Let X = (x, y) Z Z : x^2 8 + y^2 20 < 1 and y^2 < 5x . Three distinct points P, Q and R are randomly chosen from X. Then the probability that P, Q and R form a triangle whose area is a positive integer, is

JEE Advanced 2023 Mathematics question

Let . Three distinct points , and are randomly chosen from . Then the probability that , and form a triangle whose area is a positive integer, is

(A)
(B)Correct
(C)
(D)

Answer: (B)

Solution

forces , and gives . : and , so (5 points). : , so (7 points). and there are choices. A triangle needs points on both vertical lines; with two points on one line

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Question ID VK-034067