ECAT Pre Engineering Mathematic MCQ Test With Answer for Chapter 21 (Linear Inequalities and Linear Programming)

Which of the following ordered pair is a solution of the inequality x+2y<6?

• (2,3) A
• (2,2) B
• (6,0) C
• (1,1) D

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

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

x = ________ is in the solution of 2x - 3 < 0

• 2 A
• -2 B
• 3 C
• 4 D

3x + 4 = 0 is

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

A point where two of its boundary lines intersect is called

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

(1,0) is in the solution of the inequality

• 3x + 2y > 8 A
• 2x - 3y < 4 B
• 2x + 3y > 3 C
• x - 2y < -5 D

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

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

ab > 0 and a > 0 then

• a > b A
• a < b B
• a = b C
• None D

The real numbers which satisfy an inequality form its

• solution A
• coefficient B
• domain C
• range D

3x + 4 < 0 is

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

The graph of the linear equation of the form ax =by = c is a line which divided the plane into:

• Two similar regions A
• Two disjoint regions B
• Four equal parts C
• One region D

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

3x + 4 < 0 is

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

The point ________ is in the solution of the inequality 2x - 3y > 5

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

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

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

x = ________ is in the solution of 2x - 5 > 0

• 0 A
• 2 B
• -2 C
• 3 D

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

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

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

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

(1, 1) is the in the solution of the inequality

• 3x + 4y > 3 A
• 2x + 3y < 2 B
• 4x = 3y > 5 C
• 2c - 3y > 2 D

If 4 - x >5, then

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

There may be ______ feasible solution in the feasible region

• Infinite A
• Finite B
• Defined C
• None of above 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

The graph of linear equation 2x + 3y = 10

• Parabola A
• Circle B
• Hyperbola C
• Straight line D

A ________ divides the plane into left and right half planes.

• Vertical line A
• Horizontal line B
• Non vertical line C
• Inequality 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

Which is in the solution set of 4x - 3y < 2

• (3, 0) A
• (4, 1) B
• (1, 3) C
• None D

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

• Vertex of the solution A
• Feasible point B
• Point of inequality C
• Null point of the solution region 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