The incentre of the $$\triangle A B C$$, whose vertices are $$A(0,2,1), B(-2,0,0)$$ and $$C(-2,0,2)$$, is

The acute angle between the line joining the points $$(2,1,-3),(-3,1,7)$$ and a line parallel to $$\frac{x-1}{3}=\frac{y}{4}=\frac{z+3}{5}$$ through the point $$(-1,0,4)$$ is

A random variable $$X$$ has the probability distribution

For the events $$E=\{X$$ is a prime number $$\}$$ and $$F=\{x<5\}, P(E U F)$$ is

The shaded area in the given figure is a solution set for some system of inequations. The maximum value of the function $$z=10 x+25 y$$ subject to the linear constraints given by the system is