JEE Important Topics

Cheatsheet Content

### Mathematics: Calculus - **Limits, Continuity, and Differentiability:** - L'Hopital's Rule - First Principle of Differentiation - Mean Value Theorems (Rolle's, Lagrange's) - **Applications of Derivatives:** - Tangents and Normals - Maxima and Minima (first and second derivative test) - Rate of Change - **Indefinite Integration:** - Integration by Substitution, Parts, Partial Fractions - Standard Integrals - **Definite Integration:** - Properties of Definite Integrals - Area Under Curves (using definite integrals) - **Differential Equations:** - Formation of Differential Equations - Solution of First Order and First Degree (Variable Separable, Homogeneous, Linear) ### Mathematics: Algebra - **Complex Numbers:** - Argand Plane, Modulus, Argument - Euler's Form, De Moivre's Theorem - Roots of Unity - **Quadratic Equations:** - Nature of Roots, Relation between Roots and Coefficients - Common Roots, Transformation of Equations - **Sequences and Series:** - Arithmetic Progression (AP), Geometric Progression (GP), Harmonic Progression (HP) - Arithmetico-Geometric Progression (AGP) - Sum to N terms of special series - **Permutations and Combinations:** - Fundamental Principle of Counting - Permutations (arrangements) - Combinations (selections) - **Binomial Theorem:** - General Term, Middle Term - Properties of Binomial Coefficients - Applications to Summation of Series - **Matrices and Determinants:** - Types of Matrices, Operations - Determinant properties, Adjoint, Inverse - Solving System of Linear Equations (Cramer's Rule, Matrix Method) ### Mathematics: Coordinate Geometry - **Straight Lines:** - Various forms of lines, Slope, Intercepts - Distance of a point from a line, Angle between lines - Family of lines, Concurrency - **Circles:** - Various forms of equations, Tangent, Normal - Chord of Contact, Pair of Tangents - Radical Axis, Radical Centre - **Parabola:** - Standard equation, Focus, Directrix, Latus Rectum - Tangents and Normals - **Ellipse:** - Standard equation, Eccentricity, Foci, Directrices - Tangents and Normals - **Hyperbola:** - Standard equation, Eccentricity, Foci, Directrices - Tangents and Normals ### Physics: Mechanics - **Kinematics:** - Motion in 1D, 2D, 3D - Relative Motion, Projectile Motion - **Newton's Laws of Motion:** - Free Body Diagrams - Friction, Pulley Systems - **Work, Energy, and Power:** - Work-Energy Theorem - Conservation of Mechanical Energy - Power - **Rotational Motion:** - Moment of Inertia - Torque, Angular Momentum (Conservation) - Rolling Motion - **Gravitation:** - Newton's Law of Gravitation - Gravitational Potential Energy, Escape Velocity - Kepler's Laws - **Simple Harmonic Motion (SHM):** - Equation of SHM, Velocity, Acceleration - Energy in SHM, Simple Pendulum ### Physics: Electromagnetism - **Electrostatics:** - Coulomb's Law, Electric Field, Electric Potential - Gauss's Law and its Applications - Capacitance, Dielectrics, Energy Stored - **Current Electricity:** - Ohm's Law, Resistance, Resistivity - Kirchhoff's Laws - Wheatstone Bridge, Potentiometer - **Magnetic Effects of Current:** - Biot-Savart Law, Ampere's Law - Force on a moving charge and current-carrying conductor - Torque on a current loop, Galvanometer - **Electromagnetic Induction (EMI):** - Faraday's Laws, Lenz's Law - Self and Mutual Inductance - AC Generator - **Alternating Current (AC):** - RMS and Average Values - LC, LR, RC, LCR Series Circuits (Resonance) - Power in AC Circuits, Transformers ### Physics: Optics & Modern Physics - **Ray Optics:** - Reflection and Refraction at plane and spherical surfaces - Lenses, Prisms, Optical Instruments (Microscope, Telescope) - **Wave Optics:** - Huygens' Principle - Interference (Young's Double Slit Experiment) - Diffraction (Single Slit) - **Dual Nature of Matter and Radiation:** - Photoelectric Effect (Einstein's Equation) - De Broglie Wavelength - **Atomic Physics:** - Bohr's Model of Hydrogen Atom - Energy Levels, Spectral Series - **Nuclear Physics:** - Radioactivity (Alpha, Beta, Gamma Decay) - Half-life, Nuclear Fission and Fusion ### Chemistry: Physical Chemistry - **Atomic Structure:** - Bohr's Model, Quantum Numbers - Aufbau Principle, Hund's Rule, Pauli Exclusion Principle - Electronic Configuration - **Chemical Bonding and Molecular Structure:** - Lewis Structures, VSEPR Theory - Hybridization, Molecular Orbital Theory (MOT) - Dipole Moment - **Gaseous State:** - Ideal Gas Equation, Gas Laws - Kinetic Theory of Gases - Real Gases (Van der Waals Equation) - **Chemical Thermodynamics:** - First Law of Thermodynamics, Enthalpy - Hess's Law, Bond Energies - Spontaneity, Gibbs Free Energy - **Chemical Equilibrium:** - Law of Mass Action, Equilibrium Constant ($K_c, K_p$) - Le Chatelier's Principle - **Ionic Equilibrium:** - Acids and Bases (Arrhenius, Bronsted-Lowry, Lewis) - pH, Buffer Solutions, Solubility Product - **Redox Reactions and Electrochemistry:** - Oxidation Numbers - Electrochemical Cells (Galvanic, Electrolytic) - Nernst Equation, Kohlrausch's Law - **Chemical Kinetics:** - Rate of Reaction, Order and Molecularity - Integrated Rate Laws (Zero, First Order) - Activation Energy, Arrhenius Equation ### Chemistry: Inorganic Chemistry - **Periodic Classification and Periodicity:** - Modern Periodic Table, Periodic Trends (Atomic Radii, Ionization Enthalpy, Electronegativity) - **p-Block Elements:** - General Characteristics, Trends in Groups 13-18 - Important compounds (e.g., Boron compounds, Nitrogen compounds, Sulfur compounds, Halogens) - **d- and f-Block Elements (Transition and Inner Transition):** - Electronic Configuration, Oxidation States - Properties (Colour, Magnetic Properties, Catalytic Properties) - Lanthanoids and Actinoids - **Coordination Compounds:** - Werner's Theory, IUPAC Nomenclature - Isomerism, VBT, CFT (Crystal Field Theory) - Stability of Coordination Compounds - **Metallurgy:** - Principles of Metal Extraction (Concentration, Reduction, Refining) - Important Ores and Extraction Processes ### Chemistry: Organic Chemistry - **General Organic Chemistry (GOC):** - IUPAC Nomenclature - Isomerism (Structural, Stereoisomerism) - Electronic Effects (Inductive, Resonance, Hyperconjugation) - Acidity and Basicity of Organic Compounds - **Hydrocarbons:** - Alkanes, Alkenes, Alkynes (Preparation, Reactions) - Aromatic Hydrocarbons (Benzene: Preparation, Electrophilic Substitution) - **Halogen Containing Organic Compounds:** - Haloalkanes and Haloarenes (Preparation, Nucleophilic Substitution, Elimination Reactions) - **Oxygen Containing Organic Compounds:** - Alcohols, Phenols, Ethers (Preparation, Reactions) - Aldehydes and Ketones (Preparation, Nucleophilic Addition, Oxidation, Reduction) - Carboxylic Acids and their Derivatives (Preparation, Reactions) - **Nitrogen Containing Organic Compounds:** - Amines (Basicity, Preparation, Reactions) - Diazonium Salts - **Biomolecules:** - Carbohydrates (Monosaccharides, Disaccharides, Polysaccharides) - Amino Acids, Proteins (Structure) - Nucleic Acids (DNA, RNA) - **Polymers:** - Classification, Polymerization (Addition, Condensation) - Important Polymers and their uses - **Chemistry in Everyday Life:** - Drugs, Food Preservatives, Cleansing Agents