A) 535
B) 601
C) 728
D) None of these
Correct Answer: A
Solution :
[a] The number of points of intersection of 37 straight lines is \[^{37}{{C}_{2}}.\] But 13 of them pass through the point A. Therefore instead of getting \[^{13}{{C}_{2}}\] points we get merely one point. Similarly 11 straight lines out of the given 37 straight lines intersect at B. therefor instead of getting \[^{11}{{C}_{2}}\] points, we get only one point. Hence, the number of intersection points of the lines is \[^{37}{{C}_{2}}{{-}^{13}}{{C}_{2}}{{-}^{11}}{{C}_{2}}+2=535.\]
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