ECAT Pre Engineering MCQ Test With Answer for Chapter 21 Mathematics

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

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

• Solution A
• Domain B
• Range C
• None 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

Optimal solution is found by evaluation the objective function at

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

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

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

If 4 - x >5, then

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

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

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

There may be ______ feasible solution in the feasible region

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

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 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

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

3x + 4 = 0 is

• not inequality A
• equation B
• identity C
• inequality 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 point ________ is in the solution of the inequality 2x - 3y < 4

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

The graph of y < 2 is the

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

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

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

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

Optimize means ______ a quantity under certain constraints

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

Each point of the feasible region is called

• Solution A
• feasible solution B
• Both a & b C
• None 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 solution set of x < 4 is

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

3x + 4 > 0 is

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

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