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

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

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

ax + by < c is linear inequality in

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

3x + 4 > 0 is

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

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

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

r + 3 >5 then which is true

• r + 2 > 4 A
• r + 2 < 4 B
• r + 2 = 4 C
• None D

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

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

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

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

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

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

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

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

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

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

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

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

3x + 4 > 0 is

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

Optimize means ______ a quantity under certain constraints

• Minimize A
• Maximize B
• Maximize or minimize C
• None of these D

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

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

The graph of y < 2 is the

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

Inequalities have ______ symbol

• 2 A
• 3 B
• 4 C
• 1 D

Order (or sense) of an inequality is changed by multiplying or dividing its each side by a:

• Zero A
• one B
• negative constant C
• Non negative constant 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

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

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

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

3x + 4 = 0 is

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