XAT 2019 — QA & DI Question 18
What is the maximum number of points that can be placed on a circular disk of radius 1 metre (some of the points could be placed on the bounding circle of the disk) such that no two points are at a distance of less than 1 metre from each other?
Answer & solution
- A
5
- B
8
- C
6
- D
9
7
If we take one point at the centre of the circle, the remaining points can only be at the circumference of the circle as the minimum distance between any 2 points is at least 1 m (which is the radius of the circle).
Also, the remaining points on the circumference of the circle have to be such that 2 points are at a distance of less than one.
Now circumference of the circle = 2 × 22/7 × 1 = 44/7 ≈ 6.28 m
As the circumference or the length of the boundary is 6.28 m, we can have a maximum of 6 points on the circumference such that the distance between any 2 points is at least 1 m.
So, in all we can have a maximum of 6 points on the circumference and 1 point at the centre of the circle, making a total of 7 points.
Hence, option (e).