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

The probability mass function of a random variable X is given by
$P(X = x) = \dfrac{{}^{5}C_x}{2^5}$, for $x = 0, 1, 2, 3, 4, 5$ and $= 0$, otherwise.
Then which of the following is correct?