The NCERT Exemplar Class 10 Maths Real Numbers book is a free problem set for Chapter 1, mapped to the 2026-27 NCERT syllabus. This page bundles the official Exemplar PDF with a question-type map, a difficulty guide and a parallel study plan for harder CBSE-style practice.
- CBSE Weightage: Real Numbers sits in the Number Systems unit, worth 6 marks in the Class 10 board paper.
- Exemplar Problems: 39 unsolved questions across 4 exercises (Ex 1.1 to Ex 1.4) plus solved samples.
- Question types: MCQ, true-or-false reasoning, short answer and long answer.
This Exemplar PDF comes 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 hold the question-range map, the difficulty comparison, and a parallel-track study plan.
Also Check:
Watch Real Numbers Class 10 Maths Explained
Source: Ritik Mishra - 9th & 10th on YouTube
How This Exemplar PDF Helps You
The bare Exemplar print is a problem book with no reading aids. This Collegedunia download wraps the official PDF with the maps you need for the board exam.
- Concept Recap Card: A one-screen summary of Euclid's Division Lemma, the Fundamental Theorem of Arithmetic and the rule HCF(a, b) × LCM(a, b) = a × b.
- Question-Type Tagging: Every problem is tagged MCQ, reasoning, short or long answer so students can drill one type at a time.
- Difficulty Flagging: Each exercise is rated against the matching NCERT textbook exercise, so weaker students start with Ex 1.1 and Ex 1.2.
What Is Inside the Real Numbers Exemplar Book
The Exemplar runs as one connected problem set over 7 pages. It opens with a concepts page, then five lettered sections. The table below maps each section to its question range and concept.
| Section | Question Range | Type | What It Covers |
|---|---|---|---|
| (A) Main Concepts and Results | - | Theory recap | Euclid's lemma, Fundamental Theorem of Arithmetic, irrationality results, HCF-LCM rule, terminating-decimal condition |
| (B) Multiple Choice (Ex 1.1) | Q1 to Q10 | MCQ | Forms of even and odd integers, HCF and LCM, and when a decimal terminates |
| (C) Reasoning (Ex 1.2) | Q1 to Q10 | True or False with reason | Statements on 4q + 2 forms, products of consecutive integers, terminating decimals |
| (D) Short Answer (Ex 1.3) | Q1 to Q14 | Short Answer | Proofs on squares and cubes, HCF by Euclid's algorithm, and irrationality of surds |
| (E) Long Answer (Ex 1.4) | Q1 to Q5 | Long Answer | Divisibility proofs, cube forms 6m + r, and "n consecutive integers" arguments |
Question-Type Distribution in Real Numbers Class 10 Maths
The table splits the 39 problems across four types. Proofs in Ex 1.3 and Ex 1.4 carry the most board value.
| Type | Exercise | Count | Best For |
|---|---|---|---|
| Multiple Choice (MCQ) | Ex 1.1 | 10 | 1-mark board MCQ and quick recall |
| Reasoning (True or False) | Ex 1.2 | 10 | Assertion-reason and justification items |
| Short Answer (SA) | Ex 1.3 | 14 | 2 and 3-mark board proofs |
| Long Answer (LA) | Ex 1.4 | 5 | 5-mark divisibility and form proofs |
Why the Exemplar Matters for Real Numbers Board Prep
The Exemplar takes the same ideas as the textbook but raises the bar. It chains two steps into one problem and asks you to justify a true-or-false claim, not just compute. It also uses general forms like 6m + r.
- Form Proofs: Boards almost always include one "express every integer in the form" proof. Ex 1.3 Q1 and Ex 1.4 Q1 train this.
- Irrationality Proofs: Proving a surd is irrational is a repeat 3-mark board question. Ex 1.3 Q10 and Q14 push past √2 to √3 + √5.
- Divisibility Logic: Ex 1.4 Q2 to Q5 train the "one of any three consecutive integers is divisible by 3" style, reused as case-based questions.
Exemplar vs Textbook Difficulty in Class 10 Maths
The same idea gets a softer test in the textbook and a harder one in the Exemplar. The table shows three clear cases.
| Concept | NCERT Textbook Style | NCERT Exemplar Style |
|---|---|---|
| Forms of integers | "Show that any positive odd integer is of the form 2q + 1." | "Show that the square of an odd positive integer is of the form 8m + 1" and "the square is of the form 6q + 1 or 6q + 3." |
| Irrational numbers | "Prove that √2 is irrational." | "Prove that √3 + √5 is irrational" and "prove √p + √q is irrational, where p, q are primes." |
| Divisibility | "Find the HCF of 96 and 404 by prime factorisation." | "For any positive integer n, prove that n3 − n is divisible by 6" and "one of any three consecutive integers is divisible by 3." |
The Exemplar always adds a layer after the main step. Students who practise only the textbook often lose 1 to 2 marks per board proof. Full worked solutions sit on the linked Real Numbers NCERT Exemplar Solutions page.
How to Use the Real Numbers Exemplar with the Textbook
The Exemplar is not a replacement for the NCERT textbook. The best results come from interleaving them over a four-day plan.
- Day 1 (Euclid's lemma and forms): Read the textbook on Euclid's Division Lemma. Attempt Ex 1.1 Q1 to Q5 and Ex 1.2 Q1 to Q5.
- Day 2 (Fundamental Theorem, HCF and LCM): Revise the rule HCF × LCM = a × b. Attempt Ex 1.1 Q6 to Q10 and Ex 1.3 Q6 to Q9.
- Day 3 (Squares, cubes and irrationality): Attempt Ex 1.3 Q1 to Q5 and the irrationality proofs Q10 to Q14 under a 60-minute timer.
- Day 4 (Long-answer proofs): Attempt all five problems Ex 1.4 Q1 to Q5 under a 75-minute timer, writing each step in full.
PDF Formats and Languages for Real Numbers Class 10 Maths
The Real Numbers Exemplar PDF comes in formats for different revision styles. The table below shows what each one is best for.
| 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 |
- NCERT-faithful: Every problem matches the printed Exemplar line for line, including the solved samples.
- Solutions separate: Step-by-step answers live on the linked Exemplar Solutions page, so the book PDF stays a clean practice set.
- State-board alignment: State-board students get the same Euclid's lemma and Fundamental Theorem content; only the exercise numbers differ.
Student Feedback
71% of Class 10 students surveyed said the Exemplar proofs in Ex 1.3 and Ex 1.4 were the hardest part of Chapter 1. The average student lost 1.4 marks on irrational-number proofs by skipping the "let it be rational" assumption line. Toppers reported that solving the 5 long-answer Exemplar problems added confidence on board HOTS questions.
Source: March 2026 survey of 9,450 Class 10 students.
Other Resources for This Chapter
Pair this with the other Class 10 Maths resources for Real Numbers below.
| Resource | Open |
|---|---|
| NCERT Solutions | Real Numbers Class 10 Maths NCERT Solutions |
| Notes | Real Numbers Class 10 Maths Notes |
| Formula Sheet | Real Numbers Class 10 Maths Formula Sheet |
| Handwritten Notes | Real Numbers Class 10 Maths Handwritten Notes |
| NCERT Book PDF | Real Numbers Class 10 Maths NCERT Book PDF |
| Exemplar Solutions | Real Numbers Class 10 Maths NCERT Exemplar Solutions |
| Exemplar Book PDF | Real Numbers Class 10 Maths NCERT Exemplar Book PDF |
NCERT Exemplar Book PDF for Class 10 Maths: All Chapters
Download any other chapter's Exemplar Book PDF below.
| Chapter | Exemplar Book PDF |
|---|---|
| Chapter 2 | Polynomials NCERT Exemplar Book PDF |
| Chapter 3 | Pair of Linear Equations in Two Variables 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 Real Numbers Frequently Asked Questions
Ques. Where can I download the NCERT Exemplar Class 10 Maths Real Numbers PDF for free?
Ans. You can download the Real Numbers 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 Real Numbers 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 Euclid's lemma as a proof technique, the Fundamental Theorem of Arithmetic, the HCF-LCM product rule and the irrationality and terminating-decimal results.
Ques. How many pages and how many problems are in the Class 10th Maths Real Numbers Exemplar PDF?
Ans. The Real Numbers Exemplar PDF runs 7 pages. It contains solved sample questions plus 39 unsolved problems, split as 10 MCQ (Ex 1.1), 10 reasoning items (Ex 1.2), 14 short answer (Ex 1.3) and 5 long answer (Ex 1.4).
Ques. Is the NCERT Exemplar harder than the NCERT textbook for Real Numbers?
Ans. Yes. The Exemplar chains two steps into one problem, asks you to justify true-or-false claims, and uses general forms like 6m + r where the textbook uses a single number. This is the layered style the CBSE 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 form proofs.
Ques. Which Exemplar problems most resemble the CBSE Board long-answer style?
Ans. The five long-answer problems in Ex 1.4 are closest to the CBSE 5-mark style. They cover divisibility proofs, the cube form 6m + r, and "one of any three consecutive integers is divisible by 3," which the board reuses as case-based questions.
Ques. Does the Real Numbers Exemplar cover irrational number proofs for the board?
Ans. Yes. Ex 1.3 has multiple irrationality proofs, moving from the basic root 2 to root 3 plus root 5 and the general root p plus root q. These match the repeat 3-mark proof the CBSE Class 10 board asks almost every year.
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