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 f

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Q.
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 ______. [2024]

Ans.
(101)

Let $L_{1}, L_{3}, . . ., L_{19}$ are parallel to each other and $L_{2}, L_{4}, L_{6}, \dots, L_{20}$ are passing through a point P.

$∴$ Point of intersection of pairs of lines from the set ${L_{1}, L_{2}, \dots, L_{20}} = {}^{20}{C_{2} - {}^{10}{C_{2}} - {}^{10}{C_{2}}} + 1 = 101$

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