NDA 2026 Mathematics PYQ — What is the maximum number of points of intersection of circles? … | Mathem Solvex | Mathem Solvex
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NDA 2026 — Mathematics PYQ
NDA | Mathematics | 2026
What is the maximum number of points of intersection of 5 circles?
5 वृत्तों के प्रतिच्छेदन बिंदुओं की अधिकतम संख्या क्या है ?
Choose the correct answer:
A.
10
B.
15
C.
20
(Correct Answer)
D.
25
Correct Answer:
20
Explanation
Fundamental Principle:
Any two distinct circles can intersect at a maximum of 2 points.
To achieve the maximum number of total intersection points, every pair of circles must intersect at these 2 distinct points, and no three circles should intersect at the same point.
Calculation:
The number of ways to choose 2 circles from 5 is given by the combination formula (rn), where n=5 and r=2:
(25)=2×15×4=10
Since each pair intersects at 2 points, the total maximum number of intersection points N is:
N=(25)×2
N=10×2=20
Correct Option: (c) 20
Explanation
Fundamental Principle:
Any two distinct circles can intersect at a maximum of 2 points.
To achieve the maximum number of total intersection points, every pair of circles must intersect at these 2 distinct points, and no three circles should intersect at the same point.
Calculation:
The number of ways to choose 2 circles from 5 is given by the combination formula (rn), where n=5 and r=2:
(25)=2×15×4=10
Since each pair intersects at 2 points, the total maximum number of intersection points N is:
