JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Geometrical Problems

  • question_answer
    A polygon has 35 diagonals, then the number of its sides is [AMU 2002]

    A) 8

    B) 9

    C) 10

    D) 11

    Correct Answer: C

    Solution :

    Since \[^{n}{{C}_{2}}\,-\,n\,=35\] Þ \[\frac{n!}{2!\,\,(n-2)!}-n=35\] Þ \[n(n-1)-2n=70\] Þ \[{{n}^{2}}-3n=70\] Þ \[{{n}^{2}}-3n-70=0\] Þ \[(n+7)\,\,(n-10)=0\] Þ \[n\,\,=\,\,10\].


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