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NCERT Solutions for Class 12 Maths Chapter 2 – Inverse Trigonometric Functions

NCERT Solutions for Class 12 Maths Chapter 2 – Inverse Trigonometric Functions

Chapter 2 of NCERT Class 12 Maths Inverse Trigonometric Functions plays an important role in calculus. Students must practice calculus part of class 12 to score excellent marks in the board exams. NCERT solutions provide solutions for all the problems from chapter 2 of class 12 inverse trigonometric functions. Students can download NCERT solutions PDF of class 12 inverse trigonometric functions, and practice for themselves at any instant of time. The concepts of Inverse trigonometry functions are also used in the higher classes in the streams of science and engineering.

Practicing calculus is very useful to score more marks because the calculus part has more weightage in the board exams as well as many competitive exams. For most of the competitive exams, the questions are given from the topics picked from the NCERT books. NCERT solutions are very clear and easy to understand for the students. Any problem from the Inverse Trigonometric Functions of NCERT Class 12 Maths can be checked from the PDF below if you got stuck anywhere in between solving problems.

NCERT Solutions for Class 12 Maths Chapter 2 – Inverse Trigonometric Functions

Topics covered: chapter 2 inverse trigonometric functions         

☛Definition
☛Range
☛domain
☛principal value branch
☛inverse trigonometric functions
☛properties of inverse trigonometric functions
☛Graphs of inverse trigonometric functions
☛Elementary properties of inverse trigonometric functions.

Inverse trigonometric functions Definition:

Inverse trigonometric functions also called as “anti-trigonometric” functions are nothing but the inverses of the basic trigonometric functions (i.e. sine, cosine, tangent, cotangent, secant, and cosecant) with suitable restricted domains.

Inverse trigonometric functions Notation

(i)sine inverse- \sin^{-1}x (ii)cos inverse- \cos^{-1}x\cdot (iii)tan inverse- \tan^{-1}x (iv)cot inverse- cot^{-1}x (v) secant inverse- Sec^{-1}x (vi)cosecant inverse- \cos ec^{-1}x

Range:

The range of the function is the set of outputs that can be generated by inputting the numbers from the domain into the function and perform the function operation. Range can also be the all real possible numbers(unlimited).

Function Range
f(x)=sin-1(x) [-π2,π2]
f(x)=cos-1(x) [0,π]
f(x)=tan-1(x) (-π2,+π2)
f(x)=cot-1(x) (0,π)
f(x)=sec-1(x) [0,π2)[π,3π2)
fx=cosec-1x (-π,π2](0,π2]

Domain:

The domain of a function is the set of possible values of the independent variable or variables of that function.

Function Domain
fx=sin1x -1,1
fx=cos-1x -1,1
fx=tan1x -,+
fx=cot-1x -,+
fx=sec-1x -,-1][1,+
fx=cosec-1x -,-1][1,+

Principal value branch:

Not even one inverse trigonometric function is one to one, Therefore, the ranges of the inverse functions are proper subsets of the domains of the original functions. when one function is desired to one value then the function may be restricted to its principal branch. With this restriction, the inverse of the sine function will evaluate to a single value, which is called the principal value.

The below-given table gives the principal value branches of the inverse trigonometric functions along with their domains and ranges.

Function Domain Range
sin-1 -1,1 -π2,π2
cos-1 -1,1 0,π
tan-1 R -π2,π2
cot-1 R 0,π
Sec-1 R--1,1 [0,π]-π2
cosec-1 R--1,1 [π2,π2]-0

 Inverse trigonometric functions: 

FunctionDomainRange
sin to the power of negative 1 end exponent x[−1,1][−π/2,π/2]
cos to the power of negative 1 end exponent x[−1,1][0,π]
tan to the power of negative 1 end exponent x(−∞,∞)[−π/2,π/2]
C o t to the power of negative 1 end exponent x(−∞,∞)[0,π]
S e c to the power of negative 1 end exponent x(−∞,−1]∪[1,∞)[0,π/2)∪(π/2,π]
cos e c to the power of negative 1 end exponent x(−∞,−1]∪[1,∞)[−π/2,0)∪(0,π/2]

properties of inverse trigonometric functions:

1. Property number 1 (i). \sin^{-1}\frac1x=\cos ec^{-1}x,x\geq1\;or\;x\leq1 (ii). \cos^{-1}x\frac1x=sec^{-1}x,x\geq1\;or\;x\leq-1 (iii). \tan^{-1}x=\mathrm{co}t^{-1}x,x>0 2. Property number 2 (i). Sin^{-1}\left(-x\right)=-\sin^{-1}x,\;x\in\lbrack-1,1\;\rbrack (ii) \tan^{-1}\left(-x\right)=-\tan^{-1}x,\;x\in R (iii) \cos ec^{-1}\left(-x\right)=-\cos ec^{-1}x,1x\vert\geq1 3. Property number 3 (i) \cos^{-1}\left(-x\right)=\pi-\cos^{-1}x,\;x\in\lbrack-1,1\;\rbrack (ii) Sec^{-1}\left(-x\right)=\pi-sec^{-1}x_,\;\left|x\right|\geq1 (iii) cot^{-1}\left(-x\right)=\pi-cot^{-1}x,\;x\in R 4. Property number 4 (i) \sin^{-1}x+\cos^{-1}x=\frac\pi2,x\in\left[-1,1\right] (ii) \tan^{-1}x+\cos^{-1}x=\frac\pi2,x\in R (iii) \cos ec^{-1}x+sec^{-1}x=\frac\pi2,\;\left|x\geq1\right| 5. Property number 5 (i) \tan^{-1}x+\tan^{-1}y=\tan^{-1}\frac{x+y}{1-xy},xy<1 (ii) \tan^{-1}x-\tan^{-1}y=\tan^{-1}\frac{x-y}{1+xy},xy>-1 (iii) \tan^{-1}x+\tan^{-1}y=\pi+\tan^{-1}\left(\frac{x+y}{1-xy}\right),\;xy>1;\;x,y>0 6. Property number 6 (i) 2\tan^{-1}x=\sin^{-1}\frac{2x}{1+x^2},\;\vert x\vert\leq1 (ii) 2\tan^{-1}x=\cos^{-1}\frac{1-x^2}{1+x^2},x\geq0 (iii) 2\tan^{-1}x=\tan^{-1}\frac{2x}{1-x^2},-1<x<1

Graphs of inverse trigonometric functions:

EXERCISESHORT ANSWERSLONG ANSWERSTOTAL SOLUTIONS
EXERCISE 2.114014
EXERCISE 2.141721

NCERT Solutions for class 12 to class 1✅(All Subjects)

NCERT Solutions – CBSE Students & others Can Download NCERT Solution for Class 10 Math’s, Science, English, Hindi, Social Science available in a FREE PDF format Class 11 and class 12 being the academic wise turning points need a plethora of basics to run-in success. Class 1 to class 10 is a level of basics and class 11, class 12 are the application of the basics. Therefore, it is very important to learn everything in a detailed manner. NCERT (National Council of Educational Research and Training) aims to provide qualitative education for the students. Hence it provides textbooks, materials, journals, school kits, multimedia packages, etc. to the students to develop their skills

NCERT publication is much more useful and can be used as a reference too. Many students who are ambitious to crack the competitive exams can gaily use these NCERT books and materials for the preparation of their competitive exams. Students must solve and practice a greater number of questions in order to succeed in any exam. There must be a guide or a reference to help us out at times of rigidity in solving problems.

NCERT Solutions

NCERT Solutions of NCERT book is then used for checking or understanding the problems. These solutions are written stack-dab like what should be written or known to save time. Because competitive exams also require time management skills along with the knowledge. These solutions help in understanding and solving problems in case you are stuck. Here are the links to access NCERT Solution. Keep reading to browse the solutions of different classes and different subjects.

NCERT Solutions for all Class – Overview

NCERT Solutions for Class 12 to 7

NCERT Solutions for Class 6 to 1

NCERT Solutions for class 12 NCERT Solutions for class 6
NCERT Solutions for class 11 NCERT Solutions for class 5
NCERT Solutions for class 10 NCERT Solutions for class 4
NCERT Solutions for class 9 NCERT Solutions for class 3
NCERT Solutions for class 8 NCERT Solutions for class 2
NCERT Solutions for class 7 NCERT Solutions for class 1

NCERT solutions provide a detailed view of each and every question. At the end of each chapter’s solutions, a brief summary and important points and formulas to be remembered are given. This succor in the preparation for the final exams in a short period of time.

NCERT Solutions for Class 1 to 12 in PDF

Students can easily expect more No. of questions directly from the textbook. NCERT solutions could assist in solving problems if you are stuck somewhere in between solving problems. keep reading for subjects wise list from class 1 to class 12.

The given below are the links to access the chapters of each subject of class 1 to class 12. The links redirect to the chapter-wise solutions. Click on the required link and you can reach the solutions of each chapter. NCERT solutions also hold keynotes and important points. Students get attuned to further state-wise or competitive exams. Practicing or revising more helps them to build up confidence levels.

Class 12 to Class 1 NCERT Solutions Index

Subjects and topics are interlinked with each other. Thus, it is important to put more focus on the topics covered and practice them. All the solutions are detailed very clearly and in an understandable way. Keep scrolling for the solutions of other classes.

Class 12 NCERT Solutions Index

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Class 12 Subject wise Solution

1. ☛NCERT Solutions for Class 12 Math’s
2. ☛NCERT Solutions for Class 12 Physics
3. ☛NCERT Solutions for Class 12 Chemistry
4. ☛NCERT Solutions for Class 12 Biology
5. ☛NCERT Solutions for Class 12 Business Studies
6. ☛NCERT Solutions for Class 12 Accountancy
7. ☛NCERT Solutions Class 12 Accountancy Part 1
8. ☛NCERT Solutions Class 12 Accountancy Part 2
9. ☛NCERT Solutions Class 12 Economics
10. ☛NCERT Solutions Class 12 Micro-Economics
11. ☛NCERT Solutions Class 12 Macro-Economics
12. ☛NCERT Solutions Class 12 Macro-Economics

Class 11 NCERT Solutions Index

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Class 11 Subject wise Solution

1. ☛NCERT Solutions for Class 11 Math’s
2. ☛NCERT Solutions for Class 11 Physics
3. ☛NCERT Solutions for Class 11 Chemistry
4. ☛NCERT Solutions for Class 11 Biology
5. ☛NCERT Solutions for Class 11 Accountancy
6. ☛NCERT Solutions for Class 11 Business Studies
7. ☛NCERT Solutions Class 11 Economics
8. ☛NCERT Solutions Class 11 Statistics
9. ☛NCERT Solutions Class 11 Commerce

Class 10 NCERT Solutions Index

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Class 10 Subject wise Solutions

1. ☛NCERT Solutions for Class 10 Math’s
2. ☛NCERT Solutions for Class 10 Science
3. ☛NCERT Solutions for Class 10 English
4. ☛NCERT Solutions for Class 10 Social Science
5. ☛NCERT Solutions for Class 10 Social Science History
6. ☛NCERT Solutions for Class 10 Social Science Geography
7. ☛NCERT Solutions for Class 10 Social Science Political Science
8. ☛NCERT Solutions for Class 10 Social Science Economics

Class 9 NCERT Solutions Index

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Class 9 Subject wise Solutions

1. ☛NCERT Solutions for Class 9 Maths
2. ☛NCERT Solutions for Class 9 Science
3. ☛NCERT Solutions for Class 9 English
4. ☛NCERT Solutions for Class 9 Social Science
5. ☛NCERT Solutions for Class 9 Social Science History
6. ☛NCERT Solutions for Class 9 Social Science Geography
7. ☛NCERT Solutions for Class 9 Social Science Political Science
8. ☛NCERT Solutions for Class 9 Social Science Economics

Class 8 NCERT Solutions Index

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Class 8 Subject wise Solutions

1. ☛NCERT Solutions for Class 8 Maths
2. ☛NCERT Solutions for Class 8 Science
3. ☛NCERT Solutions for Class 8 English
4. ☛NCERT Solutions Class 8 Social science
5. ☛NCERT Solutions for Class 8 Social Science History
6. ☛NCERT Solutions for Class 8 Social Science Geography
7. ☛NCERT Solutions for Class 8 Social Science Political Science (Civics)

Class 7 NCERT Solutions Index

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Class 7 Subject wise Solutions

1. ☛NCERT Solutions for Class 7 Maths
2. ☛NCERT Solutions for Class 7 Science
3. ☛NCERT Solutions for Class 7 English
4. ☛NCERT Solutions Class 7 Social science
5. ☛NCERT Solutions for Class 7 Social Science History
6. ☛NCERT Solutions for Class 7 Social Science Geography
7. ☛NCERT Solutions for Class 7 Social Science Political Science (Civics)

Class 6 NCERT Solutions Index

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Class 6 Subject wise Solutions

1. ☛NCERT Solutions for Class 6 Maths
2. ☛NCERT Solutions for Class 6 Science
3. ☛NCERT Solutions for Class 6 English
4. ☛NCERT Solutions Class 6 Social science
5. ☛NCERT Solutions for Class 6 Social Science History
6. ☛NCERT Solutions for Class 6 Social Science Geography
7. ☛NCERT Solutions for Class 6 Social Science Political Science (Civics)

NCERT Solution chapter-wise PDF Format Download Free

Go through the links below and ingress the NCERT solutions written by the experts in vidyanidhi. Every chapter has key points and important formulae to be noted at the completion of the chapter. All the solutions can be downloaded for free in PDF form from the links given below. Keep scrolling for exhaustive information.

NCERT Solutions for Class 12 – NCERT Solutions for Class 12 – Maths Math’s

Students who can solve math flawlessly are considered to learn any subject predominantly. Thus, it is important to learn and practice all the sums once the chapter is explained. Class 12 math’s is not so easy, as well as not so hard for those who vigorously practice when they get time. The below-given links lead you to the solutions of every chapter in an understandable way.

NCERT Class 12 Mathematics

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Chapter No.

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

NCERT Solutions for Class 12 – E = mc² NCERT Solutions for Class 12 Physics Physics

The below-given links lead you to the solutions of every chapter in an understandable way. Physics can be learned and can be used to create wonders in any field.

NCERT Class 12 Physics

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Chapter No.

Class 12 Physics Chapter Names
1. Chapter 1. Electric Charges and Fields
2. Chapter 2 Electrostatic Potential and Capacitance
3. Chapter 3 Current Electricity
4. Chapter 4 Moving Charges and Magnetism
5. Chapter 5 Magnetism and Matter
6. Chapter 6 Electromagnetic Induction
7. Chapter 7 Alternating Current
8. Chapter 8 Electromagnetic Waves
9. Chapter 9 Ray Optics and Optical Instruments
10 Chapter 10 Wave Optics
11. Chapter 11 Dual Nature of Radiation and Matter
12 Chapter 12 Atoms
13. Chapter 13  Nuclei
14. Chapter 14 Semiconductor Electronics
15. Chapter 15 Communication Systems

NCERT Solutions for Class 12- NCERT Class 12 - Chemistry Chemistry

Here are the links to download PDFs of NCERT Class 12 Chemistry with the chapter wise. Click on the required link to download the PDF doc of the chapters.

NCERT Class 12 Chemistry

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Chapter No.

Class 12 Chemistry Chapter Names
1. Chapter 1. The Solid State
2. Chapter 2 Solutions
3. Chapter 3 Electrochemistry
4. Chapter 4 Chemical Kinetics
5. Chapter 5 Surface Chemistry
6. Chapter 6 General Principles and Processes of Isolation of Elements
7. Chapter 7 p-Block Elements
8. Chapter 8 d and f Block Elements
9. Chapter 9 Coordination Compounds
10 Chapter 10 Haloalkanes and Haloarenes
11. Chapter 11 Alcohols, Phenols, and Ethers
12 Chapter 12 Aldehydes, Ketones, and Carboxylic Acids
13. Chapter 13 Organic compounds containing Nitrogen
14. Chapter 14 Biomolecules
15. Chapter 15  Polymers
16. Chapter 16 Chemistry in Everyday life

NCERT Solutions for Class 12- NCERT Class 12 - Biology Biology

Here are the links to download PDFs of every NCERT Class 12 Biology chapters wise. Click on the required link to download the PDF of the chapter.

NCERT Class 12 Biology

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Chapter No.

Class 12 Biology Chapter Names
1. Chapter 1. Reproduction in Organisms
2. Chapter 2 Sexual Reproduction in Flowering Plants
3. Chapter 3 Human Reproduction
4. Chapter 4 Reproductive Health
5. Chapter 5 Principles of Inheritance and Variation
6. Chapter 6 Molecular Basis of Inheritance
7. Chapter 7 Evolution
8. Chapter 8 Human Health and Diseases
9. Chapter 9 Strategies for Enhancement in Food Production
10 Chapter 10 Microbes in Human Welfare
11. Chapter 11 Biotechnology Principles and Processes
12 Chapter 12 Biotechnology: and its Application
13. Chapter 13 Organisms and Populations
14. Chapter 14 Ecosystem
15. Chapter 15 Biodiversity and Conservation
16. Chapter 16 Environmental Issues

NCERT Solutions for Class 11- NCERT Class 11 Maths Math’s

NCERT Class 11 Maths forms a base for the class 12 mathematics. Practicing it and solving other questions out of the book could help in achieving the goal. Here are the links to download PDFs of every chapter. Click on the required link to download the PDF of the chapter.

NCERT Class 11 Mathematics

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Chapter No.

Class 11 Maths Chapter Names
1. Chapter 1. Sets
2. Chapter 2 Relations and Functions
3. Chapter 3 Trigonometric Functions
4. Chapter 4 Principle of Mathematical Induction
5. Chapter 5 Complex Numbers and Quadratic Equations
6. Chapter 6 Linear Inequalities
7. Chapter 7 Permutations and Combinations
8. Chapter 8 Binomial Theorem
9. Chapter 9 Sequences and Series
10 Chapter 10 Straight Lines
11. Chapter 11 Conic Sections
12 Chapter 12 Introduction to Three-Dimensional Geometry
13. Chapter 13 Limits and Derivatives
14. Chapter 14 Mathematical Reasoning
15. Chapter 15 Statistics
16. Chapter 16 Probability

NCERT Solutions Class 11- NCERT Class 11- PhysicsPhysics

NCERT books contain exercise questions at the end of each chapter. Students must solve them in order to improve their skills. Click on the required link to download the PDF of the chapter. Here are the links to download PDFs of every chapter.

NCERT Class 11 Physics

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Chapter No.

Class 11 Physics Chapter Names
1. Chapter 1. Physical World
2. Chapter 2 Units and Measurement
3. Chapter 3 Motion in a Straight Line
4. Chapter 4 Motion in a Plane
5. Chapter 5 Laws of Motion
6. Chapter 6 Work, Energy, and Power
7. Chapter 7 System of Particles and Rotational Motion
8. Chapter 8 Gravitation
9. Chapter 9 Mechanical Properties of Solids
10 Chapter 10 Mechanical Properties of Fluids
11. Chapter 11 Thermal Properties of Matter
12 Chapter 12 Thermodynamics
13. Chapter 13  Kinetic Theory
14. Chapter 14 Oscillations
15. Chapter 15 Waves

NCERT Solutions Class 11- NCERT-Class-11-Chemistry Chemistry

Here are the links to download PDFs of every chapter. Click on the required link to download the PDF of the chapter. Every experiment and the usage of chemicals is explained in a very easy and understandable method

NCERT Class 11 Chemistry

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Chapter No.

Class 11 Chemistry Chapter Names
1. Chapter 1. Some Basic Concepts of Chemistry
2. Chapter 2 Structure of Atom
3. Chapter 3 Classification of Elements and Periodicity in Properties
4. Chapter 4 Chemical Bonding and Molecular Structure
5. Chapter 5 States of Matter
6. Chapter 6 Thermodynamics
7. Chapter 7 Equilibrium
8. Chapter 8 Redox Reactions
9. Chapter 9 Hydrogen
10 Chapter 10 s-Block Elements
11. Chapter 11 p-Block Elements
12 Chapter 12 Organic Chemistry – Some Basic Principles and Techniques
13. Chapter 13 Hydrocarbons
14. Chapter 14 Environmental Chemistry

NCERT Solutions Class 11- NCERT Class 11 Biology Biology

Click on the required link to download the PDF of the chapter. Here are the links to download PDFs of every chapter.

NCERT Class 11 Biology

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Chapter No.

Class 11 Biology Chapter Names
1. Chapter 1. The Living World
2. Chapter 2 Biological Classification
3. Chapter 3 Plant Kingdom
4. Chapter 4 Animal Kingdom
5. Chapter 5 Morphology of Flowering Plants
6. Chapter 6 Anatomy of Flowering Plants
7. Chapter 7 Structural Organization in Animals
8. Chapter 8 Cell the Unit of Life
9. Chapter 9 Biomolecules
10 Chapter 10 Cell Cycle and Cell Division
11. Chapter 11 Transport in Plants
12 Chapter 12 Mineral Nutrition
13. Chapter 13 Photosynthesis in Higher Plants
14. Chapter 14 Respiration in Plants
15. Chapter 15 Plant Growth and Development
16. Chapter 16 Digestion and Absorption
17. Chapter 17 Breathing and Exchange of Gases
18. Chapter 18 Body Fluids and Circulation
19. Chapter 19 Excretory Products and their Elimination
20. Chapter 20 Locomotion and Movement
21. Chapter 21 Neural Control and Coordination
22. Chapter 22 Chemical Coordination and integration

Class 12 NCERT Solutions Maths PDF Download

Class 12 NCERT Solutions Maths – Mathematics is an interesting and lengthy subject to be learned especially the class12 Maths, it forms a base for the upcoming studies. And it is also a prime subject to score marks at any level of the academics. Vidyanidh NCERT solutions provide a step by step solving process of each and every problem present in the NCERT publications Textbook.

Students are intended to solve more and more questions in order to top in any of the exams. This Class 12 NCERT Solutions Maths PDF helps the students at the time of difficulty, whenever they are stuck in any step of solving a problem. A thorough learning and a continuous practice from the NCERT books help the students to do well in their exams. Here are the links to browse and download PDFs of all the chapters and exercises of Class 12 NCERT Maths Solutions.

Class 12 NCERT Solutions Maths Chapter-wise PDF

Chapter No.Name of the Chapter
Chapter 1Relations and Functions
Chapter 2Inverse Trigonometric Functions
Chapter 3Matrices
Chapter 4Determinants
Chapter 5Continuity and Differentiability
Chapter 6Applications of Derivatives
Chapter 7Integrals
Chapter 8Applications of Integrals
Chapter 9Differential Equations
Chapter 10Vector Algebra
Chapter 11Three-dimensional Geometry
Chapter 12Linear Programming

NCERT Solutions for Class 12 Maths Briefing all 13 Chapters

For Better Understanding, to the Class 12 Students, we have Briefed Each chapter & Exercises

Chapter 1: Relations and Functions

S.no

Name of the Topics

1. Relations and functions
2. Types of relation
☛reflexive 
☛Symmetric
☛Transitive
☛equivalence
3. Types of functions
4. The composition of functions and invertible function
5. Binary operations.

Relations and Functions Exercises wise Solutions PDF

Relations and Functions Chapter Exercises Solutions
Exercise 1.1
Exercise 1.2
Exercise 1.3
Exercise 1.4
Miscellaneous Exercise

The above-mentioned concepts are explained very well through examples. Solutions to the exercises from the chapter can be accessed from here


Chapter 2: Inverse Trigonometric Functions

S.no Name of the Topics
1 Inverse trigonometric functions
2 Properties of inverse trigonometric functions
☛Definition
☛Range
☛domain 
☛principal value branch
☛Graphs of inverse trigonometric functions
☛Elementary properties of inverse trigonometric functions. 

Inverse Trigonometric Functions Exercises wise Solutions PDF

Inverse Trigonometric Functions Chapter Exercises Solutions
Exercise 2.1
Exercise 2.2
Miscellaneous Exercise

The above-mentioned concepts are explained very well through examples. Solutions to the exercises from the chapter can be accessed from here –


Chapter 3: Matrices

S.no Name of the Topics
1. Definition of a matrix
2. Types of matrices
3. Equality of matrices
4. Operations on matrices
☛addition of matrices
☛multiplication of a matrix by a scalar
5. Properties of matrix addition
6. Properties of scalar multiplication
7. Multiplication of matrices
8. Properties of multiplication of matrices
9. Transpose of a matrix
10. Properties of the transpose of the matrix
11. Symmetric and skew-symmetric matrices
12. Elementary operation or transformation of a matrix
13. The inverse of a matrix by elementary operations

NCERT Class 12 Solutions for Maths, Physics, Chemistry, Biology

NCERT Solutions for Class 12 All Subjects

Class 12 is the strongest base forming year of academics. Being clearer and more perfect in the core subjects i.e. Maths, Physics, Chemistry, and Biology is very much important to crack all the competitive exams. To help students who want to top in their board exams NCERT an autonomous organization run by the government developed books in such a way that each and every student is clear with all the subjects and topics of class 12.

NCERT Solutions for Class 12, Maths, Physics, Chemistry, and Biology

NCERT Class 12th Solution for all Subjects like Maths, Physics, Chemistry, Biology
NCERT Class 12 Solutions for Maths, Physics, Chemistry, Biology Subjects

NCERT solutions thus provide a clean and clear way of explanation for all the problems and questions given in the textbook. Students who find difficulty in solving problems and answering the questions can take the help of these NCERT solutions links and reach the solutions of the topics or subjects that they are stuck in. students can visit the official website of NCERT to access the NCERT publications

Here we provide all the answers to all the questions and solutions to all the problems on one click. The links below lead you to the solutions page of the desired subject. One can download the NCERT solutions in the PDF format, and practice them at any time. These NCERT Class 12 solutions not only help in the board exams but also in many competitive exams like JEE, NEET, BITSAT, etc. Download the solutions by clicking the links below and try solving as many as problems you can.

All the competitive exams, as well as board exams, include a maximum of questions from the topics covered in the NCERT books. NCERT books are designed in such a manner that helps the students to understand any topic in a very easy way.

NCERT Class 12 Solutions Subject wise

S.no

name of the NCERT Class 12 Subjects
1. NCERT Class 12 Maths
2. NCERT Class 12 Physics
3. NCERT Class 12 Chemistry
4. NCERT Class 12 Biology

All the above links guide to the NCERT solutions of class 12, maths, physics, chemistry, and biology subjects. Students can download and learn all the topics from the PDF at one’s convenience. If followed, NCERT books can be the best guide to score good marks in the board exams and crack almost all of the competitive exams.

Salient Features of NCERT Solutions

  • The NCERT solutions are very easy to acknowledge
  • NCERT Solutions for Class 12 are thorough
  • All the exercise problems are covered From NCERT Class 12 Textbook
  • For maths Subject, Step by Step solutions are provided
  • Diagrams are provided wherever required for a better understanding

Guidelines to Learn Core Subjects of NCERT Class 12th

  1. All the competitive exams like JEE, NEET, etc. include questions merely from the physics, maths, chemistry, and biology subjects. So, it is important to learn the fundamental basics of the chapters from every subject to the top in the exams.
  2. Focus and spend more time on core subjects like physics, maths, chemistry, and biology.
  3. Keep referring to a number of books, and keep on practicing and learning till you have enough grip and revision.
  4. Keeping books handy while learning new or prime topics is a good idea so that you can note down the key points and important formulae.
  5. Learn the conceptual part thoroughly so that you don’t face any issue in solving the intellectual questions.
  6. Spend more time in understanding the topic perfectly than just mugging it up.
  7. Keep solving a greater number of problems out of the textbooks in order to solve any kind of a question in the exam

FAQs about NCERT Class 12 Solution for All Subjects

How to download NCERT solutions PDF?

visit the official website of NCERT and find the links to download NCERT publications. Or visit the NCERT Vidyanidhi official page and click on the links to download the desired subjects and classes.

What is the official website of NCERT?

http://ncert.nic.in/ is the official website link. One can find all the required stuff regarding the academics on the page.

Can NCERT books be used as a reference to competitive exams?

NCERT books can be the best resources to prepare for any competitive exams. Because most of the questions covered in the exams are picked from the topics covered in NCERT books.