 NCERT Solutions of Class 12 Maths in Hindi and English Medium are modified and revised for Session 2023-24 as per the rationalised NCERT books published for board exams. Class 12 Maths solutions refer to the answers, explanations with step-by-step solutions provided by Tiwari academy for the mathematics textbook of the 12th grade in the National Council of Educational Research and Training (NCERT) curriculum in Bharat.

## NCERT Solutions of Class 12 Maths

Class 12 Maths solutions are designed to help students understand and solve the complex mathematical problems presented in the Class 12 Maths. Class 12 Chapter Wise Maths NCERT Solutions are as follows:
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 NCERT solutions in Bharat serve several important purposes for students and educators. Class 12 mathematics is a critical year for students in Bharat as they prepare for their board exams, such as the Central Board of Secondary Education (CBSE) exams and various state board exams. NCERT solutions provide comprehensive and well-structured solutions to the problems and exercises in the NCERT mathematics textbook for class 12. This helps students prepare effectively for their board exams, as these exams often follow the NCERT curriculum closely.

Class 12 Solutions App

NCERT solutions offer clear and detailed explanations for various mathematical concepts and problem-solving techniques. They help students understand the underlying principles and logic behind mathematical concepts. This is crucial for building a strong foundation in mathematics, which is beneficial not only for board exams but also for various competitive exams and future academic pursuits.

It also includes examples that will help students better understand the concepts. Oswaal CBSE Question Banks Class 12 2023-24 for 2024 Board Exam | Trusted by 3 Lakh Teachers, 50000 Schools, and 13M Parents. The Tiwari Academy provides NCERT Solutions of Class 12 Maths which can be of great help to students.

NCERT solution provide a wide range of solved exercises and problems. Students can use these solutions for practice and revision, helping them become proficient in solving mathematical problems of varying complexity. Regular practice is essential to improve problem-solving skills and gain confidence in mathematics.

When you encounter problems in the Class 12 NCERT Maths textbook, refer to the NCERT Solutions provided by Tiwari Academy. Follow these steps:
1. Read the solution carefully to understand the approach.
2. Attempt to solve the problem on your own first.
3. Compare your solution with the provided solution.
4. Analyze any differences and learn from them.

 Class: 12 Mathematics Number of Chapters: 13 (Thirteen) Content: NCERT and Extra Questions with Papers Content Type: Images, Text, PDF and Video Format Mode of Study: Online and Offline Format Academic Session: Year 2023-24 Medium: Hindi and English Medium

Many competitive exams in Bharat, such as engineering and medical entrance exams (e.g., JEE Main, NEET), require a strong foundation in mathematics. Class 12 mathematics NCERT solutions can be valuable for students preparing for these exams, as they cover essential topics and concepts commonly tested in such competitive exams.

Teachers often use NCERT solutions as teaching aids to explain concepts and solve problems in the classroom. These solutions provide structured explanations and solutions that can assist teachers in delivering effective math lessons. NCERT textbooks and solutions are widely recognized and accepted across Bharat. They ensure a standardized curriculum and help maintain consistency in mathematics education across different states and regions.

Key Points of 12th Maths Solutions

Class 12 Maths NCERT solutions cover advanced mathematical concepts and topics suitable for students in their final year of secondary education. Oswaal CBSE Sample Papers Class 12 2023-24 for 2024 Board Exam | Trusted by 3 Lakh Teachers, 50000 Schools, and 13M Parents.

Here are some key points to consider about Class 12 Maths NCERT solutions:

1. The 12th Maths solutions cover a wide range of topics such as calculus, linear algebra, differential equations, Inverse Trigonometry, probability, and vectors. These concepts are important for building a strong foundation in mathematics and preparing for higher studies.

2. The solutions provide step-by-step explanations for various problems, helping students understand the logic and reasoning behind each step. This approach promotes better comprehension and problem-solving skills.

3. The Maths solutions in grade 12th include a variety of problems, ranging from basic to complex. This allows students to gradually build their skills and tackle more challenging problems. These often provide real-world applications of mathematical concepts, helping students see the practical relevance of what they are learning.

4. Class 12 Maths involves more abstract and analytical thinking. The solutions emphasize mathematical reasoning and logic, helping students develop a deeper understanding of the subject. These are designed to align with the CBSE board exam pattern and guidelines. Practicing with these solutions can help students prepare effectively for their exams.

5. Instead of just memorizing formulas, the solutions encourage students to understand the underlying concepts. This approach is crucial for mastering mathematics. Class 12 Maths often involves graphical representations of functions and equations mainly in chapter 8 and 12. The solutions help students interpret and draw various types of graphs accurately.

6. The solutions of 12th Mathematics include a wide range of practice questions at the end of each chapter, allowing students to reinforce their learning and improve their problem-solving skills. These can be used as a valuable resource by teachers to guide their teaching and help them explain concepts effectively to their students. The official NCERT website and various educational platforms like Tiwari Academy offers Class 12 Maths NCERT solutions online, making them easily accessible for students. Remember that Class 12 Maths can be challenging, but with consistent practice and a strong grasp of the concepts, you can excel in the subject. It’s a good idea to use the NCERT solutions in conjunction with additional study materials and possibly seek guidance from teachers or tutors if needed.

In summary, class 12 mathematics NCERT solutions are a valuable resource for students and educators in Bharat. They aid in exam preparation, concept clarity, and skill development, making them an essential tool for students aiming to excel in mathematics and related fields.

These solutions are prepared by expert mathematicians and can help students understand the concepts better and score good marks in the exams. NCERT Solutions for Class 12 Maths in English and Hindi Medium updated for CBSE session. It provides a detailed explanation to promote a better conceptual understanding in students for all the topics included in CBSE Class 12 Maths Syllabus.

NCERT Solutions Class 12, designed by our Expert Maths Teacher to facilitate smooth and clear understanding of concepts and logic. These solution covers all the formulae and theorems with step by step method so that student can easily understand. You can get all chapter wise all exercise solutions for the Class 12 Maths NCERT Books. Students who are practising with these class 12th Maths solution for the academic year 2023-24 can pass the 12th class board exam.

You can download NCERT Class 12 Maths Solutions App for all exercises by just click these links here. Class 12 Maths solutions play a vital role in supporting students’ learning and understanding of complex mathematical concepts. It covers advanced topics like calculus, verctor-3D, and probability, which can be challenging to grasp. Solutions provide clear explanations, breaking down complex concepts into digestible steps, helping students understand the underlying principles.

Board exams are a significant milestone. Class 12 Maths solutions align with the CBSE curriculum, providing practice questions similar to those that might appear in the exams. This helps students prepare effectively and boosts their performance.

### NCERT Class 12 Maths all Chapters

Class 12 Maths covers advanced topics in mathematics such as calculus, matrix and determinants, differential equations, probability, and vectors. The solutions for these topics aim to provide a clear understanding of the concepts and guide students through solving various types of mathematical problems.

It’s important to note that Class 12 Maths solutions are not only meant for providing answers but also for enhancing understanding and building problem-solving skills. They serve as a valuable resource for students, helping them master the concepts and excel in their studies. #### NCERT Solutions for Class 12 Maths Chapter 1 – Relations and Functions

Class 12 Maths, Relations and Functions is the first chapter of the Class 12 Maths NCERT Book. There are 3 exercises in this NCERT Solutions for class 12 Maths Chapter 1.
Class 12 Maths Exercise 1.1
Class 12 Maths Exercise 1.2
Class 12 Maths Miscellaneous 1
Class 12 Maths Exercise 1.1 in Hindi
Class 12 Maths Exercise 1.2 in Hindi
Class 12 Maths Miscellaneous 1 in Hindi

These exercises cover types of relations and functions, the composition of functions, domain, co-domain, and composite functions, the inverse of a function and invertible function etc. NCERT Solutions for class 12 Maths Chapter 1 Relations and Functions is an important chapter which provides detail knowledge of relation and functions. All 12th class Maths book solution given here are well solved each problem sums by the experienced Maths teacher. The solution of class 12 Maths chapter 1 are in dual language – Hindi and English.

#### NCERT Solutions for Class 12 Maths Chapter 2- Inverse Trigonometric Functions

NCERT Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions covers various topics such as concepts of inverse trigonometric functions, inverse trigonometric functions properties, and miscellaneous examples.

There are two exercises which explain ranges of trigonometric functions and observe the behaviour in the graphical representation. Study Material for Class 12 Maths Chapter 2 for all exercises are prepared by Mathematics teacher and solutions are well-structured so that it would be easier to learn and understand.

#### NCERT Solutions for Class 12 Maths Chapter 3 – Matrices

NCERT Solutions for Class 12 Maths Chapter 3 Matrices you can get the definition of Matrices, various types of matrices, equality of matrices, operations on matrices such as the addition of matrices and multiplication of matrices by a scalar.

You will learn here about the properties of matrices addition, properties of scalar multiplication, multiplication of matrices, properties of multiplication of matrices, transpose of matrices, properties of the transpose of the matrices, symmetric and elementary operation or transformation of a matrix, skew symmetric matrices, inverse of a matrix with by elementary operations, and at last, it covers miscellaneous examples. Matrices exercise answers of 12th Maths are given here in Hindi and English medium text and videos format.

#### NCERT Solutions for Class 12 Maths Chapter 4 – Determinants

NCERT Solutions for Class 12 Maths Chapter 4 Determinants covers all topic of determinants. You can learn and study here about the definition and meaning of determinants.

There are six exercises in this chapter which explains remarks based on the order of determinants, properties of determinants, finding the area of a triangle using determinants, minors, adjoint, and cofactors of determinants, systems of linear equation in two as well as three variables using the inverse of matrices.

#### Class 12 Maths Chapter 5 – Continuity and Differentiability

Class 12 Maths Chapter 5 Continuity and Differentiability textbook has eight exercises which are based on 12th Class Maths Book Solution, in the 1st exercise you just learn about the definition of continuity.

Then you proceed with continuity, algebra of continuous function, definition and meaning of differentiability, derivative of implicit functions, derivatives of composite functions, derivative of inverse trigonometric functions, logarithmic differentiation, Concept of exponential and logarithmic functions, derivatives of functions in parametric forms, exponential and logarithmic functions, second order derivatives, mean value theorem with different examples for practice in board preparation.

#### NCERT Solutions for Class 12 Maths Chapter 6 – Applications of Derivatives

NCERT Solutions for Class 12 Maths Chapter 6 Applications of Derivatives has five exercises which cover the definition of derivatives, tangents and normal, and rate of change of quantities, increasing and decreasing functions.

It describes the use of derivatives in approximation maxima and minima, approximations, first derivative test, function in a closed interval and miscellaneous examples. Here in this NCERT Solutions for 12th Mathematics Chapter 6 you can get a detailed knowledge of Applications of Derivatives. Student can learn Chapter 6 in Hindi and English Medium as per their requirement.

#### NCERT Solutions for Class 12 Maths Chapter 7 – Integrals

Class 12 Maths Chapter 7 Integration has twelve exercises which cover the definition of integration, definite and indefinite integrations and limit of sums based questions.
Class 12 Maths Exercise 7.1
Class 12 Maths Exercise 7.2
Class 12 Maths Exercise 7.3
Class 12 Maths Exercise 7.4
Class 12 Maths Exercise 7.5
Class 12 Maths Exercise 7.6
Class 12 Maths Exercise 7.7
Class 12 Maths Exercise 7.8
Class 12 Maths Exercise 7.9
Class 12 Maths Exercise 7.10
Class 12 Maths Miscellaneous 7

In mathematics, integration is the process of finding the integral of a function. Integrals are used to calculate areas, volumes, and other quantities. The fundamental theorem of calculus states that integration and differentiation are inverse operations. This means that the integral of the derivative of a function is equal to the original function, plus a constant.

#### NCERT Solutions for Class 12 Maths Chapter 8 – Applications of Integrals

In NCERT Solutions for Class 12 Maths Chapter 8 Applications of Integrals, students can get an overall knowledge about the Integrals and specific application of integrals.

It covers the definition of Integrals, especially lines, circles/ parabolas/ellipses, area under simple curves, area between two curves and at last miscellaneous examples. There are two exercises in NCERT Solutions for Class 12 Maths Chapter 8. We have prepared the solutions based on 12th Class Maths NCERT Book part 2. Get Applications of Integrals Class 12 Maths Solutions in Hindi medium.

#### NCERT Solutions for Class 12 Maths Chapter 9 – Differential Equations

Students can find concentrate on the definition of Differential Equations in the NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations.

It clears basic concepts related to differential equations and many more with step by step solutions so that students can easily understand. It covers all the solutions based on 12th Class Maths Book Solution including the degree of a differential equation, order of a differential equation, general and particular solutions of a differential equation, homogeneous differential equations, linear differential equations, procedure involved formation of a differential equation etc. Student can use Differential Equations of 12th standard in Hindi and English medium.

#### NCERT Solutions for Class 12 Maths Chapter 10 – Vector Algebra

NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra, you can understand the introduction of vector algebra. And you can know how to find position vector, some basic concepts related to vector algebra etc.

In this chapter, you can also learn about algebraic as well as geometric properties. And multiplication of a vector by a scalar, r, vector joining two points, components of a vector, section formula, product of two vector etc. This chapter 10 has four exercises excluding miscellaneous. All solutions are based on 12th Class Maths Book Solution. Get the complete solutions with step by step description in Hindi and English medium. #### NCERT Solutions for Class 12 Maths Chapter 11 – Three Dimensional Geometry

NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry, you can get know about Three Dimensional Geometry. The student can constitute topics related to three dimensional geometry, direction cosines and direction ratios.

Learn the properties of line, equation of a line through a given point and parallel direction cosines of a line passing through two points, relation between the direction cosines of a line, equation of a line in space, plane passing through the intersection of two given planes, angle between two planes, co-planarity of two lines and many more. And last it contains miscellaneous examples. There are three exercises and a miscellaneous exercise in chapter 11 of 12th Mathematics NCERT.

#### NCERT Solutions for Class 12 Maths Chapter 12 – Linear Programming

You can get introduced with to NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming. Here this chapter covered linear programming problem and its mathematical formulation.

You will learn about the mathematical formulation of the problem, different types of all linear programming problems graphical feasible and infeasible method solution. NCERT Solutions for Class 12 Maths Chapter 12 covers two exercises in all. Take the Linear Programming of 12th Mathematics in Hindi and English medium here.

#### NCERT Solutions for Class 12 Maths Chapter 13 – Probability

In this last NCERT Solutions for Class 12 Maths Chapter 13 Probability, you can find deals with probability and Multiplication rule of Probability.

You can understand here the concept of random variables and its probability in this chapter. Other than this chapter also covers mean of random variable, variance of random variable, and binomial distribution and Bernoulli trials with miscellaneous examples. NCERT Solutions for Class 12 Maths Chapter 13 describes about the five topics with well-defined solutions by the expert math teacher.

As Class 12 Maths is an important subject that plays a vital role in next classes and future career. Class 12 Maths NCERT Solutions acts as the best tool for students in their exam Class 12 boards and undergraduate competitive examination in future. These above NCERT Class 12 Maths solutions for all chapter exercises can be your best education support for board exam preparations.

Mathematics is a subject you cannot get good marks in the exam by reading and memorizing the formulae. So you need to practice well to succeed. Learning from Tiwari Academy’s NCERT solutions will help students of Class 12 to clear all the logic of every problem quite effectively.

##### Importance of Learn NCERT Solutions for Class 12 Maths from Tiwari Academy

Students can get many benefits if they learn and practice with Maths Class 12 NCERT Solutions from Tiwari Academy. Class 12th Maths plays an important role for the preparation of many undergraduate competition exams. So well described Maths solution at Tiwari Academy help you to clear all doubts and concepts of all chapters. It is the best study material to score more marks in your class 12 board exam and competitive exams in future.

There are total of 13 chapters which are given by the expert math teachers with extensive reviewed. By learning properly and practice this NCERT solution for Class 12 Maths, you will be top on 12th class board exam.
Provides Authentic Information to the Students
All Maths Class 12 NCERT Solutions are provided by the experienced Math after extensive research on each and every chapter to provide correct and authentic information to the students.

Follows the CBSE Curriculum

This is another most prominent reason that why you learn NCERT Solutions from us. These solutions for every chapter strictly adhere to the CBSE curriculum.

Clears all Fundamental Logic & Concepts

These NCERT solutions help the students to make their concepts crystal clear once you clear the concept then you no need to read the whole stuff again and again.

These all solutions are designed in such a way that Students can revise quickly during their Examinations.

The well-defined solution saves your revision time by providing all the necessary logic and formulae in a proper way.

###### How are CBSE 12 Maths Solutions of NCERT Helpful for Board Exams?

CBSE 12 Maths Solutions help you secure marks in the 12 class Board exam as efficiently as they clear your conceptual doubts. The class 12 Maths NCERT solutions help students solve all the exercises given in the textbooks prescribed by the NCERT, which are easy to understand the concepts and get good marks in their board exam.

If the students do practice and revise CBSE 12 Maths Solutions of NCERT in a proper way then you may surely passed your Class 12 Board Exams with above 90% marks in the subject Maths. It is seen that most of the student achieved a high score in math by learning CBSE 12 Maths Solutions of NCERT.

12th Maths Solutions are an invaluable resource for self-study. They allow students to revisit topics at their own pace, helping them reinforce their understanding and address any doubts. It serve as a reference for checking answers while doing homework or practice exercises. This helps students identify errors and rectify mistakes, contributing to accurate learning. With grade 12 Math solutions, students gain insights into the logic behind mathematical techniques rather than memorizing formulas. This clarity enhances their comprehension and critical thinking.

Many solutions include real-world applications of mathematical concepts, demonstrating their practical significance and fostering an appreciation for mathematics in daily life. Solutions aid teachers in explaining complex topics effectively, ensuring a consistent understanding among students.

Teachers can also use these solutions as teaching aids to supplement their lessons. A strong understanding of Class 12 Maths concepts is essential for pursuing higher education in fields like engineering, mathematics, economics, and sciences. Class 12 Maths solutions are available in various formats, including books, online platforms, and mobile apps. This accessibility ensures that students can choose the format that suits their learning preferences. In summary, Class 12 Maths solutions provide clarity, guidance, and practice for students facing intricate mathematical challenges.

### How to get class 12 Maths NCERT Solutions?

Get the revised and modified Class 12 Maths NCERT Solutions to prepare for board exams. As you know the syllabus is reduced for academic year 2023-24. So, follow the instruction to get appropriate NCERT textbook solution for final exams. If you still have doubts or questions, don’t hesitate to ask your teacher or a peer for clarification. Clearing up any confusion is essential to build a strong foundation in mathematics. Follow the steps given here to get Class 12 Maths solutions in Hindi and English Medium.

#### Step 1: Search the website for class 12 Maths NCERT Solutions. You can download Class 12 Maths NCERT solutions from various sources, including the official NCERT website, Tiwari Academy website and other educational websites. Here’s a step-by-step guide on how to download Class 12 Maths NCERT solutions. You’ll typically find chapter-wise solutions for Class 12 Mathematics. Click on the chapter you want to download solutions for. The solutions will be displayed on the website. Look for a Download or PDF option to save the solutions to your device. Remember to verify the credibility of the website you choose to download from to ensure the accuracy of the solutions. Always cross-reference the solutions with your textbook to confirm correctness.

#### Step 2: Visit to Class 12 Maths solutions based Educational Websites like Tiwari Academy. Several educational websites and apps offer NCERT solutions for Class 12 Mathematics. You can use these platforms to access and download the solutions. Using your web browser visit a popular educational website that provides NCERT solutions. Websites like Tiwari Academy, Khan Academy and others often offer NCERT solutions for free. Use the search bar on the website to search for Class 12 Mathematics NCERT solutions. Select the appropriate result that matches your requirements, usually labelled by class and subject.

#### Step 3: Use Class 12 Maths Solutions App to get Hindi and English medium content. Downloading Class 12 Maths NCERT solutions App can be a helpful step in your exam preparation, as it provides you with detailed explanations and solutions to practice questions, which are essential for scoring well in the CBSE Class 12 Mathematics exam. NCERT Solutions can be a valuable resource to help you prepare for your Class 12 Maths exams effectively. Here’s a step-by-step guide on how to use NCERT Solutions for Class 12 Maths App to improve your exam performance. Familiarize yourself with the layout of the NCERT Solutions for Class 12 Maths. Each chapter typically includes a summary of important concepts, solved examples, and exercises with solutions.

#### Step 4: Prepare Class 12 Maths for board exams using NCERT Solutions. Start by reading the relevant chapter in your Class 12 Maths textbook. Understand the concepts and principles explained in the chapter. Pay attention to key formulas, theorems, and definitions. After reading the chapter, go through the solved examples provided in the NCERT Solutions. These examples demonstrate how to apply the concepts to solve problems. Pay close attention to the steps and methods used to solve each example. Work through the exercises at the end of each chapter in your textbook. Try to solve the problems on your own first. If you get stuck, refer to the NCERT Solutions for guidance.

#### Step 5: Crosscheck the answers and Solution using NCERT Solutions of Class 12 Maths. Compare your solutions to the problems with the solutions provided in the NCERT Solutions. Identify any mistakes or discrepancies in your answers and try to understand where you went wrong. Don’t just rely on the final answers in the NCERT Solutions. Examine the step-by-step solutions provided. Understand the logic and reasoning behind each step. This will help you grasp the problem-solving techniques. While going through the NCERT Solutions, take notes of important formulas, theorems, and concepts. Create a concise summary of each chapter that you can refer to for last-minute revision. Consistent practice is key to success in mathematics. Keep practicing problems from the textbook and use the NCERT Solutions whenever you need help or clarification.

### Is NCERT Enough for Class 12 Maths Board Exams?

Yes, NCERT Class 12 Maths Books are enough to score maximum marks in the Class 12 Board exams. Just do practice all the exercise and learn the theorems. Also, do not skip any topic of CBSE 12th Maths syllabus and do revision 2-3 times before your class 12 board exam. The NCERT books for Class 12 are prescribed by the CBSE itself. So these NCERT books are known for their clear explanation of each topic and a good level of practice questions. It the best study material for Class 12 Board’s Maths. These NCERT textbooks are enough for you to score well in your CBSE Class 12 Maths board exam.

### Which Book is Best for Class 12 Maths Board Exam?

NCERT Book is the best and most trusted book for Class 12 board exam. Students can clear their concepts and logics through NCERT Class 12 Maths book by solving the examples and all exercise problems. Students are recommended to solve the NCERT book as this book follows the CBSE syllabus and pattern.

### Is Class 12 Maths Difficult?

No, Class 12 Maths is not difficult than class 11 in CBSE board. It is easier than the syllabus of class 11 Maths. By the practicing in perfectly you can score more marks in Class 12 Maths. The student who have cleared all concept of the early class 11 Maths syllabus, then no need to worry about the Class 12 Maths topic, they can easily understand all topics. If the student faces any doubt about the syllabus then they can learn and get solutions from Class 12 Maths NCERT solutions. It can help you to clear all doubts and concept of all topics.

### Which website is best for Class 12 maths NCERT solutions?

You can find many websites online which are providing Maths NCERT solutions for class 12. But tiwariacademy.com provides a solid conceptual base for all the topics included in CBSE Class 12 Maths Syllabus. All solutions cover all the important theorems and formulae with detailed explanations so that student can easily clear the concept. A detailed step-by-step explanations of problems given in the NCERT textbooks on tiwariacademy.com website. Apart from solutions for each chapter of CBSE Class 12 Maths are the best study materials for students who are preparing for their Class 12 board exams. From this website, you can get FREE Class 12 maths NCERT solutions with unlimited solution PDFs.

Last Edited: September 21, 2023