For the linear programming problem, $x + 2y \leq 10,\ 3x + y \leq 12,\ x, y \geq 0$, the maximum value of $z = 5x + 10y$ occurs at every point on the line segment joining the points..

The region satisfying the inequalities $y - x \geq 2,\ x + y \leq 5,\ x \geq 0$ and $y \geq 0$ is

If the mean and the variance of a binomial variate X are 1 and 0.75 respectively, then which of the following is true?

A box contains 8 red and N green balls. Two balls are drawn at random from it. If X is the random variable representing the number of green balls drawn and $E(X) = 1.2$, then $N = \ldots$