The lines L 1 , L 2 , . .. , L 20 are distinct. For n = 1 , 2 , 3 , . .. , 10 all the lines L 2 n − 1 are parallel to each other and all the lines L 2 n pass through a given point P . The maximum number of points of intersection of pairs of lines from the set L 1 , L 2 , . .. , L 20 is equal to:

Step-by-step solution

Given: Out of 20 numbered lines, even numbered lines are concurrent, odd number lines are parallel. So, the maximum number of intersection points will be given by, N = 1 → point of intersection when both lines are even + 0 → point of intersection when both lines are parallel + C 1 10 × C 1 10 → point of intersection when 1 odd and 1 even line meets ⇒ N = 1 + 0 + 100 ⇒ N = 101