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

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

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

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

The points (x, y) which satisfy a linear inequality in two variables x and y from its

• domain A
• range B
• solution C
• none of these D

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

• (3, 0) A
• (4, 1) B
• (1, 3) 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

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

• (0, -2) A
• (1, -3) B
• (2, 2) 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

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

• b A
• -b B
• -a C
• (a - b)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

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

3x + 4 > 0 is

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

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

• 0 A
• 2 B
• -1 C
• -2 D

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

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

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

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

ab > 0 and a > 0 then

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

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

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

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

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 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 feasible region which can be enclosed within a circle is called

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

3x + 4 = 0 is

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

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

• 2x + y > 8 A
• 2x + y < 6 B
• 2x - y > 1 C
• 2x + 3y < 2 D

x = ________ is in the solution of 2x + 3 > 0

• 1 A
• -2 B
• -3 C
• -4 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

3x + 4 > 0 is

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

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

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

The solution set of the inequality ax + by < c is

• straight line A
• half plane B
• parabola C
• none of these D