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

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

The graph of y < 2 is the

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

The real numbers which satisfy an inequality form its

• solution A
• coefficient B
• domain C
• range 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

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

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

The solution set of x < 4 is

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

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

• Solution A
• Domain B
• Range C
• None 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 linear equation 2x + 3y = 10

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

ab > 0 and a > 0 then

• a > b A
• a < b B
• a = b C
• None 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

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

3x + 4 > 0 is

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

Each point of the feasible region is called

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

Inequalities have ______ symbol

• 2 A
• 3 B
• 4 C
• 1 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

2x + 3y > 4 is a linear inequality in

• one variable A
• two variables B
• three variables C
• none of these 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

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

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

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

• 2 A
• -2 B
• 3 C
• 4 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

Which is not a half plane

• ax + by < c A
• ax + by > c B
• Both A and B C
• None D

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

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

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

• 1 A
• -2 B
• -3 C
• -4 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

3x + 4 = 0 is

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

r + 3 >5 then which is true

• r + 2 > 4 A
• r + 2 < 4 B
• r + 2 = 4 C
• None D

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