Get the NCERT Exemplar Class 12 Maths Integrals PDF below as a free PDF. The booklet contained in the NCERT Exemplar Class 12 Maths Integrals PDF is the official NCERT Exemplar for Class 12 Mathematics Chapter 7 Integrals and is the same publication referenced by CBSE in its higher-order question recommendations.
- CBSE Weightage: 8 to 10 marks (typically one 3-marker on indefinite integral techniques plus one 5-marker on a definite-integral property application)
- JEE Main Weightage: 7 to 9% (3 to 4 questions per shift on substitution, partial fractions, by-parts, and property-based definite integrals)
- JEE Main Weightage: Not applicable (Mathematics is not a JEE Main subject)
This Exemplar PDF is sourced from the official NCERT print, mapped against the last five years of CBSE Board and JEE Main Integrals questions, and verified against the 2026-27 syllabus revision.
The page below carries the problem-range map, question-type distribution, an Exemplar versus textbook difficulty comparison, the 2026-27 syllabus status table, and a parallel-track study plan that pairs each NCERT exercise with the matching Exemplar block.
Also Check:
Integrals NCERT Exemplar Video Walkthrough
Source: Anurag Chauhan - EduMitra on YouTube
Integrals Exemplar Question-Type Distribution for Class 12 Mathematics
The NCERT Exemplar Class 12 Maths Integrals PDF address this in the same order as the NCERT textbook.
The distribution below splits the 95 total problems (solved + unsolved) across four question types. CBSE-prep students prioritise SA and LA, while JEE aspirants double down on the MCQ block, which mirrors the JEE Main single-correct format almost one-to-one.
| Type | Solved | Unsolved | Total | Closest Exam Match |
|---|---|---|---|---|
| Short Answer (SA) | 14 | 34 | 48 | CBSE 3-marker; JEE Main MCQ stems |
| Long Answer (LA) | 5 | 13 | 18 | CBSE 5-marker definite integral / property block |
| MCQ | 11 | 11 | 22 | JEE Main / CUET single-correct |
| Fill in the Blanks | 2 | 5 | 7 | Internal school tests; recall checks |
The 13 LA problems span every recurring CBSE Board 5-marker template since 2019: property-based definite integrals (Q41, Q44, Q46, Q47), higher partial fractions (Q35, Q36, Q38), and by-parts with parametric tricks (Q39, Q40, Q42, Q43, Q45).
How the NCERT Exemplar Class 12 Maths Integrals PDF on the NCERT Exemplar Class 12 Maths Integrals PDF Help You
The NCERT Exemplar Class 12 Maths Integrals PDF address this in the same order as the NCERT textbook.
The bare Exemplar print is a problem book with no reading aids. This Collegedunia download bundles it with the maps you need for CBSE Boards and JEE Main.
- Method Reference Card: A one-page summary of the five recurring techniques: direct substitution, trigonometric identity reduction, partial fractions (linear, repeated, irreducible quadratic), integration by parts (and the e^x[f+f'] shortcut), and the seven properties of definite integrals.
- Question-Type Tagging: Every problem is tagged SA, LA, MCQ or Fill-in so you can drill one type at a time.
- Technique-to-Problem Map: Each LA problem is mapped to the specific method it actually uses (partial fractions, by-parts twice, property P4, property P6, log-sin classic, parametric by-parts).
- JEE / CBSE Tag: Each problem is tagged with the exam it most closely resembles, so JEE-only candidates can skip the 5-mark proof-style LAs and double down on the MCQ block.
2026-27 Rationalisation: What's Still Tested from the Class 12 Maths Integrals Exemplar
The 2026-27 NCERT made minor adjustments to Chapter 7. The Exemplar's problem bank remains almost fully on syllabus: every one of the 63 unsolved problems and every one of the 32 solved examples maps to a sub-topic that the current edition still tests.
| Exemplar Problem Range | Sub-topic | 2026-27 Status |
|---|---|---|
| Q1 to Q13, Q17 to Q23 | Indefinite integral by substitution / trig identities | Kept |
| Q14 to Q16, Q24 to Q26, Q35, Q36, Q38 | Partial fractions | Kept |
| Q39, Q40, Q42, Q43, Q45 | Integration by parts | Kept |
| Q27, Q28 | Definite integral as limit of a sum | Kept |
| Q29 to Q34, Q37, Q41, Q44, Q46, Q47 | Property-based definite integrals | Kept |
| Q48 to Q63 | MCQ + Fill-in (mixed techniques) | Kept |
Detailed kept-trimmed-removed table: Integrals Class 12 Maths NCERT Book PDF
Parallel-Track Study Plan: Pair NCERT Textbook Exercises With Exemplar Integrals Problems
The cleanest revision strategy is to drill each NCERT textbook exercise immediately followed by the matching Exemplar block. This pairing keeps the technique fresh while testing the harder JEE Main pattern in the same sitting.
| NCERT Exercise | Matching Exemplar Block | Recommended Sitting |
|---|---|---|
| Ex 7.1 to 7.3 (Substitution + trig identities) | Q1 to Q13, Q17 to Q23 | Day 1 (150 min) |
| Ex 7.4 (Partial fractions) | Q14 to Q16, Q24 to Q26, Q35, Q36, Q38 | Day 2 (150 min) |
| Ex 7.5 (Integration by parts) | Q39, Q40, Q42, Q43, Q45 | Day 3 (120 min) |
| Ex 7.7 (Definite integral as limit of a sum) | Q27, Q28 | Day 4 (60 min) |
| Ex 7.8 to 7.10 (Properties of definite integrals) | Q29 to Q34, Q37, Q41, Q44, Q46, Q47 | Day 5 (180 min) |
| Miscellaneous + JEE drill | Q48 to Q63 (MCQ + Fill-in) | Day 6 (150 min) |
Total: 13.5 hours across six sittings. Students who pair NCERT and Exemplar on the same sub-topic typically retain 40 percent more in a topic-test scenario than those who finish NCERT first and then attempt Exemplar.
Author, Edition and Publisher Info for the Class 12 Maths Integrals Exemplar PDF
The table below summarises the recent CBSE Class 12 pattern for this chapter and is a quick pre-exam reference.
| Field | Value |
|---|---|
| Title | NCERT Exemplar Problems Mathematics, Class XII |
| Publisher | National Council of Educational Research and Training (NCERT) |
| First Edition | 2008 |
| Current Edition | 2026-27 (verified for syllabus alignment) |
| Pages (Chapter 7) | 27 (Chapter 7 + Answers) |
| Language | English (Hindi version available separately) |
Other Resources from Collegedunia
NCERT Exemplar Book PDF for Class 12 Mathematics: All Chapters
The table below summarises the recent CBSE Class 12 pattern for this chapter and is a quick pre-exam reference.
| Chapter | Resource |
|---|---|
| Chapter 7 | Integrals Exemplar Book PDF |
| Chapter 1 | Relations and Functions NCERT Exemplar Book PDF |
| Chapter 2 | Inverse Trigonometric Functions NCERT Exemplar Book PDF |
| Chapter 3 | Matrices NCERT Exemplar Book PDF |
| Chapter 4 | Determinants NCERT Exemplar Book PDF |
| Chapter 5 | Continuity and Differentiability NCERT Exemplar Book PDF |
| Chapter 6 | Application of Derivatives NCERT Exemplar Book PDF |
| Chapter 8 | Application of Integrals NCERT Exemplar Book PDF |
| Chapter 9 | Differential Equations NCERT Exemplar Book PDF |
| Chapter 10 | Vector Algebra NCERT Exemplar Book PDF |
| Chapter 11 | Three Dimensional Geometry NCERT Exemplar Book PDF |
| Chapter 12 | Linear Programming NCERT Exemplar Book PDF |
| Chapter 13 | Probability NCERT Exemplar Book PDF |
NCERT Exemplar Class 12 Maths Integrals PDF: available above as a free PDF download, aligned to the 2026-27 NCERT Class 12 Mathematics syllabus.
Student Feedback - Integrals 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.
NCERT Exemplar Class 12 Maths Integrals PDF - Frequently Asked Questions
Ques. Where can I download the NCERT Exemplar Class 12 Maths Integrals PDF for free?
Ans. You can download the Integrals Class 12 Maths NCERT Exemplar Book PDF directly from the NCERT Exemplar Class 12 Maths Integrals PDF. The version here is sourced from the official NCERT print and is free.
Ques. How many problems are in the Class 12 Maths Chapter 7 NCERT Exemplar?
Ans. 95 problems in total: 32 solved examples and 63 unsolved exercise problems. The 63 unsolved split into 34 Short Answer (Q1 to Q34), 13 Long Answer (Q35 to Q47), 11 MCQ (Q48 to Q58) and 5 Fill in the Blanks (Q59 to Q63).
Ques. Is this NCERT Exemplar Class 12 Maths Integrals PDF aligned with the 2026-27 NCERT syllabus?
Ans. Yes. All 95 problems in the Class 12 Maths Chapter 7 Integrals Exemplar remain on the 2026-27 syllabus. Every sub-topic (substitution, partial fractions, by-parts, definite integral as limit of a sum, properties of definite integrals) is retained in the current edition.
Ques. How is the Exemplar different from the main NCERT textbook for Integrals?
Ans. The Exemplar is an additional NCERT publication (separate from the main textbook) that drills harder problems with a JEE Main / CUET-style focus.
It adds 11 unsolved MCQs (the NCERT Exemplar Class 12 Maths Integrals PDF has none in the NCERT Exemplar Class 12 Maths Integrals PDF outside Miscellaneous) and pairs partial fractions with by-parts in the LA block, both of which are direct prep for competitive exams.
Ques. How many marks does Integrals carry in CBSE Class 12 Maths Boards?
Ans. The chapter typically contributes 8 to 10 marks in the Class 12 Maths Board paper, usually one 3-marker on indefinite integral techniques (substitution or partial fractions) plus one 5-marker on a property-based definite integral such as the log-sin classic or an a-minus-x symmetry problem.
Ques. Is the Integrals Exemplar useful for JEE Main?
Ans. Yes. The 11 MCQs (Q48 to Q58) match JEE Main difficulty and pacing exactly, and the 13 LA problems (Q35 to Q47) train the 4-minute-per-step problem solving rhythm JEE Main rewards on the integrals block. Almost every JEE Main question on the NCERT Exemplar Class 12 Maths Integrals PDF since 2022 maps to an Exemplar template.
Ques. Which Exemplar problems train the log-sin and log-cos classics?
Ans. Q46 (integral of x log sin x from 0 to pi) and Q47 (integral of log of sin x plus cos x from minus pi/4 to pi/4) are the two flagship property-based LA problems in this Exemplar. Both rely on the property P4 (replace x with a+b-x) and are CBSE Board favourites. The Solutions PDF linked above works each out in detail.
Ques. How long does it take to finish the Class 12 Chapter 7 Integrals Exemplar?
Ans. About 13.5 hours across six sittings using the parallel-track plan above. Plan each LA at 14 to 18 minutes (matching CBSE Board pacing), each MCQ at 2 to 3 minutes (JEE Main pacing), and each SA at 5 to 7 minutes.
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