Mathematics is one of the main pillars of science and technology, and class 12 is the time when students learn about the advanced concepts of mathematics that build a strong foundation for their higher education and many competitive exams. With concepts like Calculus, Matrices, Probability, and three-dimensional geometry, the students will require a clear understanding, practice, patience, and the right guidance. This is where the NCERT solutions for Class 12 Maths come into play. These NCERT solutions provide a detailed step-by-step explanation of every problem in the NCERT textbook, making these advanced concepts of class 12 very easy to understand. For syllabus, notes, and PDF, refer to this link: NCERT
This Story also Contains
- NCERT Solutions for Class 12 Math, All Chapters 2025–26
- Class 12 Maths NCERT Solutions Exercises
- NCERT Exemplar solutions for class 12 - subject-wise
- NCERT solutions for class 12 - subject-wise
- NCERT Books and NCERT Syllabus
NCERT Solutions for Class 12 Math, All Chapters 2025–26
Chapter-wise Class 12 Maths NCERT solutions are listed below.
Here you will find all the class 12 maths NCERT solutions PDF downloads in a single place, which will be helpful when you are not able to solve the NCERT practice questions on your own. Also, you can use these NCERT solutions for Class 12 as a quick revision of concepts.
CBSE Class 12 Maths Marks Distribution: Unit Wise Weightage
|
Units |
Marks |
|
Relations & Functions |
08 |
|
Algebra |
10 |
|
Calculus |
35 |
|
Vector & 3-Dimensional Geometry |
14 |
|
Linear Programming |
05 |
|
Probability |
08 |
|
Total |
80 |
Class 12 Maths NCERT Solutions Exercises
Students can download the NCERT Solution of Maths of Class 12, chapter-wise, from the links given below.
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.
In the NCERT Class 12 Maths solutions, you will learn about types of relations, reflective, transitive, and equivalence relations, functions, range, domain, and co-domain of a function, which have already been introduced in the Maths of NCERT Class 11. Class 12 Maths NCERT solutions for chapter 1 have 3 exercises. Click on the above link to get Class 12 NCERT solutions exercise-wise for this chapter.
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 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. This chapter contains 3 exercises, which are provided below.
Chapter 3: Matrices
The array of numbers or mathematical objects called "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.
In this chapter of NCERT Class 12 Maths solutions, you will learn about matrices and their properties. Also, you are going to study the types, operations, transpose, and inverse of the matrix, as well as the properties of matrices, which are one of the most powerful tools of mathematics. This tool simplifies our work when compared with other straightforward methods. In Class 12 Maths NCERT Solutions Chapter 3, there are 5 exercises. Students can study using the matrices class 12 Solutions.
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.
In Class 12 NCERT Maths solutions for this chapter, you will get questions about the determinants of a square matrix, properties of determinants, consistency, inconsistency, the number of solutions of linear equations, and solving systems of linear equations, which are important parts of matrices. So, we are dealing with determinants of order up to three only. In this chapter, there are 6 exercises. Practice all the exercises, including exercise 4.6 class 12, to get a good grasp on the concepts.
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
The important concepts that you will study are continuity, differentiability, the derivative of a composite function, a derivative of a trigonometric function, the derivative of the inverse trigonometric functions, a derivative of the logarithm, the derivative of the exponential function, chain rule, role's theorem, Lagrange mean value theorem, etc. In this chapter, there are a total of eight exercises. Students can practice all exercises, including exercise 5.2 class 12, exercise 5.6 class 12, and exercise 5.7 class 12, to command the concepts discussed in this chapter that are listed below.
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.
This chapter of NCERT Class 12 Maths Solutions "Application of Derivatives" will cover the rate of change, maxima, minima of functions, equations of tangents and normals, etc. There are five exercises in this chapter, and here you will find the solutions to all exercises, including exercise 6.5, class 12.
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.
The function is integrable only if it is already differentiated. Remember, every function is not integrable, which means you can't integrate every function. In this chapter, you will learn about the integrals of various functions and also discuss their applications, like the calculation of areas under graphs. There are 11 exercises in this chapter of the NCERT 12th Maths solutions. All of them are listed below, including exercise 7.9, class 12. Practice them to score well in the exam.
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.
In this chapter, you will study a specific application of integrals to find the area between the lines and arcs of circles, ellipses, and parabolas, as well as the area under simple curves. The two exercises of this chapter deal with finding the area bounded by the above-mentioned curves.
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. All the exercises, including exercise 9.4 class 12, exercise 9.6 class 12, are listed below. Practice them to get a deeper understanding of the concepts. 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.
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.
In Physics and engineering, you often come across these quantities. In the class 12 NCERT Maths solutions of this chapter, you will learn about some basic concepts of vectors, types of vectors, the component of vectors, algebraic properties of addition, multiplication by a scalar, dot product, cross product, and their geometric properties. All the exercises, including exercise 10.2 class 12, exercise 10.3 class 12, are helpful for students. They can practice all of the exercise solutions listed below.
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". To visualise in 3-D geometry it 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
This chapter makes the study of 3-D geometry simple. In the class 12 maths solutions of this chapter, "Three Dimensional Geometry," you will study the direction ratio and direction cosines of a line joining two points, equations of planes and lines in space under different conditions, the angle between two planes, two lines, a plane, and a line, and other important concepts.
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.
In Class 12 NCERT Maths solutions of this chapter, we deal with some problems on linear programming, different types of linear programming and their solutions by the graphical method, feasible and infeasible region, feasible and infeasible solutions, optimal feasible solutions, and also about many other methods to solve such problems. There are two exercises in Chapter 12, Linear programming. The exercises, including exercise 12.2 class 12, are important for students; practice them to get benefits.
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 be helpful in understanding 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.
In Class 12 Maths NCERT Solutions Chapter 13, you will also get questions on random variables and their probability distributions, as well as the mean and variance of a probability distribution.
NCERT Exemplar solutions for class 12 - subject-wise
Given below are the subject-wise links for the NCERT exemplar solutions of class 12:
NCERT solutions for class 12 - subject-wise
Here are the subject-wise links for the NCERT solutions of class 12:
NCERT Books and NCERT Syllabus
Here are some useful links for NCERT books and the NCERT syllabus for class 12:
Frequently Asked Questions (FAQs)
Only knowing the answer is not enough to perform well in the board exams. One should know how to write an answer in order to get good marks. CBSE class 12 maths solutions are provided by experts who know how best to answer in the board exam in order to get good marks. Follow NCERT syllabus for a good score. Students can practice questions from the NCERT exemplar for Class 12 Maths. Also, they can take help from class 12th cbse maths solutions. practice all exercise including exercise 5.2 class 12,
NCERT books are considered a top resource for Class 12 students. Memorizing information just before exams is not an effective strategy for achieving high grades. It's crucial to have a thorough understanding of concepts. Daily practice with textbook problems will give students an idea of what to expect on exams and improve their performance. Also, students can use BCSE class 12 maths ncert solutions to get good hold in the concepts.
There are 13 chapters starting from Relations and Functions to Probability in the CBSE Class 12 Maths. The chapters are from Algebra, Trigonometry, Calculus and Probability. Students can practice these ncert solutions class 12 maths to get deeper understanding of the concepts. Maths class 12 ncert solutions are very important as these are provide comprehensive explanation of all the problems.
Class 12 is a crucial year for students, as their grades will impact their future career aspirations. They can access class 12 maths ncert book solutions online or download them as PDFs and use them while working through textbook problems. The chapter-wise Maths Class 12 NCERT Solutions available for download at Careers360 enhance understanding of concepts and aid in scoring well on exams. Practice these ncert maths class 12 solutions to get best benefit during the exams.
While NCERT Maths Solutions are an excellent resource, it's recommended to supplement them with additional study materials, reference books, and practice tests, especially if you're aiming for competitive exams. Athoug these class 12th maths ncert solutions are covered comprehensively, keeping in mid of latest syllabus of CBSE, practice additional resources with ncert maths solutions class 12.
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