The probability that 3 vertices of a cube chosen at random form an equilateral triangle be `a/b` when a and b are co-prime, then `|a - b| =`

If triangles are formed by joining the vertices of a cube then number of equilateral triangles formed is

If three vertices of a regular hexagon are chosen at random, then the chance that they form an equilateral triangle is :

If the vertices of an equilateral triangle ABC are (1,1),(-1,-1) and (a,b) then

Two different numbers are selected at random from the set S={1, 2, 3, ……10}, then the probability that sum of selected numbers is divisible by 2 a/b, where a and b are co-prime then b is equal to ___.

Two different numbers are selected at random from the set S={1, 2, 3, ……10}, then the probability that sum of selected numbers is divisible by 2 a/b, where a and b are co-prime then b is equal to ___.

Show that the points (a,b,c),(b,c,a),(c,a,b) are the vertices of an equilateral triangle.

Show that A(a,b,c),B(b,c,a) and C(c,a,b) are the vertices of an equilateral triangle.