Mathematics ECAT Pre Engineering Chapter 21 Linear Inequalities and Linear Programming Online Test

The point _________ is in the solution of the inequality 2x + 3y < 5

• (1,1) A
• (2,2) B
• (0,1) C
• (0,2) D

The graph of y> 0 is the upper - half of:

• y-axis A
• x-axis B
• 1st and 4th quandrant C
• 2nd and 3rd quadrant D

2x + 3y > 4 is a linear inequality in

• one variable A
• two variables B
• three variables C
• none of these D

The liner equation ax + by = c is called _________ of the inequality ax +by > c.

• Associated equation A
• Non-associated equation B
• disjoint equation C
• Feasible equation D

Inequalities have ______ symbol

• 2 A
• 3 B
• 4 C
• 1 D

A point (x,y) which satisfy a linear inequality in two variables form its

• Solution A
• Domain B
• Range C
• None D

If 4 - x >5, then

• x > 1 A
• x > -1 B
• x < 1 C
• x < -1 D

Corner point of the system x - y≤ 2,x + y≤ 4,2x -y≤ 6,x≥ 0,y≥ 0

• (1,4) A
• (4,2) B
• (3,1) C
• (4,1) D

For graphing a linear inequality, solid line is drawn if the inequality involves the symbols:

• > or < A
• > or < B
• = or≠ C
• = or > D

The feasible region which can be enclosed within a circle is called

• Bounded region A
• Convex region B
• Unbounded region C
• None D

Optimal solution is found by evaluation the objective function at

• All point of feasible region A
• Corner point B
• Origin C
• None D

The solution set of x < 4 is

• -∞< x < 4 A
• -∞> x > 4 B
• -∞< x < 2 C
• -∞> x > 2 D

3x + 4 < 0 is

• not inequality A
• equation B
• identity C
• inequality D

A point of a solution region where two of its boundary lines intersect, is called

• Boundary A
• Inequality B
• Half plane C
• Vertex D

x = _________ is in the solution of 2x + 3 < 0

• 0 A
• 2 B
• -1 C
• -2 D

A farmer possesses 100 hectometers of land and wants to grow corn and wheat. Cultivations of corn requires 3 hours per hectometer while cultivation of wheat requires 2 hours per hectometer. Working hours cannot exceed 240. If he gets a profit of Rs. 20 per hectometer for corn and Rs. 15 per hectometer for wheat. The profit function for the farmer is

• P(x, y) = 20x + 15y A
• P(x, y) = 2x + 3y B
• P(x, y) = x + y C
• P(x, y) = 3x + 2y D

Sum of two quantities is at least 20 is denoted by

• x +y =20 A
• x +y≥ 20 B
• x +y≠ 20 C
• x +y≤20 D

An expression involving any of the symbols <,>,< or > is called

• equation A
• inequality B
• linear equation C
• identity D

• p < r A
• p > rr B
• p + r < 0 C
• p - r < 0 D

If 4 - x >5, then

• x > 1 A
• x > -1 B
• x < 1 C
• x < -1 D

A point where two of its boundary lines intersect is called

• Corner point A
• Feasible point B
• Vertex C
• Feasible solution D

s > t then

• (s - t)²> (t - s)² A
• (s - t)²< (t - s)² B
• (s - t)²= (t - s)² C
• None D

The point ________ is in the solution of the inequality 4x - 3y < 2

• (0,1) A
• (2,1) B
• (2,2) C
• (3,3) D

ax + by < c is linear inequality in

• four variables A
• three variables B
• two variables C
• one variable D

Multiplying each side of an inequality by (-1) will:

• Not effect A
• Change the sign B
• Become zero C
• Not defined D

The corner point of the boundary lines, x-2y

2x + y = 2 is:

• (2,6) A
• (6,2) B
• (-2,2) C
• (2,-2) D

Optimal solution is found by evaluation the objective function at

• All point of feasible region A
• Corner point B
• Origin C
• None D

A function which is to be maximized or minimized is called an

• Explicit function A
• Implicit function B
• Objective function C
• None D

If -1 < x < 0, which of the following statements must be true?

• x < x²< x³ A
• x < x³< x² B
• x²< x³< x C
• x²< x < x³ D

The graph of y < 2 is the

• Left half plane A
• upper half plane B
• Right half plane C
• Lower half plane D