**NCERT Solutions Class 12 Maths in Hindi and English Medium**

CBSE Syllabus Class 12 Maths for 2024-25

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

## NCERT Solutions of Class 12 Maths

Tiwari Academy NCERT Solutions for Class 12 Maths have emerged as a simple tool for students preparing for their board exams in the 2024-25 session. These NCERTNational Council of Educational Research and Training | Official Website: https://ncert.nic.in/ textbook solutions, available in both Hindi and English, are carefully revised to stay in sync with the recent rationalized NCERT textbooks. They are tailored to meet the needs of students aiming for excellence in their board examinations, ensuring a comprehensive understanding of the latest curriculum.

Each solution is tailored to meet the National Council of Educational Research and Training (NCERT) curriculum, empowering students to confidently tackle and understand the intricacies of every Maths challenge. Class 12 Chapter Wise Maths NCERT Solutions are as follows:

Chapters | Marks |
---|---|

1. Relations and Functions, 2. Inverse Trigonometric Functions | 08 |

3. Matrices, 4. Determinants | 10 |

5. Continuity and Differentiability, 6. Application of Derivatives, 7. Integrals, 8. Application of Integrals, 9. Differential Equations | 35 |

10. Vector Algebra, 11. Three Dimensional Geometry | 14 |

12. Linear Programming | 05 |

13. Probability | 08 |

Periodic Tests ( Best 2 out of 3 tests conducted) | 10 |

Mathematics Activities | 10 |

Total | 100 |

Class 12 Maths NCERT solutions in India serve several important purposes for students and educators. Class 12 mathematics is a critical year for students in India as they prepare for their board exams, such as the Central Board of Secondary Education (CBSE) exams and various state board exams. Please provide your valuable Review and Feedback for further improvement. 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 follow the NCERT curriculum 2024-25.

Class 12 Solutions Apps for iOS and Android

NCERT solutions for Class 12 Mathematics delve deep into mathematical techniques and principles. These comprehensive solutions guide help in building a solid Maths foundation, ensuring students excel in board exams, competitive tests, and further academic pursuits.

It also includes examples that will help students better understand the concepts. **Oswaal CBSE Question Banks Class 12 2024-25 for 2025 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 for class 12 Maths provide a wide range of solved exercises and problems. Students can use these solutions for practice and revision during the board exams, helping them become proficient in solving mathematical problems of varying complexity. Regular practice is essential to improve problem-solving skills and gain confidence in 12th mathematics particularly in Calculus, that is, Differentiation and Integration.

**The Essence of Mathematics**

Mathematics is a vast field that encompasses the study of numbers, formulas, structures, shapes, spaces, and the changes in quantities. It is divided into major subdisciplines like number theory, algebra, geometry, and analysis. Interestingly, there’s no universally accepted definition of mathematics among mathematicians, highlighting its diverse and evolving nature. 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 how the formulae have been applied.

2. Attempt to solve the problem on your own first.

3. Compare your solution with the solution provided by Tiwari Academy.

4. Analyze any differences and learn from them. Carry on the process to master the subject.

NCERTNational Council of Educational Research and Training | Official Website: https://ncert.nic.in/ Solutions for Class 12 Maths are indeed valuable resources for students preparing for their Class 12 Mathematics exams. Here’s why these solutions can be helpful for CBSE exams. NCERT Solutions are designed to align with the curriculum prescribed by educational boards in India. This means they cover the topics and concepts that are essential for the Class 12 Mathematics exam.

Preparing for Class 12 Maths board exam becomes more effective with a structured approach, especially when incorporating NCERT Solutions for Class 12 Maths. Initially, it’s vital to build a solid foundation in basic concepts. Make sure you have a clear understanding of the principles from previous grades, as Class 12 Maths is often an extension of those basic principles. Regular review and practice of these earlier concepts can greatly enhance your comprehension. Then, acquaint yourself with the Class 12 Maths syllabus. Identify the topics to be covered, focusing first on those that extend from your existing knowledge. This method eases the transition into more advanced topics. Use NCERT textbooks and other educational materials at Tiwari Academy, to gain a thorough understanding of each subject area. Moreover, solving a variety of problems is crucial for a better grasp of the subject and for preparation of board examination questions.

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 Year: | CBSE Session 2024-25 |

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.

Class 12 Maths NCERT Solutions at Tiwari Academy are known for their clarity and accuracy. They provide step-by-step explanations for solving problems, making it easier for students to understand and follow the solutions. These solutions provide a wide range of practice problems and exercises. Practice is crucial for math exams, as it helps students become more comfortable with the concepts and improves problem-solving skills.

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 assist teachers in explaining the mathematical concepts effectively. NCERTNational Council of Educational Research and Training | Official Website: https://ncert.nic.in/ textbooks and solutions are widely recognized and accepted across India. They ensure a standardized curriculum and help maintain consistency in mathematics education across different states and regions. Solutions provided by Tiwari Academy are a valuable resource for teachers and students alike.

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 2024-25 for 2025 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 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 meet 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 explain the mathematical terms and principles 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 like past year papers. It is suggested that students seek guidance from teachers or tutors if needed.

Class 12th Maths Solutions focus on developing a deep understanding of the underlying mathematical concepts. This is essential for scoring well in exams, as questions may be designed to test your understanding rather than testing your memorizing ability. Since NCERT textbooks and solutions are created to cater to the syllabus of the respective boards, they are highly relevant to the exams. Questions in the exams are often drawn from NCERT textbooks and similar resources.

Class 12 mathematics NCERT solutions are valuable for all students and educators in India. They aid in exam preparation and build conceptual clarity.

Class 12 Solutions App Download

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 have been 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.

Users can easily update iOS and Android apps to access error-free solutions. This ensures that students always have access to the most accurate and up-to-date information. Using Tiwari Academy apps for NCERT solutions reduces the need for physical textbooks, contributing to a more Eco-friendly learning environment.

Class 12 Maths NCERT Solutions include solutions to previous years CBSE board question, which can be extremely helpful for practice and understanding the exam pattern. In addition to the basic solutions, there are often additional exercises and problems provided in the NCERT textbooks and solutions. These can be used to challenge yourself and further strengthen your skills.

NCERT Solutions Class 12, designed by our Expert Maths teachers 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.

However, it’s important to note that while NCERT Solutions of 12th Maths are a valuable resource, they may not cover every possible type of question or provide extensive practice for highly competitive exams. Depending on your goals and the level of your preparation, you may also want to explore other textbooks, reference books, online resources and practice past years papers.

NCERT Solutions for Class 12 Maths are an excellent starting point for your exam preparation, but it is advisable to supplement your study with a variety of resources to ensure comprehensive preparation for your Class 12 Mathematics exam.

You can download NCERT Class 12 Maths Solutions App for all exercises by just clicking 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. Tiwari Academy solutions provide clear explanations, breaking down complex concepts in a way that can be more absorbing. They also help students in understanding the underlying principles.

Board exams are a significant milestone. Class 12 Maths solutions align with the CBSE curriculum 2024-25, providing practice questions similar to those that might appear in the exams. This helps students prepare effectively and boosts their performance.

In the next phase, concentrate on problem-solving and practical application, utilizing NCERT Solutions for Class 12 Maths. Engage in consistent practice with different problem types, including exercises from textbooks, previous exam papers, and additional questions from various math workbooks or online platforms. If you face challenges, seek assistance from teachers, tutors, or educational resources like videos and online forums. It is also important to understand the theories underlying mathematical concepts, as this can make problem-solving more intuitive. Furthermore, managing your time and stress effectively is crucial.

Develop a study plan that includes regular mathematics practice, using NCERT Solutions for Class 12 Maths, while also balancing time for other subjects and activities. Remember, consistent study is more beneficial than last-minute cramming for exams.

### Class 12 Maths Syllabus Revised for 2024-25

### 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. Class 12th Maths book solutions given by Tiwari Academy are solved by experienced Maths teachers. The solutions of class 12 Maths chapter 1 are available in dual languages – 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.

Class 12 Maths Exercise 2.1

Class 12 Maths Exercise 2.2

Class 12 Maths Miscellaneous 2

Class 12 Maths Exercise 2.1 in Hindi

Class 12 Maths Exercise 2.2 in Hindi

Class 12 Maths Miscellaneous 2 in Hindi

There are two exercises which explain range 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 experienced mathematics teachers 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 understand 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.

Class 12 Maths Exercise 3.1

Class 12 Maths Exercise 3.2

Class 12 Maths Exercise 3.3

Class 12 Maths Exercise 3.4

Class 12 Maths Miscellaneous 3

Class 12 Maths Exercise 3.1 in Hindi

Class 12 Maths Exercise 3.2 in Hindi

Class 12 Maths Exercise 3.3 in Hindi

Class 12 Maths Exercise 3.4 in Hindi

Class 12 Maths Miscellaneous 3 in Hindi

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.

Class 12 Maths Exercise 4.1

Class 12 Maths Exercise 4.2

Class 12 Maths Exercise 4.3

Class 12 Maths Exercise 4.4

Class 12 Maths Exercise 4.5

Class 12 Maths Miscellaneous 4

Class 12 Maths Exercise 4.1 in Hindi

Class 12 Maths Exercise 4.2 in Hindi

Class 12 Maths Exercise 4.3 in Hindi

Class 12 Maths Exercise 4.4 in Hindi

Class 12 Maths Exercise 4.5 in Hindi

Class 12 Maths Miscellaneous 4 in Hindi

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.

Class 12 Maths Exercise 5.1

Class 12 Maths Exercise 5.2

Class 12 Maths Exercise 5.3

Class 12 Maths Exercise 5.4

Class 12 Maths Exercise 5.5

Class 12 Maths Exercise 5.6

Class 12 Maths Exercise 5.7

Class 12 Maths Miscellaneous 5

Class 12 Maths Exercise 5.1 in Hindi

Class 12 Maths Exercise 5.2 in Hindi

Class 12 Maths Exercise 5.3 in Hindi

Class 12 Maths Exercise 5.4 in Hindi

Class 12 Maths Exercise 5.5 in Hindi

Class 12 Maths Exercise 5.6 in Hindi

Class 12 Maths Exercise 5.7 in Hindi

Class 12 Maths Miscellaneous 5 in Hindi

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.

Class 12 Maths Exercise 6.1

Class 12 Maths Exercise 6.2

Class 12 Maths Exercise 6.3

Class 12 Maths Miscellaneous 6

Class 12 Maths Exercise 6.1 in Hindi

Class 12 Maths Exercise 6.2 in Hindi

Class 12 Maths Exercise 6.3 in Hindi

Class 12 Maths Miscellaneous 6 in Hindi

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.

**Class 12 Maths Chapter 7 in Hindi Medium**

Class 12 Maths Exercise 7.1 in Hindi

Class 12 Maths Exercise 7.2 in Hindi

Class 12 Maths Exercise 7.3 in Hindi

Class 12 Maths Exercise 7.4 in Hindi

Class 12 Maths Exercise 7.5 in Hindi

Class 12 Maths Exercise 7.6 in Hindi

Class 12 Maths Exercise 7.7 in Hindi

Class 12 Maths Exercise 7.8 in Hindi

Class 12 Maths Exercise 7.9 in Hindi

Class 12 Maths Exercise 7.10 in Hindi

Class 12 Maths Miscellaneous 7 in Hindi

#### 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 area bounded and specific application of integrals.

Class 12 Maths Exercise 8.1

Class 12 Maths Miscellaneous 8

Class 12 Maths Exercise 8.1 in Hindi

Class 12 Maths Miscellaneous 8 in Hindi

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. The solutions to area bounded Class 12 Maths are available in Hindi and English medium.

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

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

Class 12 Maths Exercise 9.1

Class 12 Maths Exercise 9.2

Class 12 Maths Exercise 9.3

Class 12 Maths Exercise 9.4

Class 12 Maths Exercise 9.5

Class 12 Maths Miscellaneous 9

Class 12 Maths Exercise 9.1 in Hindi

Class 12 Maths Exercise 9.2 in Hindi

Class 12 Maths Exercise 9.3 in Hindi

Class 12 Maths Exercise 9.4 in Hindi

Class 12 Maths Exercise 9.5 in Hindi

Class 12 Maths Miscellaneous 9 in Hindi

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. Students can take help for 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, can help the students to understand about the introduction of vector algebra, position vector and some basic concepts related to vector algebra.

Class 12 Maths Exercise 10.1

Class 12 Maths Exercise 10.2

Class 12 Maths Exercise 10.3

Class 12 Maths Exercise 10.4

Class 12 Maths Miscellaneous 10

Class 12 Maths Exercise 10.1 in Hindi

Class 12 Maths Exercise 10.2 in Hindi

Class 12 Maths Exercise 10.3 in Hindi

Class 12 Maths Exercise 10.4 in Hindi

Class 12 Maths Miscellaneous 10 in Hindi

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 master topics on three dimensional geometry, direction cosines and direction ratios.

Class 12 Maths Exercise 11.1

Class 12 Maths Exercise 11.2

Class 12 Maths Miscellaneous 11

Class 12 Maths Exercise 11.1 in Hindi

Class 12 Maths Exercise 11.2 in Hindi

Class 12 Maths Miscellaneous 11 in Hindi

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. 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 are introduced to NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming. Here this chapter covers linear programming problem and its mathematical formulation.

Class 12 Maths Exercise 12.1 in Hindi

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. Solutions to the Linear Programming Problems of 12th Mathematics are available in Hindi and English medium both.

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

In this last chapter of NCERT Solutions for Class 12 Maths Chapter 13 Probability, you will learn what is probability and Multiplication rule of the same.

Class 12 Maths Exercise 13.1

Class 12 Maths Exercise 13.2

Class 12 Maths Exercise 13.3

Class 12 Maths Miscellaneous 13

Class 12 Maths Exercise 13.1 in Hindi

Class 12 Maths Exercise 13.2 in Hindi

Class 12 Maths Exercise 13.3 in Hindi

Class 12 Maths Miscellaneous 13 in Hindi

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 teachers.

Class 12 Maths is an important subject that plays a vital role in next classes and future career. Class 12 Maths NCERT Solutions act as the best tool for students in their exam Class 12 boards, undergraduate as well as 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 in which you can score good marks by continuous practice. You can not merely read and memorize formulae. Solutions given by Tiwari Academy help you to understand the logic clearly and effectively.

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

Students can get the following benefits if they learn and practice from Tiwari Academy App/website for class 12 Mathematics:

1. Clears your doubt easily through simple explanation.

2. Provides best study material for the preparation of academic and competitive exams.

3. Helps you to build a strong base for higher classes.

There are a total of 13 chapters-solutions for which are given by experienced mathematics teachers reviewed too. By learning properly and practice this NCERT solution for Class 12 Maths, will enable you to score well in class 12th board exams.

**Provides Authentic Information to the Students**

All Maths Class 12 NCERT Solutions are provided by the experienced Maths teachers after extensive research on each and every chapter to provide correct and authentic information to the students.

**Follows the CBSE Curriculum**

This is yet another most important reason why you should follow NCERT Solutions given by us. These solutions for every chapter strictly adhere to the CBSE curriculum 2024-25.

**Clears all Fundamental Logic & Concepts**

These NCERT solutions help the students to make their concepts crystal clear. Once you clear the concept then there is no need to read the whole chapter again and again.

**Helpful For Revisions during Examinations**

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

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

CBSE 12 Maths Solutions help you to secure good marks in the 12th class Board exams since they make your concepts crystal clear.

By practicing and revising class 12 solutions of Maths NCERT given by us, there is probability of scoring above 90 percent marks in the board examination. In the past, students have scored high marks in mathematics class 12th by following and learning from our website and apps.

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. These solutions ensure that students understand the topics thoroughly.

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 science.

### 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 2024-25. 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.
- Step 2: Visit to Class 12 Maths solutions based Educational Websites like Tiwari Academy.
- Step 3: Use Class 12 Maths Solutions App to get Hindi and English medium content.
- Step 4: Prepare Class 12 Maths for board exams using NCERT Solutions.
- Step 5: Crosscheck the answers and Solution using NCERT Solutions of Class 12 Maths.

#### Step 1: Search the website for class 12 Maths NCERT Solutions.

#### Step 2: Visit to Class 12 Maths solutions based Educational Websites like Tiwari Academy.

#### Step 3: Use Class 12 Maths Solutions App to get Hindi and English medium content.

#### Step 4: Prepare Class 12 Maths for board exams using NCERT Solutions.

#### Step 5: Crosscheck the answers and Solution using NCERT Solutions of Class 12 Maths.

Class 12 Maths textbook part 1 and part 2 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. Class 12 Maths solutions provide clarity, guidance, and practice for students facing intricate mathematical challenges.

### 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 practice all the exercise and learn the theorems. Also, do not skip any topic of CBSE 12th Maths syllabus and revise 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 is the best study material for Class 12 Boards 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 advised to solve questions from the NCERT book as this book follows the pattern prescribed by CBSE.

### Is Class 12 Maths Difficult?

For students who have understood the concepts of class 11, there no need to worry about the class 12th mathematics. By sufficient practice of questions, students can score good marks in board exams. In case of any doubt, students can refer to solutions provided by Tiwari Academy and understand the concepts behind the solutions.

### 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.

Tiwari Academy is one of the best websites because of the following reasons:

1. A detailed step-by-step explanations of problems is given for NCERT textbooks questions.

2. Apart from solutions, the best study materials for students who are preparing for their Class 12 board exams is given.

3. From this website, you can get FREE Class 12 Maths NCERT solutions in PDF formats.