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JEE Advance 2023
Paper-2 2023
Question
PARAGRAPH "I" Consider an obtuse angled triangle ABC in which the difference between the largest and the smallest angle is $\frac{\pi}{2}$ and whose sides are in arithmetic progression. Suppose that the vertices of this triangle lie on a circle of radius 1 . (There are two questions based on PARAGRAPH "I", the question given below is one of them)

PARAGRAPH "II" Consider the $6 \times 6$ square in the figure. Let $A_1, A_2, \ldots . . A_{49}$ be the points of intersections (dots in the picture) in some order. We say that $A_i$ and $A_j$ are friends if they are adjacent along a row or along a column. Assume that each point $\mathrm{A}_{\mathrm{i}}$ has an equal chance of being chosen.


(There are two questions based on PARAGRAPH “II”, the question given below is one of them)
Two distinct points are chosen randomly out of the points $\mathrm{A}_1, \mathrm{~A}_2, \ldots . . \mathrm{A}_{49}$. Let p be the probability that they are friends. Then the value of $7 p$ is
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