NIMCET 2024 Paper

Section: Mathematics

Question : 43 of 120

Marks: +1, -0

Lines

L_1, L_2, . . ., L_{10}

are distinct among which the lines

L_2, L_4, L_6, L_8, L_{10}

are parallel to each other and the lines

L_1, L_3, L_5, L_7, L_9

pass through a given point

C

. The number of points of intersection of pairs of lines from the complete set

L_1, L_2, L_3, . . ., L_{10}

Solution:

Total number of intersection points (in normal case when no two lines are parallel or no three pass through the same point)

{ }^{10} C_2

But the five lines

L_2, L_4, L_6, L_8, L_{10}

are parallel, hence these lines do not intersect.
Also the five lines

L_1, L_3, L_5, L_7, L_9

intersect at the same point, hence these lines create only one intersecting point.
Number of intersecting points is:

{ }^{10} C_2-{ }^5 C_2-{ }^5 C_2+1=26

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