ECAT (Pre-Eng) Mathematics MCQ's Test For Chapter 21 Linear Inequalities & Linear Programming

x = -1 is in the solution of the inequality

• x + 5 < 0 A
• 2x + 3 < 0 B
• x > 0 C
• 2x + 3 > 0 D

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

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

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

3x + 4 < 0 is

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

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

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

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

• 1 A
• -2 B
• -3 C
• -4 D

Which is not a half plane

• ax + by < c A
• ax + by > c B
• Both A and B C
• None 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 where two of its boundary lines intersect is called

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

There may be ______ feasible solution in the feasible region

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

The graph of y < 2 is the

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

An expression involving any of the symbols <,>,< or > is called

• equation A
• inequality B
• linear equation C
• identity 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

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

Inequalities have ______ symbol

• 2 A
• 3 B
• 4 C
• 1 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

ax + by < c is linear inequality in

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

The real numbers which satisfy an inequality form its

• solution A
• coefficient B
• domain C
• range 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

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

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

ab > 0 and a > 0 then

• a > b A
• a < b B
• a = b C
• None 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

Which of the following is not a solution of system of inequalities 2x- 3y ≤6,2x +y≥ 2,x +2y≤ 8, x≥ 0,y ≥ 0

• (1,0) A
• (0,4) B
• (3,0) C
• (8,0) D

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

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