Jee Main 2024 01 02 2024 Shift 2 - Question16
Question 16
There are 20 lines numbered as $1,2,3 \ldots 20$
All the odd numbered lines intersect at a point and all the even numbered lines are parallel
Find the maximum number of point of intersections.
Show Answer
Answer: (101)
Solution:
10 lines are concurrent, 10 lines are parallel.
Odd lines $\in{I _1, l _3 \ldots, l _{19} }$
Even lines $\in{I _2, I _4 \ldots, I _{20} }$
For maximum intersection:
(Even lines) $C _2 \times$ (zero point of intersection)
- (One line from odd lines) (one line from even lines) +1 point of intersection of concurrent lines
$$ \begin{aligned} & \Rightarrow{ }^{10} C _2(0)+{ }^{10} C _1 \cdot{ }^{10} C _1+1 \\ & \Rightarrow(101) \end{aligned} $$
BETA
