NCERT Solutions for Class 12 Maths Chapter Wise Solutions

Chapter 1 Relations and Functions

Relationships and functions, relation types, function types, function composition, invertible functions, binary operations, and other examples are covered in Chapter 1 of the NCERT textbook. The links to the exercise solutions for the subjects discussed in this chapter are provided here.

Maths Class 12 NCERT Solutions Chapter 1 Exercises
Exercise 1.1
Exercise 1.2
Exercise 1.3
Exercise 1.4
Miscellaneous Exercise

Chapter 2 Inverse Trigonometric Functions

Chapter 2, Inverse Trigonometric Functions of NCERT Class 12 Maths, provides an overview of a number of subjects, including properties of inverse trigonometric functions, remarks based on fundamental ideas of inverse trigonometric functions, and different examples. The examples used to illustrate these ideas are excellent. You may find the answers to the chapter's exercises here.

Maths Class 12 NCERT Solutions Chapter 2 Exercises
Exercise 2.1
Exercise 2.2
Miscellaneous Exercise

Chapter 3 Matrices

The definition of a matrix, matrix types, matrix equality, operations on matrices, including matrix addition and matrix multiplication by a scalar, matrix addition properties, scalar multiplication properties, matrix multiplication properties, matrix transpose properties, symmetric and skew-symmetric matrices, elementary operation or transformation of a matrix, the inverse of a matrix by elementary operations, and various examples are all covered in Chapter 3 of the NCERT textbook. The links to the exercise solutions for the subjects discussed in this chapter are provided here.

Maths Class 12 NCERT Solutions Chapter 3 Exercises
Exercise 3.1
Exercise 3.2
Exercise 3.3
Exercise 3.4
Miscellaneous Exercise

Chapter 4 Determinants

Determinants are covered in Chapter 4 of the 12 Class NCERT Maths Solution. The definition and meaning of determinants, remarks based on their order, properties, finding the area of a triangle using determinants, determining determinants' minors and cofactors, adjoint of a matrix, inverse of a matrix, applications of determinants and matrices, and various examples will all be covered for the students. Links to all of the exercise solutions discussed in this chapter are included below.

Maths Class 12 NCERT Solutions Chapter 4 Exercises
Exercise 4.1
Exercise 4.2
Exercise 4.3
Exercise 4.4
Exercise 4.5
Exercise 4.6
Miscellaneous Exercise

Chapter 5 Continuity and Differentiability

The definition of continuity opens Chapter 5 of the NCERT textbook. Through a variety of examples, students learn about the following topics: continuity, algebra of continuous functions, concept and meaning of differentiability, derivatives of composite functions, derivatives of implicit functions, derivatives of inverse trigonometric functions, exponential and logarithmic functions, logarithmic differentiation, derivatives of parametric functions, second order derivatives, and mean value theorem. Students can find tasks that adequately explain these ideas along with solutions below.

Maths Class 12 NCERT Solutions Chapter 5 Exercises
Exercise 5.1
Exercise 5.2
Exercise 5.3
Exercise 5.4
Exercise 5.5
Exercise 5.6
Exercise 5.7
Exercise 5.8
Miscellaneous Exercis

Chapter 6 Applications of Derivatives

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 other examples are all covered in Chapter 6 of the NCERT textbook. Students can find tasks that adequately explain these ideas here.

Maths Class 12 NCERT Solutions Chapter 6 Exercises
Exercise 6.1
Exercise 6.2
Exercise 6.3
Exercise 6.4
Exercise 6.5
Miscellaneous Exercise

Chapter 7 Integrals

The definition and meaning of definite integrals, definite integral as the limit of a sum, fundamental theorem of calculus, evaluation of definite integrals by substitution, properties of definite integrals, geometrical interpretation of indefinite integrals, geometrical interpretation of indefinite integrals, comparison between differentiation and integration, and methods of integration such as integration by substitution, integration using partial fractions, integration by parts, integration using trigonometric identities, integration of some integral functions are all covered in Chapter 7, Integrals. Based on these chapter topics, we have provided exercises and solutions here.

Maths Class 12 NCERT Solutions Chapter 7 Exercises
Exercise 7.1
Exercise 7.2
Exercise 7.3
Exercise 7.4
Exercise 7.5
Exercise 7.6
Exercise 7.7
Exercise 7.8
Exercise 7.9
Miscellaneous Exercise

Chapter 8 Applications of Integrals

We continue the topic of integrals in Chapter 8 of the NCERT textbook, covering definition, area under simple curves, area of the region enclosed by a curve and a line, area between two curves, and other examples. Students can access the exercises with solutions that explain the concepts from this chapter by clicking on the links provided below.

Maths Class 12 NCERT Solutions Chapter 8 Exercises
Exercise 8.1
Exercise 8.2
Miscellaneous Exercise

Chapter 9 Differential Equations

Chapter 9, Differential Equations , focuses on solving equations involving derivatives, fundamental to understanding change and motion. It covers formation, order, degree, and methods of solving differential equations, including variable separable, homogeneous, and linear types. This chapter builds essential skills for calculus and its applications in physics, engineering, and real-world problems.

Maths Class 12 NCERT Solutions Chapter 9 Exercises
Exercise 9.1
Exercise 9.2
Exercise 9.3
Exercise 9.4
Exercise 9.5
Exercise 9.6
Miscellaneous Exercise

Chapter 10 Vector Algebra

Chapter 10, Vector Algebra , explores the mathematical study of vectors, essential for physics and engineering. It covers vector operations like addition, subtraction, scalar multiplication, and dot and cross products. These concepts simplify spatial problems and provide tools for understanding geometry, motion, and forces in three-dimensional space effectively.

Maths Class 12 NCERT Solutions Chapter 10 Exercises
Exercise 10.1
Exercise 10.2
Exercise 10.3
Exercise 10.4
Miscellaneous Exercise

Chapter 11 Three Dimensional Geometry

Chapter 11, Three-Dimensional Geometry , delves into the spatial representation of points, lines, and planes. It covers direction cosines, direction ratios, the equation of lines and planes, and their intersections. This chapter equips students with tools to analyze and solve complex spatial problems, crucial for engineering, physics, and architecture applications.

Maths Class 12 NCERT Solutions Chapter 11 Exercises
Exercise 11.1
Exercise 11.2
Exercise 11.3
Miscellaneous Exercise

Chapter 12 Linear Programming

Students learn about linear programming in this chapter. This chapter covers the following topics: the mathematical formulation of linear programming problems, the mathematical formulation of the problem, the graphical way of addressing linear programming problems, and many forms of linear programming problems with various examples. Students can locate exercises that provide solutions and a proper explanation of these ideas.

Maths Class 12 NCERT Solutions Chapter 12 Exercises
Exercise 12.1
Exercise 12.2

Chapter 13 Probability