Three of six vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral is (a) `1/2` (b) `1/5` (c) `1/10` (d) `1/20`

If four vertices a regular octagon are chosen at random, then the probability that the quadrilateral formed by them is a rectangle is

Find the area of the triangle with vertices are(3,5)(2,4)(5,1).

Three vertices are chosen randomly from the seven vertices of a regular 7 -sided polygon. The probability that they form the vertices of an isosceles triangle is

The incentre of the triangle with vertices (1, sqrt3 ) (0,0) (2,0) is

A triangle with vertices (4, 0), (-1, -1), (3, 5) is

The orthocentre of the triangle whose vertices are (5,-2), (-1, 2) and (1,4) is

A three-digit number is selected at random from the set of all three-digit numbers. The probability that the number selected has all the three digits same is 1//9 b. 1//10 c. 1//50 d. 1//100