If the distance of point $B(2,1,-3)$ from the line passing through the point $A(4,-2,2)$, and parallel to the vector $\vec{c} = -4\hat{i} - 6\hat{j} - 2\hat{k}$ is $x$, then $x^4 + x^2 + 541 =$

In the following figure, the shaded region represents the system of constraints:

On average, one out of 10 persons is busy. If six persons are selected at random, then the probability that at least 5 of them will be busy is...

If a discrete random variable $X$ takes the values $1, 2, 3, 4$ such that $2P(X = 1) = 3P(X = 2) = P(X = 3) = 5P(X = 4)$, then $P(X = 4) = \ldots$