assignment of maths class 12

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CBSE Worksheets for Class 12 Maths

CBSE Worksheets for Class 12 Maths: One of the best teaching strategies employed in most classrooms today is Worksheets. CBSE Class 12 Maths Worksheet for students has been used by teachers & students to develop logical, lingual, analytical, and problem-solving capabilities. So in order to help you with that, we at WorksheetsBuddy have come up with Kendriya Vidyalaya Class 12 Maths Worksheets for the students of Class 12. All our CBSE NCERT Class 12 Maths practice worksheets are designed for helping students to understand various topics, practice skills and improve their subject knowledge which in turn helps students to improve their academic performance. These chapter wise test papers for Class 12 Maths will be useful to test your conceptual understanding.

Board: Central Board of Secondary Education(www.cbse.nic.in) Subject: Class 12 Maths Number of Worksheets: 42

CBSE Class 12 Maths Worksheets PDF

All the CBSE Worksheets for Class 12 Maths provided in this page are provided for free which can be downloaded by students, teachers as well as by parents. We have covered all the Class 12 Maths important questions and answers in the worksheets which are included in CBSE NCERT Syllabus. Just click on the following link and download the CBSE Class 12 Maths Worksheet. CBSE Worksheets for Class 12 Maths can also use like assignments for Class 12 Maths students.

CBSE Class 12 Definite Integrals Worksheets

• CBSE Class 12 Definite integrals Assignment 1
• CBSE Class 12 Definite integrals Assignment 2
• CBSE Class 12 Definite integrals Assignment 3
• Class 12 Maths CBSE Worksheets for Definite integrals Assignment 4
• CBSE Class 12 Maths Worksheets Definite integrals Assignment 5
• CBSE Worksheets for Class 12 Maths Definite integrals Assignment 6
• CBSE Maths Worksheets for Class 12 Definite integrals Assignment 7

CBSE Determinants Class 12 Worksheets

• CBSE Worksheets for Class 12 Maths Determinants Assignment 1
• CBSE Class 12 Maths Determinants Assignment 2
• CBSE Class 12 Maths Determinants Assignment 3
• CBSE Class 12 Maths Determinants Assignment 4
• CBSE Class 12 Maths Determinants Assignment 5
• CBSE Class 12 Maths Worksheets for Determinants Assignment 6
• CBSE  Class 12 Maths Worksheets for Determinants Assignment 7

CBSE Class 12 Integration Worksheets

• CBSE Worksheets for Class 12 Maths Integration Assignment 1
• CBSE Worksheets for Class 12 Maths Integration Assignment 2
• CBSE Worksheets for Class 12 Maths Integration Assignment 3
• CBSE Worksheets for Class 12 Maths Integration Assignment 4
• CBSE Class 12 Maths Integration Assignment 5
• CBSE Class 12 Maths Integration Assignment 6
• CBSE Class 12 Maths Integration Assignment 7

CBSE Class 12 Relations and Functions Worksheets

• CBSE Class 12 Maths Relations and Functions Assignment 1
• CBSE Class 12 Maths Relations and Functions Assignment 2
• CBSE Class 12 Maths Relations and Functions Assignment 3
• CBSE Class 12 Maths Relations and Functions Assignment 4
• CBSE Class 12 Maths Relations and Functions Assignment 5
• CBSE Class 12 Maths Relations and Functions Assignment 6

CBSE Class 12 Maths Linear Programming Worksheets

• CBSE Class 12 Maths Linear Programming Assignment 1
• CBSE Class 12 Maths Linear Programming Assignment 2
• CBSE Class 12 Maths Linear Programming Assignment 3
• CBSE Class 12 Maths Linear Programming Assignment 4

Application of Derivatives CBSE Class 12 Maths Worksheets

• CBSE Worksheets for Class 12 Maths Application of Derivatives

Application of Integrals CBSE Class 12 Maths Worksheets

• CBSE Worksheets for Class 12 Maths Application of Integrals

Continuity and Differentiation Class 12 Worksheets

• CBSE Worksheets for Class 12 Maths Continuity and Differentiability Assignment 01
• CBSE Class 12 Maths Continuity and Differentiability Assignment 02

Differential Equations CBSE Class 12 Mathematics Worksheets

• CBSE Class 12 Differential Equations Assignment 01
• CBSE Class 12 Differential Equations Assignment 02

CBSE Class 12 Inverse Trigonometric Functions Worksheets

• CBSE Class 12 Maths Inverse Trigonometric Functions Assignment 01
• CBSE Class 12 Maths Inverse Trigonometric Functions Assignment 02

Continuity Class 12 Maths Worksheets

• CBSE Class 12 Maths Continuity Assignment

Class 12 CBSE Maths Matrices Worksheets

• CBSE Class 12 Maths Matrices
• CBSE Class 12 Maths Matrices and determinants

Class 12 Vector Algebra CBSE Maths Worksheets

• CBSE Class 12 Maths Vector Algebra Assignment

Advantages of CBSE Class 12 Maths Worksheets

• By practising NCERT CBSE Class 12 Maths Worksheet , students can improve their problem solving skills.
• Helps to develop the subject knowledge in a simple, fun and interactive way.
• No need for tuition or attend extra classes if students practise on worksheets daily.
• Working on CBSE worksheets are time-saving.
• Helps students to promote hands-on learning.
• One of the helpful resources used in classroom revision.
• CBSE Class 12 Maths Workbook Helps to improve subject-knowledge.
• CBSE Class 12 Maths Worksheets encourages classroom activities.

Worksheets of CBSE Class 12 Maths are devised by experts of WorksheetsBuddy experts who have great experience and expertise in teaching Maths. So practising these worksheets will promote students problem-solving skills and subject knowledge in an interactive method. Students can also download CBSE Class 12 Maths Chapter wise question bank pdf and access it anytime, anywhere for free. Browse further to download free CBSE Class 12 Maths Worksheets PDF .

Now that you are provided all the necessary information regarding CBSE Class 12 Maths Worksheet and we hope this detailed article is helpful. So Students who are preparing for the exams must need to have great solving skills. And in order to have these skills, one must practice enough of Class 12 Maths revision worksheets . And more importantly, students should need to follow through the worksheets after completing their syllabus.  Working on CBSE Class 12 Maths Worksheets will be a great help to secure good marks in the examination. So start working on Class 12 Maths Worksheets to secure good score.

CBSE Worksheets For Class 12

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Class 12 Maths NCERT Solutions PDF for 2024-25

• NCERT Solutions

NCERT Solutions Class 12 Maths Solutions PDF - Free Download All Chapters

If you are looking for the most accurate Class 12 Maths NCERT Solutions PDF , then Vedantu is the perfect website to download it in PDF format free of cost. NCERT Solutions for Class 12 Maths offer a strong foundational understanding for all topics in the CBSE Class 12 Maths Syllabus . It covers essential theorems and formulas with thorough explanations to enhance student’s understanding. These solutions are invaluable for preparation for undergraduate Engineering entrance exams like JEE Mains, BITSAT, VITEEE, etc., scheduled for the years 2024-25.

NCERT Maths class 12 solutions PDF is crafted by Vedantu’s Maths expert teachers to facilitate clear understanding of concepts. These 12th CBSE Maths solutions provide detailed, step by step explanations for problems found in the textbooks. Additionally, alongside solutions for each chapter of CBSE Class 12 Maths, Vedantu offers Class 12 Maths notes, solved exemplar problems, important questions, formulas and more as effective study materials for students preparing for their Class 12 board exams.

NCERT Solutions for Class 12 Maths | Chapter-wise List

Given below are the chapter-wise NCERT 12 Maths solutions PDF. Using these chapter-wise class 12th maths ncert solutions, you can get clear understanding of the concepts from all chapters.

Glance on NCERT Solutions Class 12 Maths

Class 12th Maths NCERT solutions for all the chapters and exercises from Chapters 1 to 13 are provided.

Using these CBSE class 12 maths solutions to practice textbook questions can assist students in assessing their preparation level and understanding of concepts.

The link also provides details about the exam pattern, marks weightage, and question paper design for CBSE Class 12 Maths.

The chapters cover topics like Relations and Functions, Inverse Trigonometric Functions, Matrices, Determinants, Continuity and Differentiability, Application of Derivatives, Integrals, and more.

Additionally, it offers resources such as class notes, important questions and formulas, exemplar solutions, RD Sharma and RS Aggarwal solutions for further study.

Get an idea about: Is NCERT for class 12 (maths) sufficient for board exams?

NCERT Solutions Class 12 Maths - Chapter Details, Formulas and Exercises PDF

  ncert 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. Throughout this chapter, students will develop a solid understanding of relations and functions, which are essential for understanding various mathematical concepts. They will also learn to analyse and interpret graphical representations of functions, which are used extensively in calculus, algebra, and other branches of mathematics. This chapter serves as a foundation for the more advanced topics covered in later chapters of Class 12 Maths.

Topics covered in Class 12 Maths Chapter 1 Relations and Functions.

Types of Relations

Equivalence.

Types of functions

One to one functions

Onto functions

Composite functions

Invertible functions.

Binary operations.

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

Students can find below the supplementary study materials for Relations and Functions on Vedantu. These resources are downloadable, providing extra assistance for your Maths preparation.

Relations and Functions Important Questions

Relations and Functions Revision Notes

Relations and Functions Formulas

Relations and Functions NCERT Exemplar Solutions

Relations and Functions RD Sharma Solutions

Relations and Functions RS Aggarwal Solutions

NCERT Class 12 Maths Chapter 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.

The inverse trigonometric functions hold great value in calculus, for they serve to define many integrals. The concepts of inverse trigonometric functions are applied vastly in science and engineering.

Here is the list of topics covered in Class 12 Maths Chapter 2 inverse trigonometric function:

Definition, range, domain, principal value branches. 

Graphs of inverse trigonometric functions.

Elementary properties of inverse trigonometric functions.

NCERT Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Function Exercises are given in the table below:

Students can find below the supplementary study materials for Real Numbers on Vedantu. These resources are downloadable, providing extra assistance for your Maths preparation.

Inverse Trigonometric Functions Important Questions

Inverse Trigonometric Functions Revision Notes

Inverse Trigonometric Functions Formulas

Inverse Trigonometric Functions NCERT Exemplar Solutions

Inverse Trigonometric Functions RD Sharma Solutions

Inverse Trigonometric Functions RS Aggarwal Solutions

NCERT Class 12 Maths Chapter 3 Matrices

It covers basic operations like addition, subtraction, multiplication, and scalar multiplication of matrices, which are fundamental in various fields such as computer graphics, quantum mechanics, and economics. Matrices provide a systematic way to solve systems of linear equations.

Chapter 3 of NCERT Class 12 Maths covers the following topics:

What are Matrices?

Types of Matrices

Properties of Matrix Addition

Properties of Scalar Multiplication

Multiplication of Matrices

Properties of Multiplication of Matrices

Symmetric and Skew-symmetric Matrices

Elementary Operation or Transformation of a Matrix

Inverse of a Matrix by Elementary Operations

Students can find below the supplementary study materials for Matrices on Vedantu. These resources are downloadable, providing extra assistance for your Maths preparation.

Matrices Important Questions

Matrices Revision Notes

Matrices Formulas

Matrices NCERT Exemplar Solutions

Matrices RD Sharma Solutions

Matrices RS Aggarwal Solutions

NCERT 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.

Topics Covered in Class 12 Maths Chapter 4 Determinants:

Determinant of a square matrix (up to 3 × 3 matrices), properties of determinants, minors, cofactors and applications of determinants in finding the area of a triangle.

Adjoint and inverse of a square matrix. 

Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.

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

Students can find below the supplementary study materials for Determinants on Vedantu. These resources are downloadable, providing extra assistance for your Maths preparation.

Determinants Important Questions

Determinants Revision Notes

Determinants Formulas

Determinants NCERT Exemplar Solutions

Determinants RD Sharma Solutions

Determinants RS Aggarwal Solutions

NCERT Class 12 Maths Chapter 5 Continuity and Differentiability

Understanding continuity and differentiability helps in analysing the behaviour of functions. It provides insights into where functions are smooth and where they have sharp corners or discontinuities. These are the fundamental concepts in calculus. They form the basis for studying limits, derivatives, and integrals, which are extensively used in physics, engineering, economics, and other sciences.

The important concepts that students will get to learn from Class 12 Maths NCERT Solutions are as follows:

Algebra of continuous function

Derivatives of composite functions, Implicit functions, Inverse trigonometric functions, Exponential and logarithmic functions

Logarithmic differentiation

Derivatives of functions in parametric forms

Second order derivatives

Rolle’s and Lagrange’s Mean Value Theorems

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

Here are the links for some important study materials that are available on our website for CBSE Class 12 Maths Chapter 5.

Continuity and Differentiability Important Questions

Continuity and Differentiability Revision Notes

Continuity and Differentiability Formulas

Continuity and Differentiability NCERT Exemplar Solutions

Differentiability RD Sharma Solutions

Continuity RD Sharma Solutions

Continuity and Differentiability RS Aggarwal Solutions

NCERT 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.

Topics Covered in Class 12 Maths Chapter 6 Application of Derivatives:

Rate of Change

Increasing and Decreasing Functions

Tangents and Normals

Approximations

Maxima and Minima

Optimization Problems

Rate of Change of Quantities

Students can find below the supplementary study materials for Application of Derivatives on Vedantu. These resources are downloadable, providing extra assistance for your Maths preparation.

Application of Derivatives Important Questions

Application of Derivatives Revision Notes

Application of Derivatives Formulas

Application of Derivatives NCERT Exemplar Solutions

Derivatives RD Sharma Solutions

Application of Derivatives RS Aggarwal Solutions

NCERT Class 12 Maths Chapter 7 Integrals

Integrals are used to find the area under curves. This is particularly useful in various fields like physics, where it helps in calculating quantities such as displacement, velocity, and acceleration. Definite integrals are used for precise calculation of quantities such as total distance travelled, total work done, and total profit earned. It is extensively used in economics, engineering, and physics.

Topics in this chapter include an introduction to indefinite integrals, integration as inverse to differentiation, its geometrical interpretation, and properties. Other topics that are discussed in this chapter are the following:

Comparison of integration and differentiation

Integration methods including substitution, partial fraction, by parts, and trigonometric identities. 

Definite integrals

Fundamental theorem of calculus

How to evaluate definite integrals by substitution

Students can find below the supplementary study materials for Integrals on Vedantu. These resources are downloadable, providing extra assistance for your Maths preparation.

Integrals Important Questions

Integrals Revision Notes

Integrals Formulas

Integrals NCERT Exemplar Solutions

Definite Integrals RD Sharma Solutions

Indefinite Integrals RD Sharma Solutions

Definite Integrals RS Aggarwal Solutions

Indefinite Integrals RS Aggarwal Solutions

NCERT 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.

Topics Covered in Chapter 8 Application of Integrals:

Area Under Simple Curves

Area Between Two Curves

Area Enclosed Between Two Curves

Application in Finding Lengths

Application in Finding Volumes

Volume by Cross-Sectional Areas

Volume of Solids with Known Cross-Sections

Application in Physics and Engineering

Students can find below the supplementary study materials for Application of Integrals on Vedantu. These resources are downloadable, providing extra assistance for your Maths preparation.

Chapter 8: Application of Integrals Important Questions

Chapter 8: Application of Integrals Revision Notes

Chapter 8: Application of Integrals Formulas

Chapter 8: Application of Integrals NCERT Exemplar Solutions

Application of Integrals RD Sharma Solutions

Application of Integrals RS Aggarwal Solutions

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.

Topics Covered in Class 12 Maths Chapter 9 Differential Equations

Introduction to Differential Equations

Basic Concepts and Terminology

Formation of Differential Equations

Methods of Solving First Order, First Degree Differential Equations

Linear Differential Equations of Second and Higher Order

Applications of Differential Equations

Students can find below the supplementary study materials for Differential Equations on Vedantu. These resources are downloadable, providing extra assistance for your Maths preparation.

Differential Equations Important Questions

Differential Equations Revision Notes

Differential Equations Formulas

Differential Equations NCERT Exemplar Solutions

Differential Equations RD Sharma Solutions

Differential Equations RS Aggarwal Solutions

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: 

Negative of a vector

Operations of vectors such as addition

Properties of vector addition

Components of vectors

Multiplication of a vector by a scalar

Section formulae

Vector joining two points

Dot product of two vectors

Product of two vectors

Cross product of two vectors

Projection of a vector on a line

Students can find below the supplementary study materials for Vector Algebra on Vedantu. These resources are downloadable, providing extra assistance for your Maths preparation.

Vector Algebra Important Questions

Vector Algebra Revision Notes

Vector Algebra Formulas

Vector Algebra NCERT Exemplar Solutions

Vector Algebra RD Sharma Solutions

Vectors and Their Properties RS Aggarwal Solutions

Scalar, or Dot, Product of Vectors RS Aggarwal Solutions

Cross, or Vector, Product of Vectors RS Agarwal Solutions

Product of Three Vectors RS Agarwal Solutions

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.

Topics Covered in Class 12 Maths Chapter 11 Three Dimensional Geometry

Equation of a Line in Space

Angle between Two Lines

Shortest Distance between Two Lines

Cartesian and Vector Equation of a Plane

Angle between Two Planes

Distance of a Point from a Plane

Coplanarity of Two Lines

Students can find below the supplementary study materials for Dimensional Geometry on Vedantu. These resources are downloadable, providing extra assistance for your Maths preparation.

Three Dimensional Geometry Important Questions

Three Dimensional Geometry Revision Notes

Three Dimensional Geometry Formulas

Three Dimensional Geometry NCERT Exemplar Solutions

Three Dimensional Geometry RS Aggarwal Solutions

NCERT Solutions 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.

Topics Covered in Class 12 Maths Chapter 12 Linear Programming

Introduction to Linear Programming Problems

Formulation of L.P. Problems

Graphical Method of Solution

Non-negative Constraints and Feasible Region

Solution of L.P. Problems by Graphical Method

Corner Points and Optimum Solution

L.P. Problems with More than Two Variables

Students can find below the supplementary study materials for Linear Programming on Vedantu. These resources are downloadable, providing extra assistance for your Maths preparation.

Linear Programming Important Questions

Linear Programming Revision Notes

Linear Programming Formulas

Linear Programming NCERT Exemplar Solutions

Linear Programming RD Sharma Solutions

Linear Programming RS Aggarwal Solutions

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.

Topics Covered in Class 12 Maths Chapter 13 Probability

Introduction to Probability

Conditional Probability

Properties of Conditional Probability

Multiplication Theorem on Probability

Independent Events

Bayes'Theorem

Random Variables and Probability Distribution

Probability Important Questions

Probability Revision Notes

Probability Formulas

Probability NCERT Exemplar Solutions

Probability RD Sharma Solutions

Probability RS Aggarwal 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.

Internal Assessment Class 12 Marks Distribution

CBSE Class 12 Maths Exam Pattern

The CBSE Class 12 Maths Exam Pattern for 2024 follows a competency-based approach, focusing on application and concept understanding. Here's a breakdown:

Total Marks: 100 (80 Theory + 20 Internal Assessment)

Theory Paper (80 Marks):

Exam Duration: 3 Hours

Question Paper Format: Five sections (A, B, C, D, and E) - all compulsory with internal choices in some sections.

Internal Assessment (20 Marks):

Conducted by the school throughout the year

May include projects, assignments, practical work, or quizzes

The Class 12 Maths NCERT Solutions provided on Vedantu have been written to help you understand all the chapter-wise problems in the latest and updated textbooks prescribed by NCERT . Being the most preferred study material , NCERT Solutions will help the students in various ways. Let us look into this.

Key Benefits of Maths NCERT Solutions Class 12 from Vedantu

You can easily clear your doubts by accessing this PDF anytime and also be able to learn some important tips to answer some complex questions in a detailed manner. 

You no longer have to turn in several pages for revision before the examination. The NCERT Maths Class 12 PDF Download is available on our website for FREE, which you can access anytime, anywhere.

Also, all the NCERT Class 12 Maths solutions are arranged in a sequential manner which enables smooth learning. Maths is a sequential subject, and it is important that it is studied in the right manner.

The solutions are explained in a detailed manner. Step by step solutions provided for all the exercise questions helps you to know the subject in a detailed manner.

The topic-wise detailed solutions will help you to take your preparation to the next level. Vedantu’s Class 12 Maths NCERT Solutions will definitely help you in improving your mathematical skills as well.

Go through these Chapter-wise Exercise Solutions that are provided for CBSE Class 12 Maths and begin your preparation for the Class 12 Board exam confidently. For any more information and study materials, visit Vedantu’s website.

Important Related Links for NCERT Class 12 Maths

NCERT Solutions for Class 12 Math in Hindi Chapter wise free pdf

Important Questions for CBSE Class 12 Maths

RS Aggarwal Class 12 Solutions for Math book

FAQs on Class 12 Maths NCERT Solutions PDF for 2024-25

1.  Is NCERT Maths Textbook a Good Study Material for Cracking JEE Main Exam?

NCERT Maths textbook is the best book to get your concepts cleared regarding the subject. For many studen ts, the Maths paper of JEE Main is considered one of the toughest subjects to clear. NCERT book is a good book to start your preparations for the exam. However, it is not just sufficient to clea r the exam as students need to have enough practice of the concepts. Referring to other books that are specialized for JEE preparation would give students an idea of different types of questions. If a student practices NCERT books enough, they will have a strong grip on the subject to start with. For any assistance regarding JEE preparation, students can log in to Vedantu’s platform.

2. Which is the Best Book Available in the Market for NCERT Maths Class 12 Board Exam Preparation?

NCERT textbook is considered the most valuable resource for board exam preparation. If a student concentrates well on the concepts given in NCERT textbook chapters and practices the exercise and example problems regularly, he/she can get good marks in the Class 12 Board exam . CBSE students must have a clear concept of the NCERT books before referring to other books for revision. 

3. Where Can I Get Free to Download Class 12 Maths NCERT Solutions?

The one-stop solution where you can get all the free materials for Class 12 board exam preparation is Vedantu. On Vedantu’s site, you can find the best NCERT Solutions for Class 12 Maths for free in PDF format. Vedantu is a trusted name when it comes to availing of the most authentic study materials. NCERT Solution of Maths Class 12 is designed by expert teachers who are well versed in the exam pattern and syllabus and have years of experience in the field of teaching.

4. How many chapters are there in NCERT Class 12 Maths Textbook?

NCERT Class 12 Maths Textbook consists of 2 parts. Part 1 of the NCERT Textbook includes 6 chapters, i.e., chapter 1 to chapter 6, whereas part 2 contains 7 chapters, i.e., chapter 7 to chapter 13. Therefore, a total of 13 chapters are included in the NCERT Class 12 Maths Textbook , which includes the following:

Inverse Trigonometric Functions

Relations and Functions

Determinants

Applications of Derivatives

Continuity and Differentiability

Applications of Integrals

Vector Algebra

Differential Equations

Three Dimensional Geometry

Probability

Linear Programming.

5. Are NCERT Exemplar Solutions available online?

Yes, NCERT Exemplar Solutions are available online. Students can also download the NCERT Exemplar Solutions for all classes and subjects from Vedantu in free PDF format. 

6.  How can Maths NCERT Solutions Class 12 help me score better marks in exams?

Maths NCERT Solutions Class 12 offer a structured approach to exam preparation. By practicing with these solutions, students can understand the logic behind each solution, learn different problem-solving techniques, and gain confidence in tackling complex mathematical problems, ultimately leading to improved performance in exams.

7. Which is the hardest chapter in Maths class 12?

The perception of the hardest chapter can vary among students. However, some commonly considered challenging chapters in Class 12 Maths include Differential Equations, Application of Integrals, and Linear Programming.

8. Is Class 12th maths hard?

Class 12 Maths can be challenging for some students due to its complexity and the introduction of new topics like Differential Equations, Three Dimensional Geometry, and Linear Programming. However, with consistent practice and understanding, it can become manageable.

9. How many exercises are there in AOD?

There are a total of 6 exercises in the Chapter Application of Derivatives (AOD).

10. Which topic is easiest in Maths Class 12?

The perception of the easiest topic may vary from student to student. However, some students find Relations and Functions, Matrices, and Determinants relatively easier compared to other chapters.

11. How can I improve my maths in class 12?

To improve in Maths in Class 12, it's essential to practice regularly, understand the concepts thoroughly, and seek help from teachers or tutors when needed. Solving previous years' question papers and additional practice exercises can also be beneficial.

12. How long does it take to complete class 12 maths?

The time required to complete Class 12 Maths varies depending on individual pace, understanding, and study habits. On average, it may take a few months if studied consistently and thoroughly.

13. How many marks are required to pass in maths class 12?

The passing marks in Class 12 Maths are generally 33% of the total marks. However, it's always better to aim for higher marks to secure good grades and improve overall performance.

NCERT Solutions for Class 12

Cbse study materials for class 12, important update.

NCERT Solutions for Class 12 Maths

Ncert solutions for class 12 maths – free pdf solutions.

Maths NCERT Solutions for Class 12 acts as a vital tool when students are preparing for their Board examinations and even while solving the home work or any assignments. It also helps students to crack any competitive exam such as IIT JEE, AIIMS, NDA, UPSC, NEET, BITSAT, VITEEE or any government exam. In short, any undergraduate engineering entrance exam or government exam requires NCERT solutions since they are your best ally and foot forward towards your exam preparations. Scoring in Maths can be very difficult process as it is not plain wrote-learning but practical application of the conceptual knowledge you have learned. This can be only done by mere practice and hardwork.

Class 12 NCERT Maths Solutions prepare a strong foundation of conceptual learning of all the chapters and topics covered in 12 th standard portion as prescribed by CBSE. The solution PDF compromises of important formulas, theorems and equations. Each point is further explained with detailed explanations so that students can grasp it easily and understand the concepts efficiently. Mathongo provides detailed step by step explanation of the problems. They are free download and in PDF format. They are designed by the best professors and teachers to ensure students get good marks in their examination.

The maths solutions of CBSE NCERT Class 12 gives in-depth clarity answers to all the questions asked in the NCERT textbook. All the topics of NCERT are equally important and must be studied thoroughly to attain good marks. Students should study chapters like probability, calculus, coordinate geometry, trigonometry with consistence as they can become very easy to solve with proper practice and then these units will help in fetching high marks.

NCERT Class 12 Maths Chapterwise Solutions

• Chapter 1 Relations and Functions
• Chapter 2 Inverse Trigonometric Functions
• Chapter 3 Matrices
• Chapter 4 Determinants
• Chapter 5 Continuity and Differentiability
• Chapter 6 Application of Derivatives
• Chapter 7 Integrals
• Chapter 8 Applications of Integrals
• Chapter 9 Differential Equations
• Chapter 10 Vector Algebra
• Chapter 11 Three-Dimensional Geometry
• Chapter 12 Linear Programming
• Chapter 13 Probability

Why Go for Mathongo’s NCERT Maths Solutions for Class 12

Mathongo provides NCERT class 12 maths solution at free of cost online and it’s easily accessible in the form of PDF. Each PDF constitutes of the chapter in which exercise wise solutions are given. It is very easy for the students to locate any answer from the exercise.

All the solutions are made with the help of the best teachers and academicians. The solutions are plain easy and can be understood by anyone. The approaches and the methods used to solve the questions are also given in step by step method so that students score good in paper. For additional conceptual clarity, diagrams and formulas are also used.

Mathongo has provided the best solutions for class 12 maths Ncert textbooks. Students can refer these solutions which will help them in solving the previous year question papers. These NCERT maths class 12 solution will help the students to study more effectively and also present the answers in the most effective way to get the highest scores.

The back-end exercise questions given in NCERT books are very important for the class 12 finals. These exercises often test the conceptual clarity and the subject knowledge of the student. NCERT Solutions will help you to understand these concepts better. On the other hand, the students who have problem in solving maths and require assistance and guidance can also refer class 12 Ncert Maths Solutions to clarify the complex questions concepts.

Maths is all about practice. The more you practice, the better you will be. Ncert maths class 12 pdf download can help students to solve all their problems and also save their time as everything is at one place, one click away.

Which book is best for class 12 Maths?

The best book for not only class 12 Mathematics but for any class is the NCERT textbook which is prescribed by CBSE. The conceptual base required to solve HOTs (High Order Thinking Problems) is built by practicing NCERT maths book examples and exercise questions. Once the students have studied thoroughly the NCERT textbook, the students can through books like RD Sharma and RS Aggarwal for further practice. However, students must not underestimate the power of solving NCERT since majority of the questions in the boards come either directly from NCERT or are NCERT based.

Is NCERT enough for Class 12 board Maths?

NCERT textbook is well enough for class 12 board examinations for Maths. Solving questions from NCERT textbook helps student to grasp concepts easily. If they wish to practice more as Maths is all about practice, they can use other reference books or even solve question banks and past year question papers.

Is class 12 NCERT Maths difficult?

The idea of the subject being difficult or easy lies in the mind of the beholder. Some students since childhood have Maths phobia engraved in their minds. But I would like to clear that. NCERT Maths of class 12 is not difficult. Once you get the conceptual clarity, you can start solving solved examples and problems followed by exercise questions. The only way you can master Maths is by practicing variety of questions.

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NCERT Solutions for Class 12 Maths Free PDF Download

Ncert solutions for class 12 maths.

NCERT Solutions for Class 12 Maths free PDF format is available to download from the links below. NCERT stands for National Council of Education Research and Training is the most preferred curriculum by all the boards like CBSE, Gujarat board, Madhya Pradesh board, etc. The NCERT Solutions for Class 12 Maths will help you to solve the answer the faster and it will clear each and every concept very clearly. NCERT Solutions also helps in cracking many entrance exams like JEE Main, JEE Advanced, NEET, etc. Questions and answers in these solutions will help in scoring better marks in exams.

Download NCERT solutions for other subjects here .

Following NCERT Solutions for Class 12 Maths are free to download. And if you signup on Toppr or download Toppr app you will also get last 10 years of question papers, 1000+ hours of video lectures, mock tests, live doubt solving and much more. Download Toppr app for Android and iOS now and join our 7 Million Students!

NCERT Solutions for Class 12 Maths Chapterwise

Chapter 1 – Relations and Functions

Chapter 2 – Inverse Trigonometric Functions

Chapter 3 – Matrices

Chapter 4 – Determinants

Chapter 5 – Continuity and 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

Class 12 Maths Chapterwise NCERT Solutions Free PDF Download

Ncert solutions of class 12 maths chapter 1 relations and functions.

In this chapter, you will learn about the Relations between two items and other topics like the Cartesian product of set. You will get more than 40 problems solved in this chapter in this free NCERT solutions PDF .

NCERT Solutions for Class 12 Maths Chapter 2  Inverse Trigonometric Functions

We covered trigonometric functions in Class 11. Now it is time to learn about Inverse Trigonometric functions. In this chapter, you will learn how to measure the angles between the two sides of the right angle and properties of angle. We have solved more than 40 problems in NCERT solutions for inverse trigonometric functions .

NCERT Solutions for Class 12 Maths Chapter 3 Matrices

Matrix is one of the most important applications of Maths. Understand matrices will also help you in further courses. In this chapter, you will learn different topics on matrices like transpose of matrices, multiplication of matrices, etc. Download NCERT Solutions for Matrices here .

NCERT Solutions for Class 12 Maths Chapter 4  Determinants

Learning matrices is not complete without learning Determinants. The inverse of the matrix depends upon the Determinants. In this chapter, Determinant of a matrix, properties of determinants and more. We have solved more than 100 problems for this chapter. Download NCERT solution for Class 12 Maths Determinants here .

NCERT Solutions for Class 12 Maths Chapter 5  Continuity and Differentiability

Continuity and differentiability are all about derivates and its algebra. You will get more than 100 problems solved in this NCERT Solutions for Continuity and Differentiability .

NCERT Solutions for Class 12 Maths Chapter 6  Application of Derivatives

Tangents and normal, Maxima and minima and some more applications of derivatives you will learn in this chapter. Download NCERT Solutions free PDF for applications of derivates here .

NCERT Solutions for Class 12 Maths Chapter 7  Integrals

Integrals are the most important and toughest topic in mathematics. It is very important to understand integrals very clearly and NCERT solutions will definetly help you in that. Our team of experts has solved more than 200 problems in this chapter for you. Download NCERT Solutions for Class 12 Integrals here .

NCERT Solutions for Class 12 Maths Chapter 8  Application of Integrals

Integrals have a lot of applications in Engineering. In this chapter, we will learn how to measure how to find area under simple curves, area between two curves, area bounded by curve and line. We have solved more than 50 problems in this chapter. Download NCERT Solutions for this chapter here .

NCERT Solutions for Class 12 Maths Chapter 9  Differential Equations

In this chapter, you will learn about Linear and homogenous Differential equations and how to find the order of differential equations. We have solved more than 50 problems solved in this chapter. Download NCERT Solutions for Differential equations here .

NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra

Vector algebra is a really important topic for cracking exams like JEE Main and Advanced. This topic can be helpful in real life scenarios too. In this chapter, you will learn different types of vectors, product, and addition of vectors. We have solved more than 50 problems solved in this chapter. Download NCERT Solutions of Vector algebra here .

NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry

Three Dimensional Geometry is an interesting topic. In this chapter, you will learn to measure the distance between parallel lines, the distance between skew lines, etc. Download NCERT Solutions for three-dimensional geometry here .

NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming

Linear programming problems have wide applications in business mathematics, economics, and statistics. In this chapter, you will learn about types of linear programming, graphical method of linear programming and more. Download NCERT Solutions for Linear programming here .

NCERT Solutions for Class 12 Maths Chapter 13 Probability

Probability is one of the most important topics in Mathematics which helps in real life applications as well. In this chapter, we will learn about Baye’s theorem, Bernoulli trials and more. Download NCERT Solutions for this chapter here .

Toppr – Best Learning App for Class 5 to Class 12

Toppr is the best learning app for Class 5 to Class 12 and also for competitive entrance exams like JEE Main, JEE Advanced, NEET, AIIMS, etc. In Toppr you will get 1000+ hours of free video lectures on each and every topic. Our experts at Toppr has created an important set of questions for you. You will also get the last 10 years of question papers, mock tests, and live doubts solving. Download Toppr for Android and iOS or signup on Toppr and start learning now.

Solved Questions For You:

Question 1. Find the rate of change of the area of a circle with respect to its radius  r  when

(i)  r = 3  cm (ii)  r = 4  cm

Question 2.  Let  f : R → R  be defined as  f ( x ) = 3 x . Choose the correct answer.

f : R → R  is defined as  f ( x ) = 3 x .

Let  x , y  ∈  R  such that  f ( x ) = f ( y )

⇒ 3 x = 3 y ⇒ x = y ∴ f  is one-one Also, for any real number  ( y )  in co-domian  R , there exists \(\frac{y}{3}\)  in  R  such that f (\(\frac{y}{3}\))  = 3 (\(\frac{y}{3}\) ) = y

∴ f  is onto.

Hence, function  f  is one-one and onto The correct answer is  A .

Let  A = { 4 , 6 , 8 }

a , b ∈ R .

Relation  R  is not transitive since  ( 4 , 6 ) , ( 6 , 8 ) ∈ R , but  ( 4 , 8 ) \(\notin\)  R .

Question 4: Let  R  be the relation in the set  { 1 , 2 , 3 , 4 }  given by  R = { ( 1 , 2 ) , ( 2 , 2 ) , ( 1 , 1 ) , ( 4 , 4 ) , ( 1 , 3 ) , ( 3 , 3 ) , ( 3 , 2 ) } . 

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NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12

NCERT Solutions For Class 12 Maths (2023-2024)

NCERT Solutions for Class 12 Maths (2023-2024) has been written to help students like you who are appearing for different board exams as well as the JEE. It provides sound knowledge and understanding of all important concepts covered in each chapter in the Class 12 Maths NCERT textbook. There are 13 important chapters from the NCERT textbook. Both problems and their detailed solutions are provided. The solutions have been devised by India’s best teachers to help students grasp basic concepts better and faster.

NCERT Solutions for Class 12 Maths All Chapters 2023-2024

NCERT Maths Class 12 Solutions are given below for all chapter. Select chapter number to view Class 12 Maths NCERT chapter wise solutions.

• Chapter 1 Relations and Functions
• Chapter 2 Inverse Trigonometric Functions
• Chapter 3 Matrices
• Chapter 4 Determinants
• Chapter 5 Continuity and 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

If you are looking for Class 12 Maths NCERT Solutions, there is no better place to be than right here. We provide Maths NCERT solutions class 12 that are precise, to the point and absolutely error free. With NCERT reputed to be the best textbooks for school education, we make the solutions that are at par with the excellent textbooks.

Important Questions for Class 12 Maths Chapter wise 2023-24

Relations and Functions

• Concept of Relations and Functions
• Binary Operations
•   Inverse Trigonometric Functions
• Matrix and Operations of Matrices
• Transpose of a Matrix and Symmetric Matrix
• Inverse of a Matrix by Elementary Operations

Determinants

• Expansion of Determinants
• Properties of Determinants
• Inverse of a Matrix and Application of Determinants and Matrix

Continuity and Differentiability

• Differentiability

Application of Derivatives

• Rate Measure Approximations and Increasing-Decreasing Functions
• Tangents and Normals
• Maxima and Minima
• Types of Integrals

Differential Equation

• Formation of Differential Equations
• Solution of Different Types of Differential Equations

Vector Algebra

• Algebra of Vectors
• Dot and Cross Products of Two Vectors

Three Dimensional Geometry

• Direction Cosines and Lines

Linear Programming

Probability

• Conditional Probability and Independent Events
• Baye’s Theorem and Probability Distribution

NCERT Exemplar Class 12 Maths

• Chapter 3 Matrices
• Chapter 5 Continuity and Differentiability
• Chapter 6 Application of Derivatives
• Chapter 7 Integrals
• Chapter 8 Applications of Integrals
• Chapter 9 Differential Equations
• Chapter 10 Vector Algebra
• Chapter 11 Three Dimensional Geometry
• Chapter 12 Linear Programming
• Chapter 13 Probability

RD Sharma Class 12 Maths Solutions

Class 12 Maths NCERT Solutions

Class 12 Maths is key in the preparation for boards as well as JEE Main and Advance, and our solutions are made keeping in mind the very same thing. The solutions are concise, and also discuss alternative methods to solve some problems. We make it a point to provide the students the best help they can get, and the solutions reflect just that.

The National Council of Educational Research and Training ( NCERT ) is an autonomous organization of the Government of India that was established in 1961 as a literary, scientific and charitable society under the Societies’ Registration Act (Act XXI of 1860). Its headquarters are located at Sri Aurobindo Marg in New Delhi. It sets the curriculum for all schools that follow the Central Board of Secondary Education (CBSE) across the country. Class 12 Maths NCERT Solutions is the perfect guide to help you prepare for CBSE exams as well as engineering entrances like the JEE.

Your performance in the board exams will play a role in determining your admission into a good college or even your dream college! That will undoubtedly induce a lot of pressure upon you and you may tend to get demotivated or stressed out. To help you overcome such situations, LearnCBSE is a platform all the way helps you to crack your target. if you have any queries leave in the comments box.

NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions

The chapter builds up on the concepts of relations, functions, domain and codomain introduced in Class 11. The students explore several real valued functions, and their graphs. The chapter comprises of four exercises that consolidate the concepts explained in the chapter.

NCERT Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions

This chapter plays in the restricted range of trigonometric functions that enables them to be one on one, and hence makes inverse of the functions visible. This chapter explores the inverse trigonometric through two exercises that teach the students the behavior of the functions, their graphical representations, and the elementary properties. These prove to be of more value in integration later.

NCERT Solutions for Class 12 Maths Chapter 3 Matrix

This chapter takes you through the properties of one of the most important tools of Mathematics, namely Matrices. The students learn the basics of Matrices and Matrix Algebra..

NCERT Solutions for Class 12 Maths Chapter 4 Determinants

Correctly preceded by Matrix, this chapter deals with an important part of Matrices, namely Determinants. The chapter deals with determinants of orders upto 3, and their cofactors and inverses.This chapter also talks about the applications of determinants, like calculation of area of triangles, adjoint of matrices, consistency of a set of linear equations.

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability

This chapter picks up after the Differentiation of Functions introduced in Class 11. The chapter explores the important concepts of Continuity, Differentiability and establishes the relationship between them. It also deals with the continuity and differentiability of Inverse Trigonometric Functions. It also introduces exponential and logarithmic functions.

NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives

With Continuity and Differentiability marking the start of Calculus, this chapter deals with the differentiability of functions, and introduction to derivatives. It delves into the derivatives of specific functions, and their applications, namely the tangents and normal to curves, and the rate of change in some quantities. It also talks about increasing and decreasing functions.

NCERT Solutions for Class 12 Maths Chapter 7 Integrals

This is one of the most important and time consuming chapters in the whole Class 12 Mathematics. This chapter deals with integration of functions, and its applications in terms of calculation of areas. This marks the introduction to Integral Calculus. There are a total of 11 exercises in this chapter, making it a very practice driven part of the syllabus.

NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals

This chapter deals with the applications of integrals in calculating areas under simple curve, lines, parabolas and ellipses. The two exercises provide enough questions for practicing the area calculations.

NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations

This chapter introduces the concept of Differential equations, the general and particular solutions, and the order and degree of an equation. This also talks about the applications of differential equations in the six exercises.

NCERT Solutions for Class 12 Maths Chapter 10 Vector Equations

This chapter deals with the vector quantities, that is, the quantities with both magnitude and direction. The Vector algebra summarises the rules of addition of vector quantities, and other important properties. Vector Algebra plays a big role in Physics.

Class 12 Maths Chapter 11 Three Dimensional Geometry

This chapter utilises vectors to calculate the distance between lines, a point and a line, and a line and a plane, along with the angles between them.It also introduces the concept of direction cosines

Class 12 Maths Chapter 12 Linear Programming

This chapter explores the concept of linear programming problems, and their solutions using graphical method only.

Class 12 Maths Probability

This chapter deals with the concept of Conditional Probability and the encounters of the same in our daily lives. This explores Bayes’ Theorem, the multiplication rule, and the independence of events. This chapter is best understood by practicing as many questions as possible.

NCERT Solution

We hope you will have great learning experience while using the solutions. You can download the solutions by clicking on the links above in the description.

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Chapter 10 Class 12 Vector Algebra

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Learn Chapter 10 Class 12 Vector Algebra free with solutions of all NCERT Questions, Examples as well as Supplementary Questions from NCERT.

Suppose we have to go 10km from Point A to Point B.

This 10km is the distance travelled.

It is only value - 10, nothing else.

This is a scalar quantity.

Now, suppose we say, 

We go 10 km East from Point A to Point B.

So, we have travelled 10 km East

It has value - 10, and direction - East.

So, this is a vector quantity .

In this chapter, we will talk about vectors. The topics include

• Basics - Difference between scalars and vectors , with example
• Graphical Displacement - Where we represent Displacement like 40 km, 30° East of North, in the Graph.
• We also discuss what is a position vector, and different types of vectors
• Then we learn what happens when a scalar is multiplied to a vector
• We learn what are Equal Vectors and Unit Vectors , and do some questions on them
• Finding Direction Ratios and Direction Cosines
• Then, adding two vectors
• Finding vector joining two points
• Section formula in vectors
• Checking if 3 points make a right angled triangle
• Checking if 2 vectors are collinear
• Checking if 3 points (or vectors) are collinear
• Then, Scalar Product of Vectors and its properties
• Finding projection using scalar product
• Vector product of vectors, and its properties
• Finding area using vector product (Area of parallelogram = Vector Product)

All the questions are solved, with step by step explanation. Click on an exercise or a topic to start learning

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• Chapter Wise Extra Questions...

Chapter Wise Extra Questions of Class 12 Mathematics

Chapter Wise Extra Questions of Class 12 Mathematics myCBSEguide has just released question for Class 12 Mathematics There chapter wise latest exam questions with complete solutions are available for download in myCBSEguide   website and the app for CBSE students. We have taken care of every single concept given in  CBSE Class 12 Mathematics syllabus  and questions are framed as per the latest marking scheme and blue print issued by CBSE. There are around 4-5 set of solved important questions from each and every chapter. The students will not miss any concept in these Test papers that are specially designed to tackle CBSE class 12 board exam.

Maths Class 12 Chapter Wise Extra Questions

• Relations and Functions
• Inverse Trigonometric Functions
• Determinants
• Continuity and Differentiability
• Application of Derivatives
• Application of Integrals
• Differential Equations
• Vector Algebra
• Three Dimensional Geometry
• Linear Programming
• Probability

To download  Mathematics, Science, Social Science, English Communicative, English Language and Literature, Hindi Course A, Hindi Course B, and Other subjects; do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, guess papers and CBSE important question papers. Sample Paper all are made available through  the best app for CBSE students  and myCBSEguide website.

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CLASS XII RELATIONS AND FUNCTIONS

CLASS XII INVERSE TRIGONOMETRY

CLASS XII MATRICES

CLASS XII DETERMINANTS

CLASS XII CONTINUITY & DIFFERENTIABILITY

CLASS XII APPLICATION OF DERIVATIVES

CLASS XII INTEGRATION

CLASS XII APPLICATIONS OF INTEGRATION

CLASS XII DIFFERENTIAL EQUATIONS

CLASS XII VECTOR ALGEBRA

CLASS XII THREE DIMENTIONAL GEOMETRY

CLASS XII LINEAR PROGRAMMING PROBLEMS

CLASS XII PROBABILITY

CLASS XII ASSIGNMENTS (Old)

Ch 1 Relation and Function

Ch 2 Inverse Trigonometry

Ch 3 Matrices

Ch 4 Determinants

Ch 5 Continuity and Differentiability

Ch 6 Application of Derivatives

Ch 7 Integrals

Ch 8 Applications of Integrals

Ch 9 Differential Equations

Ch 10 Vector Algebra

Ch 11 3D Geometry

Ch 13 Probability

Formula List (Book 1 Based)

Formula List (Book 2 Based)

• NCERT Solutions
• NCERT Class 12
• NCERT 12 Maths
• Chapter 1: Relations And Function

NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions

Ncert solutions for class 12 maths chapter 1 – free pdf download.

NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions provides solutions for all the questions enlisted under the chapter, which is included in the CBSE syllabus 2023-24. All exercise questions are solved using a step-by-step approach. Solving the questions from the Class 12 Maths NCERT textbook helps grasp the concepts correctly. Students can download and go through these NCERT Solutions for Class 12 Maths  to sharpen their Maths skills.

Students should understand not only the basics of this chapter but also the advanced portions to get a command over the chapter Relations and Functions. Practising these NCERT Solutions for Class 12 Maths will help the students in their exam preparation in such a way that they will find even the difficult questions from this chapter to be extremely easy. Download the NCERT Solutions PDF of this chapter from the link provided below.

Download PDF of NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions

Access answers of class 12 ncert maths chapter 1 relations and functions.

In NCERT Class 12 Maths Chapter 1, students study different types of relations and equivalence relations, composition of functions, invertible functions and binary operations. Students can utilise the NCERT Solutions for Class 12 Maths Chapter 1 for any quick reference to comprehend complex topics.

The main features of this chapter are as follows:

• Empty relation
• Universal relation
• Reflexive relation
• Symmetric relation
• Transitive relation
• Equivalence relation
• A function f: X → Y is one-one (or injective) if f (x 1 ) = f(x 2 ) ⇒ x 1 = x 2 ∀ x 1 , x 2 ∈ X.
• A function f: X → Y is onto (or surjective) if given any y ∈ Y, ∃ x ∈ X such that f(x) = y.
• A function f: X → Y is one-one and onto (or bijective), if f is both one-one and onto.
• A function f: X → Y is invertible if and only if f is one-one and onto.

NCERT Solutions For Class 12 Maths Chapter 1 Exercises:

Get detailed solutions for all the questions listed under the below exercises:

Exercise 1.1 Solutions : 16 Questions (14 Short Answers, 2 MCQ)

Exercise 1.2 Solutions : 12 Questions (10 Short Answers, 2 MCQ)

Exercise 1.3 Solutions : 14 Questions (12 Short Answers, 2 MCQ)

Exercise 1.4 Solutions : 13 Questions (12 Short Answers, 1 MCQ)

Miscellaneous Exercise Solutions : 19 Questions (7 Long answers, 9 Short Answer Type, 3 MCQs)

The main topics covered in this chapter include:

Key Features of NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions

• These NCERT exercises are meticulously solved by subject experts.
• Simple and easy language is used.
• All questions are solved with the best possible explanations given.
• These NCERT Solutions are a valuable help to students in their assignments and competitive exams.

Students can also access the NCERT Solutions for Class 12 of any subject while preparing for the board examinations apart from Mathematics. All the solutions are in accordance with the latest CBSE Syllabus and guidelines.

Disclaimer – 

Dropped Topics – 1.4 Composition of Functions and Invertible Function (upto ‘This leads to the following definition’), Page 13-14 Full Pages, Page 15 Examples 24 and 25, Page 16-25 Full Pages, Page 26 Question 12 and 13, Page 27-28 Examples 45 and 49, Page 29-31 Ques. 1–3, 6–7, 9, 11–14, 18–19, Page 31-32 Summary points 11-13 and 15-19.

Frequently Asked Questions on NCERT Solutions for Class 12 Maths Chapter 1

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Class 12 Mathematics Matrices and Determinants Assignments

We have provided below free printable Class 12 Mathematics Matrices and Determinants Assignments for Download in PDF. The Assignments have been designed based on the latest NCERT Book for Class 12 Mathematics Matrices and Determinants . These Assignments for Grade 12 Mathematics Matrices and Determinants cover all important topics which can come in your standard 12 tests and examinations. Free printable Assignments for CBSE Class 12 Mathematics Matrices and Determinants , school and class assignments, and practice test papers have been designed by our highly experienced class 12 faculty. You can free download CBSE NCERT printable Assignments for Mathematics Matrices and Determinants Class 12 with solutions and answers. All Assignments and test sheets have been prepared by expert teachers as per the latest Syllabus in Mathematics Matrices and Determinants Class 12. Students can click on the links below and download all Pdf Assignments for Mathematics Matrices and Determinants class 12 for free. All latest Kendriya Vidyalaya Class 12 Mathematics Matrices and Determinants Assignments with Answers and test papers are given below.

Mathematics Matrices and Determinants Class 12 Assignments Pdf Download

We have provided below the biggest collection of free CBSE NCERT KVS Assignments for Class 12 Mathematics Matrices and Determinants . Students and teachers can download and save all free Mathematics Matrices and Determinants assignments in Pdf for grade 12th. Our expert faculty have covered Class 12 important questions and answers for Mathematics Matrices and Determinants as per the latest syllabus for the current academic year. All test papers and question banks for Class 12 Mathematics Matrices and Determinants and CBSE Assignments for Mathematics Matrices and Determinants Class 12 will be really helpful for standard 12th students to prepare for the class tests and school examinations. Class 12th students can easily free download in Pdf all printable practice worksheets given below.

Topicwise Assignments for Class 12 Mathematics Matrices and Determinants Download in Pdf

Advantages of Class 12 Mathematics Matrices and Determinants Assignments

• As we have the best and largest collection of Mathematics Matrices and Determinants assignments for Grade 12, you will be able to easily get full list of solved important questions which can come in your examinations.
• Students will be able to go through all important and critical topics given in your CBSE Mathematics Matrices and Determinants textbooks for Class 12 .
• All Mathematics Matrices and Determinants assignments for Class 12 have been designed with answers. Students should solve them yourself and then compare with the solutions provided by us.
• Class 12 Students studying in per CBSE, NCERT and KVS schools will be able to free download all Mathematics Matrices and Determinants chapter wise worksheets and assignments for free in Pdf
• Class 12 Mathematics Matrices and Determinants question bank will help to improve subject understanding which will help to get better rank in exams

Frequently Asked Questions by Class 12 Mathematics Matrices and Determinants students

At https://www.cbsencertsolutions.com, we have provided the biggest database of free assignments for Mathematics Matrices and Determinants Class 12 which you can download in Pdf

We provide here Standard 12 Mathematics Matrices and Determinants chapter-wise assignments which can be easily downloaded in Pdf format for free.

You can click on the links above and get assignments for Mathematics Matrices and Determinants in Grade 12, all topic-wise question banks with solutions have been provided here. You can click on the links to download in Pdf.

We have provided here topic-wise Mathematics Matrices and Determinants Grade 12 question banks, revision notes and questions for all difficult topics, and other study material.

We have provided the best collection of question bank and practice tests for Class 12 for all subjects. You can download them all and use them offline without the internet.

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WELCOME TO THE EXCITING WORLD OF MATHEMATICS

Sunday, august 28, 2016, assignments -mathematics - class xii, 3 comments:.

Sir, Your blogs are very helpful to me.{specially this one} These assignments are fabulous. BUT I am facing some serious problem in physics. Please can you provide such assignments for physics or send link of some other physics teacher blog providing assignment like yours. I am student of 2019-20 batch from M.P. Expecting Helpful answer from you sir -Harish

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Assignments For Class 12

Assignments for Class 12 have been developed for Standard 12 students based on the latest syllabus and textbooks applicable in CBSE, NCERT, and KVS schools. Parents and students can download the full collection of class assignments for class 12 from our website as we have provided all topic-wise assignments free in PDF format which can be downloaded easily. Students are recommended to do these assignments daily by taking printouts and going through the questions and answers for Grade 12. You should try to do these test assignments on a daily basis so that you are able to understand the concepts and details of each chapter in your book and get good marks in class 12 exams.

Assignments Class 12 for all subjects Free Pdf

Students can refer to the below subject-wise assignments for class 12 which the students can download in Pdf format for free. This is the best and largest collection of standard 12th assignments with important questions and answers for grade 12th subjects and their chapters to help the students properly practice and gain more marks in Class 12 class tests and exams

Subject wise Assignments for Class 12 for download in Pdf

Some advantages of Free Assignments for Class 12

• Solving Assignments for Class 12 helps to further enhance understanding of the topics given in your NCERT text book which will help you to get better marks
• By solving one assignments given in your class by teacher for class 12 will help you to keep in touch with the topic thus reducing dependence on last minute studies
• You will be able to understand the type of questions which are expected in your class test
• You will be able to revise all topics given in the ebook for Class 12 as all questions have been provided in the question banks
• NCERT Class 12 Workbooks will surely help you to make your concepts stronger and better than anyone else in your class.
• Parents will be able to take print out of the assignments and give to their child easily.

All free Printable practice assignments are in PDF single lick download format and have been prepared by Class 12 teachers after full study of all topics which have been given in each chapter so that the students are able to take complete benefit from the worksheets. The Chapter wise question bank and revision assignments can be accessed free and anywhere. Go ahead and click on the links above to download free CBSE Class 12 Assignments PDF.

You can download free assignments for class 12 from https://www.assignmentsbag.com

You can get free PDF downloadable assignments for Grade 12 from our website which has been developed by teachers after doing extensive research on each topic.

On our website we have provided assignments for all subjects in Grade 12, all topic-wise test sheets have been provided in a logical manner so that you can scroll through the topics and download the worksheet that you want.

You can easily get question banks, topic wise notes and questions, and other useful study material from https://www.assignmentsbag.com without any charge

Yes, all test papers for Class 12 are available for free, no charge has been put so that the students can benefit from it. And off-course, all are available for download in PDF format and with a single click, you can download all assignments.

https://www.assignmentsbag.com is the best portal to download all assignments for all classes without any charges.

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Important questions on Inverse Trigonometric Functions, Maths Assignment on trigonometric functions, extra questions on inverse trigonometric functions class XII chapter 2

• First of all students should learn and  revise all  basic concepts and formulas  of Inverse Trigonometric Functions.
• Revise Chapter 2 Inverse Trigonometric Functions from  NCERT book of Mathematics.
• Revise all examples of chapter 2 of  NCERT book.
• Now start the Assignment.

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Lesson Plan Maths Class XII | For Maths Teacher

• Assignment 10 15
• Assignment 11 12
• Assignment 12 14
• Assignment 8 8
• Assignment 9 5
• Lesson plan 10 15
• Lesson Plan 12 14
• Lesson Plan 8 10
• Maths 10 20
• Maths 11 21
• Maths 12 17

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HBSE Class 12 Mathematics Syllabus Available For The Academic Year 2024-25

Hbse class 12 mathematics syllabus 2024-25: the hbse class 12 syllabus plays a crucial role in the student’s exam preparation. it makes them familiar with the course content of the mathematics exam. check the latest syllabus for the hbse class 12 mathematics board exam. .

HBSE Class 12 Mathematics Syllabus 2024-25 Free PDF Download: Most students might be looking for the complete syllabus to prepare for the test and give their best. Knowing the complete syllabus before preparing for the exam is very important. So, here we are providing the full HBSE Class 12 Mathematics 2024-25 syllabus. You can also download the PDF for free.

The very first thing students can take a look at is the general instructions for the exam. 

• There will be an Annual Examination based on the entire syllabus. 
• The Annual Examination will be of 80 marks and 20 marks weightage will be for Internal Assessment. 
• For Internal Assessment: There will be a Periodic Assessment that will include: 

i) For 04 marks- Two SAT exams will be conducted and will have a weightage of 04 marks towards the final Internal Assessment. 

ii) For 02 marks- One half-yearly exam will be conducted and will have a weightage of 02 marks towards the final Internal Assessment.

For 02 marks- One pre-board will be conducted and will have a weightage of 02 marks towards the final Internal Assessment. 

iv) For 02 marks- The subject teacher will assess and give a maximum of 02 marks for CRP (Classroom participation). 

v) For 05 marks- A project work to be done by students and will have a weightage of 05 marks towards the final Internal Assessment. 

vi) For 05 marks- Attendance of student will be awarded 05 marks as: Above 75% up to 80% - 01 marks 

Above 80% up to 85% - 02 marks 

Above 85% up to 90% - 03 marks 

Above 90% up to 95% - 04 marks

Core Structure For HBSE Class 12 Mathematics Exam 2024-25

Class: 12th 

Subject: Mathematics 

Total Chapters For The Exam

Chapter 1: Relations and Functions

1.1: Introduction

1.2 Types of Relations: Empty Relation, Universal Relation, Reflexive Relation, Symmetric Relation, Transitive Relation, Equivalence Relation

1.3 Types of Functions: Injective Function, Surjective Function, Bijective Function

1.4: Composition of Functions and Invertible Function: fog, of, Invertible Function definition

Miscellaneous Exercise

Chapter 2: Inverse Trigonometric Functions

2.1 Introduction

2.2 Basic Concepts: Domain, Range, Graphs, and Principal Value of Trigonometric Functions

2.3 Properties of Inverse Trigonometric Functions: Related to sin(sin1x) = x, x € [-1,1] and sin-1 (sin x) = x, x € [-π/2,π/2], Conversion of some trigonometric functions in their simplest forms using trigonometric properties

Chapter 3: Matrices

3.1 Introduction

3.2 Matrix: Definition and Order of a matrix

3.3 Types of Matrices: Column Matrix, Row Matrix, Square Matrix, Diagonal Matrix, Scalar Matrix, Identity Matrix, Zero Matrix

3.3.1 Equality of Matrices

3.4 Operations on Matrices: Addition of matrices, Multiplication of a matrix by a scalar, Properties of matrix addition, Properties of scalar multiplication of a matrix, Multiplication of matrices, Properties of multiplication of matrices

3.5 Transpose of a Matrix: Properties of the transpose of the matrices

3.6 Symmetric and Skew Symmetric Matrices

3.7 Invertible Matrices: Definition of invertible matrix, Uniqueness of Inverse (Theorem and its applications)

Chapter 4: Determinants

4.1 Introduction

4.2 Determinant: Determinants of matrices of order one, two, and three

4.3 Area of a Triangle

4.4 Minors and Cofactors

4.5 Adjoint and Inverse of a Matrix

4.6 Applications of Determinants and Matrices: Solution of a system of linear equations using the inverse of a matrix

Chapter 5: Continuity and Differentiability

5.1 Introduction

5.2 Continuity: Definition of continuity, Algebra of continuous functions

5.3 Differentiability: Derivatives of composite functions, Chain Rule, Derivatives of implicit functions, Derivatives of inverse trigonometric functions

5.4 Exponential and Logarithmic Functions

5.5 Logarithmic Differentiation

5.6 Derivatives of Functions in Parametric Forms

5.7 Second Order Derivative

Chapter 6: Application of Derivatives

6.1 Introduction

6.2 Rate of Change of Quantities

6.3 Increasing and Decreasing Functions

6.4 Maxima and Minima: Local Maxima, Local Minima, First Derivative Test, Second Derivative Test, Maximum and Minimum Values of a Function in a closed Interval, Absolute Maximum, Absolute Minimum

Chapter 7: Integrals

7.1 Introduction

7.2 Integration as an Inverse Process of Differentiation: Some properties of indefinite integral

7.3 Methods of Integration: Integration by Substitution, Integration using Trigonometric Identities

7.4 Integrals of Some Particular Functions

7.5 Integration by Partial Fractions

7.6 Integration by Parts: Integral of the type ∫ ex [ f (x)+f1 (x) ] dx, Integrals of some more types

7.7 Definite Integral

7.8 Fundamental Theorem of Calculus: Area function and related numerical problems

7.9 Evaluation of Definite Integrals by Substitution

7.10 Some Properties of Definite Integrals and Related Problems

Chapter 8: Application of Integrals

8.1 Introduction

8.2 Area under Simple Curves Using Definite Integrals

Chapter 9: Differential Equations

9.1 Introduction

9.2 Basic Concepts: Order and Degree of a Differential Equation

9.3 General and Particular Solutions of a Differential Equation

9.4 Methods of Solving First-Order, First-Degree Differential Equations: Differential Equations with variables separable, Homogeneous Differential Equations, Linear Differential Equations

Chapter 10: Vector Algebra

10.1 Introduction

10.2 Some Basic Concepts: Definition of Vector, Position Vector, Direction Cosines

10.3 Types of Vectors: Zero Vector, Unit Vector, Coinitial Vector, Collinear Vector, Equal Vectors, Negative of a Vector

10.4 Addition of Vectors

10.5 Multiplication of a vector by a Scalar: Components of a Vector, Vector joining Two Points, Section Formula

10.6 Product of Two Vectors: Scalar (or dot) Product of Two Vectors, Projection of a Vector on a line, Vector ( or cross ) product of Two Vectors

Chapter 11: Three-Dimensional Geometry

11.1 Introduction

11.2 Direction Cosines and Direction Ratios of a Line: Direction cosines of a line passing through two points

11.3 Equation of a Line in Space: Equation of a Line through a given point and parallel to a given vector

11.4 Angle between two Lines

11.5 Shortest Distance between Two Lines: Distance between two skew lines, the Distance between two parallel lines

Chapter 12: Linear Programming

12.1 Introduction

12.2 Linear Programming Problem and its Mathematical Formation: Mathematical Formulation of the Problem, Graphical Method of solving Linear Programming Problems

Chapter 13: Probability

13.1 Introduction

13.2 Condition Probability: Properties of conditional probability

13.3 Multiplication Theorem on Probability

13.4 Independent Events

13.5 Bayes’ Theorem and Related Problems: Partition of a sample space, Theorem of total probability

Prescribed Books:

1. Textbook for class 12th : Mathematics Part-1 , NCERT- Latest Edition

  Mathematics Part-2, NCERT- Latest Edition

HBSE Class 12 Mathematics Exam Weightage And Marks

HBSE Class 12 Mathematics Exam Question Typology

This is the syllabus and the question paper design for HBSE Class 12 Mathematics. The students can start preparing for the exams as the holidays are approaching. 

HBSE Class 12 Mathematics Syllabus 2024-25 Free PDF Download

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HBSE Class 11 Philosophy Syllabus 2024-25 Free PDF Download!

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