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

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

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

Optimize means ______ a quantity under certain constraints

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

x = ________ is in the solution of 2x - 3 < 0

• 2 A
• -2 B
• 3 C
• 4 D

A function which is to be maximized or minimized is called an

• Explicit function A
• Implicit function B
• Objective function C
• None D

The graph of y < 2 is the

• Left half plane A
• upper half plane B
• Right half plane C
• Lower half plane 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 ab > 0 and a < 0, which of the following is negative?

• b A
• -b B
• -a C
• (a - b)² 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

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

• Solution A
• Domain B
• Range 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

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

• 0 A
• 2 B
• -1 C
• -2 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

3x + 4 > 0 is

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

Maximum value of z =15x +20y subject to 3x+ 4y≤ 12,x,y≥ 0 is given by

• 46 A
• 60 B
• 50 C
• 70 D

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

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 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

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

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

The solution set of x < 4 is

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

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

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

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

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

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

Optimal solution is found by evaluation the objective function at

• All point of feasible region A
• Corner point B
• Origin 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

x = ________ is in the solution of 2x - 5 > 0

• 0 A
• 2 B
• -2 C
• 3 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