The lines L 1 , L 2 , ldots, L 20 are distinct. For n =1,2,3, ldots, 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 , ldots, L 20 \ is equal to :

Mathematics · Permutations and Combinations

JEE Main 2024 — 1 February, Shift 2 — Question 26

The lines $\mathrm{L}_{1}, \mathrm{~L}_{2}, \ldots, \mathrm{~L}_{20}$ are distinct. For $\mathrm{n}=1,2,3, \ldots, 10$ all the lines $\mathrm{L}_{2 \mathrm{n}-1}$ are parallel to each other and all the lines $\mathrm{L}_{2 n}$ pass through a given point $P$ . The maximum number of points of intersection of pairs of lines from the set $\left\{L_{1}, L_{2}, \ldots, L_{20}\right\}$ is equal to :

Answer: 101

Numerical answer — enter this value.

Step-by-step solution

$\mathrm{L}_{1}, \mathrm{~L}_{3}, \mathrm{~L}_{5},--\mathrm{L}_{19}$

are Parallel $\mathrm{L}_{2}, \mathrm{~L}_{4}, \mathrm{~L}_{6},--\mathrm{L}_{20}$

are Concurrent Total points of intersection

$={ }^{20} \mathrm{C}_{2}-{ }^{10} \mathrm{C}_{2}-{ }^{10} \mathrm{C}_{2}+1$

$=101$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 1 February, Shift 2
Subject: Mathematics
Chapter: Permutations and Combinations
Topic: Applications of Permuations and Combination