The sum of all two digit positive numbers which when divided by 7 yield 2 or 5 as remainder is -

Consider the quadratic equation (c – 5)x² – 2cx + (c – 4) = 0, c $$ \ne $$ 5. Let S be the set of all integral values of c for which one root of the equation lies in the interval (0, 2) and its other root lies in the interval (2, 3). Then the number of elements in S is -

If the area enclosed between the curves y = kx² and x = ky², (k > 0), is 1 square unit. Then k is -

A point P moves on the line 2x – 3y + 4 = 0. If Q(1, 4) and R (3, – 2) are fixed points, then the locus of the centroid of $$\Delta $$PQR is a line :