NCERT Solutions for Class 12 Maths - Download Chapter Wise Solution PDF

NCERT Solutions for Class 12 Maths 2025–26

To support students' preparation, Careers360 has compiled all Class 12 Maths NCERT solutions here for quick, convenient access.

Class 12 Maths NCERT Solutions Exercises

Students can download the NCERT Solution of Maths of Class 12, chapter-wise, from the links given below.

NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions

NCERT Solutions for Class 12 Maths Chapter 1: Relations and Functions are provided here. If two sets of elements are related in some way, we say these two sets have a relation. Father, mother, sister, and brother are real-life examples of relations. A relation becomes a function when, for every input, there is only one output. For different inputs, the output can be the same. Every function is a relation, but not every relation represents a function. For PDF and notes, refer to Class 12 Maths Chapter 1 Relations and Functions Notes. Also, for the exemplar solutions of Relations and functions, refer to the NCERT Exemplar Solutions for Class 12 Maths Chapter 1 Relations and Functions.

Topics:

1.1 Introduction
1.2 Types of Relations
1.3 Types of Functions
1.4 Composition of Functions and Invertible Functions

Find detailed, step-by-step solutions to the exercises through the links given below.

NCERT Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions

In Class 11 Maths, you have already learned about trigonometric functions. The inverse trigonometric function is the inverse of a trigonometric function. If you are good at trigonometric functions, it won't take much effort to get a command of the inverse trigonometric functions. Students can study using the inverse trigonometric function class 12 Solutions PDF. For PDF and notes, refer to Class 12 Maths Chapter 1 Inverse Trigonometric Functions Notes. Also, for the exemplar solutions of inverse trigonometric functions, refer to NCERT Exemplar Solutions for Class 12 Maths Chapter 1 Inverse Trigonometric Functions.

In the NCERT Class 12 Maths solutions of this chapter, you will learn concepts related to the definition of inverse trigonometric functions, domain, range, principal value, graph, and properties of inverse trigonometric functions. In class 11, you have already learned that trigonometric functions are not one-to-one and onto in their natural ranges. We restrict domains and ranges of trigonometric functions to enable their inverse to be one-one and onto.

Topics:

2.1 Introduction
2.2 Basic Concepts
2.3 Properties of Inverse Trigonometric Functions

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NCERT Solutions for Class 12 Maths Chapter 3 Matrices

The array of numbers or mathematical objects called a "Matrix" is used for operations like addition and multiplication. It was introduced to solve simultaneous linear equations. Matrix has a lot of applications in engineering, scientific studies, computer graphics (images or videos that you see are matrices of colour intensities), storage of big data, etc. For PDF and notes, refer to Class 12 Maths Chapter 3 Matrices Notes. Also, for the exemplar solutions of matrices, refer to NCERT Exemplar Solutions for Class 12 Maths Chapter 3 Matrices.

Topics:

3.1 Introduction
3.2 Matrix
3.3 Types of Matrices
3.4 Operations on Matrices
3.5 Transpose of a Matrix
3.6 Symmetric and Skew Symmetric Matrices
3.7 Invertible Matrices

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NCERT Solutions for Class 12 Maths Chapter 4 Determinants

In the previous chapter, you have already learned about matrices and their properties. For every square matrix, you can compute a number called "Determinant". It shows the factor by which the area or volume of a linear transformation has changed. For PDF and notes, refer to Class 12 Maths Chapter 4 Determinants Notes. Also, for the exemplar solutions of determinants, refer to the NCERT Exemplar Solutions for Class 12 Maths Chapter 4 Determinants.

Topics:

4.1 Introduction
4.2 Determinant
4.3 Area of a Triangle
4.4 Minors and Cofactors
4.5 Adjoint and Inverse of a Matrix
4.6 Applications of Determinants and Matrices

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NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability

In Class 11 NCERT, you have learned about the differentiation of certain functions. In Class 12 NCERT Solutions for this chapter, you will learn about differentiability, continuity, and how differentiability is related to continuity. For PDF and notes, refer to Class 12 Maths Chapter 5 Continuity and Differentiability Notes. Also, for the exemplar solutions of Continuity and Differentiability, refer to Ncert Exemplar Solutions For Class 12 Maths Chapter 5 Continuity and Differentiability

Topics:

5.1 Introduction
5.2 Continuity
5.3 Differentiability
5.4 Exponential and Logarithmic Functions
5.5 Logarithmic Differentiation
5.6 Derivatives of Functions in Parametric Forms
5.7 Second Order Derivative

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NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives

In Chapter 5, you have learned how to find the derivative of implicit functions, composite functions, exponential functions, inverse trigonometric functions, and logarithmic functions. In this chapter, you are going to study the applications of derivatives in various fields like science, social science, engineering, and many other fields. For PDF and notes, refer to Class 12 Maths Chapter 6 Application of Derivatives Notes. Also, for the exemplar solutions of Application of Derivatives, refer to Ncert Exemplar Solutions For Class 12 Maths Chapter 6 Application of Derivatives.

Topics:

6.1 Introduction
6.2 Rate of Change of Quantities
6.3 Increasing and Decreasing Functions
6.4 Maxima and Minima

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NCERT Solutions for Class 12 Maths Chapter 7 Integrals

Differential calculus is centred around the concepts of differentiation, defining tangent, and calculating the slope of a line. Integral calculus is centred around defining and calculating the area of the region bounded by the graph of a function. Integration means 'bringing together, which is the inverse process of differentiation (set-apart). For PDF and notes, refer to Class 12 Maths Chapter 7 Integrals Notes. Also, for the exemplar solutions of Integrals, refer to Ncert Exemplar Solutions for Class 12 Maths Chapter 7 Integrals.

Topics:

7.1 Introduction
7.2 Integration as an Inverse Process of Differentiation
7.3 Methods of Integration
7.4 Integrals of Some Particular Functions
7.5 Integration by Partial Fractions
7.6 Integration by Parts
7.7 Definite Integral
7.8 Fundamental Theorem of Calculus
7.9 Evaluation of Definite Integrals by Substitution
7.10 Some Properties of Definite Integrals

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NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals

In the previous chapter, you learned about the integration of different complicated functions. Well, it has a lot of applications, like calculating the area between curves, calculating distance, velocity, acceleration, finding the average value of a function, probability, surface area, etc. For PDF and notes, refer to Class 12 Maths Chapter 9 Applications of Integrals Notes. Also, for the exemplar solutions of Application of Integrals, refer to NCERT Exemplar Solutions for Class 12 Maths Chapter 8 Applications of Integrals.

Topics:

8.1 Introduction
8.2 Area under Simple Curves

Click on the links below to explore step-by-step explanations for all exercise questions.

NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations

You have learned about differentiation and integration. A differential equation is an equation of a function with one or more derivatives. In this chapter, you are going to learn some basic concepts related to differential equations, particular and general solutions of a differential equation, different methods to solve a first-order-first-degree differential equation, solutions of linear differential equations, the formation of differential equations, and discuss some applications of differential equations in different areas. For PDF and notes, refer to Class 12 Maths Chapter 9 Differential Equations Notes. Also, for the exemplar solutions of Differential Equations, refer to NCERT Exemplar Solutions for Class 12 Maths Chapter 9 Differential Equations.

Topics:

9.1 Introduction
9.2 Basic Concepts
9.3 General and Particular Solutions of a Differential Equation
9.4 Methods of Solving First Order, First Degree Differential Equations

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NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra

Think about the situation where you are applying force to a box. So it has two quantities: the magnitude that you are applying and the direction in which you are applying the force. Such quantities with both magnitude and direction are termed vector quantities. For PDF and notes, refer to NCERT Notes for Class 12 Maths Chapter 10 Vector Algebra. Also, for the exemplar solutions of Vector Algebra, refer to NCERT Exemplar Solutions for Class 12 Maths Chapter 10 Vector Algebra.

Topics:

10.1 Introduction
10.2 Some Basic Concepts
10.3 Types of Vectors
10.4 Addition of Vectors
10.5 Multiplication of a Vector by a Scalar
10.6 Product of Two Vectors

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NCERT Solutions for Class 12 Maths Chapter 11 Three-Dimensional Geometry

In the previous class, you learned 2-D geometry. 3-D geometry is an extension of 2-D geometry that takes into consideration three orthogonal axes. Augustus De Morgan quotes, "the moving power of mathematical invention is not reasoning but imagination". Visualising in 3-D geometry requires more of your imagination. For PDF and notes, refer to Class 12 Maths Chapter 11 Three-Dimensional Geometry Notes. Also, for the exemplar solutions of Three Dimensional Geometry, refer to the NCERT Exemplar Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry

Topics:

11.1 Introduction
11.2 Direction Cosines and Direction Ratios of a Line
11.3 Equation of a Line in Space
11.4 Angle between Two Lines
11.5 Shortest Distance between Two Lines

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NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming

You often come across problems where you seek to maximise profit or minimise cost. Linear programming is useful to find the optimal solution for such problems. We formulate these real-life problems into a mathematical model. For PDF and notes, refer to Class 12 Maths Chapter 12 Linear Programming Notes. Also, for the exemplar solutions of Linear Programming, refer to Ncert Exemplar Solutions For Class 12 Maths Chapter 12 Linear Programming.

Topics:

12.1 Introduction
12.2 Linear Programming Problem and its Mathematical Formulation

Find detailed, step-by-step solutions to the exercises through the links given below.

NCERT Solutions for Class 12 Maths Chapter 13 Probability

In previous classes, you have learned that probability means how likely something is to happen. In this chapter, you will learn the important concept of the conditional probability of an event given that another event has occurred, which will help you understand the multiplication rule of probability, Bayes' theorem, and independence of events. For PDF and notes, refer to Class 12 Maths Chapter 13 Probability Notes. Also, for the exemplar solutions of Probability, refer to NCERT Exemplar Solutions for Class 12 Maths Chapter 13 Probability.

Topics:

13.1 Introduction
13.2 Conditional Probability
13.3 Multiplication Theorem on Probability
13.4 Independent Events
13.5 Bayes' Theorem

Access complete solutions for each exercise by following the links provided here.

Why are Class 12 Maths NCERT Solutions Important?

Class 12 Maths is an important subject that builds a base for higher studies and competitive exams. It covers many topics like Calculus, Algebra, Probability, and Geometry that are useful in real life too. These NCERT Class 12 Maths Solutions help students understand each concept clearly and practice different types of questions. Here are some more points on why these solutions are important.

• These solutions make it easier to learn tough topics like Integrals, Differential Equations, and Vector Algebra through step-by-step answers.

• Using these solutions helps us save time during revision and improves accuracy in solving problems.

• These NCERT Solutions for Class 12 Maths also prepare us for higher classes, especially for courses like engineering, data science, and economics.

• Regular practice with these solutions boosts confidence for board exams and builds a strong base for future studies.

NCERT Exemplar Solutions for Class 12 - subject-wise

Given below are the subject-wise links for the NCERT exemplar solutions of class 12:

• NCERT Exemplar Class 12 Chemistry Solutions
• NCERT Exemplar Class 12 Mathematics Solutions
• NCERT Exemplar Class 12 Biology Solutions
• NCERT Exemplar Class 12 Physics Solutions

NCERT Solutions for Class 12 - subject-wise

Here are the subject-wise links for the NCERT solutions of class 12:

• NCERT Solutions class 12 chemistry
• NCERT Solutions for class 12 physics
• NCERT Solutions for class 12 biology

NCERT Books and NCERT Syllabus

Here are some useful links for NCERT books and the NCERT syllabus for class 12:

• NCERT Books Class 12 Maths
• NCERT Syllabus Class 12 Maths
• NCERT Books Class 12
• NCERT Syllabus Class 12