If the straight line, 2x – 3y + 17 = 0 is perpendicular to the line passing through the points (7, 17) and (15, $$\beta $$), then $$\beta $$ equals :

Considering only the principal values of inverse functions, the set
A = { x $$ \ge $$ 0: tan^$$-$$1(2x) + tan^$$-$$1(3x) = $${\pi \over 4}$$}

The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now form an A.P. Then the sum of the original three terms of the given G.P. is :

Let y = y(x) be the solution of the differential equation, x$${{dy} \over {dx}}$$ + y = x log_e x, (x > 1). If 2y(2) = log_e 4 $$-$$ 1, then y(e) is equal to :