If the lines $\dfrac{x-1}{2} = \dfrac{y+1}{3} = \dfrac{z-1}{4}$ and $\dfrac{x-3}{1} = \dfrac{y-c}{2} = \dfrac{z}{1}$ intersect, then the radius of circle $x^2 + y^2 - 4x + 10y + c = 0$ is

The corner points of the feasible region determined by a system of linear constraints are $(0, 3), (1, 1)$ and $(3, 0)$. If the objective function is $z = px + qy$, where $p, q > 0$, then the condition on p and q such that the minimum of z occurs at both $(3, 0)$ and $(1, 1)$ is _____

If $X \sim B(n, p)$, then the value of $\dfrac{P(X = k)}{P(X = k - 1)}$ is

A player tosses two fair coins, he wins Rs. $5$ if two heads appear, Rs. $3$ if one head appears and Rs. $2$ if no head appears, then the variance of the winning amount is