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

• p < r A
• p > rr B
• p + r < 0 C
• p - r < 0 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 set of ordered pairs (x,y) such that ax+ by < c, and (x,y) such that ax + by>0, are called

• Half planes A
• Boundary B
• Linear Inequalities C
• Feasible regions 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

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

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

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

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

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

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

• Solution A
• Domain B
• Range C
• None 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

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

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

Optimize means ______ a quantity under certain constraints

• Minimize A
• Maximize B
• Maximize or minimize 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 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

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

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

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

x = 0 is in the solution of the inequality

• x > 0 A
• 3x + 4 < 0 B
• x + 3 < 0 C
• x - 2 < 0 D

For which of the following ordered pairs (s, t) is s + t > 2 and s - t < -3?

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

ax + by < c is linear inequality in

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

The real numbers which satisfy an inequality form its

• solution A
• coefficient B
• domain C
• range 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

3x + 4 = 0 is

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

3x + 4 < 0 is

• inequality A
• equation B
• identity C
• not 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

The graph of y < 2 is the

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

There may be ______ feasible solution in the feasible region

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