The integer 'k', for which the inequality x² $$-$$ 2(3k $$-$$ 1)x + 8k² $$-$$ 7 > 0 is valid for every x in R, is :

A tangent is drawn to the parabola y² = 6x which is perpendicular to the line 2x + y = 1. Which of the following points does NOT lie on it?

The total number of positive integral solutions (x, y, z) such that xyz = 24 is :

A man is observing, from the top of a tower, a boat speeding towards the lower from a certain point A, with uniform speed. At that point, angle of depression of the boat with the man's eye is 30$$^\circ$$ (Ignore man's height). After sailing for 20 seconds, towards the base of the tower (which is at the level of water), the boat has reached a point B, where the angle of depression is 45$$^\circ$$. Then the time taken (in seconds) by the boat from B to reach the base of the tower is :