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NDA 2025
Exam
NDA
Year
2025
Subject
Mathematics
Chapter
Permutation and Combination

NDA 2025 · Mathematics · Permutation and Combination

How many sides are there in a polygon which has 20 diagonals?

How many sides are there in a polygon which has 20 diagonals?

Options

  1. A66
  2. B77
  3. C88
  4. D1010

Correct answer

C. 88

Step-by-step solution

The number of diagonals of an nn-sided polygon is given by nC2−n=n(n−3)2^{n}C_{2} - n = \dfrac{n(n-3)}{2}.

Given that the number of diagonals is 2020.

n(n−3)2=20\dfrac{n(n-3)}{2} = 20

n2−3n−40=0n^2 - 3n - 40 = 0

(n−8)(n+5)=0(n-8)(n+5) = 0

Since the number of sides nn must be a positive integer, n=8n = 8.

Answer: 88
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