KEAM Syllabus and Exam Pattern

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• Mechanics

  Kinematics, Dynamics, Energy, Per KEAM Official Notification

  ~1 marks
  • Kinematics — Motion in 1D/2D/3D, Projectile, Circular, Relative Motion
  • Newton's Laws, Friction, Work-Energy-Power, Circular Motion, Gravitation
  • Rotational Mechanics — Torque, Angular Momentum, Moment of Inertia, Rolling
  • Properties of Matter — Elasticity, Fluid Mechanics, Surface Tension, Viscosity
  • SHM, Oscillations, Waves, Sound, Doppler Effect, Beats, Resonance
  • Heat & Thermodynamics — Laws, Calorimetry, Heat Transfer, Kinetic Theory
  • Mechanical Engineering Topics (for GATE — Machine Design, TOM, SOM, FMS)
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• Electrodynamics & Optics

  Electrostatics, Magnetism, Optics, Per KEAM Official Notification

  ~1 marks
  • Electrostatics — Coulomb's Law, Electric Field, Potential, Capacitance, Dielectrics
  • Current Electricity — Ohm's Law, Kirchhoff, Circuits, Wheatstone Bridge, Potentiometer
  • Magnetism — Biot-Savart, Ampere's Law, Magnetic Field, Earth's Magnetism
  • EMI & AC — Faraday, Lenz, Transformer, Generator, AC Circuits, RLC
  • Optics — Reflection, Refraction, Lens, Prism, Wave Optics, Diffraction, Polarization
  • Modern Physics — Photoelectric Effect, Bohr Model, Atomic, Nuclear, Radioactivity
  • Semiconductors & Electronics — Diode, Transistor, Logic Gates, Communication
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• Mechanics (Physics)

  Kinematics, Dynamics, Rotational Motion, Gravitation

  ~4 marks
  • Kinematics — Motion in 1D/2D/3D, Projectile, Circular, Relative Motion
  • Newton's Laws of Motion, Friction, Pseudo Forces, Constraint Motion
  • Work, Energy, Power, Kinetic and Potential Energy, Conservation
  • Circular Motion, Banking of Roads, Conical Pendulum, Vertical Circle
  • Rotational Mechanics — Torque, Angular Momentum, Moment of Inertia, Rolling
  • Gravitation — Kepler's Laws, Universal Law, Gravitational Field, Satellite
  • Elasticity — Stress, Strain, Hooke's Law, Young's Modulus, Bulk Modulus, Shear Modulus
  • Fluid Mechanics — Pressure, Buoyancy, Bernoulli's Theorem, Viscosity, Surface Tension
  • Mechanical Waves — SHM, Oscillations, Spring, Pendulum, Wave Motion, Sound
  • Properties of Matter, Units, Dimensions, Error Analysis, Significant Figures
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• Heat & Thermodynamics (Physics)

  Heat Transfer, Laws, Kinetic Theory

  ~4 marks
  • Heat and Temperature — Scales, Thermometry, Thermal Expansion
  • Calorimetry — Specific Heat, Latent Heat, Heat Capacity
  • Heat Transfer — Conduction, Convection, Radiation, Thermal Conductivity
  • Thermodynamics — Zeroth, First, Second, Third Law, PV Diagram, Work, Heat
  • Kinetic Theory of Gases — Pressure, RMS Speed, Mean Free Path, Degrees of Freedom
  • Gas Laws — Boyle's, Charles', Gay-Lussac's, Ideal Gas Equation, Real Gases
  • Thermodynamic Processes — Isothermal, Adiabatic, Isobaric, Isochoric, Cyclic
  • Heat Engines, Refrigerators, Carnot Cycle, Entropy
  • Calorimetry, Phase Changes, Latent Heat, Triple Point, Critical Point
  • Thermal Radiation, Black Body, Stefan-Boltzmann Law, Wien's Displacement Law
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• Optics & Modern Physics

  Light, EM Waves, Relativity, Quantum, Nuclear

  ~4 marks
  • Ray Optics — Reflection, Refraction, Total Internal Reflection, Prism
  • Lenses and Mirrors — Image Formation, Formulae, Power, Combination
  • Optical Instruments — Microscope, Telescope, Magnifying Glass, Camera
  • Wave Optics — Interference, Diffraction, Polarization, Young's Double Slit
  • Electromagnetic Waves — EM Spectrum, Properties, Maxwell's Equations
  • Photoelectric Effect — Einstein's Equation, Work Function, Threshold Frequency
  • Bohr's Atomic Model, Hydrogen Spectrum, Atomic Structure
  • Nuclear Physics — Atomic Structure, Radioactivity, Half-Life, Decay
  • Modern Physics — Photoelectric Effect, X-rays, Lasers, Optical Fibers
  • Semiconductor Physics — Diode, Transistor, Logic Gates, Communication
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• Electrostatics & Current Electricity

  Charges, Fields, Circuits, EM

  ~4 marks
  • Electrostatics — Coulomb's Law, Electric Field, Electric Potential, Equipotential
  • Capacitance, Capacitors, Series-Parallel, Energy Stored, Dielectrics
  • Current Electricity — Ohm's Law, Resistance, Resistivity, Conductivity
  • Circuits — Series, Parallel, Combination, Kirchhoff's Laws, Wheatstone Bridge
  • DC Circuits, EMF, Internal Resistance, Potentiometer, Meter Bridge
  • Heating Effect of Current, Joule's Law, Electric Power, Commercial Units
  • Magnetic Effects — Biot-Savart Law, Ampere's Law, Solenoid, Cyclotron
  • Electromagnetic Induction — Faraday's Law, Lenz's Law, Self/Mutual Induction
  • AC Circuits — RLC, Resonance, Impedance, Transformer, Generator, AC
  • EM Waves, Maxwell's Equations, Communication Systems, Modulation
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• Modern Physics

  Quantum, Nuclear, Solid State, Electronics

  ~4 marks
  • Quantum Mechanics — Wave-Particle Duality, De Broglie Wavelength, Heisenberg
  • Schrodinger Equation (Qualitative), Quantum Numbers, Atomic Orbitals
  • Nuclear Physics — Nuclear Structure, Binding Energy, Mass Defect
  • Radioactivity — Alpha, Beta, Gamma Decay, Half-Life, Decay Constant
  • Nuclear Reactions — Fission, Fusion, Chain Reaction, Atomic Reactor
  • Particle Physics — Quarks, Leptons, Bosons, Hadrons, Standard Model
  • Solid State Physics — Crystal Structure, Band Theory, Semiconductors
  • Electronics — Diodes, Transistors, Amplifiers, Oscillators, Logic Gates
  • Digital Electronics — Boolean Algebra, Logic Families, Flip-Flops
  • Communication — AM, FM, AM Modulation, Antenna, Propagation of EM Waves
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• Units, Measurement & Practical Physics

  ~4 marks
  • Units and Dimensions — SI Units, Dimensional Analysis, Conversion
  • Measurement — Vernier Caliper, Screw Gauge, Significant Figures, Errors
  • Vectors — Addition, Subtraction, Dot Product, Cross Product, Resolution
  • Kinematics — 1D, 2D, 3D Motion, Projectile, Relative Velocity, Circular
  • Newton's Laws — Inertia, F=ma, Action-Reaction, Free Body Diagrams
  • Friction, Work, Energy, Power, Collisions (Elastic, Inelastic)
  • Gravitation — Universal Law, g, Escape Velocity, Kepler's Laws, Satellites
  • Properties of Matter — Elasticity, Fluid Statics, Surface Tension, Viscosity
  • Oscillations and Waves — SHM, Wave Motion, Sound, Doppler Effect
  • Practical Physics — Lab Equipment, Experiments, Error Analysis, Data Interpretation
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• Electromagnetism

  Magnetic, EM Induction, AC, Communication

  ~4 marks
  • Magnetic Effects — Magnetic Field, Oersted, Ampere, Biot-Savart, Right-Hand Rule
  • Magnetic Materials — Dia, Para, Ferromagnetic, Hysteresis, Curie Temperature
  • Earth's Magnetism — Magnetic Declination, Dip, Magnetic Maps, Compass
  • Electromagnetic Induction (EMI) — Faraday's Experiments, Faraday's Law, Lenz's Law
  • Eddy Currents, Self-Inductance, Mutual Inductance, Inductors, Transformers
  • AC Generator, Motor, Alternating Current, RMS, Peak Value, Phase
  • AC Circuits — R, L, C, RLC Series/Parallel, Resonance, Impedance, Power Factor
  • EM Waves — Generation, Properties, Spectrum, Applications, Communication
  • Communication Systems — Modulation (AM, FM, PM), Antenna, Propagation
  • Modern Physics Applications — X-ray, Laser, Fibre Optics, Solar Cell
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• Atomic Structure & Chemical Bonding

  Quantum, Periodic Table, Bonds

  ~4 marks
  • Atomic Structure — Bohr's Model, Quantum Numbers, Electronic Configuration, Shapes
  • Atomic Models — Thomson, Rutherford, Bohr, Schrodinger (Qualitative), Heisenberg
  • Photoelectric Effect, Wave-Particle Duality, de Broglie Wavelength, Heisenberg
  • Periodic Table — Periodicity, Atomic Radius, Ionization Energy, Electronegativity
  • Chemical Bonding — Ionic, Covalent, Coordinate, Hydrogen Bonding, Metallic
  • Hybridization — sp, sp2, sp3, sp3d, sp3d2 with Examples (CH4, NH3, H2O)
  • VSEPR Theory, VBT (Valence Bond Theory), MOT (Molecular Orbital Theory)
  • Bond Parameters — Bond Length, Angle, Energy, Polarity, Dipole Moment
  • Resonance, Hyperconjugation, Inductive Effect, Mesomeric Effect, Electromeric
  • Lattice Energy, Born-Haber Cycle, Fajan's Rules, Polarizing Power
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• States of Matter & Solutions

  Gas, Liquid, Solid, Solutions, Colloids

  ~4 marks
  • Gas Laws — Boyle's Law, Charles' Law, Gay-Lussac's Law, Avogadro's Law, Ideal Gas
  • Kinetic Molecular Theory — Postulates, Derivation of Gas Laws, RMS Speed
  • Real Gases — van der Waals Equation, Critical Constants, Liquefaction
  • Liquid State — Properties, Vapor Pressure, Surface Tension, Viscosity
  • Solid State — Crystalline, Amorphous, Crystal Systems, Bravais Lattices
  • Unit Cell, Coordination Number, Packing Efficiency, Density Calculations
  • Imperfections in Solids — Point Defects, Schottky, Frenkel, F-Centers
  • Solutions — Types, Concentration (Molarity, Molality, Normality, Formality)
  • Colligative Properties — Lowering of VP, Elevation of BP, Depression of FP, Osmotic
  • Colloids — Types, Preparation, Properties, Emulsions, Gels, Tyndall Effect
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• Thermodynamics, Equilibrium, Kinetics

  Energetics, Rate, Ionic

  ~4 marks
  • Thermodynamics — System, Surroundings, Internal Energy, Enthalpy, Entropy, Gibbs
  • First Law of Thermodynamics — Work, Heat, Energy Conservation, Enthalpy
  • Thermochemistry — Enthalpy of Formation, Combustion, Neutralization, Solution
  • Second Law of Thermodynamics — Entropy, Spontaneity, Carnot Cycle
  • Chemical Equilibrium — Equilibrium Constant (Kc, Kp), Le Chatelier's Principle
  • Ionic Equilibrium — Acids, Bases, pH, Buffer Solutions, Indicators, Solubility Product
  • Chemical Kinetics — Rate Law, Order, Molecularity, Integrated Rate Equations
  • Arrhenius Equation, Activation Energy, Catalysis, Collision Theory
  • Electrochemistry — Cells, EMF, Nernst Equation, Electrolysis, Faraday's Laws
  • Colligative Properties of Electrolytes — van't Hoff Factor, Osmotic Pressure
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• Inorganic Chemistry

  Periodic Table, s/p/d/f Block, Coordination, Metallurgy

  ~4 marks
  • Periodic Table — Classification, Periodicity, Properties, s/p/d/f Block Elements
  • Hydrogen, s-Block Elements — Properties, Compounds, Uses (Na, K, Ca, Mg)
  • p-Block Elements — Group 13-18, Properties, Compounds, Allotropes
  • Boron, Carbon, Nitrogen, Oxygen, Phosphorus, Sulfur, Halogen Families
  • Noble Gases — Properties, Compounds, Clathrates, Xenon Compounds
  • d-Block / Transition Elements — Properties, Variable Valency, Catalysis
  • f-Block Elements — Lanthanides, Actinides, Properties, Uses
  • Coordination Compounds — Werner's Theory, IUPAC, Isomerism, Bonding
  • Metallurgy — Ore, Mineral, Extraction, Refining, Alloys, Properties
  • Environmental Chemistry, Pollution, Green Chemistry, Bioinorganic Chemistry
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• Organic Chemistry I

  Basic, Hydrocarbons, Functional Groups, Reactions

  ~4 marks
  • Organic Chemistry Basics — Tetravalent Carbon, Hybridization, Bonding, Isomerism
  • IUPAC Nomenclature — Alkanes, Alkenes, Alkynes, Functional Groups
  • Isomerism — Structural (Chain, Position, Functional, Metamerism, Tautomerism)
  • Stereoisomerism — Geometrical (cis-trans), Optical (d, l, meso), E/Z, R/S
  • Alkanes — Properties, Reactions (Substitution, Combustion, Cracking, Reforming)
  • Alkenes — Properties, Reactions (Addition, Polymerization, Markownikoff, Peroxide)
  • Alkynes — Properties, Reactions (Addition, Acidity, Ozonolysis, Polymerization)
  • Aromatic Hydrocarbons — Benzene, Aromaticity, Electrophilic Substitution (EAS)
  • Alkyl/Aryl Halides — Properties, Reactions (Substitution, Elimination, Grignard)
  • Alcohols, Phenols, Ethers — Properties, Reactions, Acidity, Preparation
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• Organic Chemistry II

  Aldehydes, Amines, Biomolecules, Polymers, Practical

  ~4 marks
  • Aldehydes and Ketones — Carbonyl Compounds, Nucleophilic Addition, Aldol
  • Carboxylic Acids — Properties, Acidity, Reactions, Derivatives (Esters, Amides)
  • Amines — Properties, Basicity, Reactions, Diazonium Salts, Aniline
  • Amino Acids, Peptides, Proteins — Structure, Properties, Zwitterions, Isoelectric
  • Carbohydrates — Mono, Di, Polysaccharides, Glucose, Fructose, Starch, Cellulose
  • Lipids, Fats, Oils, Waxes, Phospholipids, Steroids, Cholesterol
  • Vitamins, Hormones, Enzymes, Nucleic Acids (DNA, RNA), Genetic Code
  • Polymers — Natural, Synthetic, Addition, Condensation, Plastics, Rubber, Fibers
  • Chemistry in Everyday Life — Drugs, Food Preservatives, Cleansing Agents, Cosmetics
  • Practical Organic Chemistry — Qualitative Analysis, Quantitative Analysis, Lab Tests
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• Organic Chemistry III

  Spectroscopy, Biomolecules, Polymers, Chemistry in Action

  ~4 marks
  • Spectroscopy — UV, IR, NMR (Principles, Applications to Organic Compounds)
  • Reaction Mechanisms — SN1, SN2, E1, E2, Addition, Elimination, Substitution
  • Named Reactions — Aldol, Cannizzaro, Perkin, Reformatsky, Wittig, Diels-Alder
  • Reagents — Grignard, LDA, NaBH4, LiAlH4, PBr3, SOCl2, KMnO4, K2Cr2O7
  • Heterocyclic Compounds — Furan, Pyrrole, Thiophene, Pyridine, Indole, Quinoline
  • Biomolecules — Amino Acids, Proteins, Enzymes, Carbohydrates, Nucleic Acids
  • Drugs and Pharmaceuticals — Analgesics, Antipyretics, Antibiotics, Antiseptics
  • Polymers — Classification, Polymerization, Natural and Synthetic Polymers
  • Chemistry in Industries — Petroleum, Petrochemicals, Pharmaceuticals, Dyes, Paints
  • Environmental Chemistry — Pollution, Water Treatment, Green Chemistry, Waste
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• Algebra (Advanced)

  Sets, Relations, Functions, Complex Numbers, P&C

  ~4 marks
  • Sets, Relations, Functions, Venn Diagrams, Equivalence Relations
  • Complex Numbers — Algebra, Argand Plane, Modulus-Argument, De Moivre's
  • Quadratic Equations, Polynomials, Identities, Factorization, Remainder Theorem
  • Sequences and Series — AP, GP, HP, Sum, Special Series, Method of Differences
  • Permutations and Combinations, Binomial Theorem, Multinomial Theorem
  • Probability — Conditional, Bayes, Independent Events, Random Variables
  • Matrices and Determinants — Types, Operations, Inverse, Cramer's Rule
  • Linear Algebra — Vector Spaces, Eigenvalues, Linear Programming, Graph Theory
  • Logarithms, Antilogarithms, Partial Fractions, Induction, Mathematical Reasoning
  • Number Theory — Divisibility, Modular Arithmetic, Fermat's, Wilson's Theorem
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• Trigonometry (Advanced)

  Ratios, Identities, Equations, Inverse, Heights

  ~4 marks
  • Trigonometric Ratios (sin, cos, tan, cot, sec, cosec) — Sign Conventions
  • Trigonometric Identities — Pythagorean, Sum-Difference, Product-to-Sum
  • Trigonometric Equations — General Solutions, Specific Solutions
  • Inverse Trigonometric Functions — sin^-1, cos^-1, tan^-1, Properties
  • Heights and Distances — Angle of Elevation, Depression, Problems
  • Properties of Triangles — Sine Rule, Cosine Rule, Half-Angle, Napier Analogy
  • Trigonometric Series — Taylor Series, Maclaurin Series for sin, cos
  • Multiple and Sub-multiple Angles — sin 2θ, cos 2θ, sin 3θ, cos 3θ
  • Conditional Trigonometric Identities, Maxima and Minima
  • Heights and Distances — Bearing, Compass, Survey Problems, Real-World Applications
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• Coordinate Geometry (Advanced)

  2D/3D, Conics, Vectors, Transformations

  ~4 marks
  • Straight Lines — Slope, Equation, Distance, Angle Between Lines, Family of Lines
  • Circles — Standard Form, General Form, Tangent, Normal, Chord of Contact, Pole-Polar
  • Conic Sections — Parabola, Ellipse, Hyperbola (Standard Forms, Focus, Directrix, Eccentricity)
  • 3D Coordinate Geometry — Distance, Section Formula, Direction Cosines, Ratios
  • Plane and Line in 3D — Equation, Angle, Distance, Symmetric Form
  • Sphere, Cone, Cylinder — Equations, Tangent Plane, Generator, Curved Surface
  • Vectors — Types, Addition, Subtraction, Dot, Cross, Triple Product
  • Vector Algebra — Position Vector, Section Formula, Projection, Resolution
  • Coordinate Transformations — Translation, Rotation, Reflection, Scaling
  • Locus, Curve Tracing, Parametric Equations, Applications to Motion
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• Calculus (Advanced)

  Limits, Derivatives, Integration, Differential Equations

  ~4 marks
  • Limits — Algebraic, Trigonometric, Logarithmic, Exponential, L'Hopital's Rule
  • Continuity, Discontinuity, Types of Discontinuity, Intermediate Value Theorem
  • Differentiation — First Principles, Product, Quotient, Chain Rule, Implicit
  • Applications of Derivatives — Tangent, Normal, Maxima, Minima, Rate of Change
  • Higher-Order Derivatives, Successive Differentiation, Leibnitz Theorem
  • Integration — Indefinite, Definite, Methods (Substitution, Parts, Partial Fractions)
  • Applications of Integration — Areas, Volumes, Arc Length, Surface Area
  • Differential Equations — First Order, First Degree, Second Order, Exact Equations
  • Differential Equations Applications — Population Growth, Newton's Law of Cooling
  • Integral Calculus — Beta, Gamma Functions, Multiple Integrals, Improper Integrals
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• Probability & Statistics (Advanced)

  Probability, Stats, Linear Programming

  ~4 marks
  • Probability — Classical, Axiomatic, Conditional, Independent Events, Bayes
  • Random Variables — Discrete, Continuous, PMF, PDF, Expectation, Variance
  • Probability Distributions — Binomial, Poisson, Normal, Geometric, Exponential
  • Statistics — Mean, Median, Mode, Standard Deviation, Variance, Skewness, Kurtosis
  • Correlation and Regression — Pearson, Spearman, Least Squares, Coefficient
  • Sampling Methods — Random, Stratified, Systematic, Cluster, Multistage
  • Hypothesis Testing — Null, Alternative, t-test, z-test, Chi-square, F-test, ANOVA
  • Linear Programming — Formulation, Graphical Method, Simplex Method, Duality
  • Game Theory — Pure, Mixed Strategy, Saddle Point, Dominance, Two-Person Zero-Sum
  • Operations Research — Transportation, Assignment, Sequencing, Replacement, Inventory
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• Modern Mathematics

  Sets, Relations, Boolean Algebra, Number Theory

  ~4 marks
  • Sets, Relations, Functions, Equivalence Relations, Partial Order
  • Boolean Algebra — Boolean Operations, Laws, Simplification, Karnaugh Maps
  • Logic — Propositional, Predicate, Quantifiers, Truth Tables, Inference Rules
  • Graph Theory — Types, Euler, Hamiltonian, Coloring, Planar, Trees, BFS, DFS
  • Number Theory — Primes, GCD, LCM, Modular Arithmetic, Fermat, Wilson, Euler
  • Combinatorics — Permutation, Combination, Pigeonhole, Inclusion-Exclusion
  • Group Theory — Definitions, Subgroups, Cyclic, Permutation, Lagrange, Cosets
  • Mathematical Induction, Recurrence Relations, Generating Functions
  • Linear Algebra — Matrices, Determinants, Eigenvalues, Eigenvectors, Systems
  • Topology (Basic) — Open Sets, Closed Sets, Continuity, Compactness
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