JEE Main 2024 — Permutation Combination Question with 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,

$N=\left(1\to \text{point of intersection when both lines are even}\right)+\left(0\to \text{point of intersection when both lines are parallel}\right)+\left({}^{10}C_1\times {}^{10}C_1\to \text{point of intersection when }1\text{ odd and }1\text{ even line meets}\right)$

$\Rightarrow N=1+0+100$

$\Rightarrow N=101$