Free Linear Equations MCQs with Answers
78 Linear Equations MCQs from Mathematics, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.
Linear equations contain variables only to the first power and produce straight-line relationships when represented graphically. Problems involve solving equations with brackets, fractions, and variables on both sides, forming equations from statements, and handling simultaneous linear equations, which differ from quadratic equations by having no squared variable.
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78 questions · page 4 of 4
- A. decision variables
- B. problem constraints
- C. feasible solution
- D. None
Explanation: Each point of the feasible region is called a feasible solution. A feasible solution is a point within the feasible region that satisfies…
Correct answer: feasible solution- A. objective function
- B. explicit function
- C. feasible function
- D. optimal solution
Explanation: A function which is to be maximized or minimized in optimization problems is called the objective function.
Correct answer: objective function- A. infinite
- B. finite
- C. two
- D. three
Explanation: In some theoretical scenarios or special cases, the feasible solution region may be unbounded or extend infinitely in some directions.
Correct answer: infinite- A. simple solution
- B. feasible solution
- C. optimal solution
- D. None
Explanation: The feasible solution that maximizes or minimizes the objective function is called the optimal solution.
Correct answer: optimal solution- A. closed half plane
- B. open half plane
- C. line only
- D. full plane
Explanation: The graph of the inequality \(3x + 2y > 3\) represents an open half plane.
Correct answer: open half plane- A. Circle
- B. Open half plane
- C. Parabola
- D. Plane
Explanation: The solution set of the inequality \(ax + by < c\) is an open half plane.
Correct answer: Open half plane- A. an equation
- B. an inequality
- C. both a and b
- D. None
Explanation: A statement that contains at least one of the symbols < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or…
Correct answer: an inequality- A. variables
- B. constraints
- C. solution
- D. None
Explanation: Nonnegative constraints often refer to constraints on variables in optimization problems, requiring them to be nonnegative.
Correct answer: variables- A. Ellipse
- B. Circle
- C. Region
- D. None
Explanation: The graph of a linear inequality with two variables represents a region in the coordinate plane.
Correct answer: Region- A. convex
- B. bounded
- C. unbounded
- D. None
Explanation: A feasible region is typically defined as convex, meaning that any line segment connecting two points within the region lies entirely…
Correct answer: convex- A. Vertex
- B. solution
- C. boundary
- D. none of these
Explanation: In linear programming, the set of values of decision variables that satisfy all the constraints is referred to as a solution.
Correct answer: solution- A. finite
- B. infinite
- C. unique
- D. None
Explanation: In many cases, the number of ordered pairs that satisfy an inequality is infinite.
Correct answer: infinite- A. corner point
- B. test point
- C. boundary point
- D. None
Explanation: In the context of linear inequalities and half planes, a test point is a point used to determine which side of the boundary line (or…
Correct answer: test point- A. I
- B. II
- C. III
- D. IV
Explanation: The feasible region in the context of linear programming is the region of the coordinate plane that satisfies all the constraints of the…
Correct answer: I- A. optimization
- B. solution
- C. both a & b
- D. none of these
Explanation: The process of maximizing or minimizing a quantity, often subject to certain constraints, is known as optimization.
Correct answer: optimization- A. bounded
- B. unbounded
- C. dashed line
- D. closed
Explanation: A convex region is characterized by the property that the line segment connecting any two points within the region lies entirely within…
Correct answer: dashed line- A. negative
- B. non negative
- C. feasible region
- D. None
Explanation: In the context of linear inequalities and optimization problems, the variables used typically represent quantities that cannot be…
Correct answer: non negative- A. open right half plane
- B. closed right half plane
- C. open left half plane
- D. closed left half
Explanation: The inequality \(x + 2 > 0\) represents all points \(x\) that are greater than 2.
Correct answer: open right half plane