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NCERT Solutions for Class 12 Maths (Updated 2023-24)

NCERT Solutions for Class 12 Maths (Updated 2023-24)

Edited By Ramraj Saini | Updated on Sep 11, 2023 05:59 PM IST

NCERT Solutions for Class 12 Maths - Chapter Wise

Class 12 Maths NCERT Solutions are provided here. These Solutions are created by expert team at careers360 in accordance of latest CBSE syllabus and pattern comprehensively covering all the steps. Maths is an important subject for Class 12 students. So you should clear all your doubts and prepare for exams. In NCERT 12 maths solution, there are 13 chapters that cover important theorems and formulas. You will find the chapter-wise NCERT Solutions for Class 12 Maths that will help you to perform well in the board exams.

This Story also Contains
  1. CBSE Class 12 Weightage Distribution Of Mathematics
  2. Class 12 maths chapter 1 NCERT Solutions - Chapter wise
  3. NCERT Solutions for Class 12 Maths Chapter 1
  4. NCERT Solutions for Class 12 Maths Chapter 2
  5. NCERT Solutions for Class 12 Maths Chapter 3
  6. NCERT Solutions for Class 12 Maths Chapter 4
  7. NCERT Solutions for Class 12 Maths Chapter 5
  8. NCERT Solutions for Class 12 Maths Chapter 6
  9. NCERT Solutions for Class 12 Maths Chapter 7
  10. NCERT Solutions for Class 12 Maths Chapter 8
  11. NCERT Solutions for Class 12 Maths Chapter 9
  12. NCERT Solutions for Class 12 Maths Chapter 10
  13. NCERT Solutions for Class 12 Maths Chapter 11
  14. NCERT Solutions for Class 12 Maths Chapter 12
  15. NCERT Solutions for Class 12 Maths Chapter 13
  16. How to use Class 12 Maths NCERT Solutions
  17. Key Features Of NCERT Solutions Class 12 Maths
NCERT Solutions for Class 12 Maths (Updated 2023-24)
NCERT Solutions for Class 12 Maths (Updated 2023-24)

Practising NCERT questions from class 12 maths chapters is very important in Mathematics, to understand the concepts. If you are not able to solve this, you can take the help of these Class 12 Maths NCERT solutions. In this article of NCERT solutions, you can click on the chapter you wish to study.

Here you will find all class 12 maths ncert solutions pdf Download 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 solutions of NCERT as a quick revision of concepts before the exam to score more marks.

CBSE Class 12 Weightage Distribution Of Mathematics

Units

Marks

Relations & Functions

10

Algebra

13

Calculus

44

Vector & 3-Dimensional Geometry

17

Linear Programming

6

Probability

10

Total

100

NCERT Solutions for Class 12 Subject-wise:

Class 12 maths chapter 1 NCERT Solutions - Chapter wise

Chapter 1

Chapter 2

Inverse Trigonometric Functions

Chapter 3

Matrices

Chapter 4

Determinants

Chapter 5

Differentiability

Chapter 6

Application of Derivatives

Chapter 7

Integrals

Chapter 8

Application of Integrals

Chapter 9

Differential Equations

Chapter 10

Vector Algebra

Chapter 11

Three Dimensional Geometry

Chapter 12

Linear Programming

Chapter 13

Probability

NCERT Solutions for Class 12 Maths Chapter 1

NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions provided here. If two sets of elements are related in some ways, we say these two sets have a relation. Father, mother, sister and brother are real-life examples of relations. Relation becomes a function when for every input there is only only one output. For different inputs, the output can be the same. Every function is a relation, but every relation doesn't represent a function. Students can study using relations and function class 12 pdf free download.

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NCERT Class 12 Maths solutions, you will learn about types of relations, reflective, transactive and equivalence relation, functions, range, domain and co-domain of function, which have already been introduced in Maths of NCERT Class 11. Class 12 Maths NCERT solutions for chapter 1 has 4 exercises. Click on the above link to get Class 12 NCERT solutions exercise wise of this chapter.

NCERT Solutions for Class 12 Maths Chapter 2

NCERT Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions provided here. In Class 11 Maths, you have already learnt trigonometric function. The inverse trigonometric function is the inverse of a trigonometric function. If you are good at trigonometric function, it won't take much effort to get a command on the inverse trigonometric functions. Students can study using inverse trigonometric function class 12 pdf free download.

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In NCERT Class 12 Maths solutions of this chapter, you will learn concepts related to the definition of inverse trigonometric functions, domain, range, and principal value, graph, and properties of inverse trigonometric functions. In class 11, you have already learnt 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 one-one and onto. This chapter contains 2 exercises with 35 questions. all the exercises including the exercise 2.2 class 12 maths solutions are provided below.

NCERT Solutions for Class 12 Maths Chapter 3

NCERT Solutions for Class 12 Maths Chapter 3 Matrices provided here. The array of numbers or mathematical objects called "Matrix", for that operation like addition, multiplications are defined. It was introduced to solve simultaneous linear equations. Matrix has a lot of applications in engineering, scientific studies, computer graphics (image or video that you see are matrices of color intensities), storage of big data, etc.

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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, operation transpose and the inverse of the matrix, and properties of matrices which is one of the most powerful tools of mathematics. This tool simplifies our work when compared with other straight forward methods. In Class 12 Maths NCERT Solutions Chapter 3, there are 4 exercises with 62 questions. Students can study using matrices class 12 pdf free download.

NCERT Solutions for Class 12 Maths Chapter 4

NCERT Solution for Class 12 Maths Chapter 4 Determinants provided here. In the previous chapter, you have already learnt matrices and their properties. For every square matrix, you can compute a number called "Determinant". It shows the factor by which times area or volume of linear transformation has changed. Students can study using determinants class 12 pdf free download.

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 system of linear equations which is an important part of matrices. So, we are dealing with determinants of order up to three only. In this chapter, there are 6 exercises. Practice all the exercise includeing exercise 4.6 class 12 to get good hold on the concepts.

NCERT Solutions for Class 12 Maths Chapter 5

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability provided here. In Class 11 NCERT, you have learnt 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. Students can study using continuity and differentiability class 12 pdf free download.

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, and Lagrange mean value theorem, etc. In this chapter, there are a total of eight exercises. Students can practice all exercises including ex 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.

NCERT Solutions for Class 12 Maths Chapter 6

NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives provided here. 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. Students can study using application of derivatives class 12 pdf free download.

This chapter of NCERT Class 12 Maths Solutions "Application of Derivatives" will cover the rate of change, maxima, minima of functions, equation of tangents and normal, etc. There are five exercises in this chapter and here you will find the solutions to all exercises including exercise 6.5 class 12.

NCERT Solutions for Class 12 Maths Chapter 7

NCERT Solutions for Class 12 Maths Chapter 7 Integrals provided here. Differential calculus is centred around the concept of differentiation, defining tangent and calculating the slope of the 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). Students can study using integrals class 12 pdf free download.

The function is integrable only if the function is already differentiated. Remember every function is not integrable means you can't integrate every function. In this chapter, you will learn about the integrals of various functions and also discuss their application like the calculation of areas under the graphs. There are 11 exercises in this chapter of NCERT 12th Maths solutions. All of them are listed below including exercise 7.9 class 12, practice them to score well in the exam.

NCERT Solutions for Class 12 Maths Chapter 8

NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals provided here. In the previous chapter, you have learnt 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. Students can study using application of integrals class 12 pdf free download.

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 and area under simple curves. The two exercises of this chapter deal with finding the area bounded by the above-mentioned curves.

NCERT Solutions for Class 12 Maths Chapter 9

NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations provided here. You have learnt about differentiation and integration. The differential equation is an equation of a function and with its one or more derivatives. In this chapter, you are going to learn some basic concepts related to the differential equation, 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 deeper understanding of the concepts. Students can study using differential equations class 12 pdf free download.

NCERT Solutions for Class 12 Maths Chapter 10

NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra provided here. Think about the situation where you are applying force on a box. So it has two quantities, one the magnitude that you are applying and second the direction in which you are applying the force. Such quantities with both magnitude and direction are termed vector quantities. Students can study using vector algebra class 12 pdf free download.

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 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 very benificial for students. they can practice all at once that are listed below.

NCERT Solutions for Class 12 Maths Chapter 11

NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry provided here. In the previous class, you have learned 2-D geometry. 3-D geometry is an extension of 2-D geometry with taking consideration of 3 orthogonal axes. Augustus De Morgan quotes "the moving power of mathematical invention is not reasoning but imagination". To visualize in 3-D geometry, it requires more of your imagination power. Students can study using three dimensional geometry class 12 pdf free download.

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.

NCERT Solutions for Class 12 Maths Chapter 12

NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming provided here. You often come across problems where you seek to maximize profit or minimize cost. Linear programming is useful to find the optimal solution for such problems. We formulate these real-life problems into a mathematical model. Students can study using linear programming class 12 pdf free download.

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 benefit.

NCERT Solutions for Class 12 Maths Chapter 13

NCERT Solutions for Class 12 Maths Chapter 13 Probability provided here. In previous classes, you have learnt 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. Students can study using probability class 12 pdf free download.

In Class 12 Maths NCERT solutions chapter 13, you will also get questions on random variable and its probability distribution and also the mean and variance of a probability distribution.

NCERT Solutions for Different Classes:

How to use Class 12 Maths NCERT Solutions

  • Stick to the NCERT Class 12 Maths syllabus and study it completely including all examples and all exercises. As NCERT maths 12th guide you in the whole preparation.

  • First, try to solve every question on your own from ncert 12 maths, if you are not able to do it, you can take the help of NCERT solutions for Class 12 Maths that are provided here. Don't ever think that reading the solutions is enough. You have to solve on your own, even after reading the solutions

  • If you have solved all NCERT questions then you can solve previous years paper CBSE board to get familiar with the question paper which you can study as class 12th maths solution book pdf download.

  • If you have difficulties in remembering the formulas of some chapters, you can use the formula sheet of that chapter but if you really want to remember the formulas do just one thing "write all the formulas which you are using in every question when you are solving the problems"

  • A formula sheet is always helpful in revision before the exam.

Key Features Of NCERT Solutions Class 12 Maths

  1. Structured Content: The class 12 math ncert solution are well-structured and organized according to the chapters and topics in the NCERT Class 12 Mathematics textbook. This makes it easy for students to find relevant solutions.
  2. Comprehensive Approach: The class 12 math ncert solution cover all the exercises and examples present in the NCERT textbook. This ensures that students have access to solutions for all types of problems, from basic to advanced. also includes deleted exercise of maths class 12 in these solutions.

  3. Step-by-Step Solutions: Each cbse 12th maths solutions is presented in a step-by-step manner. This helps students grasp the logical sequence of solving mathematical problems, making it easier to follow and understand.

  4. Clarity and Conciseness: The NCERT 12 maths solutions are written in a clear and concise language, avoiding unnecessary jargon. This ensures that students can easily comprehend the concepts and procedures involved in solving problems.

  5. Conceptual Understanding: NCERT class 12th maths NCERT solutions focus on promoting a deep understanding of mathematical concepts rather than rote memorization. The solutions often include explanations and insights to help students grasp the underlying principles.

Also check NCERT Exemplar Class 12 Solutions

Benefits of Class 12 Maths NCERT Solutions

  • Before solving the NCERT exercise question, understand the concept and solve the solved examples of the NCERT books for 12 Maths.

  • You should try to solve every question including examples on your own, if you are not able to do, you can take help with these Class 12 Maths NCERT solutions in which detailed explanation using a step-by-step approach is there to facilitate an easy and smooth understanding of concepts. It will give you a new insight to solving CBSE maths problems.

  • These Class 12 NCERT Maths solutions will help you to learn CBSE Class 12 Maths as well as the crack JEE Main and other competitive exams like BITSAT, VITEEE, etc.

  • With the help of these NCERT solutions for Class 12 Maths, you can grasp the concepts based on their application very easily.

Also Check NCERT Books and NCERT Syllabus here:

Frequently Asked Question (FAQs)

1. How are the NCERT solutions beneficial in the CBSE Class 12 board exams?

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, 

2. Are NCERT Solutions for maths class 12 chapters considered the best reference material for students?

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.

3. How many chapters are there in the Class 12 Maths?

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.

4. Where can class 12 mathematics NCERT solutions be downloaded?

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.

5. Can I rely solely on 12th cbse maths solutions for exam preparation?

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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