# NCERT Solutions for Class 12

## NCERT Solutions for Class 12 - All Subjects

Now get access to comprehensively researched NCERT Class 12 PDFs to prepare well for your exams. 12th is one of the most integral grades of every student’s life. It not only is the deciding factor for your higher studies but also shapes you as an individual. Students tend to go through extreme stress while finding the right study material for preparing for their exams. NCERT Solutions for Class 12 are extensively designed after thorough research by experts to ensure that students have a less stressful and enjoyable learning experience. All the PDF solutions are available for all subjects, along with meticulous additional question banks to help students reach their highest potential. Now visit our official webpage to clear your doubts and find the PDFs of chapters you’re looking for.

The NCERT Solutions for Maths provide detailed explanations and solutions of all the chapters. In Class 12 Maths, there are 13 chapters. You can download NCERT solutions PDF chapter-wise as well.

#### Chapter 1 – Relations and Functions

This chapter is important and you must learn it properly. In this chapter, you will learn about relations, types of relation, such as empty, universal, etc. Next, you will learn about functions and types of functions. To understand the concepts, practice the exercise examples. Solve additional questions from previous year's papers and also solve sample papers once you complete the chapter.

#### Chapter 2 – Inverse Trigonometric Functions

In this chapter, there are three exercises. You will learn about inverse trigonometric functions, their basic concepts, and their properties. You need to practice questions and solve sample papers. Be very thorough with the chapter. You will be asked both short and long question answers from this chapter, so prepare well.

#### Chapter 3 – Matrices

This chapter is easy and you can score well with proper preparation. There are eight exercises in this chapter. You will learn about the types of matrices and you should also solve questions related to them. Learn about the elementary operation and invertible matrices. Solve examples for a better understanding of the concepts and practice as many questions as possible. From this chapter, you will also be asked both short and long questions. Use the NCERT solutions for Class 12 for practising the textbook questions and other additional questions.

#### Chapter 4 – Determinants

This chapter is also easy and you can prepare it from NCERT Solutions. There are seven exercises in this chapter. Use the NCERT solutions to learn properties of determinants, area of a triangle, applications, etc. Practice examples and exercise questions and be thorough. Maintain separate notes for the questions as you can use them for quick revisions. Long questions will be asked from this chapter.

#### Chapter 5 – Continuity and Differentiability

This chapter is very important and you must learn it properly. There are 13 exercises in this chapter. Use the solutions to learn Algebra. The topics you will find here include continuous functions, differentiability, and more. It is also important that you practice questions related to them. In these exercises, you will learn about second-order derivatives and the mean value theorem. Practice examples and solve additional questions too, as you may encounter them during your class tests and examinations.

#### Chapter 6 – Application of Derivatives

Another important chapter in the Class 12 Maths is the application of derivatives. In this chapter, there are eight exercises. The rate of change of quantities is one of the topics and in this exercise, you will learn about the rate of change of distance, and velocity. Learn the formulas and how to implement them. Practice examples and questions related to them. Next, you will learn about increasing and decreasing functions. Practice exercise questions and learn the concept properly. Use the NCERT solutions for additional help and reference. You can also get the 12th Business Maths Guide for additional help.

#### Chapter 7 – Integrals

In this chapter, there are ten exercises. To score well in this topic you have to practice as much as possible. Use the NCERT Solutions for easy learning and understanding of the concepts. In the methods of integration exercise, you will learn the methods and how to implement them. Integration by parts is another important exercise that you have to focus on. Practice the formulas and solve as many questions as possible. Go through the examples and use the NCERT solutions for help. You will also learn about definite integrals and their properties.

#### Chapter 8 – Application of Integrals

This chapter is small compared to others, there are only 3 exercises. Mainly, two important topics are area under simple curve and area between two curves. Practice and learn the concept properly. Solve exercise questions and use the NCERT solutions. From this chapter, you will get long questions. The Class 12 Maths NCERT PDF is also available along with the solutions.

#### Chapter 9 – Differential Equations

In this chapter, there are five exercises. You will get short and medium marks questions from this chapter. Learn about differential equations and their basic concepts. You will learn all the methods for solving first-order and first-degree differential equations. Practice examples and solve exercise questions. Solve both exercise questions and additional questions from the NCERT solutions.

#### Chapter 10 – Vector Algebra

This is a fun chapter and easy to learn. There are 6 exercises in this chapter. Types of vectors, in this exercise, learn about the types of vectors and their properties. Go through a few examples to understand properly. In the exercise addition of vectors, you will learn how to add vectors. Practice the exercise examples and questions. Next, you will learn how to multiply a vector by a scalar. Practice questions using the NCERT solutions and understand the topics and concepts properly. From this chapter, long questions can be asked.

#### Chapter 11 – Three-Dimensional Geometry

In this chapter, there are ten exercises. The three-dimensional geometry NCERT solutions are designed by experts and have explained the chapter in simple terms. Equation of line space, this exercise is very important to learn the concept and practise the exercise questions using the NCERT solutions. You will learn about the plane, angle between two lines, etc. You will also learn about the theorems. Solve additional questions from question banks, sample papers, etc.

#### Chapter 12 – Linear Programming

In this chapter, there are three exercises. Learn about linear programming problems and different types of linear programming problems. Practice examples and solve the exercise questions using the NCERT solutions. 4 marks questions can be asked from this chapter.

#### Chapter 13 – Probability

This is the last chapter in your Class 12 Maths Syllabus. There are seven exercises in this chapter. You will learn conditional probability, multiplication theorem, Bayes’ theorem, random variables, etc. Practice examples and solve the exercise questions using the NCERT solutions. Solve sample papers and write mock tests once you complete your syllabus. Revise using the NCERT Solutions and go through the important topics and questions.

### NCERT Solutions for Class 12 Physics

In Physics, there are 15 chapters. The NCERT solutions for physics provide well-explained solutions for all the chapters. You can also download NCERT solutions PDF chapter-wise. Learn and practice all the chapters thoroughly.

Some of the important chapters that you can learn using the NCERT solutions are as follows:

#### Chapter 1 – Electric Charges and Fields

In this chapter, there are 15 exercises. This chapter is very important and you have to learn and practice it properly. Some of the salient topics that you will cover in this chapter are Coulomb’s law, electric field, flux, Gauss’s law, electric field lines, etc. Use the NCERT Solutions for a proper understanding of the concepts. Solve the exercise questions also by using the solutions as the questions are explained simply and they are easy to understand and learn.

#### Chapter 2 – Current Electricity

This is another important chapter. There are 16 exercises in this chapter. You will learn about topics such as Ohm’s law, limitations of Ohm’s law, electrical energy and power, resistivity, etc. Learn all the concepts and practice. Next, you will learn about combinations of resistors, learn the method and solve examples for better understanding. Solve questions related to it. You will also learn about Kirchoff’s law, and types of bridges such as the Wheatstone bridge and meter bridge. Use the NCERT solutions for practising and learning all the exercises as they are explained properly with additional examples.

#### Chapter 3 – Moving Charges and Magnetism

In this chapter, there are 11 exercises. You will learn about magnetic force, the motion of the magnetic field, etc. Use the NCERT solutions to learn this chapter. The solutions are designed to help you understand the concepts and questions better and in a simple way. You will also learn Ampere’s circuital law, solenoid, and toroid, etc.

#### Chapter 4 – Electromagnetic Induction

In this chapter, there are ten exercises. You will learn about magnetic flux, Faraday’s law of induction, Lenz’s law, Eddy current, etc. Practice all the derivations and use the solutions to learn and solve the exercise questions. You will also learn about inductance and AC generators.

#### Chapter 5 – Alternating Current

This is another important chapter and you have to learn and practice this chapter properly. There are nine exercises in this chapter. You will learn about alternating current, AC voltage applied to an inductor, capacitor, LCR circuit, etc. Learn the concept and methods properly by using the solutions and solve questions related to each topic. The last topic is transformers, in this exercise, you will learn about transformers, their formulas, and applications.

#### Chapter 6 – Wave Optics

In this chapter, there are seven exercises. Learn about Huygens principle, refraction, and reflection of a plane wave, diffraction, polarization, etc. Practice all the topics and solve exercise questions and examples. Use the NCERT solutions as a reference.

#### Chapter 7 – Atoms

In this chapter, there are six exercises. You will learn about alpha particle scattering and Rutherford’s nuclear model of the atom. Learn and understand the concept properly. These questions can be asked for six marks. This chapter is fairly easy and you can complete it easily with the help of the solutions.

#### Chapter 8 -Nuclei

In this chapter, there are 7 exercises. You will learn about atomic masses, size of nucleus, nuclear force, radioactivity, etc. Practice and learn all the exercise questions using the NCERT physics solutions.

### NCERT Solutions for Class 12 Chemistry

The list of chapters in class 12 chemistry is given below.

#### Chapter 1 - Solid State

In this chapter, students will study about general characteristics of solid-state, amorphous and crystalline solids, crystal lattice and unit cell, various types of voids and close-packed structures.

#### Chapter 2 - Solutions

In this chapter, the types of solutions, their formation and their properties are discussed in detail. Other major topics are abnormal molar masses, Raoult's law, the vapour pressure of liquid solutions, the concentration of solutions, colligative properties, etc.

#### Chapter 3 - Electrochemistry

The important topics of this chapter are the electrochemical cell, the galvanic cell and the electrolytic cell, the standard potential of the cell, Gibbs energy of cell reaction and other applications of electrochemistry.

#### Chapter 4 - Chemical Kinetics

The chapter deals with the chemical kinetics and rate of reactions.

#### Chapter 6 - General Principles and Processes of Isolation of Elements

Students will get to know about the thermodynamic and electrochemical principles of metallurgy.

#### Chapter 7 - p-Block Elements

The chapter is about p-block elements of the periodic table.

#### Chapter 8 - d and f Block Elements

The chapter is about d and f-block elements of the periodic table.

#### Chapter 9 - Coordination Compounds

The major topics of this chapter are Werner’s theory of coordination compounds, Isomerism, bonding in coordination compounds etc.

#### Chapter 10 - Haloalkanes and Haloarenes

The chapter contains information on the preparation, properties and reactions of haloalkanes and haloarenes.

#### Chapter 11 - Alcohols, Phenols and Ethers

The chapter explains the preparation, properties and reactions of alcohol, phenols and ethers.

#### Chapter 12 - Aldehydes, Ketones and Carboxylic Acids

Chapter 12 is related to the preparation, properties and chemical reactions of aldehydes, ketones and carboxylic acids. Students will also learn about the factors that affect carboxylic acids’ acidity and their reactions.

#### Chapter 13 - Organic Compounds Containing Nitrogen

Chapter 13 is related to the preparation, properties and chemical reactions of organic compounds containing nitrogen i.e., amines.

#### Chapter 14 - Biomolecules

In this chapter, biomolecules such as proteins, carbohydrates and nucleic acids etc. are discussed in detail. Students will also learn about the difference between RNA and DNA, and the role of biomolecules in the biosystem.

#### Chapter 15 - Polymers

In this chapter, students will be able to learn about polymers, types of polymers, and polymerisation processes. The preparation of synthetic polymers and their properties are also discussed in this chapter.

#### Chapter 16 - Chemistry in Everyday Life

An important chapter to know the application of chemistry in everyday life. After going through this chapter, students will be able to learn the term ‘chemotherapy’, the classification of drugs and their function in the body. Students will also know about food preservatives and artificial sweetening agents.

### NCERT Solutions for Class 12 Biology

The list of chapters in class 12 biology is given below:

(The unit count begins with unit 6 as the continuation of class 11 biology.)

#### VI) Reproduction

• Chapter-01 Reproduction in Organisms

• Chapter-02 Sexual Reproduction in Flowering Plants

• Chapter-03 Human Reproduction

• Chapter-04 Reproductive Health

#### VII) Genetics and Evolution

• Chapter-05 Principles of Inheritance and Variation

• Chapter-06 Molecular Basis of Inheritance

• Chapter-07 Evolution

#### VIII) Biology in Human Welfare

• Chapter-08 Human Health and Disease

• Chapter-09 Strategies for Enhancement in Food Production

• Chapter-10 Microbes in Human Welfare

#### IX) Biotechnology

• Chapter-11 Biotechnology: Principles and Processes

• Chapter-12 Biotechnology and its Applications

#### X) Ecology

• Chapter-13 Organisms and Populations

• Chapter-14 Ecosystem

• Chapter-15 Biodiversity and Conservation

• Chapter-16 Environmental Issues

### NCERT Solutions for Class 12 in Hindi Medium

Finding the right study material for preparing for the 12th standard is exceptionally crucial to ace your exams. We offer a plethora of PDFs of all subjects for 12th-grade students to learn and prepare well for their exams. Now download the free Class 12 NCERT PDFs here.

### NCERT Class 12 Solutions Advantages

Class 12 board exams are one of the most fundamental exams of every student’s life. These exams are a prime aspect that helps you create a smooth path for your career and higher studies. Thus, it comes as no surprise that studying well for this exam is of paramount importance. Scoring good marks is the key to getting into top-notch and prestigious universities for your higher studies. Simultaneously, graduating from a prestigious university can help open up doors of opportunities for your future.

In a nutshell, Class 12 solution PDFs are the one-stop solution to gaining deep insights into what you should study for your board exams. With the right study materials, students can now achieve their desired marks. 12th board exams are the pillars of building a strong and successful career path for your life. NCERT Solution for Class 12 PDFs will thus help you discover how you can reach your fullest potential. Here are some advantages of revising Class 12th NCERT guides.

• Class 12 NCERT PDFs aim to help students grasp knowledge on the vital concepts of every chapter. You can refer to distinguishing guides for every subject and every chapter.

• Class 12th NCERT guides are written in easy to understand and readable language to help students enjoy the learning process.

• You can refer to a wide range of question banks outside your class textbooks to prepare better for your exams.

• Class 12th NCERT Solutions are designed to help students score maximum marks in their upcoming board exams.

• Every solution offered in these guides comes with elaborate explanations to help students boost their level of understanding.

### Some Tips to Consider While Preparing for Your Exams

The Class 12th NCERT PDFs are made with maximal research to ensure that the students gain optimum knowledge of even the difficult concepts. As the CBSE board exams are nearing, students might be overwhelmed, trying to get the motivation to study. Students are advised to prepare beforehand for their exams, not to experience extreme anxiety during exams. You can carefully look for certain strategies to boost your exam preparation skills as a whole. Following are some tips and tricks that can save you on your upcoming exams.

• Choose relevant study material while preparing for your board exams. Remember to study smart instead of study hard.

• Regularly work out to keep yourself fresh throughout your study sessions.

• Jot down a timetable and maintain a good schedule to stay organized.

• Make use of previous year's question papers while revising and practising.

• Revise each and every topic before your exam to remember better.

• Take sufficient and regular study breaks to avoid over-exhaustion.

• For subjects like maths, ensure solving even the optional exercises so that you are well-prepared.

• If you have enough time, practice by writing down the answers every now and then to remember the answer thoroughly.

• Stay hydrated and meditate every now and then to stay woke during your study hours.

• Get enough sleep so that you have effective study hours. Lack of sleep may lead to forgetting everything you’ve learned.

### Strategies to Score Well in Class 12 Board Exams

Every student dreams to score well in their upcoming board exams. If you’re daunted about how to study for your exams, here are some strategies to keep in mind.

Stay Positive:

• Students may feel extremely unmotivated on some days. Do not let this get the best of you. Stay positive throughout your journey of learning. Take these exams as challenging and work hard so that you can accomplish everything you desire to.

• Make sure to keep a balance between studying and other activities to relieve your stress. Study all the concepts thoroughly and ensure eating and exercising properly to relieve your stress levels.

Practising is the Key:

• Lastly, do not forget to practice and revise what you’ve learned so far consistently.

## FAQs on NCERT Solutions for Class 12

1. How is NCERT Different From CBSE?

The CBSE board chiefly advises students to use NCERT books as study materials while preparing for their exams.

2. Why is NCERT Reliable for Studying for Your Boards?

Class 12 NCERT solutions are designed after doing extensive research. They are ideal for preparing for CBSE board exams as the CBSE board itself recommends them. These study materials have information incorporated from popular books of study like RD Sharma and RS Aggarwal.

3. What is the Aim of NCERT?

NCERT is an autonomous organization established to help motivate students to prepare well for their exams, design textbooks incorporating all sorts of the relevant information required to gain knowledge, and even organize in-Service training and pre-service training of teachers.

4. Why are Class 12 board exams important?

Board exams are probably one of the most important exams that high school students have to appear for. These exams can determine your future and where you go to college based on how well you score. Board exams are the final class 12 exams conducted by the CBSE for students all over the country. The students study and practice all year for this. The students should work hard and give these exams their all and aim to score the highest.

5. Are the Vedantu Solutions PDF reliable for revision?

Vedantu is a leading online platform that provides solutions for students of all classes and for all subjects. The online PDFs that are available for free download are curated and written by a team of professional teachers and experts who aim at making the subject easier for the students to learn. It provides solutions, practice questions, summaries and questions from previous years. It is a good source to revise from. All the study material is available on the Vedantu app. Also, all the material is free of cost.

6. Should I practice sample papers while preparing for board exams?

Yes, attempting sample papers and papers from previous years is very important while preparing for the board exams. A lot of the time questions can be asked directly from sample papers or be repeated from question papers of previous years. The sample papers help you understand the kind of questions to expect in the exam and also how to answer them. Practicing sample papers regularly also helps you manage time well.

7. What is a good time-table to prepare for board exams?

Students should study and be thorough with their syllabus throughout the year. Do not leave a major chunk of the syllabus for the end moment. Prepare a timetable depending on your strengths and weaknesses. Give more time and practice to topics or subjects you think to require it. Be diligent in studying. Remember to not overwork yourself and give yourself regular breaks as well. Keep time to revise before the exam as well.

8. What subjects are covered in the Solutions PDF for Class 12?

Vedantu provides PDF solutions for all subjects that are offered in Class 12. All the subjects are covered chapter-wise. The students can download whichever chapter or subject-specific PDF they require to prepare from. The PDFs are available for free download on the Vedantu website. The aim of these is to make learning and revision easier for students and help them understand the subject better. It consolidates the information and provides extra questions for practice as well. SHARE TWEET SHARE SUBSCRIBE