The Best JEE Maths + Chemistry + Physics Handwritten Notes

Sets and their Representation, Operations on Sets, Counting with Sets (Practical Problems), Relations, Composition of Functions, Standard Real Functions, Fractional part {x} and modulus, Even and Odd Functions, Graph Transformations.

The Number i and Complex Numbers, Square Root of a Complex Number, Conjugate and Modulus, Properties of the Argument, Euler Form and De Moivre’s Theorem, Triangle Inequality, Quadratic Equations, Quadratic Expression: Graph and Sign, Polynomial Equations.

Matrices and their Order, Types of Matrices, Algebra of Matrices, Transpose; Symmetric and Skew-symmetric, Determinants / Minors and Cofactors, Area of a Triangle, Adjoint and Inverse of a Square Matrix, Elementary Row and Column Operations, Simultaneous Linear Equations.

Fundamental Principle of Counting, Permutations (Arrangements), Restricted Arrangements: Methods, Circular Permutations, Combinations (Selections), Standard Counting Results, Grouping and Distribution.

Binomial Theorem for a Positive Integral Index, General Term, Middle Terms and Greatest Coefficient, Properties of Binomial Coefficients, Methods for Sums of Binomial Coefficients, Simple Applications.

Sequences and Series, Arithmetic Progression (AP), Geometric Progression (GP), Infinite Geometric Series, Inserting Means between a and b, Relation between AM and GM, Arithmetico-Geometric Progression (AGP), Sums of Special Series.

Real Functions: Quick Review, Algebra of limits, Sandwich Theorem and Limits with [x], Continuity, Differentiation: Rules, Rate of Change of Quantities, Tangents and Normals, Increasing and Decreasing Functions, Maxima and Minima.

Integration as an Anti-derivative, Integration by Substitution, Integration using Trigonometric Identities, Integrals of Irrational Functions, Integration by Parts, Definite Integral and the Fundamental Theorem, Properties of Definite Integrals, Standard Results, Area under Curves.

Order / Degree and Solutions, Formation of a Differential Equation, Variables Separable, Homogeneous Differential Equations, Linear Differential Equations, Exact Differentials, Applications.

Distance / Section Formula and Area, Slope / Parallel and Perpendicular Lines, Distance / Foot and Image, Angle Bisectors of Two Lines, Circle: Tangent / Normal / Chord, Conic Sections: Focus and Directrix, Parabola: Tangents and Normals, Hyperbola, Standard Results for Conics.

Coordinates and Distance, Section Formula, Direction Cosines and Direction Ratios, Angle between Two Lines, Equation of a Line in Space, Skew Lines and Shortest Distance, Equation of a Plane, Angles and Distances with Planes, Coplanar Lines.

Vectors and Scalars, Addition and Scalar Multiplication, Components of a Vector, Section Formula and Collinearity, Scalar (Dot) Product, Vector (Cross) Product, Scalar Triple Product, Vector Triple Product.

Mean / Median and Mode, Range and Mean Deviation, Variance and Standard Deviation, Random Experiments / Sample Space and Events, Addition Theorem, Conditional Probability, Independent Events, Total Probability and Bayes’ Theorem, Random Variable and Probability Distribution.

Angles and Radian Measure, Trigonometric Functions and Basic Identities, Domain / Range / Period and Graphs, Compound Angles, Multiple and Sub-multiple Angles, Sum ⇄ Product Formulas, Trigonometric Equations, Inverse Trigonometric Functions, Properties of Inverse Trigonometric Functions.

Matter and Its Nature, Dalton’s Atomic Theory, Laws of Chemical Combination, Atomic and Molecular Masses, Mole Concept and Molar Mass, Percentage Composition and Formulae, Chemical Equations and Stoichiometry, Concentration of Solutions, Equivalent Concept / Normality and Titrations.

Gas Laws and the Absolute Temperature Scale, Partial Pressures and Diffusion of Gases, Real Gases: Deviation from Ideal Behaviour, Intermolecular Interactions, Solid State: Classification of Solids, Crystal Lattice / Unit Cell and Crystal Systems, Cubic Unit Cells and Packing Efficiency, Structures of Ionic Solids, Point Defects.

Electromagnetic Radiation and Planck’s Quantum Theory, Photoelectric Effect, Atomic Spectra: Spectrum of Hydrogen, Bohr’s Model of the Hydrogen Atom, Dual Nature of Matter and the Uncertainty Principle, Quantum Numbers, Shapes of s / p and d Orbitals, Filling of Orbitals: Aufbau / Pauli / Hund, Electronic Configuration: Extra Stability.

Kossel–Lewis Approach to Chemical Bonding, Limitations of the Octet Rule, Ionic (Electrovalent) Bond and Lattice Enthalpy, Bond Parameters, Polarity and Dipole Moment, VSEPR Theory: Shapes of Molecules, Hybridisation (s / p and d Orbitals), Molecular Orbital Theory (MOT), Hydrogen Bonding and Its Applications.

System / Surroundings and Properties, Internal Energy / Heat / Work: First Law, Heat Capacity, Enthalpy (H), Hess’s Law of Constant Heat Summation, Bond Enthalpy, Born–Haber Cycle / Lattice Enthalpy, Gibbs Energy and Spontaneity, ΔG° / Equilibrium Constant and Useful Work.

Solutions and Their Concentration, Solubility of Gases: Henry’s Law, Vapour Pressure and Raoult’s Law, Ideal and Non-ideal Solutions, Colligative Properties, Abnormal Molar Mass and van’t Hoff Factor.

Equilibrium: a Dynamic State, Equilibria in Physical Processes, Degree of Dissociation: ICE Method, Factors Affecting Equilibrium, Ionization of Water and the pH Scale, Weak Acids and Bases: Ostwald’s Dilution Law, Hydrolysis of Salts and pH of their Solutions, Acid–Base Indicators and Titration Curves, Solubility Equilibria of Sparingly Soluble Salts.

Oxidation and Reduction: Electronic Concept, Oxidation Number, Balancing Redox Equations, Electrochemical Cells: Daniell Cell, Nernst Equation / Equilibrium Constant and ΔG, Electrolysis and Faraday’s Laws, Conductance of Electrolytic Solutions, Batteries and Fuel Cells, Corrosion.

Rate of a Chemical Reaction, Rate Law / Rate Constant and Order, Molecularity and Mechanism, Integrated Rate Equations and Half-Life, Temperature Dependence: Arrhenius Equation, Collision Theory, Catalysis.

Adsorption, Freundlich Adsorption Isotherm, Colloids: True Solution / Colloid / Suspension, Surfactants and Micelles, Preparation and Purification of Colloids, Properties of Colloids, Emulsions.

Modern Periodic Law and the Long Form, Electronic Configuration and Blocks, Effective Nuclear Charge and Atomic Radius, Ionic Radius, Ionization Enthalpy, Electron Gain Enthalpy, Electronegativity, Valence / Oxidation States / Anomalies, Periodic Trends and Chemical Reactivity.

Important Ores, Concentration of Ores, Calcination and Roasting, Calcination, Roasting, Extraction of Iron: Blast Furnace, Extraction of Copper and Zinc, Electrochemical Principles: Aluminium, Refining of Crude Metals.

Position of Hydrogen in the Periodic Table, Dihydrogen: Isotopes and Preparation, Properties and Uses of Dihydrogen, Hydrides, Water and Heavy Water, Hydrogen Peroxide / H2O2.

Group 1 and Group 2: Properties, Chemical Reactivity, Oxides / Hydroxides / Halides and Salts of Oxoacids, Anomalous Li and Be: Diagonal Relationship, Compounds of Sodium, Compounds of Calcium.

Aluminium Chloride and Alums, Silica / Silicones / Silicates and Zeolites, Dinitrogen / Ammonia and Nitric Acid, Nitrogen is anomalous: N≡N, Oxoacids of Phosphorus, Dioxygen and Ozone, Oxoacids of Sulphur, Chlorine / HCl / Bleaching Powder, Interhalogens and Halogen Oxoacids.

Trends in the First (3d) Series, Oxidation States and Their Stability, Magnetism / Colour / Catalysis / Complexes / Alloys, Oxoanions of Chromium: K2Cr2O7, Oxoanions of Manganese: KMnO4, Inner Transition (f-Block) Elements.

Werner’s Theory, IUPAC Nomenclature (Mononuclear Complexes), Isomerism in Coordination Compounds, Bonding: Valence Bond Theory, Crystal Field Theory (CFT), Stability of Complexes, Metal Carbonyls, Importance and Applications.

Atmospheric Pollution: Troposphere, Stratospheric Pollution: Ozone Depletion, Water and Soil Pollution, Industrial Waste / Control and Green Chemistry, Smog, Eutrophication.

Methods of Purification, Chromatography, Qualitative Analysis: Detection of Elements, Quantitative Analysis (Basic Principles), Dumas / Kjeldahl and Carius Methods, Empirical and Molecular Formula.

Carbon: Hybridisation / σ and π Bonds / Shapes, Classification of Organic Compounds, Isomerism, Stereoisomers with Two Chiral Centres, Nucleophiles and Electrophiles, Resonance and the Resonance (Mesomeric) Effect, Electromeric Effect and Hyperconjugation, Hydrogen Bonding Effects, Types of Organic Reactions.

Classification / Isomerism and Nomenclature, Alkanes: Preparation and Physical Properties, Alkanes: Reactions, Conformations of Ethane and Butane, Alkenes: Structure / Properties / Preparation, Alkynes, Benzene: Structure and Preparation, Benzene: Electrophilic Substitution, Directive Influence of Groups on Benzene.

Classification and Nomenclature, Nature of the C–X Bond, Preparation of Haloalkanes and Haloarenes, Haloalkanes: Nucleophilic Substitution, Elimination: Substitution or Elimination?, Reaction with Metals: Grignard Reagent, Haloarenes: Nucleophilic Substitution, Haloarenes: Electrophilic Substitution, Polyhalogen Compounds and the Environment.

Alcohols / Phenols / Ethers: Classes and Structure, Preparation of Alcohols and Phenols, Acidity of Alcohols and Phenols, Reactions of Alcohols, Reactions of Phenols, Reduction / Oxidation and Tests, Aldol and Cannizzaro Reactions, Carboxylic Acids: Preparation and Acidity, Carboxylic Acids: Reactions.

Amines: Structure / Classes and Names, Preparation of Amines, Basic Character of Amines, Reactions and Tests of Amines, Electrophilic Substitution in Aniline, Diazonium Salts.

Polymers and their Classification, Types of Polymerisation, Thermoplastics and Thermosetting Polymers, Important Polymers: Monomers and Uses, Cellulose / Bakelite and Biodegradable Polymers, Natural Rubber and Vulcanisation.

Carbohydrates: Classification, Glucose: Structure, Reactions of Glucose, Disaccharides and Polysaccharides, Amino Acids and Proteins, Enzymes, Vitamins, Nucleic Acids, Hormones (General Introduction).

Drug–Target Interaction, Therapeutic Action of Classes of Drugs, Antacids, Antihistamines, Antimicrobials, Artificial Sweeteners, Soaps / Detergents and Cleansing Action.

Detection of N / S and Halogens (Lassaigne’s Test), Tests for Functional Groups, Chemistry of Preparations, Titrimetric Analysis, Qualitative Salt Analysis: Anions, Qualitative Salt Analysis: Cations, Chemical Principles of the Experiments.

Units and Systems of Units, Least Count: Vernier Calipers and Screw Gauge, Screw gauge (micrometer), Significant Figures, Arithmetic with s.f., Errors in Measurement, Combination (Propagation) of Errors, Dimensions of Physical Quantities, Dimensional Analysis and its Applications.

Frame of Reference and Motion, Acceleration: Constant and Variable, Position–Time / Velocity–Time and a–t Graphs, Free Fall and Vertical Motion, Scalars and Vectors, Unit Vectors and Resolution of a Vector, Motion in a Plane, Relative Velocity, Circular Motion.

Force and Inertia, Momentum and Newton’s Second Law, Impulse, Newton’s Third Law of Motion, Equilibrium of Concurrent Forces, Constraint Relations and Spring Forces, Apparent Weight in a Lift, Non-Inertial Frames, Dynamics of Uniform Circular Motion.

Work Done by a Constant Force, Work Done by a Variable Force, Kinetic Energy and the Work–Energy Theorem, Potential Energy and the U–x Curve, Conservative and Non-conservative Forces, Potential Energy of a Spring, Power, Motion in a Vertical Circle, Collisions in One and Two Dimensions.

Rigid Body: Kinds of Motion, COM of Standard Bodies, Angular Kinematics, Moment of a Force: Torque and Couple, Moment of Inertia and Radius of Gyration, Rotation about a Fixed Axis: Dynamics, Conservation of Angular Momentum, Rolling Without Slipping, Linear vs Rotational Motion: Comparison.

Universal Law of Gravitation, Kepler’s Laws of Planetary Motion, Acceleration due to Gravity (g) and its Variation, Gravitational Field and Potential, Gravitational Potential Energy, Escape Speed, Motion of a Satellite: Orbital Speed and Period, Energy of an Orbiting Satellite.

Elastic Behaviour of Solids, Elastic Moduli: Young’s / Bulk and Rigidity, Liquids in Accelerated and Rotating Containers, Viscosity / Stokes’ Law and Terminal Velocity, Applications of Bernoulli’s Principle, Excess Pressure across a Curved Surface: Drops and Bubbles, Thermal Expansion, Heat Transfer: Conduction, Newton’s Law of Cooling.

Thermal Equilibrium / Zeroth Law and Temperature, First Law of Thermodynamics, Specific Heat Capacity of a Gas, Isothermal and Adiabatic Processes, Second Law of Thermodynamics, Kelvin–Planck statement, Reversible and Irreversible Processes, Irreversible process, Carnot Engine and its Efficiency.

Equation of State of a Perfect Gas, Work Done on Compressing a Gas, Kinetic Theory of Gases: Assumptions, Concept of Pressure: Pressure of an Ideal Gas, Kinetic Interpretation of Temperature; RMS Speed, Degrees of Freedom, Law of Equipartition of Energy, Application to Specific Heat Capacities of Gases, Mean Free Path.

Periodic and Oscillatory Motion, Velocity and Acceleration in SHM, Simple Pendulum: Time Period, Damped Oscillations, Displacement Relation for a Progressive Wave, Energy / Intensity and the Pressure Wave, Reflection and Transmission of Waves, Standing Waves in Organ Pipes (Air Columns), Doppler Effect in Sound.

Electric Charges, Forces between Multiple Charges, Continuous Charge Distribution, Electric Flux, Applications of Gauss’s Law, Potential Calculations, Conductors and Insulators, Parallel Plate Capacitor, Energy Stored in a Capacitor.

Electric Current, Drift Velocity and Mobility, Temperature Dependence of Resistance, Electrical Energy / Power and Heating Effect, EMF and Internal Resistance of a Cell, Combination of Cells in Series and Parallel, Kirchhoff’s Laws and their Applications, Wheatstone Bridge, Metre Bridge (Slide Wire Bridge).

Magnetic Field of a Current, Field due to a Straight Wire, Long Straight Solenoid, Charge in a Uniform Magnetic Field, Parallel Currents: the Ampere, Moving Coil Galvanometer (MCG), Bar Magnet as a Solenoid; Field Lines, Magnetisation / H / χ and μ, Temperature and Magnetic Properties.

Magnetic Flux and Faraday’s Law, Lenz’s Law and Conservation of Energy, Motional EMF, Eddy Currents, Self and Mutual Inductance, Alternating Current: Peak / RMS and Average, Resonance, Power / Power Factor / Wattless Current, Transformer.

Displacement Current, Maxwell’s Equations, EM Waves and their Characteristics, Energy and Momentum of EM Waves, Electromagnetic Spectrum and Applications, Microwaves, Infrared, X-rays.

Reflection of Light; Plane Mirror, Refraction of Light at a Plane Surface, Refraction at a Spherical Surface, Combinations of Lenses and Mirrors, Dispersion by a Prism, Compound Microscope, Wavefront and Huygens’ Principle, Young’s Double-Slit Experiment (YDSE), Polarisation and Polaroids.

Dual Nature of Radiation; Electron Emission, Photoelectric Effect: Hertz and Lenard, Experimental Study: Results, Einstein’s Photoelectric Equation, The Photon: Energy / Momentum / Flux, Matter Waves: de Broglie Relation.

Alpha-particle Scattering Experiment, Rutherford’s Nuclear Model of the Atom, Bohr Model, Composition and Size of the Nucleus, Mass–Energy Relation and Mass Defect, Binding Energy and the Ebn–A Curve, Law of Radioactive Decay, Nuclear Fission, Nuclear Fusion.

Semiconductors: Energy Bands, Intrinsic and Extrinsic Semiconductors, Semiconductor Diode: I–V Characteristics, Diode as a Rectifier, Zener Diode and Voltage Regulator, Optoelectronic Devices, Logic Gates.

Errors and Significant Figures, Vernier Callipers and Screw Gauge, Mechanics and Properties of Matter, Heat and Sound, Current Electricity, Optics, Semiconductor Devices, Maximum Error in Standard Experiments.