Calculate the common difference of the A.P.

For the triangle ABC formed by the points A (4, -6), B (3, -2) and C (5, 2), verify that median divides the triangle into two triangles of equal area.

The sum of first m terms of an AP is 4m² – m. If its n^th term is 107, find the value of n. Also find the 21th term of this A.P.

Two dice are thrown simultaneously. Find the probability of getting a doublet.

For what value of k, are the roots of the quadratic equation y² + k² = 2 (k + 1) y equal?