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Three distinct vertices are chosen at random form the vertices of a given regular polygon of (2n+1) sides. Let all such choices are equally likely and the probability that the centre of the given polygon lies in the interior of the triangle determined by these three chosen random points is 5/14.
Q. No. 1 The number of diagonals of the polygon is equal to
(a) 14 (b) 18 (c) 20 (d) 27
Q. No. 2 The number of points of intersection of the diagonals lying exactly inside the polygon is equal to
(a) 70 (b) 35 (c) 126 (d) 96
Q. No. 3 There vertices of the polygon are chosen at random. The probability that these vertices from an isosceles triangle is
(a) 1/3 (b) 3/7 (c) 3/28 (d) None of these
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