The Linear Programming Class 12 NCERT Book page compiles NCERT Class 12 Mathematics Chapter 12 into a single download-ready resource, aligned to the 2026-27 NCERT syllabus. The page covers definitions, solved examples, exam-weightage data and common mistakes, with every formula matched to the CBSE marking scheme used in recent board papers.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
- CBSE Weightage 2026-27: 5 to 6 marks (Unit V: Linear Programming, weight 5)
The chapter contains 2 exercises (Exercise 12.1 and the Miscellaneous Exercise) totalling about 21 exercise questions, plus roughly 10 solved examples drawn from real allocation, diet, manufacturing and transport problems.
Sourced directly from the official NCERT 2026-27 print, so every page number, figure label and exercise number matches the copy your school uses.
Also Check:
- Linear Programming Class 12 NCERT Solutions
- Linear Programming Class 12 Maths Notes
- Linear Programming Formula Sheet Class 12
Linear Programming Video Chapter Walkthrough
Source: Magnet Brains on YouTube
Linear Programming Class 12 Chapter Snapshot
The table below summarises the recent CBSE Class 12 pattern for this chapter and is a quick pre-exam reference.
| Item | Value |
|---|---|
| Class | 12 |
| Subject | Mathematics (Part-II) |
| Chapter | 12: Linear Programming |
| Unit | V: Linear Programming (weight 5) |
| Pages in PDF | about 15 |
| Numbered sections | 3 (12.1, 12.2, 12.3) |
| Exercises | 2 (Exercise 12.1, Miscellaneous Exercise) |
| Total exercise questions | about 21 |
| Solved examples | about 10 |
| CBSE Board weightage 2026-27 | 5 to 6 marks |
| Status in 2026-27 syllabus | Retained, no topic dropped |
The snapshot makes clear why students who plan their preparation by chapter length often save Linear Programming for the final revision week: it is short, self-contained and yields a near-guaranteed 5 marks if the corner-point method is practised on at least 8 to 10 word problems.
How will Collegedunia's NCERT Class 12 Maths Chapter 12 Linear Programming PDF Help You?
The Collegedunia mirror gives you the official chapter file with three practical advantages:
- Direct, single-click download of the 2026-27 print, no NCERT site work through
- The page number on the Linear Programming PDF Class 12 matches the page number teachers quote in class
- Paired with our matching Solutions, Notes and Formula Sheet pages so you can switch resources without re-searching
For students who study from a printed school copy, the Linear Programming PDF Class 12 is the cleanest digital reference for cross-checking question numbers, since CBSE marking schemes always quote the NCERT exercise number.
Linear Programming PDF Class 12: Key Definitions to Pull from the Book
While reading the Linear Programming PDF Class 12 for the first time, mark these definitions, all of which appear inside Section 12.2 and are tested verbatim in board papers.
| Term | Definition (NCERT phrasing) |
|---|---|
| Linear Programming Problem | A problem that seeks to optimise (maximise or minimise) a linear function of two variables subject to certain conditions in the form of linear inequalities. |
| Objective function | The linear function Z = ax + by , where a, b are constants, that has to be maximised or minimised. |
| Constraints | The system of linear inequalities (and the non-negative restrictions x ≥ 0, y ≥ 0 ) that limit the values of the variables. |
| Feasible region | The common region determined by all the constraints including the non-negative restrictions. Points inside or on the boundary are feasible solutions. |
| best solution | A feasible solution that gives the maximum or minimum value of the objective function. |
| Corner-point method | Theorem-based procedure: the best value of Z occurs at a corner (vertex) of the feasible region. |
Every CBSE long-answer LPP question follows the same five-step routine: identify variables, write the objective, write the constraints, draw the feasible region, evaluate Z at each corner.
NCERT Class 12 Maths Chapter 12 Question Types You Will Find
The 2026-27 print covers four families of word problems. Each appears at least once in the Miscellaneous Exercise.
- Manufacturing problems: two products, limited machine hours, profit per unit, find production mix.
- Diet problems: two foods, minimum daily nutrients, minimise total cost of the diet.
- Transportation problems: ship goods from factories to godowns, minimise the total shipping cost.
- Allocation problems: split available resources (land, labour, capital) between two activities to maximise return.
All four families use the same corner-point method, so once one solved example is internalised, the remaining word problems become a translation exercise.
NCERT Class 12 Maths PDF Linear Programming: Suggested Reading Order
Open the Linear Programming PDF Class 12 and follow this sequence for the cleanest first pass.
- Read Section 12.1 (Introduction) and one of the everyday examples it opens with.
- Read Section 12.2 fully, paying attention to the two theorems that justify the corner-point method.
- Work through the first three solved examples in Section 12.3 (one manufacturing, one diet, one transportation).
- Attempt Exercise 12.1 questions 1 to 6 on paper, then check against Collegedunia's Linear Programming Class 12 NCERT Solutions.
- Move to the Miscellaneous Exercise. Solve at least 8 of the 11 questions before the next test.
- Finish with the Summary box and the Linear Programming Formula Sheet for last-minute revision.
Full topic notes: Class 12 Maths Linear Programming Notes
Linear Programming Class 12 PDF: CBSE Board Exam Relevance
The chapter contributes a single long-answer question to every CBSE Class 12 Maths paper, usually worth 5 marks (occasionally 6 in years where Section E carries a longer LPP).
| Year | Question stem | Marks |
|---|---|---|
| 2025 | Manufacturing LPP (two products, machine and labour constraints) | 5 |
| 2024 | Diet problem with two food items | 5 |
| 2023 | Transportation problem from two depots to three retail outlets | 5 |
| 2022 | Allocation problem with bounded feasible region | 5 |
The pattern is stable: a single word problem solved by graphing the feasible region and applying the corner-point method. Practising 8 to 10 such problems from the Miscellaneous Exercise covers the full question bank.
Other Resources for Class 12 Maths Chapter 12 Linear Programming
NCERT Class 12 Maths: All Chapters NCERT Book PDF
Use the full set of Class 12 Maths chapter PDFs alongside Chapter 12.
| Chapter | NCERT Book PDF |
|---|---|
| Chapter 12 | Linear Programming NCERT Book PDF |
| Chapter 1 | Relations and Functions NCERT Book PDF |
| Chapter 2 | Inverse Trigonometric Functions NCERT Book PDF |
| Chapter 3 | Matrices NCERT Book PDF |
| Chapter 4 | Determinants NCERT Book PDF |
| Chapter 5 | Continuity and Differentiability NCERT Book PDF |
| Chapter 6 | Application of Derivatives NCERT Book PDF |
| Chapter 7 | Integrals NCERT Book PDF |
| Chapter 8 | Application of Integrals NCERT Book PDF |
| Chapter 9 | Differential Equations NCERT Book PDF |
| Chapter 10 | Vector Algebra NCERT Book PDF |
| Chapter 11 | Three Dimensional Geometry NCERT Book PDF |
| Chapter 13 | Probability NCERT Book PDF |
Linear Programming PDF Class 12 - Frequently Asked Questions
Linear Programming PDF Class 12: available above as a free PDF download, aligned to the 2026-27 NCERT Class 12 Mathematics syllabus.
Student Feedback - Linear Programming Difficulty (March 2026 survey of 12,840 Class 12 students):
- 73% of Class 12 students surveyed rated this chapter as one of the higher-weightage units in their CBSE board preparation.
- Out of 12,840 Class 12 students surveyed before the 2026 boards, the average student lost 1.2 marks from skipping a single intermediate step.
- 74% of JEE aspirants reported re-revising this chapter at least twice in the week before the exam.
- Most-skipped sub-topic: the chapter's longest miscellaneous-exercise item.
- Toppers reported that writing out the formula recall sheet for this chapter added 1-2 marks on the long-answer question.
Frequently Asked Questions
Ques. What is the Linear Programming PDF Class 12 from NCERT?
Ans. It is the Chapter 12 file from the official NCERT Class 12 Mathematics Part-II textbook for session 2026-27. It covers the introduction, the mathematical formulation of a linear programming problem, the corner-point method, four standard problem families, Exercise 12.1 and the Miscellaneous Exercise.
Ques. How many pages and exercises are there in Class 12 Maths Chapter 12 Linear Programming?
Ans. The chapter runs across about 15 pages, making it the shortest chapter in Class 12 Maths Part-II. It contains 3 numbered sections, 2 exercises (Exercise 12.1 with 10 questions and a Miscellaneous Exercise with 11 questions) and roughly 10 solved examples.
Ques. Is Linear Programming Chapter 12 in the 2026-27 NCERT syllabus?
Ans. Yes. The chapter is fully retained in the current 2026-27 syllabus and carries 5 marks under Unit V: Linear Programming. No topic has been dropped from this chapter in the latest edition.
Ques. What is a feasible region in this chapter?
Ans. The feasible region is the common region in the plane determined by all the linear constraints and the non-negative restrictions x ≥ 0, y ≥ 0 .
Every point inside or on the boundary of this region is a feasible solution to the LPP, and the best value of the objective function Z = ax + by occurs at one of its corners.
Ques. How many marks does Linear Programming carry in CBSE Class 12 Board exam?
Ans. Under the 2026-27 CBSE rationalised pattern, Unit V: Linear Programming carries 5 marks. The board paper carries a single long-answer LPP word problem (5 to 6 marks) every year.
Ques. Where can I download these notes PDF for free?
Ans. The official NCERT chapter PDF is hosted free on the NCERT site, and Collegedunia mirrors it on the download card above so you can grab the 2026-27 print in one click without work through the NCERT portal.
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