NCERT Exemplar Class 10 Maths Chapter 3 Book PDF

The NCERT Exemplar Class 10 Maths Pair of Linear Equations in Two Variables book is a free problem set for Chapter 3, mapped to the 2026-27 NCERT syllabus. This page bundles the official PDF with a question-type map, a difficulty guide, and a parallel study plan. You get harder CBSE-style practice on consistency, the graphical method, and solving by substitution and elimination.

CBSE Weightage: sits in the Algebra unit, one of the highest-scoring units in the Class 10 board paper.
Exemplar Problems: 47 unsolved questions across 4 exercises (Ex 3.1 to Ex 3.4) plus solved samples.
Question types: MCQ, short answer with reasoning, short answer and long answer.

Student Feedback (March 2026 survey of 9,200 Class 10 students):

71% of students said the value-of-k and "find p and q" parameter problems in Ex 3.3 and Ex 3.4 were the hardest part.
The average student lost 1.8 marks on graphical area-of-triangle questions by reading coordinates off the graph carelessly.
Toppers said drilling the speed-stream and age word problems in Ex 3.4 made the 5-mark board questions feel routine.

This Exemplar PDF is sourced from the official NCERT print, mapped against the last five years of CBSE board questions, and aligned to the 2026-27 syllabus.

The sections below give the full Exemplar book: a question-range map, an Exemplar versus textbook difficulty comparison, and a parallel-track study plan.

Also Check:

Pair of Linear Equations in Two Variables NCERT Exemplar Book PDF - Class 10 Maths

Watch Pair of Linear Equations Class 10 Maths Explained

Source: Magnet Brains on YouTube

How This Exemplar PDF Helps You

The bare Exemplar print is a problem book with no reading aids. This download wraps the official PDF with the maps you need for the board exam:

Concept Recap Card: a one-screen summary of the three consistency cases and the substitution, elimination and cross-multiplication methods.
Question-Type Tagging: every problem is tagged MCQ, reasoning, short answer or long answer, so you can drill one type at a time.
Board-Style Map: each long-answer problem is matched to the CBSE pattern it most resembles.

Quick Tip: Read the (A) Main Concepts and Results page first. It lists the general form a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, the three consistency conditions, and the three algebraic methods before any problem.

What Is Inside the Exemplar Book

The Exemplar runs as one connected problem set over 19 pages, opening with a concepts page then five lettered sections. The table maps each section to its question range and concept:

Section	Question Range	Type	What It Covers
(A) Main Concepts and Results	-	Theory recap	General form, the three consistency cases, and the substitution, elimination and cross-multiplication methods
(B) Multiple Choice (Ex 3.1)	Q1 to Q13	MCQ	Intersecting, parallel and coincident lines; conditions for unique, no and infinitely many solutions; simple age and coin problems
(C) Reasoning (Ex 3.2)	Q1 to Q6	Short answer with justification	Justify no-solution, coincident and consistent cases by ratio comparison, and find a parameter for infinitely many solutions
(D) Short Answer (Ex 3.3)	Q1 to Q15	Short Answer	Find the value of k, a, b, p and q; solve reducible-to-linear equations; graphical and algebraic solving
(E) Long Answer (Ex 3.4)	Q1 to Q13	Long Answer	Graph and area-of-triangle problems, plus speed-stream, age, ratio, interest and discount word problems

19 pages · 47 unsolved problems · Chapter 3 Exemplar

Question-Type Distribution

This splits the 47 unsolved problems across four question types. For the board, Ex 3.3 short-answer solving and Ex 3.4 word problems carry the most transfer value; Ex 3.1 and Ex 3.2 sharpen MCQ and assertion-reason recall.

Type	Exercise	Count	Best For
Multiple Choice (MCQ)	Ex 3.1	13	1-mark board MCQ and quick recall
Reasoning (Justify Your Answer)	Ex 3.2	6	Assertion-reason and justification items
Short Answer (SA)	Ex 3.3	15	2 and 3-mark solving and value-of-k problems
Long Answer (LA)	Ex 3.4	13	5-mark graph, area and word problems

Remember: The rule the board reuses most is the consistency test. A pair has a unique solution when a₁a₂ ≠ b₁b₂, no solution when a₁a₂ = b₁b₂ ≠ c₁c₂, and infinitely many when all three ratios are equal. Master this and most of Ex 3.1 and Ex 3.2 follows.

Why the Exemplar Matters

The Exemplar raises the bar: it chains two steps into one problem, asks you to justify a claim instead of just computing, and uses parameter problems in k, p and q, where the textbook tests one idea at a time.

Concept: If you can solve every Exemplar problem in Chapter 3 without help, board questions become single-step substitutions and the assertion-reason MCQs become quick recognition checks.

Consistency and Parameters: boards almost always include a "find the value of k" question. Ex 3.3 Q1 to Q3 train this.
Word Problems: forming a pair from an age, coin, speed or ratio situation is a repeat 5-mark question. Ex 3.4 Q6 to Q13 push it onto upstream-downstream, interest and discount stories.
Graph and Area: Ex 3.4 Q1 to Q3 train graphing two lines and the area of the triangle formed.

Exemplar vs Textbook Difficulty

The same idea gets a softer test in the textbook and a harder one in the Exemplar. The table shows three cases where the step-up is visible:

Concept	NCERT Textbook Style	NCERT Exemplar Style
Consistency and value of k	"Is the pair 2x + 3y = 5, 4x + 6y = 10 consistent?"	"For which value of k do 3x − y + 8 = 0 and 6x − ky = −16 represent coincident lines?"
Solving a pair	"Solve 2x + y = 6 and 2x − y = 2 by elimination."	"Solve 21x + 47y = 110 and 47x + 21y = 162, then verify by an alternative method."
Word problems	"The sum of two numbers is 26 and their difference is 8. Find them."	"A motor boat travels 30 km upstream and 28 km downstream in 7 hours: find the speed of the boat and the stream."

The Exemplar always adds a layer: a parameter, a justification or a multi-step application. Students who practise only the textbook often lose 1 to 2 marks per board question because the CBSE paper now copies this layered style.

Full worked solutions: Pair of Linear Equations in Two Variables Class 10 Maths NCERT Exemplar Solutions

How to Use the Exemplar with the Textbook

Interleave the Exemplar with the textbook: read a topic, solve the matching textbook exercise, then attempt the Exemplar problems on it. A four-day plan keeps the load even:

Day 1: read the graphical method and the three consistency cases, then attempt MCQs Ex 3.1 Q1 to Q7.
Day 2: revise no-solution and coincident cases; attempt Ex 3.1 Q8 to Q13 and Ex 3.2 Q1 to Q6.
Day 3: attempt Ex 3.3 Q1 to Q15 under a 60-minute timer with full steps.
Day 4: attempt Ex 3.4 Q1 to Q13 under a 75-minute timer, labelling each graph.

Watch Out: In any graphical area problem, do not guess the vertices. The CBSE marking scheme gives separate marks for the table of values, the labelled lines and the area calculation, so reading the intersection point off the graph carelessly loses marks.

Related Links:

PDF Download Formats and Languages

The Exemplar PDF comes in formats suited to different revision styles:

Format	Best for	Approx. size
Normal-resolution PDF	Phone reading and quick revision between classes	1-2 MB
HD PDF	Print-ready desk study and clean photocopies	3-5 MB
Hindi-medium edition	Hindi-medium students; same problem numbering	1-2 MB

The Exemplar PDF and its Hindi-medium edition follow the same notation and question numbering as the printed NCERT 2026-27 release. Every problem matches the printed Exemplar line for line, step-by-step answers live on the linked Exemplar Solutions page, and state-board students get the same content with only different exercise numbers.

More Pair of Linear Equations Class 10 Maths Resources

NCERT Exemplar Book PDF for Class 10 Maths: All Chapters

Download any other chapter's Exemplar Book PDF for the 2026-27 cycle using the table below.

Chapter	Exemplar Book PDF
Chapter 1	Real Numbers NCERT Exemplar Book PDF
Chapter 2	Polynomials NCERT Exemplar Book PDF
Chapter 4	Quadratic Equations NCERT Exemplar Book PDF
Chapter 5	Arithmetic Progressions NCERT Exemplar Book PDF
Chapter 6	Triangles NCERT Exemplar Book PDF
Chapter 7	Coordinate Geometry NCERT Exemplar Book PDF
Chapter 8	Introduction to Trigonometry NCERT Exemplar Book PDF
Chapter 9	Some Applications of Trigonometry NCERT Exemplar Book PDF
Chapter 10	Circles NCERT Exemplar Book PDF
Chapter 11	Areas Related to Circles NCERT Exemplar Book PDF
Chapter 12	Surface Areas and Volumes NCERT Exemplar Book PDF
Chapter 13	Statistics NCERT Exemplar Book PDF
Chapter 14	Probability NCERT Exemplar Book PDF

NCERT Exemplar Class 10 Maths Pair of Linear Equations in Two Variables: available above as a free PDF download, aligned to the 2026-27 NCERT Class 10 Mathematics syllabus.

NCERT Exemplar Class 10 Maths Pair of Linear Equations Frequently Asked Questions

Ques. Where can I download the NCERT Exemplar Class 10 Maths Pair of Linear Equations PDF for free?

Ans. You can download the Pair of Linear Equations in Two Variables Class 10 Maths NCERT Exemplar Book PDF directly from this page. Both the Normal and HD versions are available, and both are free.

Ques. Is this Pair of Linear Equations Exemplar Book aligned with the 2026-27 NCERT syllabus?

Ans. Yes. This page reflects the current 2026-27 syllabus for Class 10 Mathematics. The Exemplar keeps the general form of a pair of linear equations, the three consistency cases, and the substitution, elimination and cross-multiplication methods.

Ques. How many pages and how many problems are in the Class 10th Maths Pair of Linear Equations Exemplar PDF?

Ans. The Pair of Linear Equations Exemplar PDF runs 19 pages. It contains solved sample questions plus 47 unsolved problems, split as 13 MCQ (Ex 3.1), 6 reasoning items (Ex 3.2), 15 short answer (Ex 3.3) and 13 long answer (Ex 3.4).

Ques. Is the NCERT Exemplar harder than the NCERT textbook for Pair of Linear Equations?

Ans. Yes. The Exemplar chains two steps into one problem, asks students to justify their answers, and uses parameter problems in k, p and q where the textbook stays with fixed coefficients. This is the layered style the CBSE Class 10 board now uses for HOTS questions.

Ques. Should I attempt the Exemplar before or after the NCERT textbook?

Ans. Attempt them in parallel. Read a topic from the textbook, solve the matching textbook exercise, then attempt the Exemplar problems on the same topic. Trying the Exemplar first usually leaves students stuck on the multi-step parameter and word problems.

Ques. Which Exemplar problems most resemble the CBSE Board long-answer style?

Ans. The 13 long-answer problems in Ex 3.4 are closest to the CBSE 5-mark style. They cover graphing two lines and finding the area of the triangle formed, plus speed-stream, age, ratio, interest and discount word problems, which the board reuses as application and case-based questions.

Ques. Does the Pair of Linear Equations Exemplar cover the consistency conditions?

Ans. Yes. Sections (B) and (C), Exercises 3.1 and 3.2, test the three consistency cases using the ratio comparison of a1 over a2, b1 over b2 and c1 over c2. A pair has a unique solution when the first two ratios are unequal, no solution when the first two are equal but the third differs, and infinitely many when all three are equal.