एक अष्टभुज के शीर्षों को जोड़कर कितने विकर्ण खींचे जा सकते हैं?
Read this question in English
How many diagonals can be drawn by joining the vertices of an octagon?
(a) 20 · (b) 24 · (c) 28 · (d) 64
उत्तर और व्याख्या · explanation in English
Answer: (a) 20
Any two of the 8 vertices can be joined in C(8, 2) = 28 ways. Eight of those joins are the sides, so 20 are diagonals.
- Lines joining two vertices: C(8, 2) = 8 × 7 ÷ 2 = 28.
- Of these, 8 are sides of the octagon.
- Diagonals = 28 − 8 = 20.
- Check with the formula n(n − 3)/2 = 8 × 5 ÷ 2 = 20.
Remember · Diagonals of an n-sided polygon = n(n − 3)/2: each vertex joins n − 3 non-adjacent vertices, and each diagonal is counted twice.
Question and answer: UPSC's official GS Paper II (2018, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·