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 .....

If the following function is probability density function of r.v. X
$f(x) = kx^2(1-x)$, for $0 < x < 1 = 0$, otherwise, then the value of $k$ is