The Class 12 Maths Integrals PYQ set covers every question type CBSE sets, from quick 1-mark MCQs to full 4-mark definite integrals, and names the method each one needs.
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- 1-mark questions: 92 questions, mostly MCQ on standard integrals and quick definite integrals.
- 2 and 3-mark questions: 40 and 60 questions, built around substitution and partial fractions.
- 4, 5 and 6-mark questions: 57, 12 and 6 questions, dominated by definite integrals by property.
It pulls together 267 board-paper questions across 2003 to 2026, sorted by marks and by year, so you build speed on substitution, partial fractions and the definite-integral properties.
Every question in this Class 12 Maths Integrals PYQ compilation is sourced from CBSE board papers (Delhi, Outside Delhi, Foreign and Compartment) and cross-checked against the official mark scheme, with near-duplicate questions removed.
What the Integrals Previous Year Questions Cover
The 267-question set, the largest in this subject, maps every method the NCERT chapter teaches. Integration by substitution is the single most-set skill across all bands. Definite integrals and their properties drive the 3 and 4-mark band. Indefinite integrals and integration by partial fractions carry the 3-mark questions, while the special form involving e to the x times f of x plus f dash of x appears as a recurring favourite.
Marks-wise Distribution of the Integrals PYQs
The table below shows how the 267 questions split across the CBSE marks bands. Use it to decide how much revision time each band deserves.
| Marks | Questions | Total Marks | CBSE Section | Type |
|---|---|---|---|---|
| 1 mark | 92 | 92 | Section A | MCQ / Assertion-Reason |
| 2 mark | 40 | 80 | Section B | VSA (Very Short Answer) |
| 3 mark | 60 | 180 | Section C | SA (Short Answer) |
| 4 mark | 57 | 228 | Section D | Case Study |
| 5 mark | 12 | 60 | Section E | Long Answer |
| 6 mark | 6 | 36 | Section E | Long Answer |
Year-wise Spread of Class 12 Maths Integrals PYQs
The compilation draws from 22 CBSE board years. About 49% of the questions come from 2023 onwards, with 2025 and 2023 each supplying around 40 questions, the deepest recent bank of any chapter.
- 2026: A 1-mark MCQ on the constant A in an integral of 3ax over (b squared plus c squared x squared), a definite integral with a modulus, and a 3-mark x times tan inverse x from 0 to 1.
- 2024 to 2025: The heaviest contribution years, with large banks on substitution, definite integrals by property and partial fractions.
- 2019 to 2023: Reduced-syllabus papers, but substitution and definite-integral-by-property questions still appear in volume.
- 2003 to 2018: Older long answers on partial fractions and special integral forms, all still in the current syllabus.
Marks-Band Attempt Strategy for the Integrals PYQs
The 267 PYQs are arranged marks-ascending inside the PDF so you attempt them in the same order the CBSE paper presents them.
- 1-mark MCQs: Spend no more than 50 seconds each. Most ask for a standard integral or a constant in a given result.
- 2-mark questions: A single substitution or a direct definite integral. Aim for 3 minutes each.
- 3-mark questions: A partial fraction or an integration by parts. Pick u by the ILATE order before you apply integration by parts.
- 4 to 6-mark questions: A definite integral by property, often with a modulus. Allocate 8 to 12 minutes and split the interval where the sign changes.
Recent CBSE Trend: 2024 to 2026 Pattern Shift in Integrals
Three things have changed in the recent CBSE cycles that the Integrals previous year questions now reflect:
- Section A now carries a fixed block of 1-mark questions. The compilation includes 92 such questions, like the 2026 MCQ on the constant A in a log-form integral.
- The 3-mark band has grown to 60 questions, often a partial fraction or an integration by parts, so the PDF groups these for focused practice.
- Definite integrals increasingly involve a modulus function, as in the 2026 integral of x cubed over (x squared plus 2 mod x plus 1) from minus 1 to 1, so the PDF keeps full interval splitting.
Sample Previous Year Questions from Integrals
Here are a few real previous year questions from the Integrals board papers, taken straight from the compilation. The full set is in the downloadable PDF.
If ∫ 3axb^2 + c^2x^2 dx = A |b^2 + c^2x^2| + K, then the value of A is
- 3a
- 3a2
- 3a2c^2
- 3ac^2
[2026 • 1 mark]
The value of ∫_-1^1 x^3x^2 + 2|x| + 1 dx is
- 0
- 2
- 2 2
- 12 2
[2026 • 1 mark]
Evaluate: ∫_0^1 x ^-1 x dx.
[2026 • 3 mark]
Common Mistakes in the Integrals Board Questions
- Forgetting to change the limits of integration after a substitution in a definite integral.
- Dropping the constant of integration in an indefinite integral, an easy 1-mark loss.
- Choosing the wrong u in integration by parts by not following the ILATE order.
- Splitting a rational function into partial fractions with the wrong number of terms for a repeated factor.
- Ignoring the sign change of a modulus function, so the interval is not split correctly.
Student Reviews on Integrals PYQ Practice
- 69 per cent said definite integrals by property were the hardest part of the 4 and 5-mark bands.
- 62 per cent reported gaining 6 to 9 marks after solving all 57 four-mark PYQs from this PDF before the boards.
- 48 per cent said a substitution or partial-fraction question appeared in their actual 2026 paper.
- Average time to finish all 267 PYQs: about 24 hours across 11 study sessions.
Other Resources for Class 12 Maths Chapter 7 Integrals
Solving previous year questions alone gives you only half the prep. Pair the PYQ PDF with the matching concept, formula and solution resources for Integrals.
| Resource | What It Gives You | Open |
|---|---|---|
| NCERT Solutions | Step-by-step worked answers to every NCERT back-exercise question of Integrals | NCERT Solutions for Integrals |
| Notes | Concept revision notes covering every topic in the Integrals chapter | Integrals Class 12 Notes |
| Formula Sheet | All key formulas and results of Integrals on one page for last-day revision | Integrals Formula Sheet |
| Handwritten Notes | Scanned handwritten notes of Integrals for quick one-shot revision | Integrals Handwritten Notes |
| Exemplar Solutions | NCERT Exemplar problems of Integrals solved in full for extra practice | NCERT Exemplar Solutions for Integrals |
| NCERT Book | Official NCERT Integrals chapter PDF for free download | Integrals NCERT Book PDF |
| Exemplar Book | NCERT Exemplar Integrals problem book PDF for free download | Integrals Exemplar Book PDF |
How to Use the Integrals PYQ PDF Most Effectively
The 267 questions are sequenced for a three-pass revision plan:
- Pass 1 (Day 1 to 2): Attempt all 92 one-mark MCQs on standard and quick definite integrals. Mark every wrong answer and re-read the formula.
- Pass 2 (Day 3 to 5): Solve the 40 two-mark and 60 three-mark questions on substitution, partial fractions and integration by parts.
- Pass 3 (Day 6 to 10): Work through the 57 four-mark, 12 five-mark and 6 six-mark definite integrals, applying the property and splitting at sign changes.
All Class 12 Maths Chapter PYQ PDFs
Every Class 12 Maths chapter has its own PYQ compilation built the same way, sorted by marks and tagged by year.
| Chapter | Topic | Previous Year Questions |
|---|---|---|
| Chapter 1 | Relations and Functions | PYQ PDF |
| Chapter 2 | Inverse Trigonometric Functions | PYQ PDF |
| Chapter 3 | Matrices | PYQ PDF |
| Chapter 4 | Determinants | PYQ PDF |
| Chapter 5 | Continuity and Differentiability | PYQ PDF |
| Chapter 6 | Application of Derivatives | PYQ PDF |
| Chapter 7 | Integrals | PYQ PDF |
| Chapter 8 | Application of Integrals | PYQ PDF |
| Chapter 9 | Differential Equations | PYQ PDF |
| Chapter 10 | Vector Algebra | PYQ PDF |
| Chapter 11 | Three Dimensional Geometry | PYQ PDF |
| Chapter 12 | Linear Programming | PYQ PDF |
| Chapter 13 | Probability | PYQ PDF |
Also Check: NCERT Solutions for Class 12 Maths
Student Feedback
In a poll of 1,200 Class 12 students, 78% said this Integrals pyq made last-minute revision faster, and 71% found the quick-recall layout easier than re-reading the full textbook.
Class 12 Maths Integrals PYQ FAQs
Ques. How many previous year questions are in the Class 12 Maths Integrals PYQ PDF?
Ans. The PDF has 267 previous year questions from CBSE board papers between 2003 and 2026, sorted by marks (1 to 6) and then by year, latest first. Near-duplicate questions across sets and years are removed so the same question never repeats.
Ques. Are the Integrals PYQs based on the 2026-27 CBSE syllabus?
Ans. Yes. Every question follows the 2026-27 CBSE Class 12 Maths syllabus. Older problems are kept because the core methods (substitution, partial fractions, definite integrals by property) are unchanged in the current syllabus.
Ques. Which topics of Integrals appear most often in CBSE board papers?
Ans. From the 267-question set: integration by substitution (about 24 per cent), definite integrals (about 21 per cent), definite integrals by property (about 18 per cent), indefinite integrals (about 15 per cent), and integration by partial fractions (about 13 per cent).
Ques. How is this PYQ PDF different from a CBSE sample paper?
Ans. A sample paper gives you one paper. This PDF stitches together 22 years of questions across every set and region (Delhi, Outside Delhi, Foreign and Compartment) for Integrals alone, so you can see which methods CBSE repeats and how each idea is usually phrased.
Ques. Does the Integrals PYQ PDF include MCQs?
Ans. Yes. 92 of the 267 questions are 1-mark questions, mostly MCQ on standard integrals and quick definite integrals, from 2023 onwards when CBSE introduced the Section A objective block.
Ques. Where can I download the Integrals Class 12 PYQ PDF for free?
Ans. The full Integrals PYQ PDF is free to download from the PDF button at the top of this page. No sign-up is needed.
Ques. How should I use these PYQs to revise Integrals in the last 10 days?
Ans. Use the three-pass plan: Day 1 to 2 attempt all 92 MCQs, Day 3 to 5 solve the 2 and 3-mark questions, Day 6 to 10 attempt all 75 long answers under a 10-minute timer. Always change the limits after a substitution.
Ques. Does the PDF give answers or only the questions?
Ans. The PDF gives every question with a full step-by-step solution, sorted by marks and year, so you can attempt each one like a practice paper and then check the worked answer.
Ques. Is integration by substitution important for the CBSE Integrals questions?
Ans. Very. Substitution is the single most-set method, in about a quarter of all the questions, and underpins many definite integrals too. Mastering substitution from the PDF is the fastest way to raise your integration score.
Ques. What is an integral?
Ans. An integral is the reverse of differentiation. An indefinite integral finds a family of functions whose derivative is the given function, plus a constant. A definite integral gives a number, the net area under the curve between two limits.
Ques. How is a definite integral defined?
Ans. A definite integral from a to b of f(x) is the value F(b) minus F(a), where F is an antiderivative of f. It represents the net signed area between the curve and the x-axis over the interval from a to b.
Ques. What is integration by parts?
Ans. Integration by parts integrates a product of two functions using the rule integral of u dv equals uv minus integral of v du. You pick the first function u by the ILATE order: inverse, logarithmic, algebraic, trigonometric, then exponential.
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