If P is a point on the parabola y = x² + 4 which is closest to the straight line y = 4x $$-$$ 1, then the co-ordinates of P are :

The vector equation of the plane passing through the intersection

of the planes $$\overrightarrow r .\left( {\widehat i + \widehat j + \widehat k} \right) = 1$$ and $$\overrightarrow r .\left( {\widehat i - 2\widehat j} \right) = - 2$$, and the point (1, 0, 2) is :

The angle of elevation of a jet plane from a point A on the ground is 60$$^\circ$$. After a flight of 20 seconds at the speed of 432 km/hour, the angle of elevation changes to 30$$^\circ$$. If the jet plane is flying at a constant height, then its height is :

The probability that two randomly selected subsets of the set {1, 2, 3, 4, 5} have exactly two elements in their intersection, is :