Two dice are rolled simultaneously. The probability that the sum of the two numbers on the dice is a prime number, is

If the acute angle between the lines given by $$\mathrm{a x^2+2 h x y+b y^2=0}$$ is $$\frac{\pi}{4}$$, then $$\mathrm{4 h^2=}$$

A wire of length 20 units is divided into two parts such that the product of one part and cube of the other part is maximum, then product of these parts is

The shaded part of the given figure indicates the feasible region. Then the constraints are