Class 12 Mathematics — Chapter 12: Linear Programming
66 practice questions · 22 Easy · 22 Medium · 22 Hard
Practise Class 12 Mathematics Chapter 12, "Linear Programming", with 66 NCERT-aligned multiple-choice questions. The set is split into 22 Easy, 22 Medium and 22 Hard questions, so you can warm up on the fundamentals and then push into the exam-level problems that separate top scorers in CBSE Board exams, JEE Main and JEE Advanced.
"Linear Programming" is one of the chapters where problem-solving speed, formula recall and step-by-step reasoning really pays off. Each MCQ on this chapter is timed and uses exam-grade marking (+2 correct, −1 wrong, 0 skipped), training the same accuracy-under-pressure that real papers demand. Every question carries a short explanation, so a wrong answer becomes a quick lesson rather than a dead end — the fastest way to close gaps before a test.
Use this chapter as targeted revision: attempt the Easy set first to confirm your basics on Linear Programming, then move to Medium and Hard to test application and problem-solving. Your accuracy, streaks and XP save automatically, and the chapter feeds into your overall Class 12 Mathematics mastery score. A few sample questions are shown below; sign in free to practise all 66.
Key concepts: Linear Programming (Class 12 Mathematics)
This chapter formulates linear programming problems and solves them graphically by optimising a linear objective function over a feasible region.
- LPP components
- An objective function (to maximise or minimise), decision variables, and linear constraints (inequalities) including non-negativity.
- Feasible region
- The set of all points satisfying every constraint; it may be bounded or unbounded.
- Corner-point method
- The optimal value of the objective function (if it exists) occurs at a corner (vertex) of the feasible region.
- Bounded vs unbounded
- For a bounded region an optimum always exists; for an unbounded region it may not — this must be checked.
- Formulating problems
- Translate a real situation (diet, manufacturing, transport) into variables, constraints and an objective.
Key formulas — Linear Programming
💡 Exam tips for Linear Programming
- Evaluate Z at every corner point of the feasible region — the maximum/minimum is among them.
- For an unbounded region, verify whether the optimum actually exists before concluding.
Sample questions
In LPP, the function to optimise is called:
Maximise/minimise.
Feasible region is the:
Intersection of half-planes.
If feasible region is unbounded, optimum may:
Need to verify with check.
Linear Programming — FAQs
What are the key concepts in Class 12 Mathematics Linear Programming?+
This chapter formulates linear programming problems and solves them graphically by optimising a linear objective function over a feasible region. Key ideas include LPP components, Feasible region, Corner-point method, Bounded vs unbounded, Formulating problems.
What does Class 12 Mathematics Chapter 12 (Linear Programming) cover on XamBaaz?+
It covers 66 NCERT-aligned MCQs on "Linear Programming" — 22 Easy, 22 Medium and 22 Hard — each with a timed quiz and an instant explanation, suitable for CBSE Board exams, JEE Main 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 (limited-time launch price), with no per-chapter charges.
How should I revise "Linear Programming" for the exam?+
Start with the Easy quiz to confirm your fundamentals, then attempt Medium and Hard for application-level practice. Review each explanation, retry the questions you miss, and track your accuracy on this chapter until it is consistently high.
Practise all 66 questions free
Timed quizzes, instant scoring, streaks and XP. Sign in with Google — no card needed.
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