In the class 12th Science stream, students are provided the option to choose from Mathematics and Biology as their main subjects. This selection of subjects changes the way they approach their future. Students opting for the Biology subject go for the medical field, while those selecting Mathematics as their main subject look for their career in the Engineering and related disciplines.
In this article, we have shared the NCERT Solutions for Class 12 Maths so that all the students who have opted for Mathematics as one of their core subjects can get the right answers to all their questions and have a better understanding of the topics.
NCERT Solutions for Class 12 Maths
The Class 12th Mathematics is one of the most crucial parts of the Mathematics subject in the whole, as the CBSE Class 12 Maths Syllabus comprises of some of the most crucial and important topics that lay the foundation for the next level of education. Students aspiring to appear for the engineering entrance examinations like JEE, BITSAT, VITEE, etc., need to ensure that all their concepts and doubts are clear for all the topics mentioned in the syllabus.
Reading and learning all the algorithms and understanding the concepts is the most important protect while studying the CBSE Class 12th Mathematics. In the process, students might get stuck with several doubts and questions related to the topics; hence, to assist students with their preparation, we have added the right answers and NCERT Solutions for Class 12 Maths in the article below.
NCERT Solutions for Class 12 Maths Chapter Wise
The Mathematics subject of class 12 is considered the conceptual base for the students, as it teaches crucial topics that help students in their senior level education. The CBSE Class 12 Maths syllabus comprises various important topics, theorems, and formulas that require students to have the conceptual clarity to solve the problems. Hence, to share the right answers to all the questions of CBSE Class 12 Maths, we have shared the direct link connecting with the Chapter Wise NCERT Solutions for Class 12 Maths in the table below:
| NCERT Solutions for Class 12 Maths Chapter Wise | |
| Chapter | Link |
| NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 3 Matrices | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 4 Determinants | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 6 Applications of Derivatives | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 7 Integrals | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 8 Applications of Integrals | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 11 Three-Dimensional Geometry | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 13 Probability | Click Here |
NCERT Solutions for Class 12 Maths Chapter Wise
Each chapter in the class 12 Mathematics subject comprises multiple exercises that teach students with different aspects of the topics, hence, it is crucial that the students must first clear all their doubts about 1 certain exercise and then move to the next one. To help students get NCERT Solutions for Class 12 Maths Exercise Wise, we have added the direct links in the article below:
NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions
Chapter 1 in the NCERT Class 12 Maths textbook covers the education about topics like relations and functions, types of relations, types of functions, the composition of functions and invertible functions, binary operations, and miscellaneous examples. This chapter comprises of 4 exercises along with Miscellaneous Exercise, and the direct links to check the exercise wise NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions are added below in the table:
| NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions | |
| Exercise | Link |
| NCERT Solutions for Class 12 Maths Chapter 1 Exercise 1.1 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 1 Exercise 1.2 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 1 Exercise 1.3 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 1 Exercise 1.4 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 1 Miscellaneous Exercise | Click Here |
NCERT Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions
The Chapter 2 in the NCERT Class 12 Maths book is Inverse Trigonometric Function. This chapter covers various topics like Definition, range, domain, principal value branches, and Graphs of inverse trigonometric functions. Students, while reading this chapter, must understand all the major concepts and properties of inverse trigonometric functions as without grasping the concept, they won’t be able to solve the asked problems. Hence, to help students complete their preparations for the NCERT Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions, exercise wise links are added below:
| NCERT Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions | |
| Exercise | Link |
| NCERT Solutions for Class 12 Maths Chapter 2 Exercise 2.1 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 2 Exercise 2.2 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 2 Miscellaneous Exercise | Click Here |
NCERT Solutions for Class 12 Maths Chapter 3 Matrices
The chapter 3 in the NCERT Class 12 Maths book is Matrices, and this chapter teaches students about the basic Concept, notation, order, equality, types of matrices, zero matrix, transpose of a matrix, symmetric and skew-symmetric matrices. In the 4 exercises of this chapter, students get to read 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, etc.
The table below shares the direct links to access the exercise wise NCERT Solutions for Class 12 Maths Chapter 3 Matrices:
| NCERT Solutions for Class 12 Maths Chapter 3 Matrices | |
| Exercise | Link |
| NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.1 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.2 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.3 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.4 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 3 Miscellaneous Exercise | Click Here |
NCERT Solutions for Class 12 Maths Chapter 4 Determinants
The chapter 4 in the NCERT Class 12 Maths book is Determinants. In this chapter, students are taught about the definition and meaning of determinants, remarks based on order of determinants, properties of determinants, finding area of triangle using determinants, minors and cofactors of determinants, adjoint of a matrix, inverse of matrix, etc.
This chapter comprise of 6 exercises in which students are taught various concepts and properties of the determinants so that they can easily solve the questions and score higher in the exams. The table listed below shares the links to check and access the exercise wise NCERT Solutions for Class 12 Maths Chapter 4 Determinants:
| NCERT Solutions for Class 12 Maths Chapter 4 Determinants | |
| Exercise | Link |
| NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.1 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.2 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.3 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.4 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.5 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.6 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 4 Miscellaneous Exercise | Click Here |
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability
In the chapter 5 of the NCERT textbook, students are taught about the various aspects of Continuity and Differentiability. Students in this chapter learn about the derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, the derivative of implicit function, the Concept of exponential and logarithmic functions and their derivatives, Logarithmic differentiation, Derivative of functions expressed in parametric forms, etc.
To help students with the right answers to all the questions of Chapter 5, the direct link connecting with the NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability are added below in the table:
| NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability | |
| Exercise | Link |
| NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.1 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.2 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.3 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.4 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.5 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.6 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.7 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.8 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 4 Miscellaneous Exercise | Click Here |
NCERT Solutions for Class 12 Maths Chapter 6 Applications of Derivatives
The NCERT Class 12 Maths Chapter 6 name is Applications of Derivatives, in which students get to learn the definition of derivatives, rate of change of quantities, increasing and decreasing functions, tangents and normals, approximations, maxima and minima, first derivative test, etc.
Students, while studying this chapter, are required to prepare for topics like Rate of change, increasing/decreasing functions, tangents and normals, approximation, maxima and minima, etc. To reduce their confusion and maximise their preparations for the topics, we have added the exercise wise NCERT Solutions for Class 12 Maths Chapter 6 Applications of Derivatives in the table below:
| NCERT Solutions for Class 12 Maths Chapter 6 Applications of Derivatives | |
| Exercise | Link |
| NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.1 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.2 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.3 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.4 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.5 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 6 Miscellaneous Exercise | Click Here |
NCERT Solutions for Class 12 Maths Chapter 7 Integrals
The chapter 7, Integrals is a very crucial and important part of the CBSE class 12 Maths syllabus as students in this chapter are taught about the definition of indefinite integral, integration as an inverse process of differentiation, geometrical interpretation of indefinite integral, properties of indefinite integral, comparison between differentiation and integration, methods of integration, etc.
To complete their preparations for this chapter, the students are required to read and understand the fundamental theorem of calculus, evaluation of definite integrals by substitution, etc. To help students with their preparation phase, the direct link connecting with the exercise wise NCERT Solutions for Class 12 Maths Chapter 7 Integrals has been added in the table below:
| NCERT Solutions for Class 12 Maths Chapter 7 Integrals | |
| Exercise | Link |
| NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.1 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.2 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.3 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.4 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.5 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.6 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.7 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.8 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.9 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.10 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.11 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 7 Miscellaneous Exercise | Click Here |
NCERT Solutions for Class 12 Maths Chapter 8 Applications of Integrals
After learning about the Integrals in Chapter 7, the students will be learning about the Applications of Integrals in Chapter 8 of the NCERT Class 12 Maths textbook. Students in this chapter are taught about various topics like Applications in finding the area under simple curves, especially lines, arcs of circles/parabolas/ ellipses (in standard form only), area between the two above-said curves (the region should be clearly identifiable), etc.
The table below shares the direct link connecting students with the exercise wise NCERT Solutions for Class 12 Maths Chapter 8 Applications of Integrals:
| NCERT Solutions for Class 12 Maths Chapter 8 Applications of Integrals | |
| Exercise | Link |
| NCERT Solutions for Class 12 Maths Chapter 8 Exercise 8.1 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 8 Exercise 8.2 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 8 Miscellaneous Exercise | Click Here |
NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations
Chapter 9, named as Differential Equations, is a chapter where students are to focus on basic concepts related to differential equations, degree of a differential equation, order of a differential equation, general and particular solutions of a differential equation, formation of a differential equation, etc.
Students, while studying this chapter are required to get their understanding of the Differential Equations in a manner that helps them solving the differential equations by the method of separation of variables, homogeneous differential equations of first order and first degree.
The direct links to access the exercise wise NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations are tabulated below:
| NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations | |
| Exercise | Link |
| NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.1 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.2 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.3 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.4 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.5 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.6 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 9 Miscellaneous Exercise | Click Here |
NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra
Chapter 10 of the NCERT textbook for class 12th is named Vector Algebra, and students in this chapter are taught about various factors and concepts like how to find position vector, some basic concepts related to vector algebra, direction cosines, types of vectors such as zero vector, unit vector, collinear vector, equal vector, negative of a vector, addition of vectors, etc.
As per the CBSE Class 12 Maths Syllabus, students are taught about various topics, including Vectors and scalars, magnitude and direction of a vector, Direction cosines/ratios of vectors, Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, etc.
Below, we have tabulated the direct link to check the exercise wise NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra:
| NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra | |
| Exercise | Link |
| NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.1 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.2 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.3 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.4 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 10 Miscellaneous Exercise | Click Here |
NCERT Solutions for Class 12 Maths Chapter 11 Three-Dimensional Geometry
The NCERT textbook of class 12 Mathematics contains Three-Dimensional Geometry as chapter 11. All the students who are studying in class 12th are taught about topics related to three dimensional geometry, direction cosines and direction ratios of a line, relation between the direction cosines of a line, direction cosines of a line passing through two points, equation of a line in space, equation of a line through a given point and parallel to a given vector, etc., in this chapter.
During their preparation phase, students can now check and download the NCERT Solutions for Class 12 Maths for Chapter 11 by clicking on the exercise wise links added in the table below:
| NCERT Solutions for Class 12 Maths Chapter 11 Three-Dimensional Geometry | |
| Exercise | Link |
| NCERT Solutions for Class 12 Maths Chapter 11 Exercise 11.1 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 11 Exercise 11.2 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 11 Exercise 11.3 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 11 Miscellaneous Exercise | Click Here |
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming
The chapter 12 in the NCERT Class 12 is named as Linear Programming. Students in this chapter learn about various topics like constraints, objective function, optimization, different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions, etc.
Students, during their preparation phase of this chapter, can check the exercise wise NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming in the table below:
| NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming | |
| Exercise | Link |
| NCERT Solutions for Class 12 Maths Chapter 12 Exercise 12.1 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 12 Exercise 12.2 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 12 Miscellaneous Exercise | Click Here |
NCERT Solutions for Class 12 Maths Chapter 13 Probability
Probability is the last and 13th chapter in the NCERT Class 12 Maths textbook. All the students who are studying in class 12th will find this chapter as the easiest one in the whole syllabus, but this also requires them to have focus and learn certain areas with deep interest and understanding. Some of the topics that are discussed into this chapter are the Multiplication theorem on probability, Conditional probability, independent events, total probability, Baye’s theorem, Random variable and its probability distribution, mean and variance of haphazard variable, etc.
To help students with their preparations, the direct links connecting with the exercise wise NCERT Solutions for Class 12 Maths Chapter 13 Probability are added below in the table:
| NCERT Solutions for Class 12 Maths Chapter 13 Probability | |
| Exercise | Link |
| NCERT Solutions for Class 12 Maths Chapter 13 Exercise 13.1 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 13 Exercise 13.2 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 13 Exercise 13.3 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 13 Exercise 13.4 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 13 Exercise 13.5 | Click Here |
| NCERT Solutions for Class 12 Maths Chapter 13 Miscellaneous Exercise | Click Here |
