Question
How many sides are there in a polygon which has 20 diagonals?
NDA
Mathematics
Permutation Combination
2025
NDA 2025 (Phase 1)
NDA Mathematics Question (2025) — Solution
Options
- A. 6
- B. 7
- C. 8
- D. 10
Answer
C. 8
Step-by-step solution
The number of diagonals of an n-sided polygon is given by ^ n C_ 2 - n = n(n-3) 2 . Given that the number of diagonals is 20. n(n-3) 2 = 20 n^2 - 3n - 40 = 0 (n-8)(n+5) = 0 Since the number of sides n must be a positive integer, n = 8. Answer: 8
Related: Mathematics — Permutation Combination · All PYQ Banks