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CBSE Class XI / XII, 2021, 2022, 2023

CBSE Class XII (NCERT), 2021, 2022, 2023, Maths eBook



1. Relations and Functions 1
1.1 Introduction 1
1.2 Types of Relations 2
1.3 Types of Functions 7
1.4 Composition of Functions and Invertible Function 12
1.5 Binary Operations 19

2. Inverse Trigonometric Functions 33
2.1 Introduction 33
2.2 Basic Concepts 33
2.3 Properties of Inverse Trigonometric Functions 42

3. Matrices 56
3.1 Introduction 56
3.2 Matrix 56
3.3 Types of Matrices 61
3.4 Operations on Matrices 65
3.5 Transpose of a Matrix 83
3.6 Symmetric and Skew Symmetric Matrices 85
3.7 Elementary Operation (Transformation) of a Matrix 90
3.8 Invertible Matrices 91

4. Determinants 103
4.1 Introduction 103
4.2 Determinant 103
4.3 Properties of Determinants 109
4.4 Area of a Triangle 121
4.5 Minors and Cofactors 123
4.6 Adjoint and Inverse of a Matrix 126
4.7 Applications of Determinants and Matrices 133

5. Continuity and Differentiability 147
5.1 Introduction 147
5.2 Continuity 147
5.3 Differentiability 161
5.4 Exponential and Logarithmic Functions 170
5.5 Logarithmic Differentiation 174
5.6 Derivatives of Functions in Parametric Forms 179
5.7 Second Order Derivative 181
5.8 Mean Value Theorem 184

6. Application of Derivatives 194
6.1 Introduction 194
6.2 Rate of Change of Quantities 194
6.3 Increasing and Decreasing Functions 199
6.4 Tangents and Normals 206
6.5 Approximations 213
6.6 Maxima and Minima 216

Appendix 1: Proofs in Mathematics 247
A.1.1 Introduction 247
A.1.2 What is a Proof? 247

Appendix 2: Mathematical Modelling 256
A.2.1 Introduction 256
A.2.2 Why Mathematical Modelling? 256
A.2.3 Principles of Mathematical Modelling 257
Answers 268

7. Integrals 287
7.1 Introduction 288
7.2 Integration as an Inverse Process of Differentiation 288
7.3 Methods of Integration 300
7.4 Integrals of some Particular Functions 307
7.5 Integration by Partial Fractions 316
7.6 Integration by Parts 323
7.7 Definite Integral 331
7.8 Fundamental Theorem of Calculus 334
7.9 Evaluation of Definite Integrals by Substitution 338
7.10 Some Properties of Definite Integrals 341

8. Application of Integrals 359
8.1 Introduction 359
8.2 Area under Simple Curves 359
8.3 Area between Two Curves 366

9. Differential Equations 379
9.1 Introduction 379
9.2 Basic Concepts 379
9.3 General and Particular Solutions of a 383
Differential Equation
9.4 Formation of a Differential Equation whose 385
General Solution is given
9.5 Methods of Solving First order, First Degree 391
Differential Equations

10. Vector Algebra 424
10.1 Introduction 424
10.2 Some Basic Concepts 424
10.3 Types of Vectors 427
10.4 Addition of Vectors 429
10.5 Multiplication of a Vector by a Scalar 432
10.6 Product of Two Vectors 441

11. Three Dimensional Geometry 463
11.1 Introduction 463
11.2 Direction Cosines and Direction Ratios of a Line 463
11.3 Equation of a Line in Space 468
11.4 Angle between Two Lines 471
11.5 Shortest Distance between Two Lines 473
11.6 Plane 479
11.7 Coplanarity of Two Lines 487
11.8 Angle between Two Planes 488
11.9 Distance of a Point from a Plane 490
11.10 Angle between a Line and a Plane 492

12. Linear Programming 504
12.1 Introduction 504
12.2 Linear Programming Problem and its Mathematical Formulation 505
12.3 Different Types of Linear Programming Problems 514

13. Probability 531
13.1 Introduction 531
13.2 Conditional Probability 531
13.3 Multiplication Theorem on Probability 540
13.4 Independent Events 542
13.5 Bayes' Theorem 548
13.6 Random Variables and its Probability Distributions 557
13.7 Bernoulli Trials and Binomial Distribution 572

Answers 588


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1.Physical World
2.Units and Measurement
Kinematics
3.Motion in a Straight Line
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5.Laws of Motion
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8.Gravitation
Properties of Bulk Matter
9.Mechanical Properties of Solids
10.Mechanical Properties of Fluids
11.Thermal Properties of Matter
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Electrostatics
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17.Electrostatic Potential and Capacitance
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21.Electromagnetic Induction
22.Alternating Current
23.Electromagnetic Waves
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28.Nuclei
29.Electronic Devices
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2.Structure of Atom
3.Classification of Elements and Periodicity in Properties
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5.States of Matter
6.Thermodynamics
7.Equilibrium
8.Redox Reactions
9.Hydrogen
10.The s-block Elements
11.The p-block Elements
Organic Chemistry
12.Organic Chemistry - Some Basic Principles and Techniques
13.Hydrocarbons
14.Environmental Chemistry
15.The Solid State
16.Solutions
17.Electrochemistry
18.Chemical Kinetics
19.Surface Chemistry
20.General Principles and Processes of Isolation of Elements
21.The p-Block Elements
22.The d-and f-Block Elements
23.Coordination Compounds
24.Haloalkanes and Haloarenes
25.Alcohols, Phenols and Ethers
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27.Amines
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29.Polymers
30.Chemistry in Everyday Life
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2.Relations and Functions-1
3.Trigonometric Functions
4.Principle of Mathematical Induction
5.Complex Numbers and Quadratic Equations
6.Linear Inequalities
7.Permutations and Combinations
8.Binomial Theorem
9.Sequences and Series
10.Straight Lines
11.Conic Sections
12.Introduction to Three Dimensional Geometry
13.Limits and Derivatives
14.Mathematical Reasoning
15.Statistics
16.Probability-1
17.Infinite Series
18.Mathematical Modeling
19.Relations and Functions-2
20.Inverse Trigonometric Functions
21.Matrices
22.Determinants
23.Continuity and Differentiabilitybr /> 24.Application of Derivatives
25.Integrals
26.Application of Integrals
27.Differential Equations
28.Vector Algebra
29.Three Dimensional Geometry
30.Linear Programming
31.Probability-2
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NEET Biology
Diversity in the Living World
1.The Living World
2.Biological Classification
3.Plant Kingdom
4.Animal Kingdom
Structural Organisation in Plants and Animals
5.Morphology of Flowering Plants
6.Anatomy of Flowering Plants
7.Structural Organisation in Animals
Cell: Structure and Functions
8.Cell:The Unit of Life
9.Biomolecules
10.Cell Cycle and Cell Division
Plant Physiology
11.Transport in Plants
12.Mineral Nutrition
13.Photosynthesis in Higher Plants
14.Respiration in Plants
15.Plant Growth and Development
Human Physiology
16.Digestion and Absorption
17.Breathing and Exchange of Gases
18.Body Fluids and Circulation
19.Excretory Products and their Elimination
20.Locomotion and Movement
21.Neural Control and Coordination
22.Chemical Coordination and Integration
Reproduction
23.Reproduction in Organisms
24.Sexual Reproduction in Flowering Plants
25.Human Reproduction
26.Reproductive Health
Genetics and Evolution
27.Principles of Inheritance and Variation
28.Molecular Basis of Inheritance
29.Evolution
Biology in Human Welfare
30.Human Health and Disease
31.Strategies for Enhancement in Food Production
32.Microbes in Human Welfare
Biotechnology
33.Biotechnology : Principles and Processes
34.Biotechnology and its Applications
Ecology
35.Organisms and Populations
36.Ecosystem
37.Biodiversity and Conservation
38.Environmental Issues
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