Maths

Let S = $\left\{x\in \left[-6,3\right]-\left\{-2,2\right\}:\frac{\left|x+3\right|-1}{\left|x\right|-2}\ge 0\right\}$ and T = $\left\{x\in Z:x^2-7\left|x\right|+9\le 0\right\}.$ Then the number of element is $S\cap T$ is :

In a LPP, the maximum value of the objective function $Z=ax+by$ is always finite.

In a LPP, the minimum value of the objective function $Z=ax+by$ is always 0 if the origin is one of the corner points of the feasible region.

The maximum value of the objective function $Z=ax+by$ in a LPP always occurs at only one corner point of the feasible region.

If the feasible region for a LPP is unbounded, maximum or minimum of the objective function $Z=ax+by$  may or may not exist.

The feasible region for an LPP is always a __________ polygon.

A corner point of a feasible region is a point in the region which is the __________ of two boundary lines.

A feasible region of a system of linear inequalities is said to be __________ if it can be enclosed within a circle.

In a LPP, if the objective function $Z=ax+by$ has the same maximum value on two corner points of the feasible region, then every point on the line segment joining these two points gives the same __________ value.

If the feasible region for a LPP is __________, then the optimal value of the objective function $Z=ax+by$ may or may not exist.