A Linear Programming Problem is as follows:

Maximize/Minimize objective function Z = 2x $$-$$ y + 5

Subject to the constraints

3x + 4y $$\le$$ 60

x + 3y $$\le$$ 30

x $$\ge$$ 0, y $$\ge$$ 0

If the corner points of the feasible region are A (0, 10), B (12, 6), C (20, 0) and O (0, 0) then which of the following is true?

If x = $$-$$4 is a root of $$\left| {\matrix{ x & 2 & 3 \cr 1 & x & 1 \cr 3 & 2 & x \cr } } \right| = 0$$, then the sum of the other two roots is

The absolute maximum value of the function $$f(x) = 4x - {1 \over 2}{x^2}$$ in the interval $$\left[ { - 2,{9 \over 2}} \right]$$ is

In a sphere of radius r, a right circular cone of height h having maximum curved surface area is inscribed. The expression for the square of curved surface of cone is