If $$\int \frac{\cos 8 x+1}{\cot 2 x-\tan 2 x} \mathrm{~d} x=\mathrm{A} \cos 8 x+\mathrm{c}$$, where $$\mathrm{c}$$ is an arbitrary constant, then the value of $$\mathrm{A}$$ is

The set of all points, where the derivative of the functions $$\mathrm{f}(x)=\frac{x}{1+|x|}$$ exists, is

In triangle $$\mathrm{ABC}$$ with usual notations $$\mathrm{b}=\sqrt{3}, \mathrm{c}=1, \mathrm{~m} \angle \mathrm{A}=30^{\circ}$$, then the largest angle of the triangle is

A fair die is tossed twice in succession. If $$\mathrm{X}$$ denotes the number of fours in two tosses, then the probability distribution of $$\mathrm{X}$$ is given by