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

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

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- 2x

x+2y=10 is:

• (8,1) A
• (1,8) B
• (6,10) C
• (3,5) D

A point where two of its boundary lines intersect is called

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

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

• 0 A
• 2 B
• -1 C
• -2 D

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

• 0 A
• 2 B
• -2 C
• 3 D

The maximum value of Z = 3x+ 4y subjected to the constrains x+ y≤ 40,x+ 2y≤ 60, x≥ 0 and y≥ 0 is

• 120 A
• 100 B
• 140 C
• 160 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 ________ divides the plane into left and right half planes.

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

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

3x + 4 > 0 is

• equation A
• identity B
• inequality C
• none of these 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

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

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

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

Which of the following is not a solution of system of inequalities 2x- 3y ≤6,2x +y≥ 2,x +2y≤ 8, x≥ 0,y ≥ 0

• (1,0) A
• (0,4) B
• (3,0) C
• (8,0) 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

x = 1 is in the solution of the inequality

• x + 1 > 0 A
• x - 2 > 0 B
• 3x - 1 < 0 C
• x + 2 < 0 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

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 solution set of x < 4 is

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

x = -1 is in the solution of the inequality

• x + 5 < 0 A
• 2x + 3 < 0 B
• x > 0 C
• 2x + 3 > 0 D

Which is not a half plane

• ax + by < c A
• ax + by > c B
• Both A and B C
• None D

If ab > 0 and a < 0, which of the following is negative?

• b A
• -b B
• -a C
• (a - b)² D

ax + by < c is linear inequality in

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

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

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

The point (1,3) is one solution of

• 3x + 5y > 29 A
• 3x + 5y < 7 B
• x + 2y < 4 C
• x + 4y > 3 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