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

The graph of y < 2 is the

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

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

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

3x + 4 = 0 is

• not inequality A
• equation B
• identity 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

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

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

3x + 4 < 0 is

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

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

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

• > or < A
• > or < B
• = or≠ C
• = or > 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 corner point of the boundary lines, x- 2x

x+2y=10 is:

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

If 4 - x >5, then

• x > 1 A
• x > -1 B
• x < 1 C
• x < -1 D

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

The solution set of x < 4 is

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

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

• 1 A
• -2 B
• -3 C
• -4 D

Each point of the feasible region is called

• Solution A
• feasible solution B
• Both a & b C
• None 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

Optimize means ______ a quantity under certain constraints

• Minimize A
• Maximize B
• Maximize or minimize 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

The real numbers which satisfy an inequality form its

• solution A
• coefficient B
• domain C
• range 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

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

• 2x + y > 7 A
• x - y > 2 B
• 3x + 5y < 6 C
• 2x + y < 6 D

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

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

A point where two of its boundary lines intersect is called

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

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