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

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

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

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

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

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

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

(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

3x + 4 > 0 is

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

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

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

ax + by < c is linear inequality in

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

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 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

x is a member of the set [-1, 0, 3, 5] y is a member of the set {-2, 1, 2, 4} which is possible?

• x - y = -6 A
• x - y < -6 B
• x - y > -6 C
• None D

A point where two of its boundary lines intersect is called

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

If x < y, 2x = A, and 2y = B, then

• A = B A
• A < B B
• A < x C
• B < y 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

x = 0 is in the solution of the inequality

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

3x + 4 = 0 is

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

The graph of y < 2 is the

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

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

• 0 A
• 2 B
• -1 C
• -2 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 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 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

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

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

The total cost of 2 apples and 3 oranges is $1.70, which of the following is true

• The cost of one apple A
• The cost of one orange B
• Both have equal cost per item C
• Cost of each single item can not be determined 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