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 :

Let z₁ and z₂ be any two non-zero complex numbers such that   $$3\left| {{z_1}} \right| = 4\left| {{z_2}} \right|.$$  If  $$z = {{3{z_1}} \over {2{z_2}}} + {{2{z_2}} \over {3{z_1}}}$$  then :