               \[\frac{(n+3)!}{3!n!}=220\] \[\Rightarrow \]               \[(n+1)(n+2)(n+3)=1320\]                 \[=12\times 10\times 11\]                 \[=(9+1)(9+2)(9+3)\] \[\therefore \]  \[n=9\]


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