The equation of the plane passing through the point $(1,2,1)$ and perpendicular to the planes $x + 2y + 2z - 7 = 0$ and $3x + 3y + 2z - 5 = 0$ is

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