Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Then the probability distribution of number of jacks is

If $$\tan \theta=\frac{\sin \alpha-\cos \alpha}{\sin \alpha+\cos \alpha}, 0 \leq \alpha \leq \frac{\pi}{2}$$, then the value of $$\cos 2 \theta$$ is

The solution set of $$8 \cos ^2 \theta+14 \cos \theta+5=0$$, in the interval $$[0,2 \pi]$$, is

A ladder 5 meters long rests against a vertical wall. If its top slides downwards at the rate of $$10 \mathrm{~cm} / \mathrm{s}$$, then the angle between the ladder and the floor is decreasing at the rate of ________ rad./s when it's lower end is $$4 \mathrm{~m}$$ away from the wall.