KEAM Syllabus 2027: Physics, Chemistry, Mathematics Topics, Subject-Wise Weightage and PDF Download

Physical World; Units and Measurements; Significant Figures; Error Analysis; Dimensional Analysis and Applications.

Motion in a Straight Line; Motion in a Plane; Relative Motion; Projectile Motion; Uniform Circular Motion.

Newton’s First, Second, and Third Laws; Inertia; Momentum and Impulse; Static and Kinetic Friction; Circular Motion Dynamics; Constraint Motion.

Work-Energy Theorem; Kinetic and Potential Energy; Conservation of Mechanical Energy; Power; Elastic and Inelastic Collisions.

Centre of Mass and its Motion; Torque; Angular Momentum; Conservation of Angular Momentum; Moment of Inertia; Parallel and Perpendicular Axis Theorems; Rolling Motion.

Universal Law of Gravitation; Gravitational Field and Potential; Acceleration Due to Gravity and its Variation; Escape Velocity; Orbital Velocity; Geostationary and Polar Satellites; Kepler’s Laws.

Stress and Strain; Hooke’s Law; Fluid Pressure; Buoyancy; Bernoulli’s Theorem; Viscosity; Stokes’ Law; Surface Tension; Thermal Expansion; Specific Heat; Heat Transfer (Conduction, Convection, Radiation); Newton’s Law of Cooling.

Zeroth, First, and Second Laws of Thermodynamics; Isothermal and Adiabatic Processes; Carnot Engine and Efficiency; Heat Pumps and Refrigerators; Entropy.

Ideal Gas Equation; Kinetic Theory Postulates; RMS, Average, and Most Probable Speeds; Degrees of Freedom; Law of Equipartition of Energy; Mean Free Path.

Simple Harmonic Motion; Spring-Mass System; Simple Pendulum; Damped and Forced Oscillations; Resonance; Transverse and Longitudinal Waves; Speed of Sound; Beats; Doppler Effect; Standing Waves in Strings and Pipes.

Coulomb’s Law; Electric Field Lines; Gauss’s Law; Electric Potential and Potential Energy; Equipotential Surfaces; Capacitors and Capacitance; Energy Stored in Capacitors; Dielectrics and Polarisation.

Ohm’s Law; Resistivity and Conductivity; Drift Velocity; Kirchhoff’s Current and Voltage Laws; Wheatstone Bridge; Meter Bridge; Potentiometer; EMF and Internal Resistance; Cells in Series and Parallel.

Biot-Savart Law; Ampere’s Circuital Law; Solenoid and Toroid; Force on a Moving Charge in Magnetic Field; Galvanometer and its Conversion; Magnetic Properties of Matter; Hysteresis.

Faraday’s Laws of Electromagnetic Induction; Lenz’s Law; Induced EMF and Current; Self and Mutual Inductance; AC Generator; AC Circuits with R, L, and C; Resonance; Power Factor; Transformers.

Displacement Current; Maxwell’s Equations; Properties of Electromagnetic Waves; Electromagnetic Spectrum — Radio, Microwave, Infrared, Visible, UV, X-rays, and Gamma Rays; their Uses and Properties.

Ray Optics: Reflection at Plane and Curved Surfaces; Refraction; Total Internal Reflection; Lenses; Prism; Optical Instruments (Microscope and Telescope). Wave Optics: Huygens’ Principle; Young’s Double Slit Experiment; Single Slit Diffraction; Polarisation by Malus’s Law.

Photoelectric Effect; Einstein’s Photoelectric Equation; Work Function; Threshold Frequency; de Broglie Hypothesis; Wave-Particle Duality; Davisson-Germer Experiment; Heisenberg’s Uncertainty Principle.

Rutherford’s Nuclear Model; Bohr’s Model; Hydrogen Spectrum; Mass Defect and Binding Energy; Nuclear Fission and Fusion; Radioactivity (Alpha, Beta, Gamma Decay); Half-Life; Radioactive Decay Law.

Semiconductors and Energy Bands; Intrinsic and Extrinsic Semiconductors; p-n Junction Diode; Zener Diode; Rectifiers; Transistors (NPN and PNP); Transistor as Switch and Amplifier; Logic Gates (AND, OR, NOT, NAND, NOR).

Mole Concept; Stoichiometry; Limiting Reagent; Concentration Terms (Molarity, Molality, Mole Fraction); Empirical and Molecular Formulae.

Thomson and Rutherford Models; Bohr’s Atomic Model; Quantum Numbers; Electronic Configuration; Aufbau Principle; Hund’s Rule; Pauli Exclusion Principle.

Ionic and Covalent Bonds; VSEPR Theory; Valence Bond Theory; Hybridisation; Molecular Orbital Theory (H₂, O₂, N₂); Hydrogen Bond; Bond Parameters.

Gas Laws (Boyle’s, Charles’, Avogadro’s); Ideal Gas Equation; Kinetic Molecular Theory; van der Waals Equation; Real Gases; Liquefaction; Liquid State Properties.

System and Surroundings; Enthalpy; Hess’s Law; Bond Enthalpies; Entropy; Gibbs Free Energy; Spontaneity of Chemical Reactions.

Law of Mass Action; Equilibrium Constant (Kc and Kp); Le Chatelier’s Principle; Ionic Equilibrium; pH and pOH; Buffer Solutions; Solubility Product (Ksp); Common Ion Effect.

Oxidation States; Balancing Redox Equations by Ion-Electron Method; Disproportionation Reactions.

Types of Solutions; Raoult’s Law; Colligative Properties — Relative Lowering of Vapour Pressure, Elevation of Boiling Point, Depression of Freezing Point, Osmotic Pressure; Van’t Hoff Factor.

Galvanic Cells; Standard Electrode Potential; Electrochemical Series; Nernst Equation; Electrolytic Cells; Faraday’s Laws of Electrolysis; Kohlrausch’s Law; Conductance; Corrosion.

Rate of Reaction; Rate Laws; Order and Molecularity; Integrated Rate Equations (Zero, First, Second Order); Half-Life; Arrhenius Equation; Activation Energy; Collision Theory.

Adsorption (Physical and Chemical); Catalysis; Types of Colloids; Emulsions; Tyndall Effect; Coagulation; Brownian Motion; Protective Colloids.

Occurrence of Metals; Concentration of Ores (Gravity Separation, Froth Flotation, Leaching); Extraction by Roasting, Calcination, Smelting, and Electrolysis; Refining Methods; Extraction of Aluminium, Copper, Zinc, and Iron.

Alkali Metals (Li, Na, K) — Properties and Compounds; Alkaline Earth Metals (Mg, Ca) — Properties and Compounds; Anomalous Properties of Lithium and Beryllium; Important Compounds: NaOH, Na₂CO₃, NaHCO₃, CaO, Ca(OH)₂, CaCO₃.

Groups 13–18 Elements; Allotropy of Carbon, Phosphorus, and Sulphur; Oxides and Oxyacids of N, P, S, and Cl; Interhalogen Compounds; Noble Gases and their Compounds; Trends in Properties.

Transition Metals; Variable Oxidation States; Magnetic Properties; Catalytic Activity; Colour of Complexes; Lanthanides and Actinides; Important Compounds: KMnO₄ and K₂Cr₂O₇ — Preparation, Properties, and Uses.

Werner’s Theory; IUPAC Nomenclature of Complexes; Isomerism (Structural and Stereo); Valence Bond Theory; Crystal Field Theory; Stability Constants; Applications in Medicine, Industry, and Analysis.

Classification and Nomenclature of Organic Compounds; Inductive, Resonance, Mesomeric, and Hyperconjugation Effects; Reaction Intermediates (Carbocation, Carbanion, Free Radical); Types of Organic Reactions (Substitution, Addition, Elimination).

Alkanes — Free Radical Substitution (Halogenation); Alkenes — Electrophilic Addition (Markovnikov and Anti-Markovnikov); Alkynes — Addition Reactions; Arenes — Benzene, Aromaticity, Electrophilic Aromatic Substitution.

SN1 and SN2 Mechanisms; Elimination Reactions; Optical Activity and Stereochemistry; Environmental Effects of Haloalkanes.

Preparation and Physical Properties of Alcohols; Dehydration of Alcohols; Acidity of Phenols; Reactions of Phenols; Williamson Synthesis of Ethers; Industrial Uses.

Nucleophilic Addition; Aldol Condensation; Cannizzaro Reaction; Clemmensen and Wolff-Kishner Reductions; Tollens’ and Fehling’s Tests; Acid Derivatives — Esters, Amides, Acyl Chlorides; Relative Acidity of Carboxylic Acids.

Amines — Classification, Preparation, and Basicity; Diazonium Salts and Coupling Reactions; Cyanides and Isocyanides.

Carbohydrates (Monosaccharides, Disaccharides, Polysaccharides); Proteins and Enzymes; Nucleic Acids (DNA and RNA); Vitamins; Addition and Condensation Polymers; Rubber and Nylon; Drugs and Medicines; Cleansing Agents.

Types of Sets; Set Operations (Union, Intersection, Complement); Cartesian Product; Relations and Types; Functions (One-One, Onto, Bijection); Composite and Inverse Functions; Real-Valued Functions and Their Graphs.

Algebra of Complex Numbers; Modulus and Argument; Polar Form; De Moivre’s Theorem; nth Roots of Complex Numbers; Quadratic Equations and Nature of Roots; Cube Roots of Unity.

Types of Matrices; Matrix Operations; Transpose and Symmetric Matrices; Adjoint and Inverse; Properties of Determinants; Cramer’s Rule; Solution of System of Linear Equations.

Fundamental Counting Principle; Permutations (with and without Repetition); Circular Permutations; Combinations; Pascal’s Triangle; Binomial Theorem for Positive Integer Index; General and Middle Terms.

Arithmetic Progression — nth Term and Sum; Geometric Progression — nth Term and Sum; Harmonic Progression; Sum of Special Series (Σn, Σn², Σn³); AM-GM-HM Inequality; Infinite GP.

Solution of Linear Inequalities in One and Two Variables; Graphical Representation; Statements and Truth Values; Logical Connectives; Contrapositive, Converse, and Inverse of a Statement; Validity of Arguments.

Trigonometric Ratios and Identities; Periodicity; Compound Angle Formulae; Multiple and Sub-Multiple Angles; Product-to-Sum and Sum-to-Product Formulae; General Solutions of Trigonometric Equations; Inverse Trigonometric Functions — Domain, Range, and Principal Values; Properties of Inverse Functions.

Slope; Various Forms of Line Equations; Angle Between Two Lines; Distance of a Point from a Line; Family of Lines; Circles (Standard and General Equations); Parabola; Ellipse; Hyperbola — Standard Equations, Foci, Directrix, Eccentricity, and Asymptotes.

Direction Cosines and Direction Ratios; Equations of Lines in 3D (Vector and Cartesian Forms); Equations of Planes; Angle Between Lines and Planes; Distance of a Point from a Plane; Coplanarity of Lines; Shortest Distance Between Skew Lines.

Types of Vectors; Addition and Subtraction; Scalar (Dot) Product; Vector (Cross) Product; Scalar Triple Product; Geometrical Applications; Area of Triangle and Parallelogram Using Vectors.

Limits of Algebraic, Trigonometric, and Exponential Functions; Left-Hand and Right-Hand Limits; Continuity at a Point; Differentiability; Chain Rule; Implicit Differentiation; Derivatives of Logarithmic, Exponential, and Parametric Functions.

Rate of Change; Equations of Tangent and Normal; Increasing and Decreasing Functions; Maxima and Minima (First and Second Derivative Tests); Rolle’s Theorem; Mean Value Theorem.

Integration by Substitution; Integration by Parts; Integration Using Partial Fractions; Definite Integrals; Properties of Definite Integrals; Area Under a Curve; Area Between Two Curves; Fundamental Theorem of Calculus.

Order and Degree of Differential Equations; Formation of Differential Equations; Variable Separable Method; Homogeneous Differential Equations; Linear Differential Equations of First Order.

Mean; Median; Mode; Variance; Standard Deviation; Random Experiments; Sample Space; Events; Classical Probability; Addition Theorem; Conditional Probability; Multiplication Theorem; Bayes’ Theorem; Binomial Distribution.