Chapter 5 Linear Equations and Inequalities
MCQs Online Test
(1) What is the solution to the inequality 2x/3 – 1 < 0?
a) x > 3/2
b) x < 3/2
c) x ≥ 3/2
d) x ≤ 3/2
(2) Which of the following is a solution to the inequality x + 2y < 6?
a) (2,3)
b) (0,2)
c) (4,1)
d) (3,2)
(3) What type of line is used to graph the inequality x + 2y < 6?
a) A dashed line
b) A solid line
c) A vertical line
d) A horizontal line
(4) Which region represents the solution to x + 2y < 6?
a) The region below the line
b) The region above the line
c) The region on the line
d) The entire coordinate plane
(5) What is the boundary line for the inequality x + 2y < 6?
a) x + 2y = 6
b) x + 2y > 6
c) x – 2y = 6
d) 2x + y = 6
(6) Which of the following is a linear inequality in two variables?
a) 2x + 3y ≤ 5
b) x² + y ≤ 7
c) x³ + y < 10
d) x + y² ≥ 4
(7) What is the x-intercept of the line x + 2y = 6?
a) (6,0)
b) (0,6)
c) (3,0)
d) (0,3)
(8) What is the y-intercept of the line x + 2y = 6?
a) (0,3)
b) (3,0)
c) (0,6)
d) (6,0)
(9) Which of the following operations does not change the sense of an inequality?
a) Adding the same number to both sides
b) Multiplying by a negative number
c) Dividing by a negative number
d) Squaring both sides
(10) What is the solution set of 2x/3 − 1 < 0 represented on a real line?
a) (-∞, 3/2]
b) (-∞, 3/2)
c) (3/2, ∞)
d) [3/2, ∞)
(11) Which of the following represents a linear inequality?
a) 2x + 3y ≥ 6
b) x² + y ≥ 6
c) 3x – 4y² ≤ 8
d) x³ + y ≤ 10
(12) What is the boundary line for the inequality 3x − 4y ≤ 12?
a) 3x – 4y = 12
b) 3x – 4y ≥ 12
c) 3x + 4y = 12
d) -3x + 4y = 12
(13) Which region represents the solution to the inequality y < 2x + 1?
a) The region below the line
b) The region above the line
c) The line itself
d) The entire coordinate plane
(14) For the inequality 5x + 10y ≥ 20, which point is part of the solution region?
a) (2,2)
b) (0,1)
c) (1,0)
d) (3,-1)
(15) What is the feasible region in a system of linear inequalities?
a) The overlapping solution region
b) The entire coordinate plane
c) The region outside all constraints
d) The points where lines intersect
(16) Which of the following is a non-negative constraint?
a) x ≥ 0
b) x ≤ 0
c) x < 0
d) x = 0
(17) What is the solution region for the inequality x ≥ −3?
a) x values greater than or equal to -3
b) x values less than -3
c) All x values
d) No solution
(18) Which of the following points lies in the solution region of 2x + 3y ≤ 6?
a) (0,0)
b) (3,2)
c) (2,2)
d) (4,1)
(19) What is the boundary line for the inequality y > −2x + 4?
a) y = -2x + 4
b) y = 2x – 4
c) x = -2y + 4
d) x = 2y – 4
(20) Which of the following inequalities represents a closed half-plane?
a) y ≥ 3x + 2
b) y > 3x + 2
c) y < 3x + 2
d) x > 3y + 2
(21) Which of the following is a linear equation?
a) 2x + 1 = 1
b) x² + 3 = 7
c) 2x³ – 5 = 0
d) |x| + 4 = 10
(22) What is the solution of 5x – 10 = 10?
a) x = 4
b) x = 5
c) x = 2
d) x = 0
(23) If 7x + 4 ≤ 6x + 6, then x belongs to the interval:
a) (-∞, 2]
b) (2, ∞)
c) [2, ∞)
d) (-∞, 2)
(24) A vertical line divides the plane into:
a) Two halves
b) Three regions
c) Four quadrants
d) Infinite regions
(25) The linear equation formed out of the linear inequality is called:
a) Associated equation
b) Linear equation
c) Quadratic equation
d) None of these
(26) 3x + 4 < 0 is:
a) Inequality
b) Equation
c) Not an inequality
d) Identity
(27) Corner point is also called:
a) Vertex
b) Code
c) Curve
d) Region
(28) In linear programming, the function to be maximized or minimized is called:
a) Objective function
b) Constraint
c) Feasible region
d) Optimal solution
(29) The feasible region in a linear programming problem is defined by:
a) The constraints
b) The objective function
c) The corner points
d) The optimal solution
(30) The optimal solution in linear programming is found at:
a) The corner points of the feasible region
b) Any point in the feasible region
c) The center of the feasible region
d) Outside the feasible region
(31) Which of the following is a constraint in a linear programming problem?
a) An equation or inequality that limits the feasible region
b) The objective function
c) A point in the feasible region
d) The optimal solution
(32) The process of finding the optimal solution in linear programming involves:
a) Graphing the objective function
b) Finding the intersection of all constraints
c) Evaluating the objective function at each corner point
d) Both (b) and (c)
(33) Which of the following is true about the feasible region?
a) It is always bounded
b) It is always unbounded
c) It can be bounded or unbounded
d) It is always a triangle
(34) The point where the constraints intersect is called:
a) Feasible point
b) Corner point
c) Optimal point
d) Boundary point
(35) Which of the following is a necessary condition for a linear programming problem?
a) The objective function must be quadratic
b) The constraints must be linear
c) The feasible region must be circular
d) The solution must be at the origin
9th Class New Math Chapter 5 MCQs Online Test – Linear Equations and Inequalities
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9th Class New Math Chapter 5 MCQs Online Test
Why Take an Online Test for Linear Equations and Inequalities?
Concept Clarity – Solving multiple questions helps you understand the concepts of equations and inequalities better.
Exam Preparation – Practice tests prepare you for board exams by familiarizing you with important question patterns.
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Key Topics Covered in Chapter 5
Understanding linear equations in one variable
Solving equations using different methods
Introduction to inequalities and their properties
Graphical representation of inequalities
Solving mention word problems involving linear equations and inequalities in chapter 5
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