Linear Programming Exemplar Sums Class 12 Learncbse - Class 12...

Download the Linear Programming Exemplar Sums Class 12 Learncbse as a free PDF. The Linear Programming Exemplar Sums Class 12 Learncbse solve every problem in the Exemplar set on Class 12 Mathematics Chapter 12 Linear Programming, with the working written line by line and the answer verified at the end. The solutions PDF are suitable for JEE Main and Board preparation alike.

Curated by Collegedunia subject experts against the 2026-27 NCERT Exemplar reprint and benchmarked on the last five CBSE board cycles plus JEE Main 2025 slots.

Also Check:

• Linear Programming Class 12 Maths NCERT Exemplar Book PDF
• Linear Programming Class 12 Maths NCERT Solutions

NCERT Exemplar Class 12 Maths Solutions Chapter 12 Linear Programming: What is Inside

Chapter 12 of the NCERT Exemplar is built around four problem archetypes that recur across CBSE and JEE Main. The split below mirrors the actual question distribution in the 2026-27 print, so students know where to spend revision hours.

The Exemplar pushes harder than the main textbook in two specific ways. First, several problems use four or five constraint inequalities instead of the Linear Programming Exemplar Sums Class 12 Learncbse standard of three. Second, unbounded regions appear in roughly one-third of the SA and LA problems, where the candidate must check whether the optimum actually exists.

Linear Programming NCERT Exemplar Video Solutions

Source: Magnet Brains on YouTube

Linear Programming Problems Class 12: Concepts You Need Before Solving

Every Exemplar problem in Chapter 12 stands on six core ideas. Each solution PDF begins with the relevant idea restated so the student does not lose marks on definitions.

• Linear Programming Problem (LPP): a problem of maximising or minimising a linear objective function Z = ax + by subject to linear constraints in x and y.
• Feasible region: the intersection of all constraint half-planes plus the non-negativity restrictions x ≥ 0, y ≥ 0 .
• Corner-point theorem: if the feasible region is bounded, the optimum of Z occurs at a corner point of the region.
• Unbounded feasible region: the optimum may not exist; check by drawing ax + by > M (for max) or ax + by < m (for min) and seeing if the half-plane meets the region.
• Multiple best solutions: arise when the objective line is parallel to a constraint edge; every point on that edge is best.
• Infeasible LPP: the constraints have no common region, so no solution exists.

Roughly 60% of Exemplar Chapter 12 problems test either the unbounded-region check or the multiple-best-solution edge case, both of which the main textbook treats lightly.

How will Collegedunia's NCERT Exemplar Solutions help you?

Our Exemplar Solutions for Linear Programming are designed for the student who has finished the NCERT textbook and now needs problems that look like a real board paper. The structure stays identical on every problem so revision is fast.

• Concept Used block at the start states the formula, theorem, or corner-point rule before any algebra begins.
• Step-by-step Solution writes constraint $\rightarrow$ corner point $\rightarrow$ Z-value $\rightarrow$ optimum on separate lines, never compressing arithmetic.
• Expert Solution gives an alternate angle, often using the iso-profit line method instead of corner enumeration, which shortens JEE Main solving time.
• Tip callouts flag the three classic Exemplar traps: missing the non-negativity check, mis-shading an unbounded region, and skipping the existence check for unbounded LPPs.
• Labelled diagrams show every feasible region with vertices, intercepts, and shading direction marked, so the geometry is unambiguous.

NCERT Exemplar Class 12 Maths Linear Programming: Sample Problem Types Solved

the Linear Programming Exemplar Sums Class 12 Learncbse works through one representative problem from each archetype below. The table previews the constraint signatures so students can map an unfamiliar question back to a known type during the exam.

The transportation archetype is the most common in CBSE Long Answer slots; the diet archetype is the most common JEE Main MCQ-II setup.

Class 12 Maths Chapter 12 Linear Programming Exemplar: Common Mistakes to Avoid

Five errors account for nearly every lost mark on Exemplar LPP problems. Each solution in the Linear Programming Exemplar Sums Class 12 Learncbse carries a tip callout at the exact step where the mistake usually happens.

1. Skipping non-negativity: students forget that x ≥ 0, y ≥ 0 are constraints, so they include a corner point with a negative coordinate. This single slip costs 2 marks in CBSE LA problems.
2. Mis-shading the half-plane: using the origin test wrongly when the origin lies on the constraint line.
3. Forgetting the unbounded-region existence check: declaring an optimum without testing whether ax + by < m intersects the region.
4. Mixing maximise and minimise: writing the wrong corner point as the answer when the objective is min instead of max.
5. Computational slips at corner points: mis-substituting integer coordinates into a fractional objective.

Previous Year Paper Trend: Linear Programming in CBSE and JEE Main

Chapter 12 has appeared in every CBSE Class 12 Maths paper since 2018 as a 5-mark or 6-mark Long Answer. JEE Main coverage has stayed at roughly one MCQ per session since the rationalisation.

Full PYQ map: Linear Programming Class 12 Maths NCERT Solutions.

Other Resources for Class 12 Maths Chapter 12 Linear Programming

• these notes Maths NCERT Notes
• this chapter Maths Formula Sheet
• these notes Maths Handwritten Notes
• this Class 12 page Maths NCERT Book PDF

NCERT Exemplar Solutions for Class 12 Maths: All Chapters

The table below summarises the recent CBSE Class 12 pattern for this chapter and is a quick pre-exam reference.

Linear Programming Exemplar Sums Class 12 Learncbse: available above as a free PDF download, aligned to the 2026-27 NCERT Class 12 Mathematics syllabus.