Question

A \straight line" between two points on a sphere is dened to be an arc of the great
circle passing through these points. Given two points on the equator on the Earth
(considered as a perfect sphere), one at longitude 0 degree and the other at longitude
180 degrees, the number of \straight lines" passing through these two points is
(A) 1. (B) 2. (C) 4. (D) innite.

Answer 1

If the two points are at the ends of a diameter of Earth ie., at the opposite ends of a  diameter, then  there are infinite number of straight lines.

If the two points are some other two points, then there are  2  lines.