Download Class 12 Maths NCERT Solutions: Chapter-wise PDF for free in Hindi and English. Best Handwritten Notes for NCERT/ CBSE/ Boards – Class 12 is a turning point in every student’s academic journey, and Mathematics plays a crucial role, especially for those aspiring to pursue careers in engineering, economics, statistics, and research. The NCERT Maths textbook for Class 12 is not just a syllabus requirement—it’s the most authentic and reliable resource for mastering core concepts that appear in the CBSE board exams and competitive exams like JEE Main, BITSAT, and others.
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However, understanding every concept from scratch, solving complex questions, and revising formulas and theorems can feel overwhelming. That’s where Class 12 Maths NCERT Solutions come to your rescue. These solutions are structured chapter-wise, providing step-by-step answers to all exercises from both Part 1 and Part 2 of the textbook. These chapters are included: Relations and Functions, Inverse Trigonometric Functions, Matrices, Determinants, Continuity and Differentiability, Application of Derivatives, Integrals, Application of Integrals, Differential Equations, Vector Algebra, Three-Dimensional Geometry, Linear Programming, Probability
Whether you’re looking for quick clarification or comprehensive revision, these chapter-wise Class 12 Maths NCERT solutions PDFs are ideal for deep learning. In this post, we bring you a consolidated guide to all Class 12 Maths chapters, complete with detailed explanations, tips, and direct download links.
This single page is your go-to destination for:
- Accurate NCERT solutions curated by subject experts
- Easy-to-access chapter-wise links
- Clear explanations that follow the CBSE pattern
- Smart strategies for preparation and scoring high in board exams
Bookmark this article to stay focused and avoid distractions while studying. Let’s explore why NCERT solutions are the best companions for your board preparation.
Table of All Chaptes of Class 12 Maths NCERT Solutions
| 📚 Chapter No. | Chapter Name | Download Link |
|---|---|---|
| 1 | Relations and Functions | Download Solutions PDF |
| 2 | Inverse Trigonometric Functions | Download Solutions PDF |
| 3 | Matrices | Download Solutions PDF |
| 4 | Determinants | Download Solutions PDF |
| 5 | Continuity and Differentiability | Download Solutions PDF |
| 6 | Application of Derivatives | Download Solutions PDF |
| 7 | Integrals | Download Solutions PDF |
| 8 | Application of Integrals | Download Solutions PDF |
| 9 | Differential Equations | Download Solutions PDF |
| 10 | Vector Algebra | Download Solutions PDF |
| 11 | Three-Dimensional Geometry | Download Solutions PDF |
| 12 | Linear Programming | Download Solutions PDF |
| 13 | Probability | Download Solutions PDF |
Suggested Notes of Class 12 Maths on Amazon
Arihant NCERT Solutions for Class 12th Mathematics with Chapterwise Study Notes, including Selected Questions of DIKSHA App | Fully updated as per latest NCERT Textbook
11 Years CBSE Class 12 Mathematics Previous Year-wise Solved Papers (2013 – 2023) powered with Concept Notes 3rd Edition | Previous Year Questions PYQs
Arihant NCERT Solutions Physics,Chemistry,Maths Class 12 (Set of 3) | Latest 2025 Edition with Chapterwise Study Notes and Solved Questions
🧮 Chapter-wise Class 12 Maths NCERT Solutions (With Links & Descriptions)
📘 Chapter 1: Relations and Functions
Topics Covered: Types of relations, types of functions (one-one, onto, etc.), composition of functions, and invertible functions.
This chapter lays the foundation for advanced algebra and helps develop logical reasoning and mapping skills.
🔗 Download Class 12 Maths Chapter 1 Solutions PDF
📘 Chapter 2: Inverse Trigonometric Functions
Topics Covered: Basic concepts of inverse trigonometry, domain and range of inverse trig functions, and their properties.
This chapter is crucial for JEE aspirants and is frequently tested in boards. Understanding these concepts is also helpful in calculus.
🔗 Download Class 12 Maths Chapter 2 Solutions PDF
📘 Chapter 3: Matrices
Topics Covered: Types of matrices, operations (addition, multiplication), properties, and transpose.
An essential chapter in linear algebra, matrices have real-world applications in fields like computer science, engineering, and statistics.
🔗 Download Class 12 Maths Chapter 3 Solutions PDF
📘 Chapter 4: Determinants
Topics Covered: Determinants of matrices up to order 3, properties, minors, cofactors, adjoint, and inverse of a matrix.
This chapter directly connects with Chapter 3 and is often asked in long-form board questions. Determinants are also used in solving systems of equations.
🔗 Download Class 12 Maths Chapter 4 Solutions PDF
📘 Chapter 5: Continuity and Differentiability
Topics Covered: Continuity of functions, differentiability, rules of differentiation, logarithmic and exponential differentiation, and second-order derivatives.
This is one of the most important chapters in calculus. Mastering this chapter will help in understanding Integration and Applications of Derivatives later.
🔗 Download Class 12 Maths Chapter 5 Solutions PDF
📘 Chapter 6: Application of Derivatives
Topics Covered: Increasing/decreasing functions, maxima and minima, tangents and normals, rate of change, and approximation.
This chapter connects calculus with real-world applications such as physics and economics. It is scoring and commonly asked in board exams.
🔗 Download Class 12 Maths Chapter 6 Solutions PDF
📘 Chapter 7: Integrals
Topics Covered: Indefinite integrals, definite integrals, methods of integration (substitution, partial fractions, by parts), and properties of definite integrals.
Considered one of the most important chapters for CBSE and JEE. Integration is the backbone of calculus and is tested extensively.
🔗 Download Class 12 Maths Chapter 7 Solutions PDF
📘 Chapter 8: Application of Integrals
Topics Covered: Area under curves, area bounded by lines, parabolas, and circles.
This chapter focuses on geometrical applications of integration and is extremely scoring in the boards. Stepwise diagrams and working methods are key here.
🔗 Download Class 12 Maths Chapter 8 Solutions PDF
📘 Chapter 9: Differential Equations
Topics Covered: Order and degree of a differential equation, general and particular solutions, methods of solving first-order linear differential equations.
Very important for both CBSE exams and competitive entrance tests. Practice and understanding the methods of solutions are essential.
🔗 Download Class 12 Maths Chapter 9 Solutions PDF
📘 Chapter 10: Vector Algebra
Topics Covered: Vectors and their types, operations on vectors (addition, multiplication), scalar and vector products.
This chapter is foundational for understanding 3D Geometry and Physics. Understanding direction cosines, magnitude, and projections is crucial.
🔗 Download Class 12 Maths Chapter 10 Solutions PDF
These chapters form the calculus and algebra core of Class 12 Maths and are often considered scoring sections when prepared well. With our well-explained solutions, students can:
- Build strong conceptual understanding
- Prepare better for board and entrance exams
- Gain confidence in writing full-step answers
📘 Chapter 11: Three-Dimensional Geometry
Topics Covered: Direction cosines and direction ratios, equation of a line in space, shortest distance between two lines, angles between lines and planes.
This chapter builds upon vector algebra and introduces 3D visualization—a vital skill for JEE and CBSE board exams alike.
🔗 Download Class 12 Maths Chapter 11 Solutions PDF
📘 Chapter 12: Linear Programming
Topics Covered: Formulation of linear programming problems, graphical method of solving LPP (for two variables), feasible and infeasible regions, and optimization.
Linear Programming is one of the easiest and most scoring chapters in the syllabus. It’s commonly asked as a 6-mark question in board exams.
🔗 Download Class 12 Maths Chapter 12 Solutions PDF
📘 Chapter 13: Probability
Topics Covered: Conditional probability, multiplication theorem, Bayes’ theorem, random variables, and probability distribution (mean and variance).
This chapter is both theoretical and application-based. It’s heavily used in Data Science, Statistics, and Computer Science later on.
🔗 Download Class 12 Maths Chapter 13 Solutions PDF
Each chapter above includes:
- Solutions based on the latest CBSE Marking Scheme
- Detailed steps and justification
- Clean formatting and easy navigation
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📚 Chapter Name and 🧮 Exercises of Class 12 Maths
| 📚 Chapter Name | 🧮 Exercises |
|---|---|
| Chapter 1: Relations and Functions | Exercise 1.1, Exercise 1.2, Miscellaneous Exercise |
| Chapter 2: Inverse Trigonometric Functions | Exercise 2.1, Miscellaneous Exercise |
| Chapter 3: Matrices | Exercise 3.1, Exercise 3.2, Exercise 3.3, Miscellaneous Exercise |
| Chapter 4: Determinants | Exercise 4.1, Exercise 4.2, Exercise 4.3, Miscellaneous Exercise |
| Chapter 5: Continuity and Differentiability | Exercise 5.1, Exercise 5.2, Exercise 5.3, Exercise 5.4, Miscellaneous Exercise |
| Chapter 6: Application of Derivatives | Exercise 6.1, Exercise 6.2, Miscellaneous Exercise |
| Chapter 7: Integrals | Exercise 7.1, Exercise 7.2, Exercise 7.3, Exercise 7.4, Miscellaneous Exercise |
| Chapter 8: Application of Integrals | Exercise 8.1, Miscellaneous Exercise |
| Chapter 9: Differential Equations | Exercise 9.1, Exercise 9.2, Miscellaneous Exercise |
| Chapter 10: Vector Algebra | Exercise 10.1, Exercise 10.2, Miscellaneous Exercise |
| Chapter 11: Three Dimensional Geometry | Exercise 11.1, Exercise 11.2, Miscellaneous Exercise |
| Chapter 12: Linear Programming | Exercise 12.1, Exercise 12.2 |
| Chapter 13: Probability | Exercise 13.1, Exercise 13.2, Miscellaneous Exercise |
📚 Why Choose Our NCERT Solutions for Class 12 Maths?
If you’re wondering whether NCERT is enough for your Class 12 Maths preparation, the answer is a confident YES—especially if you’re studying under CBSE or preparing for national-level entrance exams. Here’s why:
Each solution includes:
- Step-by-step explanations
- Clean formatting
- Clear application of formulas
- Board-exam-ready answers
By working through these solutions regularly, students can eliminate doubts and build problem-solving speed and accuracy.
1. 🔍 Aligned with the Latest CBSE Curriculum
NCERT books are designed by top academic experts and are officially prescribed by CBSE. The chapter structure, topic sequence, and even the question types directly match the board exam pattern. By solving NCERT thoroughly, you are automatically preparing for your final board exams.
2. 🧠 Concept-Based Learning
Instead of promoting rote learning, NCERT focuses on conceptual understanding. Each exercise is built to challenge your problem-solving ability and strengthen your grasp of important mathematical principles.
3. 🧾 Step-by-Step Solutions
Our Class 12 Maths NCERT solutions provide clear, logical steps for every question. This helps in:
- Understanding different solving methods
- Identifying shortcuts for MCQs
- Learning how to write answers for full marks in board exams
4. 📈 Helpful for JEE, NDA, CUET & More
Topics like Determinants, Integrals, Probability, and Vectors form the backbone of several competitive exams. NCERT builds a strong foundation that helps in solving advanced problems easily.
5. ✅ Proven Track Record
Every year, the majority of Class 12 CBSE toppers claim that NCERT was their main source of preparation. Even CBSE sample papers and actual board questions are based on NCERT’s framewo
🧠 How to Use These NCERT Solutions Effectively
Getting access to all chapter-wise solutions is one thing—knowing how to use them smartly can drastically boost your performance. Here’s how you should approach these PDFs:
✅ 1. Don’t Start with Solutions
Always attempt the exercise questions on your own first. Then, use the solutions only to verify your steps, not as a shortcut.
✅ 2. Highlight Your Mistakes
When you compare your answer to the provided solution, highlight the mistake in your notebook and note down the correct concept or formula. Over time, this will reduce repetition of errors.
✅ 3. Follow a Schedule
Plan a weekly study schedule. For example:
- Monday: Algebra (Relations, Matrices)
- Wednesday: Calculus (Continuity, Differentiability, Integrals)
- Saturday: Probability + LPP
Stick to a realistic timetable with short, daily practice sessions.
✅ 4. Practice Diagram-Based and Graphical Questions
For chapters like Application of Integrals, LPP, and 3D Geometry, try to draw the diagrams by hand and learn the logical flow. It improves understanding and helps in scoring full marks.
✅ 5. Use in Revision
During your final revision, skip theory and directly go through the solved NCERT problems to refresh problem-solving techniques and formulas.
✅ 6. Solve Exemplar Problems Alongside
Once you’re confident with NCERT solutions, level up with NCERT Exemplar and previous year CBSE questions. This will give a competitive edge.
🎯 Tips to Score Maximum Marks in Class 12 Maths
Want to turn your preparation into performance? Use these smart tips to score 90+ in Maths:
✅ 1. Focus on Step-by-Step Writing
CBSE gives marks for steps. Even if the final answer is wrong, writing proper steps can still fetch partial marks.
Use our NCERT solutions to practice step-by-step writing, especially in calculus and algebra chapters.
✅ 2. Understand the Blueprint
Before exams, refer to the official CBSE marking scheme and chapter-wise weightage. Prioritize topics like:
- Integration
- Application of Derivatives
- Probability
- Matrices & Determinants
✅ 3. Time Management During Exam
- 15 minutes reading time → mark easiest questions
- Attempt 6-mark questions first (usually from calculus)
- Leave 10 minutes for final revision
✅ 4. Use Diagrams Wherever Needed
In chapters like Application of Integrals, LPP, and 3D Geometry, neatly labeled graphs or diagrams show conceptual clarity and add visual value to your answers.
✅ 5. Practice Sample Papers Regularly
Try at least 1 mock paper per week in the last 2 months. It improves:
- Speed
- Accuracy
- Time management
- Exam temperament
📚 Final Preparation Strategy Using NCERT
Follow this 3-stage plan using the solutions shared above:
🔹 Stage 1: Foundation Building
- Read the NCERT theory
- Practice each example and exercise
- Refer to the solution only after attempting the question yourself
🔹 Stage 2: Smart Practice
- Identify weak areas and focus on them
- Use chapter-wise solutions to learn alternative methods
- Start solving miscellaneous and HOTS problems
🔹 Stage 3: Exam Readiness
- Weekly mock tests
- Solve previous year CBSE papers
- Refer only to solutions for revising steps & formula application
- Keep a formula notebook for last-minute revision
Chapter-wise Important Formulas for Class 12 Maths
| 📚 Chapter | Important Formulas |
|---|---|
| 1. Relations and Functions | – Number of relations from set A to B = n(A)×n(B)n(A) \times n(B) – Types of functions: One-one, onto, bijective |
| 2. Inverse Trigonometric Functions | – sin−1x+cos−1x=π2\sin^{-1}x + \cos^{-1}x = \frac{\pi}{2} – tan−1x+cot−1x=π2\tan^{-1}x + \cot^{-1}x = \frac{\pi}{2} – sec−1x=cos−1(1x)\sec^{-1}x = \cos^{-1}\left(\frac{1}{x}\right) |
| 3. Matrices | – A+B=B+AA + B = B + A – (AB)T=BTAT(AB)^T = B^T A^T – Identity Matrix: AI=IA=AAI = IA = A |
| 4. Determinants | – ( \text{Area of triangle} = \frac{1}{2} \left |
| 5. Continuity and Differentiability | – ddx(ex)=ex\frac{d}{dx}(e^x) = e^x – ddx(lnx)=1x\frac{d}{dx}(\ln x) = \frac{1}{x} – Chain Rule: dydx=dydu⋅dudx\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx} |
| 6. Application of Derivatives | – Increasing: f′(x)>0f'(x) > 0, Decreasing: f′(x)<0f'(x) < 0 – Maxima/Minima using first and second derivative test – Equation of Tangent: y−y1=f′(x1)(x−x1)y – y_1 = f'(x_1)(x – x_1) |
| 7. Integrals | – ∫xndx=xn+1n+1+C\int x^n dx = \frac{x^{n+1}}{n+1} + C – ( \int \frac{1}{x} dx = \ln |
| 8. Application of Integrals | – Area under curve: ∫ab[f(x)−g(x)]dx\int_a^b [f(x) – g(x)] dx – Area between curves, using definite integration |
| 9. Differential Equations | – Order = highest derivative – Linear form: dydx+Py=Q\frac{dy}{dx} + Py = Q – Integrating Factor (IF) = e∫Pdxe^{\int P dx} |
| 10. Vector Algebra | – Dot product: ( \vec{a} \cdot \vec{b} = |
| 11. Three-Dimensional Geometry | – Line in space: x−x1a=y−y1b=z−z1c\frac{x – x_1}{a} = \frac{y – y_1}{b} = \frac{z – z_1}{c} – Distance between skew lines – Angle between two lines: ( \cos \theta = \frac{\vec{a} \cdot \vec{b}}{ |
| 12. Linear Programming | – No formulas, but techniques: Graphing inequalities, feasible region, corner point method – Objective function: Z=ax+byZ = ax + by |
| 13. Probability | – P(A∪B)=P(A)+P(B)−P(A∩B)P(A \cup B) = P(A) + P(B) – P(A \cap B) – Conditional Probability: ( P(A |
FAQs for “Class 12 Maths NCERT Solutions”
Answer: The best way to study Class 12 Maths NCERT is to first understand the theory, then solve all exercise questions yourself, and finally refer to chapter-wise NCERT solutions for clarifying doubts and improving step-wise presentation.
Answer: Yes, NCERT solutions are sufficient for scoring high in Class 12 Maths board exams. They are based on the latest CBSE syllabus and exam pattern, and cover all important concepts and question types.
Answer: You can download chapter-wise Class 12 Maths NCERT solutions PDFs for free from StudyCart24.com. All chapters from Relations & Functions to Probability are available with step-by-step explanations.
Answer: There are 13 chapters in Class 12 Maths NCERT, including topics like Matrices, Integrals, Application of Derivatives, Probability, and Linear Programming.
Answer: Absolutely! NCERT solutions for Class 12 Maths form the foundation for JEE Main preparation, especially in topics like Calculus, Matrices, Determinants, and Probability.
Answer: Yes, many CBSE toppers rely only on NCERT for scoring 90+ in Maths. Focus on understanding concepts, practicing all NCERT questions, and revising with solutions to strengthen your preparation.
Answer: Important chapters in Class 12 Maths include Integrals, Application of Derivatives, Probability, Differential Equations, and Three-Dimensional Geometry, as they carry high weightage in board exams.
Answer: Yes, the NCERT solutions on StudyCart24 are updated as per the latest CBSE syllabus and board exam guidelines for the academic year.
✅ Conclusion: Download Class 12 Maths NCERT Solutions & Start Today
The key to mastering Class 12 Maths lies in consistency, clarity, and confidence. Our chapter-wise NCERT solutions PDFs are designed to:
- Save your time
- Clear your doubts
- Provide exam-ready step-wise answers
- Help you score maximum marks
Whether you’re preparing for CBSE Board Exams or JEE Main, this consolidated page is all you need. Click on each chapter link, download the solutions, and start practicing.
🎓 Pro Tip: Bookmark this page and visit daily during your revision phase.
✍️ For regular updates, revision notes, and exam tips, stay connected with us at StudyCart24.com.
📣 Share this post with your classmates — let’s all score better, together!
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