Amardeep Sharma wrote:
If 25 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then in how many points do they intersect?
A 2300
B 600
C 250
D 300
E none of these
Please explaing for me to understand the concept
Amar
Responding to a pm:
We need to draw lines such that they are not parallel. Why is 'not parallel' important? Any two distinct lines drawn on the xy axis will either be parallel or will intersect in exactly one point. Lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel. Since any given two lines are not parallel, we can say that they must intersect at exactly one point. So every pair of two lines will intersect at exactly one point. We are also given that no three lines are concurrent. This means that no three lines intersect at the same point. So every pair of two lines we select will have a unique point of intersection which they will not share with any third line. So how many such unique points of intersection do we get? That depends on how many pairs of 2 lines can we select from the 25 lines?
We can select 2 lines from 25 lines in 25C2 ways i.e. 300 ways. Each one of these pairs will give us one unique point of intersection so we will get 300 points of intersection.
Answer (D)
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Karishma
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