parveen110 wrote: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 lines passes through both points A and B, no two are parallel. Then the number of intersection points the lines have is equal to:
a. 535
b. 476
c. 728
d. 601
e. None of these.
Let each line that passes through point A be known as an
A line.
Let each line that passes through point B be known as a
B line.
Let each line that passes through neither point A nor point B be known as an
N line.
Since there 13
A lines, 11
B lines, and a total of 37 lines, the number of
N lines = 37-13-11 = 13.
Case 1: An
A line intersects with a
B line
Number of options for the
A line = 13.
Number of options for the
B line = 11.
To combine these options, we multiply:
13*11 = 143.
Case 2: An
N line intersects with an
A or B line
Number options for the
N line = 13.
Number of options for the
A or B line = 13+11 = 24.
To combine these options, we multiply:
13*24 = 312.
Case 3: An
N line intersects with another
N line
Each PAIR of
N lines will yield an intersection.
From the 13
N lines, the number of ways to choose 2 = 13C2 = (13*12)/(2*1) = 78.
Case 4: Points A and B
Points A and B constitute 2 more intersections.
Total intersections = 143+312+78+2 = 535.
The correct answer is
A.
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