Class 12 Mathematics NCERT Solutions All Chapters |Free PDFs | Hand written Notes | 2026-2027

Class 12 Mathematics is an important subject for students preparing for board examinations as well as competitive exams. To understand concepts clearly and score well, students need reliable and well-structured study material. Class 12 Maths NCERT Solutions provide complete support by explaining all textbook questions in a clear and step-by-step manner.

These solutions are prepared strictly according to the latest CBSE NCERT syllabus. Each chapter is explained using simple methods so that students can easily understand difficult topics such as Calculus, Algebra, Matrices, Determinants, Probability, Vectors, and Three-Dimensional Geometry. Practicing NCERT Solutions regularly helps students build strong conceptual clarity and improve problem-solving skills.

Along with NCERT Solutions, students also get access to PDF study resources that make preparation more effective. Chapter-wise handwritten notes PDFs help students revise concepts quickly and understand problem-solving techniques in an easy format. These notes are especially useful for last-minute revision before exams.

Students can also download sample papers PDFs based on the latest exam pattern. Solving sample papers helps in understanding question formats, managing time, and improving exam confidence. In addition, important questions PDFs are provided to help students focus on frequently asked and exam-oriented questions.

Another valuable resource is the important formulas PDF, which includes all essential formulas in one place. This helps students revise formulas quickly and avoid mistakes during exams.

Class-12-Maths

Class 12 NCERT Solution Maths – Chapter -wise List

1.Relations and Functions
2. Inverse Trigonometric Functions
3. Matrices
4. Determinants
5. Continuity and Differentiability
6. Applications of Derivatives
7. Integrals
8. Applications of Integrals
9. Differential Equations
10. Vector Algebra
11. Three Dimensional Geometry
12. Linear Programming
13. Probability

Class 12 Maths NCERT Solutions – Main Topics , Formulas, Exercises

Chapter 1 - Relations and Functions

This chapter introduces relations and functions as ways to connect elements of two sets. A relation shows any type of connection, while a function is a special relation where each input has exactly one output. Students learn about domain, codomain, and range. Different types of functions like one-one and onto are also explained. This chapter builds the foundation for calculus and higher mathematics.

Important Topics

• Definition of relation and function
• Domain, codomain, and range
• Types of functions (one-one, onto)
• Algebra of real functions
• Composition of functions

Chapter 2 - Inverse Trigonometric Functions

This chapter deals with inverse trigonometric functions such as sin⁻¹, cos⁻¹, and tan⁻¹. Since trigonometric functions are not one-one in their full domain, their domains are restricted to define inverse functions properly. The chapter focuses on understanding principal values and solving problems using identities.

Important Topics

• Principal value branches
• Domain and range of inverse trigonometric functions
• Properties and identities
• Simplification of expressions

Class 12 Maths NCERT Solutions Chapter 2 Exercises

Exercise 2.1
Exercise 2.2

Chapter 3 - Matrices

Matrices are rectangular arrays of numbers arranged in rows and columns. This chapter introduces different types of matrices and explains matrix operations. It also shows how matrices can be used to solve real-life problems and systems of equations.

Important Topics

• Types of matrices
• Matrix addition and subtraction
• Matrix multiplication
• Transpose of a matrix
• Inverse of a matrix

Class 12 Maths NCERT Solutions Chapter 3 Exercises

Exercise 3.1
Exercise 3.2
Exercise 3.3
Exercise 3.4

Chapter 4 - Determinants

Determinants are numerical values related to square matrices. This chapter explains how to find determinants of matrices and use their properties. Determinants help in solving linear equations and finding the inverse of a matrix.

Important Topics

• Determinant of order 2 and 3
• Properties of determinants
• Minors and cofactors
• Adjoint of a matrix
• Solving linear equations using determinants

Chapter 5 - Continuity and Differentiability

This chapter explains how a function behaves at a point. Continuity means the function has no break at that point, while differentiability shows how smoothly it changes. Limits and derivatives form the core of this chapter.

Important Topics

• Continuity of functions
• Differentiability
• Derivatives of composite functions
• Chain rule
• Derivatives of inverse trigonometric functions

Chapter 6 - Applications of Derivatives

This chapter shows the practical use of derivatives. Students learn how derivatives help in studying the behavior of functions and solving optimization problems.

Important Topics

• Increasing and decreasing functions
• Maxima and minima
• Tangent and normal
• Rate of change
• Optimization problems

Chapter 7 - Integrals

Integration is the reverse of differentiation. This chapter introduces indefinite and definite integrals along with standard methods of integration. It is one of the most important chapters in calculus.

Important Topics

• Indefinite integrals
• Definite integrals
• Substitution method
• Integration by parts
• Partial fractions
• Properties of definite integrals

Chapter 8 - Applications of Integrals

This chapter explains how integrals are used to find areas under curves and between curves. Graphs play an important role in solving problems.

Important Topics

• Area under simple curves
• Area between two curves
• Graph-based problems

Class 12 Maths NCERT Solutions Chapter 8 Exercises

Exercise 8.1

Chapter 9 - Differential Equations

Differential equations are equations involving derivatives. This chapter teaches how to form and solve basic differential equations, which are widely used in science and engineering.

Important Topics

• Order and degree
• Formation of differential equations
• Variable separable method
• Homogeneous differential equations

Chapter 10 - Vector Algebra

Vector algebra deals with quantities having both magnitude and direction. This chapter forms the base of three-dimensional geometry and physics applications.

Important Topics

• Vector representation
• Addition of vectors
• Scalar (dot) product
• Vector (cross) product
• Projection of vectors

Chapter 11 - Three-Dimensional Geometry

This chapter studies geometry in three-dimensional space. It explains how to represent points, lines, and planes using mathematical equations.

Important Topics

• Distance between two points
• Direction ratios and direction cosines
• Equation of a line
• Angle between lines
• Shortest distance between lines

Chapter 12 - Linear Programming

Linear programming is used to find the best possible solution under given conditions. Problems are solved graphically to find maximum or minimum values.

Important Topics

• Formulation of LPP
• Constraints
• Feasible region
• Optimal solution
• Graphical method

Class 12 Maths NCERT Solutions Chapter 12 Exercises

Exercise 12.1

Chapter 13 - Probability

Probability deals with the likelihood of events. This chapter helps students understand uncertainty and decision-making using mathematical rules.

Important Topics

• Conditional probability
• Independent and dependent events
• Multiplication theorem
• Bayes’ theorem
• Real-life probability problems

Class 12 Maths – Chapter – wise Weightage Table

S.No. Units Marks
1 Relations and Functiona 7-9
2 Algebra 9-11
3 Calculus 30-35
4 Vectors and 3D Geometry 12-14
5 Linear Programming 4-5
6 Probability 7-8
Total 80
Internal Assessmen 20

Key Features of Class 12 Maths NCERT Solutions

1. Chapter-wise Structured Answers

All solutions are arranged strictly chapter-wise and exercise-wise, making it easy for students to find answers quickly and study in an organized manner.

2. Simple and Easy Language

The solutions are written in clear, student-friendly English so that even complex mathematical concepts can be understood without confusion.

3. Step-by-Step Explanation

Each problem is solved step by step, showing the complete method instead of just the final answer. This helps students learn the correct problem-solving approach.

4. Exam-Oriented Approach

The solutions are prepared keeping board exam patterns in mind, helping students understand how to present answers properly in exams.

5. Covers All NCERT Exercises

All textbook exercises and in-text questions of Class 12 Maths are fully covered, ensuring complete syllabus preparation.

6. Focus on Important Concepts

Key formulas, methods, and concepts are highlighted within the solutions to strengthen conceptual understanding.

7. Helps in Self-Study

Students can easily use these solutions for self-study, homework practice, and revision without needing constant teacher support.

8. Error-Free and Accurate Methods

Solutions are carefully prepared to follow correct mathematical rules and standard methods, reducing chances of mistakes.

9. Useful for Board and Competitive Exams

These solutions not only help in board exams but also build a strong base for competitive exams like CUET, JEE (basic level), and other entrance tests.

10. Time-Saving for Revision

Clear steps and logical flow help students revise topics quickly before exams.

11. Improves Answer Presentation

Students learn how to write neat, logical, and well-structured answers, which is important for scoring good marks.

12. Suitable for Digital Learning

The solutions are ideal for online study platforms, PDFs, mobile apps, and educational websites.

Frequently Asked Questions – Class 12 Maths NCERT Solutions

1. What are Class 12 Maths NCERT Solutions on Edutehri?

Class 12 Maths NCERT Solutions on Edutehri are step-by-step answers to all textbook questions, designed to help students understand concepts clearly and prepare confidently for board exams.

2. Are Edutehri’s Class 12 Maths NCERT Solutions free to use?

Yes, all Class 12 Maths NCERT Solutions available on Edutehri are completely free and accessible for students without any subscription or hidden charges.

3. Do these solutions cover all chapters of Class 12 Maths?

Yes, Edutehri provides solutions for all chapters of Class 12 Maths, including calculus, algebra, vectors, three-dimensional geometry, linear programming, and probability.

4. Are the solutions useful for CBSE board exam preparation?

Absolutely. The solutions on Edutehri are prepared according to the latest NCERT syllabus and follow an exam-oriented approach suitable for CBSE board exams.

5. Are the answers explained step by step?

Yes, every question on Edutehri is solved in a clear, step-by-step manner, helping students understand the method, not just the final answer.

6. Can Class 12 Maths NCERT Solutions help in competitive exams?

Yes, these solutions help build strong basics, which are useful for entrance exams like CUET and other undergraduate-level competitive exams.

7. Are Edutehri’s Maths solutions easy for self-study?

Yes, the solutions are written in simple English, making them ideal for self-study, homework practice, and last-minute revision.

8. How often are the NCERT solutions updated on Edutehri?

Edutehri regularly reviews and updates its Class 12 Maths NCERT Solutions to keep them accurate and aligned with the current syllabus and exam pattern.

9. Can I download Class 12 Maths NCERT Solutions from Edutehri?

Yes, selected chapters and solutions on Edutehri are available in downloadable formats, allowing students to study offline at their convenience.

10. Why should I choose Edutehri for Class 12 Maths NCERT Solutions?

Edutehri offers free, accurate, easy-to-understand, and exam-focused Maths solutions, making it a reliable learning platform for Class 12 students.

Class 12 NCERT Solutions For Maths Stream

Classs- 12th Mathematics NCERT Solutions All Chapters - Hand Written Notes | Free download PDF's | 2026-2027