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

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

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

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

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

Inequalities have ______ symbol

• 2 A
• 3 B
• 4 C
• 1 D

3x + 4 > 0 is

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

(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

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

Each point of the feasible region is called

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

3x + 4 < 0 is

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

Optimal solution is found by evaluation the objective function at

• All point of feasible region A
• Corner point B
• Origin C
• None 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 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 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

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

ax + by < c is linear inequality in

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

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

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

There may be ______ feasible solution in the feasible region

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

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

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

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

If 4 - x >5, then

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

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

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

Optimize means ______ a quantity under certain constraints

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