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NCERT Solutions for Class 12 Maths Exercises

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Last updated date: 15th Jul 2024
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NCERT Solutions for Class 12 Maths Exercises - PDF Solutions

Class 12 Maths syllabus is covering basic and advanced mathematical concepts and fundamental principles. To study this CBSE syllabus, you will need the assistance of the complete study material with all the exercise solutions. The experts of Vedantu have designed the NCERT Class 12 Maths All Exercises Solutions to download and refer to while studying the respective chapters. Follow how the experts have solved the questions and develop your mathematical skills accordingly.

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NCERT Solutions for Class 12 Maths Exercises

What could be better if you get the simpler and readymade solutions of your Class 12 NCERT textbook exercises? Moreover, all these are created by an experienced subject matter expert. Can you imagine how beneficial these could be? Sounds amazing, right! You must opt for these NCERT solutions for Class 12 Maths right away. You can download NCERT solutions Class 12 Maths from Vedantu official website (vedantu.com) by registering yourself with your phone number/ email address. You can also access the same study materials from Vedantu app as well. In that case, you need to download the Vedantu app first from Google play store.

You will get Class 12 Maths NCERT solutions written in a simple and lucid manner. Solve all the problems/ questions given in the exercises and evaluate your performance with these 100% accurate solutions so that you can learn how to write answers to the questions from any perspective during the final exam. Each of the answers in the Maths NCERT solutions Class 12 is student-friendly and customized by the experts. 

These NCERT solutions Class 12 Maths contain step-by-step answers to all the questions from the exercise which are considered as an invaluable aid to the students when it comes to regular study, exam preparation or doing homework. Class 12 Maths NCERT solutions will clear all your doubts in very less time. Hence your confidence will be boosted. By practising the questions from these books, you will be able to improve your time management skills. That will help you in solving all the questions in the stipulated time frame during the final exam. 

NCERT Solutions for Class 12 Maths are designed as per the latest CBSE curriculum and guidelines. Vedantu’s study materials are updated regularly as per the latest changes. Hence students of Class 12 who are referring to these materials will be able to score the best marks in the final exam. Once you start using these materials, the preparation for Class 12 exam and scoring the highest percentile amongst your peers will seem like a cakewalk at the end of the day.


Class 12 Maths Chapter 1 Relations and Functions

Chapter 1 Relations and Functions of NCERT Class 12 Maths Syllabus deals with types of relations and functions along with a few miscellaneous examples.

NCERT Solutions for Class 12 Maths Chapter 1 Exercises are given in the table below:


Chapter 1 - Relations and Functions Exercises in PDF Format

Exercise 1.1 : Types of Relations

16 Questions & Solutions (3 Short Answers, 13 Long Answers)

Exercise 1.2 : Types of Functions

12 Questions & Solutions (5 Short Answers, 7 Long Answers)

Exercise 1.3 : Composition of Functions and Invertible Function

14 Questions & Solutions (4 Short Answers, 10 Long Answers)

Exercise 1.4 : Binary Operations

13 Questions & Solutions (6 Short Answers, 7 Long Answers)


Class 12 Maths Chapter 2 Inverse Trigonometric Functions

In CBSE Class 12 Inverse Trigonometric Functions, there are only two exercises where you will study the restrictions on domains and ranges of trigonometric functions which enables the visibility of their inverses and observe their behaviour through graphical representations.

Chapter 2 - Inverse Trigonometric Functions Exercises in PDF Format

Exercise 2.1 : Basic Concepts of Trigonometric Functions

14 Questions & Solutions (14 Short Answers)

Exercise 2.2 : Properties of Inverse Trigonometric Functions

20 Questions & Solutions (4 Short Answers, 16 Long Answers)


CBSE Class 12 Maths Chapter 3 Matrices

There are 4 exercises included in this chapter. The links to these exercises are provided in the table below.

Chapter 3 - Matrix Exercises in PDF Format

Exercise 3.1

10 Questions & Solutions (5 Short Answers, 5 Long Answers)

Exercise 3.2

12 Questions & Solutions (4 Short Answers, 8 Long Answers)

Exercise 3.3

22 Questions & Solutions (3 Short Answers, 19 Long Answers)

Exercise 3.4

18 Questions & Solutions (18 Short Answers)


CBSE Class 12 Maths Chapter 4 Determinants

There are six exercises which are included in the NCERT Class 12 Maths Chapter 4 Determinants. By solving these exercises, students will be familiar with the concepts of determination, cofactors and the application of determinants in finding the area of a triangle, minors, adjoint and inverse of a square matrix. 


The free PDFs of the NCERT Solutions for Class 12 Maths Chapter 4 exercises can be downloaded from the links provided below:


Chapter 4 - Determinants Exercises in PDF Format

Exercise 4.1

8 Questions & Solutions (3 Short Answers, 5 Long Answers)

Exercise 4.2

10 Questions & Solutions (4 Short Answers, 10 Long Answers)

Exercise 4.3

5 Questions & Solutions (2 Short Answers, 3 Long Answers)

Exercise 4.4

5 Questions & Solutions (2 Short Answers, 3 Long Answers)

Exercise 4.5

18 Questions & Solutions (4 Short Answers, 14 Long Answers)

Exercise 4.6

16 Questions & Solutions (3 Short Answers, 13 Long Answers)


NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability

Class 12 Maths Chapter 5 Continuity and Differentiability explains the definition of continuity and meaning of differentiability.

The free PDFs of the NCERT Solutions for Class 12 Maths Chapter 5 exercises can be downloaded from the links provided below:


Chapter 5 - Continuity and Differentiability Exercises in PDF Format

Exercise 5.1

34 Questions & Solutions (10 Short Answers, 24 Long Answers)

Exercise 5.2

10 Questions & Solutions (2 Short Answers, 8 Long Answers)

Exercise 5.3

15 Questions & Solutions (9 Short Answers, 6 Long Answers)

Exercise 5.4

10 Questions & Solutions (5 Short Answers, 5 Long Answers)

Exercise 5.5

18 Questions & Solutions (4 Short Answers, 14 Long Answers)

Exercise 5.6

11 Questions & Solutions (7 Short Answers, 4 Long Answers)

Exercise 5.7

17 Questions & Solutions (10 Short Answers, 7 Long Answers)

Exercise 5.8

6 Questions & Solutions (2 Short Answers, 4 Long Answers)


NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives

In this chapter, you will study the applications of the derivative in various disciplines such as engineering, science, and many other fields. For instance, you will learn how the derivative can be used to determine the rate of change of quantities and to find the equations of tangent and normal to a curve at a point. You will also learn the use of derivatives to find intervals of increasing or decreasing functions, maxima and minima, along with a few simple problems based on all these concepts. 


Chapter 6 - Application of Derivatives Exercises in PDF Format

Exercise 6.1

18 Questions & Solutions (6 Short Answers, 10 Long Answers, 2 MCQs)

Exercise 6.2

19 Questions & Solutions (7 Short Answers, 10 Long Answers, 2 MCQs)

Exercise 6.3 

27 Questions & Solutions (25 Short Answers, 2 MCQs)

Exercise 6.4

9 Questions & Solutions (7 Short Answers, 2 MCQs)

Exercise 6.5 

29 Questions & Solutions (11 Short Answers, 15 Long Answers, 3 MCQs)


NCERT Solutions for Class 12 Maths Chapter 7 Integrals

Topics in this chapter include an introduction to indefinite integrals, integration as inverse to differentiation, its geometrical interpretation, and properties. 


Chapter 7 - Integrals Exercises in PDF Format

Exercise 7.1

22 Questions & Solutions (21 Short Answers, 1 MCQs)

Exercise 7.2

39 Questions & Solutions (37 Short Answers, 2 MCQs)

Exercise 7.3

24 Questions & Solutions (22 Short Answers, 2 MCQs)

Exercise 7.4

25 Questions & Solutions (23 Short Answers, 2 MCQs)

Exercise 7.5

23 Questions & Solutions (21 Short Answers, 2 MCQs)

Exercise 7.6

24 Questions & Solutions (22 Short Answers, 2 MCQs)

Exercise 7.7

11 Questions & Solutions (9 Short Answers, 2 MCQs)

Exercise 7.8

6 Questions & Solutions (6 Short Answers)

Exercise 7.9

22 Questions & Solutions (20 Short Answers, 2 MCQs)

Exercise 7.10

10 Questions & Solutions (8 Short Answers, 2 MCQs)

Exercise 7.11

21 Questions & Solutions (19 Short Answers, 2 MCQs)


NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals

Here, in this chapter, you will study some specific applications of integrals to find the area given under the simple curves, also, the area between lines and arcs of circles, parabolas and ellipses (standard forms only). There are two exercises in this chapter in which you will also deal with finding the area bounded by the above-said curves.

Chapter 8 - Application of Integrals Exercises in PDF Format

Exercise 8.1

13 Questions & Solutions (11 Short Answers, 2 MCQs)

Exercise 8.2 

7 Questions & Solutions (5 Short Answers, 2 MCQs)


NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations

In Differential Equations, you will be studying some basic concepts related to the differential equation, general and particular solutions of a differential equation, formation of differential equations, number of methods to solve a question based on first order - first-degree differential equations and some applications of differential equations in different areas.


Chapter 9 - Differential Equations Exercises in PDF Format

Exercise 9.1

12 Questions & Solutions (10 Short Answers, 2 MCQs)

Exercise 9.2

12 Questions & Solutions (10 Short Answers, 2 MCQs)

Exercise 9.3

12 Questions & Solutions (5 Short Answers, 5 Long Answers, 2 MCQs)

Exercise 9.4

23 Questions & Solutions (10 Short Answers, 12 Long Answers, 1 MCQs)

Exercise 9.5

17 Questions & Solutions (15 Short Answers, 2 MCQs)

Exercise 9.6 

19 Questions & Solutions (15 Short Answers, 2 Long Answers, 2 MCQs)


NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra

In Class 12 Maths Chapter 10  Vector Algebra, you will be studying some basic concepts of vectors, various operations on vectors, and the algebraic as well as geometric properties. You will also learn about the types of vectors such as zero, unit, equal and collinear vectors.

Other topics discussed in this chapter include the negative of a vector, operations of vectors such as addition, its properties, components and how to multiply a vector by a scalar. You will also learn about section formulae, vector joining two points, dot product of two vectors, product of two vectors, cross product of two vectors, and projection of a vector on a line.


Chapter 10 - Vector Algebra Exercises in PDF Format

Exercise 10.1

5 Questions & Solutions (5 Short Answers)

Exercise 10.2

19 Questions & Solutions (5 Short Answers, 14 Long Answers)

Exercise 10.3

18 Questions & Solutions (5 Short Answers, 13 Long Answers)

Exercise 10.4

12 Questions & Solutions (4 Short Answers, 8 Long Answers)


NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry

CBSE Class 12 Maths Chapter 11 Three Dimensional Geometry deals with the direction cosines and direction ratios of a line joining two points and also about the equations of lines and planes in space under different conditions. Along with that, you will also get to know about the angle between two lines, a line and a plane, two planes, the shortest distance between two skew lines and the distance of a point from a plane.

You will also learn about cartesian equations and vector equations of a line, skew and coplanar lines, and the cartesian and vector equations of a plane.


Chapter 11 - Three Dimensional Geometry Exercises in PDF Format

Exercise 11.1

5 Questions & Solutions (5 Short Answers)

Exercise 11.2

17 Questions & Solutions (9 Short Answers, 8 Long Answers)

Exercise 11.3

14 Questions & Solutions (5 Short Answers, 9 Long Answers)


NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming

This chapter has only two exercises in which you will study some linear programming problems and their solutions by graphical method. Other concepts in this chapter are the mathematical formulation of linear programming problems, different types of linear programming problems, terms such as objective function, optimization and constraints, as well as feasible and infeasible regions and solutions.


Chapter 12 - Linear Programming Exercises in PDF Format

Exercise 12.1

10 Questions & Solutions (10 Long Answers)

Exercise 12.2

11 Questions & Solutions (11 Long Answers)


NCERT Solutions for Class 12 Maths Chapter 13 Probability

Class 12 Maths Chapter 13 Probability will teach you the important concepts of the conditional probability of an event given that another event has occurred, which will, in turn, clarify the Bayes' theorem, multiplication rule of probability and independence of events. You will also learn the concept of a random variable and its probability distribution, mean and variance of a probability distribution, total probability theorem, Bernoulli trials and binomial distribution.


Chapter 13 - Probability Exercises in PDF Format

Exercise 13.1

17 Questions & Solutions (4 Short Answers, 13 Long Answers)

Exercise 13.2 

18 Questions & Solutions

Exercise 13.3

14 Questions & Solutions

Exercise 13.4 

17 Questions & Solutions

Exercise 13.5

15 Questions & Solutions


CBSE Class 12 Maths Weightage (2024-25)

Given below is the unit-wise mark distribution for CBSE Class 12 Maths exam for session 2024-25.

 

Unit

Unit Name

Marks

1

Relations and Functions

08

2

Algebra

10

3

Calculus

35

5

Vectors and Three - Dimensional Geometry

14

6

Linear Programming

5

7

Probability

8

Internal Assessment Marks

20

Total Marks

100


Importance of Chapter Wise List of Class 12 Maths All Exercises

The vivid exercises of a chapter in Class 12 Maths have questions that check your preparation level. This is where you will need the support of exercise solutions to learn the exact ways of answering fundamental questions.


The experts have framed the answers by following the fundamental principles explained in the chapters and the latest CBSE guidelines. The 12th Maths All Exercises Book Answers will enable students to focus on their preparation and proceed with the exam syllabus faster.


Benefits of NCERT Maths All Exercises Book Class 12 Solutions PDF

  • Resolve doubts on your own with these solutions faster.

  • Learn the ideal answering formats to follow and solve problems accurately.

  • Prepare chapters in no time by using the solutions as revision material.

  • Understand the concepts and principles of Class 12 Maths chapters from the simpler solutions easily.


Here is the list of exercise solutions for all chapters in the CBSE Class 12 Maths syllabus.


Download NCERT Maths All Exercises Book Class 12 Solutions PDF

Perform the NCERT Maths All Exercises Book Class 12 Solutions PDF free download according to your syllabus. Focus on how the experts have solved the exercise problems. Cover a syllabus faster and develop your problem-solving skills in a better way to score more in the exams.


Important Related Links for CBSE Class 12 Maths

FAQs on NCERT Solutions for Class 12 Maths Exercises

1. How can I prepare a Class 12 Maths chapter?

Complete studying the theoretical part of a chapter and solve the exercises. Refer to the solutions to compare your answers and find out where you need to change your techniques.

2. What is the advantage of using Class 12 Maths solutions?

You will the precise answers compiled following the latest CBSE guidelines to follow and develop your answering skills.

3. Can I practise using the CBSE Class 12 Maths solutions?

The solutions are to the point and comply with the NCERT guidelines. You can surely practise solving problems using the solutions.

4. How can I resolve doubts about Class 12 Maths exercises?

Refer to the exercise solutions framed by the experts to resolve all your doubts in no time.

5. What is the best way to develop my concepts for the Class 12 Maths chapters?

Apart from the notes, you can use the simpler solutions developed by the experts to learn how to use the concepts and principles of an exercise in a Class 12 Maths chapter. This is how you can develop your concepts.