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Polygon: number of diagonals or triangles formed by its vertices

This type of question, asked 4 times: 12 May 2024 S1, 14 May 2024 S2, 20 Apr 2025 S1, 14 May 2026 S1. All 4 questions below, oldest first.

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  1. Question 1

    12 May 2024 S1

    127
    If TnT_n denotes the number of triangles which can be formed using the vertices of regular polygon of nn sides and Tn+1−Tn=21T_{n+1}-T_n=21, then n=n=

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  2. Question 2

    14 May 2024 S2

    114
    In a regular polygon, the number of diagonals are 54, then the number of sides of the polygon are

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  3. Question 3

    20 Apr 2025 S1

    133
    A regular polygon has 20 sides. The number of triangles that can be drawn by using the vertices but not using the sides are

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  4. Question 4

    14 May 2026 S1

    56
    In a polygon, the number of diagonals is 5454. Then the number of sides of the polygon is

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