# NCERT Solutions for Class 12 Maths

You’re about to fly from the nest to a new world and we can understand how exciting and nervous you appear to appear on your Class 12 exams. While going through this phase, you need to make your base strong, especially in Maths subject which sets the path for you if you want to pursue a further career in a domain where Maths is very much needed. To make your work easier, GeeksforGeeks now provides Class 12 Maths NCERT Solutions for FREE here.

Class 12 Maths NCERT Solutions provides a solid conceptual base for all the topics included in CBSE Class 12 Maths Syllabus. NCERT Solutions covers all the important theorems and formulae with detailed explanations to promote a better conceptual understanding in students. Our Maths solution can help students like you build a deeper understanding of the concepts like Matrices & Determinants, Integrals, Differentials, trigonometric functions, inverse trigonometric, etc.

NCERT Solutions for Class 12 Maths include all of the answers to problems found in the NCERT Class 12th textbook. These solutions can be used as a reference by students if they get stuck when answering problems or as a source to clarify topics. Math experts meticulously create these NCERT solutions for Class 12 mathematics to guarantee that any student, regardless of intellect level, may easily comprehend the solutions.

Class 12 Mathematics NCERT solutions are incredibly valuable to students studying for the 12th board examinations since they provide students with an idea of the kind of problems that may occur in the exam. CBSE NCERT Solutions for Class 12 Maths assists students in developing a solid mathematical foundation that can also help them during college-level exams. Let’s check the following solutions:

## Chapter 1: Relations and Functions

This section covers **NCERT Solutions for Class 12 Maths Chapter 1 – ****Relation and functions** and discusses the introduction of relations and functions, types of relations, types of functions, the composition of functions and invertible functions, binary operations, and miscellaneous examples.

Here, are a total of five exercises covered in this Chapter. Exercise 1.1 is only based upon the topic types of relations: reflexive, symmetric, transitive, and equivalence relations while the rest of the exercises 1.2, 1.3, and 1.4 are based on one-to-one and onto functions, composite functions, the inverse of a function.

However, miscellaneous exercises cover standard problems based on all the mentioned topics in this Chapter.

**NCERT Solutions for Class 12 Maths of Chapter 1 are here:**

- Exercise 1.1 Set 1, Set 2
- Exercise 1.2
- Exercise 1.3
- Exercise 1.4 Set 1, Set 2
- Miscellaneous Exercise Set 1, Set 2

**More resources for CBSE Class 12 Maths Chapter 1**

- CBSE Class 12 Maths Chapter 1
- Class 12 RD Sharma Solutions Relations and Functions Chapter 1, Chapter 2, and Chapter 3
- All important formulas for Class 12 Chapter 1

## Chapter 2: Inverse Trigonometric Functions

**Inverse Trigonometric Functions **of NCERT Class 12 Maths Solutions, gives an account of various topics such as the remarks based on basic concepts of inverse trigonometric functions, properties of inverse trigonometric functions, and miscellaneous examples.

These concepts are explained very well through examples. Solutions to the exercises from the Chapter can be accessed here. Definition, range, domain, principal value branch, graphs of inverse trigonometric functions, Elementary properties of inverse trigonometric functions.

**NCERT Solutions for Class 12 Maths of Chapter 2 are here:**

- Exercise 2.1
- Exercise 2.2 Set 1, Set 2
- Miscellaneous Exercise Set 1, Set 2

**More resources for CBSE Class 12 Maths Chapter 2**

- CBSE Class 12 Maths Chapter 2
- Class 12 RD Sharma Solutions Inverse Trigonometric Functions
- All important formulas for Class 12 Chapter 2

## Chapter 3: Matrices

In **Chapter 3 of the Class 12 Maths NCERT,** we shall see the definition of a matrix, types of matrices, equality of matrices, operations on matrices such as the addition of matrices and multiplication of a matrix by a scalar, properties of matrix addition, properties of scalar multiplication, multiplication of matrices, properties of multiplication of matrices, transpose of a matrix, symmetric and skew-symmetric matrices, elementary operation or transformation of a matrix, the inverse of a matrix by elementary operations and miscellaneous examples.

Here, you can find the exercise solution links for the topics covered in this Chapter. Initial exercises like Exercise 3.1, 3.2, and 3.3 discusses the problems on Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, Symmetric and Skew Symmetric Matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar.

However, further exercises, Exercise 3.4 and Miscellaneous help to understand the concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse.

**NCERT Solutions for Class 12 Maths of Chapter 3 are here:**

- Exercise 3.1
- Exercise 3.2 Set 1, Set 2
- Exercise 3.3
- Exercise 3.4 Set 1, Set 2
- Miscellaneous Exercise

**More resources for CBSE Class 12 Maths Chapter 3**

- CBSE Class 12 Maths Chapter 3
- Class 12 RD Sharma Solutions Matrices Chapter 1 and Chapter 2
- All important formulas for Class 12 Chapter 3

## Chapter 4: Determinants

Chapter 4 of Class 12 Maths Solutions discusses the topic of **Determinants**. Students will get to learn about the definition and meaning of determinants, remarks based on the order of determinants, properties of determinants, finding the area of a triangle using determinants, minors and cofactors of determinants, adjoint of a matrix, the inverse of a matrix, applications of determinants, and matrices and miscellaneous examples.

Below we have links provided to each exercise solution covered in this Chapter. The first exercises are based on the determinant of a square matrix (up to 3 × 3 matrices), properties of determinants, minors, co-factors, and applications of determinants in finding the area of a triangle.

However, the rest of the five exercises are based on the concepts of Adjoint and inverse of a square matrix. Consistency, inconsistency, and the number of solutions of a system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using the inverse of a matrix.

**NCERT Solutions for Class 12 Maths of Chapter 4 are here:**

- Exercise 4.1
- Exercise 4.2 Set 1, Set 2
- Exercise 4.3
- Exercise 4.4
- Exercise 4.5
- Exercise 4.6 Set 1, Set 2
- Miscellaneous Exercise

**More resources for CBSE Class 12 Maths Chapter 4**

- CBSE Class 12 Maths Chapter 4
- Class 12 RD Sharma Solutions Determinants Chapter 1 and Chapter 2
- All important formulas for Class 12 Chapter 4

## Chapter 5: Continuity and Differentiability

Chapter 5 of Class 12 Maths Solutions starts with the definition of **Continuity**. Students go on to learn about continuity, algebra of continuous function, definition and meaning of differentiability, derivatives of composite functions, derivative of implicit functions, the derivative of inverse trigonometric functions, exponential and logarithmic functions, logarithmic differentiation, derivatives of functions in parametric forms, second-order derivatives, mean value theorem via miscellaneous examples.

Here, students can find the exercises explaining these concepts properly with solutions. The first five exercises deal with problems based on Continuity and differentiability, the derivative of composite functions, chain rule, inverse trigonometric functions, and the derivative of implicit functions. Concept of exponential and logarithmic functions.

While the rest of the exercises are typically based on the questions of Derivatives of logarithmic and exponential functions. Logarithmic differentiation is the derivative of functions expressed in parametric forms. Second-order derivatives. Rolle’s and Lagrange’s Mean Value Theorems (without proof) and their geometric interpretation.

**NCERT Solutions for Class 12 Maths of Chapter 5 are here:**

- Exercise 5.1 Set 1, Set 2
- Exercise 5.2
- Exercise 5.3
- Exercise 5.4
- Exercise 5.5 Set 1, Set 2
- Exercise 5.6
- Exercise 5.7
- Exercise 5.8
- Miscellaneous Exercise

**More resources for CBSE Class 12 Maths Chapter 5**

- CBSE Class 12 Maths Chapter 5
- Class 12 RD Sharma Solutions Continuity and Differentiability Chapter 1, Chapter 2, Chapter 3 and Chapter 4
- All important formulas for Class 12 Chapter 5

## Chapter 6: Applications of Derivatives

Chapter 6 of the Class 12 Maths Solutions provides a definition of **Derivatives**, rate of change of quantities, increasing and decreasing functions, tangents and normals, approximations, maxima and minima, first derivative test, maximum and minimum values of a function in a closed interval, and miscellaneous examples.

Here, students can find the exercises explaining these concepts properly. Applications of derivatives: rate of change of bodies, increasing/decreasing functions, tangents and normals, use of derivatives in approximation, maxima, and minima (first derivative test motivated geometrically, and the second derivative test is given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations).

**NCERT Solutions for Class 12 Maths of Chapter 6 are here:**

- Exercise 6.1
- Exercise 6.2 Set 1, Set 2
- Exercise 6.3 Set 1, Set 2
- Exercise 6.4
- Exercise 6.5 Set 1, Set 2
- Miscellaneous Exercise Set 1, Set 2

**More resources for CBSE Class 12 Maths Chapter 6**

**Important Resources for CBSE Class 12th provided by GeeksforGeeks:-**

**CBSE Class 12 Maths Notes****RD Sharma Solutions Maths Class 12****CBSE Class 12 Maths Formulas****CBSE Physics Class 12 Notes****CBSE Class 11 Chemistry Notes**

## Frequently Asked Questions (FAQs)

**Question 1: Which book is best for Class 12 Boards preparation for Maths?**

**Answer:**

The NCERT textbook, which is recommended by CBSE, is the best book for not only Class 12 Mathematics but any class. Practice NCERT maths book examples and exercise questions to develop the conceptual foundation needed to tackle HOTs (High Order Thinking Problems).

After properly studying the NCERT textbook, students can improve their skills by reading books like RD Sharma and RS Aggarwal. Students should not underestimate the power of NCERT solutions, as the majority of questions on the boards are either straight from NCERT or are based on NCERT.

**Question 2: Is Maths NCERT textbook enough for Class 12 Boards?**

**Answer:**

For class 12 board examinations in Maths, the NCERT textbook is sufficient. Students can readily learn ideas by answering questions from the NCERT textbook.

They can use other reference books or even solve question banks and past year question papers if they want to practise more, as Math is all about practise.

**Question 3: Is Class 12 Maths difficult?**

**Answer:**

The opinion of a subject’s difficulty or easiness is entirely subjective. Math phobia has been imprinted in the minds of some students since childhood. But we’d like to clarify something. Class 12 NCERT Maths is not challenging.

Once you have a solid grasp on the concepts, you can go on to solving solved examples and problems, which will be followed with exercise questions. The only way to master mathematics is to practise a wide range of questions.

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