The lines L _ 1 , L _ 2 , . .. , L _ 20 are distinct. For n = 1, 2,...

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,

$N = \left(1 \to \text{point of intersection when both lines are even}\right) + \left(0 \to \text{point of intersection when both lines are parallel}\right) + \left(C1 10 \times C1 10 \to \text{point of intersection when}1\text{odd and}1\text{even line meets}\right)$

$⇒ N = 1 + 0 + 100$

$⇒ N = 101$