Hi, I'm Aditya, I study in Class 12
And I Learn My Subjects Easily With Vikrant Academy®
Hi, I'm Aditya, I study in Class 12
And I Learn My Subjects Easily With Vikrant Academy®
MATHEMATICS
1. Relations and functions
1.1. Introductions
1.2. Types of Relations
1.3. Types of Functions
1.4. Compositions of Functions and Invertible Functions
1.5. Binary Operations
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2. Inverse trigonometric functions
2.1. Introduction
2.2. Basic Concepts
2.3. Property of Inverse Trigonometric functions
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3. Matrices
3.1. Introductions
3.2. Matrix
3.3. Types of Matrices
3.4. Transpose of Matrix
3.5. Symmetric and skew Symmetric Matrices
3.6. Transformation of a Matrix
3.7. Invertible Matrices
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4. Determinants
4.1. Introduction
4.2. Determinant
4.3. Properties of Determinants
4.4. Area of a Triangle
4.5. Minors and Cofactors
4.6. Adjoints and Inverse of a Matrix
4.7. Applications of Determinants and Matrices
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5. Continuity and Differentiability
5.1. Introduction
5.2. Continuity
5.3. Differentiability
5.4. Exponential and Logarithmic Functions
5.5. Logarithmic Differentiation
5.6. Derivatives of Functions in Parametric Forms
5.7. Second Order Derivatives
5.8. Mean Value Theorem
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6. Application of Derivatives
6.1. Introduction
6.2. Rate of Change of Quantities
6.3. Increasing and Decreasing Functions
6.4. Tangents and Normal
6.5. Approximations
6.6. Maxima and Minima
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7. Integrals
7.1. Introduction
7.2. Integration as an Inverse Process of Differentiation
7.3. Methods of Integration
7.4. Integrals of some particular Functions
7.5. Integrations by Parts
7.6. Definite Integral
7.7. Fundamentals Theorem of Calculus
7.8. Evaluation of Definite Integrals by Substitutions
7.9. Some Properties of Definite Integrals
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8. Application of Integrals
8.1. Introduction
8.2. Area Under Simple Curves
8.3. Area between Two Curves
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9. Differential Equations
9.1. Introduction
9.2. Basic Concepts
9.3. General and particular solution of a differential equation
9.4. Formation of a Differential Equation Whose General solution is given
9.5. Methods of Solving First order, First degree Differential Equations
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10. Vector Algebra
10.1. Introduction
10.2. Some basic Concepts
10.3. Types of Vectors
10.4. Addition of Vectors
10.5. Multiplication of a Vector by a Scalar
10.6. Product of Two Vectors
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11. Three-Dimensional Geometry
11.1. Introduction
11.2. Direction cosines and Direction of a Line
11.3. Equation of a Line in Space
11.4. Angle between two lines
11.5. Shortest Distance Between Two Lines
11.6. Plane
11.7. Coplanarity of Two Lines
11.8. Angle between two Planes
11.9. Distance of a Point from a Plane
11.10. Angle between a Line and a Plane
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12. Linear Programming
12.1. Introduction
12.2. Linear programming Problem and its Mathematical Formulation
12.3. Different Types of Linear Programming Problems
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13. Probability
13.1. Introduction
13.2. Conditional Probability
13.3. Multiplication Theorem on Probability
13.4. Independent Events
13.5. Bayes’ Theorem
13.6. Random Variables and its Probability Distributions
13.7. Bernoulli Trials and Binomial Distribution
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Question & Answers (Solved)
Chapter 13: Probability
NCERT Solutions for Class 12 Maths Chapter 13 Probability Ex 13.1 Ex 13.1 Class 12 Maths Question 1Given that E and Fare events such thatP (E) = 0.6, P (F) = 0.3 and P(E∩F) = 0.2find P(E|F)…
Chapter 7: Integrals
Integrals Ex 7.1 Class 12 Ex 7.1 Class 12 Maths Question 1.sin 2xSolution:Ex 7.1 Class 12 Maths Question 2.cos 3xSolution:Ex 7.1 Class 12 Maths Question 3.e2xSolution:Ex 7.1 Class 12 Maths Question 4.(ax + c)²Solution:Ex 7.1 Class 12 Maths Question 5.sin2x−4e3xEx 7.1 Class…
Chapter 5: Continuity and Differentiability
Class 12 Maths Continuity and Differentiability Exercise 5.2 and 5.3 Class 12 Maths Continuity and Differentiability Exercise 5.4 Class 12 Maths Continuity and Differentiability Exercise 5.5 Class 12 Maths Continuity and Differentiability Exercise 5.6 Class 12 Maths…
Chapter 4: Determinants
Class 12 Maths NCERT Solutions Chapter 4 Determinants
Chapter 3: Matrices
NCERT Solutions for Class 12th Chapter 3 Maths Chapter 3 Matrices NCERT Solutions for Class 12 Maths Exercise 3.4 Q15
PHYSICS
CHAPTER ONE
ELECTRIC CHARGES AND FIELDS
1.1. Introduction
1.2. Electric Charge
1.3. Conductors and Insulators
1.4. Charging by Induction
1.5. Basic Properties of Electric Charge
1.6. Coulomb’s Law
1.7. Forces between Multiple Charges
1.8. Electric Field
1.9. Electric Field Lines
1.10. Electric Flux
1.11. Electric Dipole
1.12. Dipole in a Uniform External Field
1.13. Continuous Charge Distribution
1.14. Gauss’s Law
1.15. Applications of Gauss’s Law
CHAPTER TWO
ELECTROSTATIC POTENTIAL AND CAPACITANCE
2.1. Introduction
2.2. Electrostatic Potential
2.3. Potential due to a Point Charge
2.4. Potential due to an Electric Dipole
2.5. Potential due to a System of Charges
2.6. Equipotential Surfaces
2.7. Potential Energy of a System of Charges
2.8. Potential Energy in an External Field
2.9. Electrostatics of Conductors
2.10. Dielectrics and Polarisation
2.11. Capacitors and Capacitance
2.12. The Parallel Plate Capacitor
2.13. Effect of Dielectric on Capacitance
2.14. Combination of Capacitors
2.15. Energy Stored in a Capacitor
CHAPTER THREE
CURRENT ELECTRICITY
3.1. Introduction
3.2. Electric Current
3.3. Electric Currents in Conductors
3.4. Ohm’s law
3.5. Drift of Electrons and the Origin of Resistivity
3.6. Limitations of Ohm’s Law
3.7. Resistivity of Various Materials
3.8. Temperature Dependence of Resistivity
3.9. Electrical Energy, Power
3.10. Combination of Resistors — Series and Parallel
3.11. Cells, emf, Internal Resistance
3.12. Cells in Series and in Parallel
3.13. Kirchhoff’s Rules
3.14. Wheatstone Bridge
3.15. Meter Bridge
3.16. Potentiometer
CHAPTER FOUR
MOVING CHARGES AND MAGNETISM
4.1. Introduction
4.2. Magnetic Force
4.3. Motion in a Magnetic Field
4.4. Motion in Combined Electric and Magnetic Fields
4.5. Magnetic Field due to a Current Element, Biot-Savart Law
4.6. Magnetic Field on the Axis of a Circular Current Loop
4.7. Ampere’s Circuital Law
4.8. The Solenoid and the Toroid
4.9. Force between Two Parallel Currents, the Ampere
4.10. Torque on Current Loop, Magnetic Dipole
4.11. The Moving Coil Galvanometer
CHAPTER FIVE
MAGNETISM AND MATTER
5.1. Introduction
5.2. The Bar Magnet
5.3. Magnetism and Gauss’s Law
5.4. The Earth’s Magnetism
5.5. Magnetisation and Magnetic Intensity
5.6. Magnetic Properties of Materials
5.7. Permanent Magnets and Electromagnets
CHAPTER SIX
ELECTROMAGNETIC INDUCTION
6.1. Introduction
6.2. The Experiments of Faraday and Henry
6.3. Magnetic Flux
6.4. Faraday’s Law of Induction
6.5. Lenz’s Law and Conservation of Energy
6.6. Motional Electromotive Force
6.7. Energy Consideration: A Quantitative Study
6.8. Eddy Currents
6.9. Inductance
6.10. AC Generator
CHAPTER SEVEN
ALTERNATING CURRENT
7.1. Introduction
7.2. AC Voltage Applied to a Resistor
7.3. Representation of AC Current and Voltage by
Rotating Vectors — Phasors
7.4. AC Voltage Applied to an Inductor
7.5. AC Voltage Applied to a Capacitor
7.6. AC Voltage Applied to a Series LCR Circuit
7.7. Power in AC Circuit: The Power Factor
7.8. LC Oscillations
7.9. Transformers
CHAPTER EIGHT
ELECTROMAGNETIC WAVES
8.1. Introduction
8.2. Displacement Current
8.3. Electromagnetic Waves
8.4. Electromagnetic Spectrum
CHAPTER NINE
RAY OPTICS AND OPTICAL INSTRUMENTS
9.1. Introduction
9.2. Reflection of Light by Spherical Mirrors
9.3. Refraction
9.4. Total Internal Reflection
9.5. Refraction at Spherical Surfaces and by Lenses
9.6. Refraction through a Prism
9.7. Some Natural Phenomena due to Sunlight
9.8. Optical Instruments
CHAPTER TEN
WAVE OPTICS
10.1. Introduction
10.2. Huygens Principle
10.3. Refraction and Reflection of Plane Waves using Huygens Principle
10.4. Coherent and Incoherent Addition of Waves
10.5. Interference of Light Waves and Young’s Experiment
10.6. Diffraction
10.7. Polarisation
CHAPTER ELEVEN
DUAL NATURE OF RADIATION AND MATTER
11.1. Introduction
11.2. Electron Emission
11.3. Photoelectric Effect
11.4. Experimental Study of Photoelectric Effect
11.5. Photoelectric Effect and Wave Theory of Light
11.6. Einstein’s Photoelectric Equation: Energy Quantum of Radiation
11.7. Particle Nature of Light: The Photon
11.8. Wave Nature of Matter
11.9. Davisson and Germer Experiment
CHAPTER TWELVE
ATOMS
12.1. Introduction
12.2. Alpha-particle Scattering and Rutherford’s Nuclear Model of Atom
12.3. Atomic Spectra
12.4. Bohr Model of the Hydrogen Atom
12.5. The Line Spectra of the Hydrogen Atom
12.6. DE Broglie’s Explanation of Bohr’s Second Postulate of Quantisation
CHAPTER THIRTEEN
NUCLEI
13.1. Introduction
13.2. Atomic Masses and Composition of Nucleus
13.3. Size of the Nucleus
13.4. Mass-Energy and Nuclear Binding Energy
13.5. Nuclear Force
13.6. Radioactivity
13.7. Nuclear Energy
CHAPTER FOURTEEN
SEMICONDUCTOR ELECTRONICS: MATERIALS, DEVICES AND SIMPLE CIRCUITS
14.1. Introduction
14.2. Classification of Metals, Conductors and Semiconductors
14.3. Intrinsic Semiconductor
14.4. Extrinsic Semiconductor
14.5. p-n Junction
14.6. Semiconductor Diode
14.7. Application of Junction Diode as a Rectifier
14.8. Special Purpose p-n Junction Diodes
14.9. Digital Electronics and Logic Gates
Question & Answers (Solved)
Chapter 15: Communication Systems
Chapter 14: Semiconductor
Chapter 13: Nuclei
Chapter 12: Atoms
Chapter 11: Dual Nature of Radiation and Matter
Chapter 10: Wave Optics
Chapter 9: Ray Optics and Optical Instruments
Chapter 8: Electromagnetic Waves
Chapter 7: Alternating Current
Chapter 6: Electromagnetic Induction
Chapter 5: Magnetism and Matter
Chapter 4: Moving Charges and Magnetism
Chapter 3: Current Electricity
Chapter 2: Electrostatic Potential and Capacitance
Class 12 Physics Chapter 1: Electric Charges And Fields
CHEMISTRY
Unit 1
The Solid State
1.1 General Characteristics of Solid State
1.2 Amorphous and Crystalline Solids
1.3 Classification of Crystalline Solids
1.4 Crystal Lattices and Unit Cells
1.5 Number of Atoms in a Unit Cell
1.6 Close Packed Structures
1.7 Packing Efficiency
1.8. Calculations Involving Unit Cell Dimensions
1.9. Imperfections in Solids
1.10. Electrical Properties
1.11. Magnetic Properties
Unit 2
Solutions
2.1. Types of Solutions
2.2. Expressing Concentration of Solutions
2.3. Solubility
2.4. Vapour Pressure of Liquid Solutions
2.5. Ideal and Non-ideal Solutions
2.6. Colligative Properties and Determination of Molar Mass
2.7. Abnormal Molar Masses
Unit 3
Electrochemistry
3.1. Electrochemical Cells
3.2. Galvanic Cells
3.3. Nernst Equation
3.4. Conductance of Electrolytic Solutions
3.5. Electrolytic Cells and Electrolysis
3.6. Batteries
3.7. Fuel Cells
3.8. Corrosion
Unit 4
Chemical Kinetics
4.1. Rate of a Chemical Reaction
4.2. Factors Influencing Rate of a Reaction
4.3. Integrated Rate Equations
4.4. Temperature Dependence of the Rate of a Reaction
4.5. Collision Theory of Chemical Reactions
Unit 5
Surface Chemistry
5.1. Adsorption
5.2. Catalysis
5.3. Colloids
5.4. Classification of Colloids
5.5. Emulsions
5.6. Colloids Around Us
Unit 6
General Principles and Processes of Isolation of Elements
6.1. Occurrence of Metals
6.2. Concentration of Ores
6.3. Extraction of Crude Metal from Concentrated Ore
6.4. Thermodynamic Principles of Metallurgy
6.5. Electrochemical Principles of Metallurgy
6.6. Oxidation Reduction
6.7. Refining
6.8. Uses of Aluminium, Copper, Zinc and Iron
Unit 7
The p-Block Elements
7.1. Group 15 Elements
7.2. Dinitrogen
7.3. Ammonia
7.4. Oxides of Nitrogen
7.5. Nitric Acid
7.6. Phosphorus – Allotropic Forms
7.7. Phosphine
7.8. Phosphorus Halides
7.9. Oxoacids of Phosphorus
7.10. Group 16 Elements
7.11. Dioxygen
7.12. Simple Oxides
7.13. Ozone
7.14. Sulphur – Allotropic Forms
7.15. Sulphur Dioxide
7.16. Oxoacids of Sulphur
7.17. Sulphuric Acid
7.18. Group 17 Elements
7.19. Chlorine
7.20. Hydrogen Chloride
7.21. Oxoacids of Halogens
7.22. Interhalogen Compounds
7.23. Group 18 Elements
Unit 8
The d-and f-Block Elements
8.1. Position in the Periodic Table
8.2. Electronic Configurations of the d-Block Elements
8.3. General Properties of the Transition Elements (d-Block)
8.4. Some Important Compounds of Transition Elements
8.5. The Lanthanoids
8.6. The Actinoids
8.7. Some Applications of d- and f-Block Elements
Unit 9
Coordination Compounds
9.1. Werner’s Theory of Coordination Compounds
9.2. Definitions of Some Important Terms Pertaining to Coordination Compounds
9.3. Nomenclature of Coordination Compounds
9.4. Isomerism in Coordination Compounds
9.5. Bonding in Coordination Compounds
9.6. Bonding in Metal Carbonyls
9.7. Importance and Applications of Coordination Compounds
Unit 10
Haloalkanes and Haloarenes
10.1. Classification
10.2. Nomenclature
10.3. Nature of C–X Bond
10.4. Methods of Preparation of Haloalkanes
10.5. Preparation of Haloarenes
10.6. Physical Properties
10.7. Chemical Reactions
10.8. Polyhalogen Compounds
Unit 11
Alcohols, Phenols and Ethers
11.1. Classification
11.2. Nomenclature
11.3. Structures of Functional Groups
11.4. Alcohols and Phenols
11.5. Some Commercially Important Alcohols
11.6. Ethers345
Unit 12
Aldehydes, Ketones and Carboxylic Acids
12.1. Nomenclature and Structure of Carbonyl Group
12.2. Preparation of Aldehydes and Ketones
12.3. Physical Properties
12.4. Chemical Reactions
12.5. Uses of Aldehydes and Ketones
12.6. Nomenclature and Structure of Carboxyl Group
12.7. Methods of Preparation of Carboxylic Acids
12.8. Physical Properties
12.9. Chemical Reactions
12.10. Uses of Carboxylic Acids384
Unit 13
Amines
13.1. Structure of Amines
13.2. Classification
13.3. Nomenclature
13.4. Preparation of Amines
13.5. Physical Properties
13.6. Chemical Reactions
13.7. Method of Preparation of Diazonium Salts
13.8. Physical Properties
13.9. Chemical Reactions
13.10. Importance of Diazonium Salts in Synthesis of Aromatic Compounds
Unit 14
Biomolecules
14.1. Carbohydrates
14.2. Proteins
14.3. Enzymes
14.4. Vitamins
14.5. Nucleic Acids
14.6. Hormones
Unit 15
Polymers
15.1. Classification of Polymers
15.2. Types of Polymerisation Reactions
15.3. Molecular Mass of Polymers
15.4. Biodegradable Polymers
15.5. Polymers of Commercial Importance
Unit 16
Chemistry in Everyday Life
16.1. Drugs and their Classification
16.2. Drug-Target Interaction
16.3. Therapeutic Action of Different Classes of Drugs
16.4. Chemicals in Food
16.5. Cleansing Agents
Question & Answers (Solved)
Chapter 16: Chemistry in Everyday Life
Chapter 15: Polymers
Chapter 14: Biomolecules
Chapter 13: Amines
Chapter 12: Aldehydes Ketones and Carboxylic Acids
Chapter 11: Alcohols Phenols and Ether
Chapter 10: Haloalkanes and Haloarenes
Chapter 9: Coordination Compounds
Chapter 8: The d and f Block Elements
Chapter 7: The p Block Elements
Chapter 6: General Principles and Processes of Isolation of Elements
Chapter 5: Surface Chemistry
Chapter 4: Chemical Kinetics
Chapter 3: Electrochemistry
Chapter 2: Solutions
Class 12 Chemistry Chapter 1: The Solid State
BIOLOGY
UNIT VI
REPRODUCTION
Chapter 1 : Reproduction in Organisms
Chapter 2 : Sexual Reproduction in Flowering Plants
Chapter 3 : Human Reproduction
Chapter 4 : Reproductive Health
Chapter 5 : Principles of Inheritance and Variation
Chapter 6 : Molecular Basis of Inheritance
Chapter 7 : Evolution
Chapter 8 : Human Health and Disease
Chapter 9 : Strategies for Enhancement in Food Production
Chapter 10 : Microbes in Human Welfare
Chapter 11 : Biotechnology : Principles and Processes
Chapter 12 : Biotechnology and its Applications
Chapter 13 : Organisms and Populations
Chapter 14 : Ecosystem
Chapter 15 : Biodiversity and Conservation
Chapter 16 : Environmental Issues
