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satish narayan chaudhary

· started a discussion

· 1 Months ago

doubt (Question: 117117.0 )

how???

Question:
There are four lines in a plane, no two of which are parallel. The maximum number of points at which any two lines intersect are :
Options:
A) four
B) five
C) six
D) seven
Solution:
Ans: (c)

Let there be 'n' lines, for maximum no. of intersections no three lines must intersect at same point, so each line must intersect at (n-1) points. For each intersection minimum two lines are required. Maximum intersection = n(n-1)/2. 

Maximum no. of intersecting points = (4*3)/2 = 6.

ASHUTOSH KUMAR

· commented

· 1 Months ago

let there be 'n' no of lines. And for the maximum possible no of intersections there should no three lines meet at the same the point. So each line will intersect all (n-1) lines. There are n total lines. However, since each intersection is caused by the intersection of exactly 2 lines, we must divide by 2 to get the final answer of n(n−1)/2.
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