Linear Programming — Class 12 MCQs with Answers
Class 12 CBSE Mathematics · Chapter 12
90 practice questions · 30 Easy · 30 Medium · 30 Hard · Updated
Practise the most important Class 12 CBSE Mathematics questions from Chapter 12, "Linear Programming". You get 9 timed quizzes made from 90 NCERT-based MCQs, with answers and explanations. The questions are split into 30 Easy, 30 Medium and 30 Hard. Warm up on the basics, then move on to the exam-level questions that set top scorers in CBSE & Maharashtra HSC Board exams, JEE Main, MHT-CET and JEE Advanced apart.
To score well in "Linear Programming", focus on fast problem-solving, formula recall and step-by-step working. Each MCQ here is timed and uses exam-style marking (+4 correct, −1 wrong, 0 skipped). This trains you to stay accurate under time pressure, as real papers need. Every question has a short explanation, so a wrong answer becomes a quick lesson. It is the fastest way to fix gaps before a test.
Use this chapter for focused revision. Start with the Easy set to check your basics on Linear Programming, then move to Medium and Hard to practise applying them. Your accuracy, streaks and XP save automatically. This chapter also adds to your overall Class 12 Mathematics mastery score. 14 sample questions are solved in full below, with the answer and a worked explanation. Sign in free to start practising.
Key concepts: Linear Programming (Class 12 Mathematics)
Linear programming optimises a linear objective Z = ax + by subject to linear inequality constraints and non-negativity. The chapter builds the feasible region graphically, identifies its corner points, and applies the corner-point method — the optimum of a bounded region lies at a vertex — with manufacturing and diet problems.
- Linear programming problem
- Optimising (maximising or minimising) a linear objective function of decision variables subject to linear constraints.
- Objective function
- The quantity to optimise, written Z = ax + by; profit is maximised, cost is minimised.
- Decision variables
- The unknowns x and y (e.g. units of two products) chosen to optimise Z; usually restricted to be non-negative.
- Constraints
- Linear inequalities such as x + y ≤ 10 that limit the variables, arising from resources, demand or capacity.
Linear Programming — important questions & MCQs with answers (Class 12 Mathematics)
14 solved questions from this chapter's difficulty levels, each with its answer and explanation. The other 76 are timed and scored when you sign in.
- Q1Easy
In LPP, the function to optimise is called:
A.VariableB.ConstraintC.Objective function✓ CorrectD.BoundaryAnswer: C. Objective function
Explanation: The expression being maximised or minimised, like Z = 3x + 4y, is the objective function — the constraints only bound where Z is evaluated, they aren't what you optimise.
- Q2Easy
Linear Programming Problem (LPP) involves:
A.Solving differential equationsB.Maximising or minimising a linear function under linear constraints✓ CorrectC.Quadratic functionsD.Random optimisationAnswer: B. Maximising or minimising a linear function under linear constraints
Explanation: An LPP means maximising or minimising a linear function subject to linear constraints — swap in a squared term or a derivative and it stops being a standard LPP.
- Q3Easy
The optimal value of the objective function of a linear programming problem, when it exists, occurs at:
A.A corner point of the feasible region✓ CorrectB.A point outside the feasible regionC.The centre of the feasible regionD.Any interior pointAnswer: A. A corner point of the feasible region
Explanation: By the corner point theorem the optimal value, if it exists, occurs at a corner point of the feasible region.
- Q4Easy
Constraints in LPP are:
A.NoneB.QuadraticC.DifferentialD.Linear inequalities✓ CorrectAnswer: D. Linear inequalities
Explanation: Every constraint in an LPP must be a linear inequality (or equation) in the decision variables — quadratic or differential terms fall outside standard LPP theory entirely.
- Q5Easy
In LPP, the function to be optimised is called:
A.Objective function✓ CorrectB.ConstraintC.Feasible regionD.VariableAnswer: A. Objective function
Explanation: The function being optimised in an LPP — for example Z = 5x + 3y — is called the objective function; constraints and the feasible region are separate concepts, not the same thing.
- Q6Easy
Constraints in LPP are:
A.ArbitraryB.QuadraticC.Differential equationsD.Linear inequalities (or equations)✓ CorrectAnswer: D. Linear inequalities (or equations)
Explanation: LPP constraints are always linear inequalities or equations, such as x + y ≤ 10 — never quadratic terms or differential equations, which would take the problem out of linear programming.
- Q7Medium
If a factory can make at most 20 units of a product, the corresponding constraint is written as:
A.x = 20B.x < 0C.x ≤ 20✓ CorrectD.x ≥ 20Answer: C. x ≤ 20
Explanation: An upper limit on production translates directly into a less-than-or-equal constraint.
- Q8Medium
Maximise Z = 3x + 4y subject to x + y ≤ 4, x ≥ 0, y ≥ 0. Vertices of feasible region:
A.RandomB.(0, 0), (4, 0), (0, 4)✓ CorrectC.Only originD.(2, 2)Answer: B. (0, 0), (4, 0), (0, 4)
Explanation: The triangle x + y ≤ 4 with x, y ≥ 0 has vertices where the boundary line meets each axis and the origin: (0, 0), (4, 0), and (0, 4) — not a random or single point.
- Q9Medium
Feasible region is the:
A.OriginB.Set of points satisfying all constraints✓ CorrectC.Single pointD.Whole planeAnswer: B. Set of points satisfying all constraints
Explanation: The feasible region is the intersection of every constraint half-plane at once, including x ≥ 0 and y ≥ 0 — satisfying just one inequality alone isn't enough.
- Q10Medium
For above LPP, maximum Z is at:
A.(0, 0)B.(4, 0)C.(0, 4) with Z = 16✓ CorrectD.(2, 2)Answer: C. (0, 4) with Z = 16
Explanation: Checking Z = 3x + 4y at every vertex gives 0 at (0,0), 12 at (4,0), and 16 at (0,4) — the largest value wins, so the maximum is 16 at (0, 4), not at the origin.
- Q11Medium
Optimum value of LPP (bounded region) occurs at:
A.MidpointB.CentreC.Origin alwaysD.A corner (vertex) of feasible region✓ CorrectAnswer: D. A corner (vertex) of feasible region
Explanation: By the corner-point theorem, on a bounded feasible region both the maximum and minimum of Z occur at a vertex, never at the centre or an interior point — always check every corner.
- Q12Hard
LPP applications include:
A.Sound wavesB.Random shufflingC.Diet, transport, manufacturing optimisation✓ CorrectD.Cooking onlyAnswer: C. Diet, transport, manufacturing optimisation
Explanation: Diet, transportation, and manufacturing problems are classic LPP applications because each optimises a linear cost or profit function under linear resource limits — not games of chance like shuffling.
- Q13Hard
Maximise Z = 4x + 5y subject to x + y ≤ 6, x + 2y ≤ 8, x, y ≥ 0:
A.At (0, 4)B.Vertices: (0, 0), (6, 0), (4, 2), (0, 4). Z max at (4, 2) = 26✓ CorrectC.At (6, 0)D.OriginAnswer: B. Vertices: (0, 0), (6, 0), (4, 2), (0, 4). Z max at (4, 2) = 26
Explanation: Z = 4x + 5y at the vertices (0,0), (6,0), (4,2), (0,4) gives 0, 24, 26, and 20 — the maximum is 26 at (4, 2), beating the larger-looking corner (6,0) which only reaches 24.
- Q14Hard
If feasible region is unbounded, optimum may:
A.Be infinity alwaysB.Always existC.Be zeroD.Not exist (problem may be unbounded)✓ CorrectAnswer: D. Not exist (problem may be unbounded)
Explanation: An unbounded region lets Z grow without limit in the open direction, so a maximum (or minimum) need not exist at all — you must test the open direction, not assume it behaves like a closed region.
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Start this chapter free →Linear Programming — FAQs
What are the key concepts in Class 12 Mathematics Linear Programming?+
Linear programming optimises a linear objective Z = ax + by subject to linear inequality constraints and non-negativity. The chapter builds the feasible region graphically, identifies its corner points, and applies the corner-point method — the optimum of a bounded region lies at a vertex — with manufacturing and diet problems. Key ideas include Linear programming problem, Objective function, Decision variables, Constraints.
What does Class 12 Mathematics Chapter 12 (Linear Programming) cover on XamBaaz?+
It has 90 NCERT-based MCQs on "Linear Programming": 30 Easy, 30 Medium and 30 Hard. Together they make 9 timed quizzes, and you never get the same set twice. Every question has an instant explanation. They help you prepare for CBSE & Maharashtra HSC Board exams, JEE Main, MHT-CET and JEE Advanced.
Are these "Linear Programming" questions free to practise?+
Yes. Sign in with Google to practise "Linear Programming" free. Full unlimited access is ₹999/year on a launch offer until 1 December 2026. No chapter is charged separately.
How should I revise "Linear Programming" for the exam?+
Start with the Easy quiz to check your basics, then try Medium and Hard to practise applying them. There are 9 timed quizzes on this chapter, so you can come back for a fresh set instead of one you have seen. Read each explanation, retry the questions you miss, and track your accuracy until it stays high.
Are these "Linear Programming" MCQs available with answers?+
Yes. 14 sample questions are shown here in full, each with the correct option and a step-by-step "Why" explanation. Sign in free with Google to start practising, with instant scoring.
Is there negative marking in the "Linear Programming" quizzes?+
Yes. The timed quizzes use exam-style marking: +4 for a right answer, −1 for a wrong one and 0 for a skip, the same negative marking as JEE Main and JEE Advanced. MHT-CET and CBSE board papers have no negative marking. Our mocks for those are scored their way.
What are the important questions from Linear Programming (Class 12 Mathematics)?+
The questions that matter most test Linear programming problem, Objective function, Decision variables, Constraints. This page shows 14 solved important MCQs with answers and explanations; all 90 questions on the chapter are available as timed quizzes once you sign in.
Is there an online quiz for Linear Programming?+
Yes — Class 12 Mathematics Linear Programming has timed online quizzes at Easy, Medium and Hard levels, with instant scoring and a worked explanation on every question. The first quiz on the chapter is free.