If the lines $L_1: \dfrac{x-1}{-3} = \dfrac{y-2}{2k} = \dfrac{z-3}{2}, L_2: \dfrac{x-1}{3k} = \dfrac{y-5}{1} = \dfrac{z-6}{-5}$ are perpendicular to each other, then the equation of a plane containing the line $L_1$ and parallel to the line $L_2$ for the value of $k$ that satisfies this condition is ...

A plane meets the coordinate axes at points A, B and C, such that the centroid of a triangle ABC is $\left(2, -\dfrac{2}{3}, \dfrac{1}{2}\right)$. The perpendicular distance from the origin to this plane is...

The point at which the maximum value of $x + y$ subject to constraints $x + 2y \leq 70$ and $2x + y \leq 95, x \geq 0, y \geq 0$ is.

Let $X \sim B(n, p)$. If $E(X) = 2$ and $\text{Var}(X) = 1$, then the probability of getting at most one success is .....