Question

In a plane there are 37 straight lines of which 13 pass through the point A and 11 pass through the point B. Besides, no three lines pass through one point, no line passes through both points A and B, and no two are parallel. Then the number of intersecting points the lines have is equal to

• A. $535$
• B. $601$
• C. $728$
• D. None of these

Answer 1

Answer: (A)

$535$

$37$ Straight lines are there

$13$ through $A$ and $11$ through $B$

No lines pass through $2$ points no parallel lines

to find point of intersection two lines are required both should not be from $A$ or $B$

${=}^{37}{C}_2{-}^{13}{C}_2{-}^{11}{C}_2+2$

$=666-78-55+2$

$=535$