The distance of the point $(1,0,-3)$ from the plane $x-y-z=9$ measured parallel to the line $\dfrac{x-2}{2} = \dfrac{y+2}{3} = \dfrac{z-6}{-6}$ is

The difference between the maximum and minimum values of the objective function $Z = 3x + 5y$, subject to the constraints $x + 3y \leq 60$, $x + y \geq 10$, $x - y \leq 0$, $x, y \geq 0$ is

For the following probability distribution, the standard deviation of the random variable X is

X	2	3	4
p(X=$x$)	0.2	0.5	0.3

A random variable X has the following probability distribution

X	1	2	3	4	5	6	7	8
P(X=$x$)	0.15	0.23	0.12	0.10	0.20	0.08	0.07	0.05

For the event E = { X is a prime number } and F = { X < 4 }, P(E$\cup$F) =