KEAM

Units and Measurement

SI units, dimensional analysis, error analysis, significant figures.

Kinematics

Motion in a straight line and plane, projectile, relative velocity, circular motion.

Laws of Motion

Newton's laws, friction, dynamics, banking, conservation of momentum.

Work, Energy and Power

Work-energy theorem, conservative forces, potential energy, collisions.

Motion of System of Particles and Rigid Body

Centre of mass, torque, angular momentum, moment of inertia, rolling motion.

Gravitation

Universal law, Kepler's laws, gravitational potential, satellites, escape velocity.

Mechanics of Solids and Fluids

Elasticity, Hooke's law, Pascal's and Bernoulli's principles, viscosity, surface tension.

Heat and Thermodynamics

Thermal expansion, calorimetry, gas laws, kinetic theory, first and second laws of thermodynamics.

Oscillations and Simple Harmonic Motion

SHM equations, energy in SHM, simple and physical pendulum, damped/forced oscillation.

Waves

Transverse and longitudinal waves, superposition, beats, standing waves, Doppler effect.

Electrostatics

Coulomb's law, electric field, Gauss's law, potential, capacitance, dielectrics.

Current Electricity

Ohm's law, Kirchhoff's laws, Wheatstone bridge, potentiometer, drift velocity.

Magnetic Effects of Current and Magnetism

Biot-Savart law, Ampere's law, force on conductor, galvanometer, Earth's magnetism.

Electromagnetic Induction and Alternating Current

Faraday's law, Lenz's law, RLC circuits, transformer, AC generator, resonance.

Electromagnetic Waves

Maxwell's equations, displacement current, EM spectrum and applications.

Optics

Ray optics — reflection, refraction, lenses, optical instruments; wave optics — interference, diffraction, polarization.

Dual Nature of Matter and Radiation

Photoelectric effect, Einstein's equation, de Broglie wavelength, Davisson-Germer.

Atomic Nucleus

Bohr's model, hydrogen spectrum, mass defect, fission, fusion, radioactive decay.

Solids and Semiconductor Devices

Energy bands, p-n junction, diode, transistor, logic gates.

Principles of Communication

Modulation (AM/FM), bandwidth, propagation, communication systems.

Some Basic Concepts of Chemistry

Mole concept, stoichiometry, empirical and molecular formula.

Structure of Atom

Atomic models, dual nature, quantum numbers, orbitals, electronic configuration.

Classification of Elements and Periodicity

Modern periodic law, periodic trends in properties.

Chemical Bonding and Molecular Structure

Ionic, covalent, hydrogen bonds, VSEPR, hybridization, MO theory.

States of Matter

Gas laws, kinetic theory, real gases, intermolecular forces, liquid state.

Chemical Thermodynamics

First law, enthalpy, Hess's law, second law, free energy, spontaneity.

Equilibrium

Chemical and ionic equilibrium, Kc, Kp, pH, buffers, Ksp.

Redox Reactions and Electrochemistry

Oxidation numbers, electrochemical cells, Nernst equation, conductance, batteries.

Chemical Kinetics

Rate, order, molecularity, integrated rate law, Arrhenius equation.

Surface Chemistry

Adsorption, catalysis, colloids, emulsions, Tyndall effect.

Hydrogen and s-Block Elements

Hydrogen, alkali and alkaline earth metals, key compounds and reactions.

p-Block Elements

Groups 13 to 18 — properties, oxoacids, anomalous behaviour, key compounds.

d- and f-Block Elements

Transition metals, lanthanoids, actinoids, properties, complex formation.

Coordination Compounds

Werner theory, IUPAC nomenclature, isomerism, VBT, CFT, applications.

General Principles and Processes of Isolation of Metals

Concentration, reduction, refining; thermodynamic principles; industrial processes.

Basic Principles of Organic Chemistry

IUPAC nomenclature, isomerism, electronic effects, reactive intermediates.

Hydrocarbons

Alkanes, alkenes, alkynes, aromatic — preparation, properties, mechanisms.

Organic Compounds with Halogens

Haloalkanes, haloarenes, SN1/SN2, elimination reactions.

Organic Compounds with Oxygen

Alcohols, phenols, ethers, aldehydes, ketones, carboxylic acids.

Organic Compounds with Nitrogen

Amines, diazonium salts, cyanides, nitro compounds.

Polymers

Classification, addition vs condensation polymerisation, important polymers.

Biomolecules

Carbohydrates, amino acids, proteins, vitamins, nucleic acids, hormones.

Environmental Chemistry

Air, water, soil pollution; greenhouse effect; ozone layer; green chemistry.

Chemistry in Everyday Life

Drugs, food additives, soaps and detergents.

Sets, Relations and Functions

Set operations, types of relations, domain/range, composition, invertibility.

Complex Numbers

Argand plane, modulus, polar form, De Moivre's theorem, roots of unity.

Quadratic Equations

Roots, nature, sum and product, equations reducible to quadratic.

Sequences and Series

AP, GP, HP, arithmetic-geometric series, sum of special series.

Permutations and Combinations

Counting principle, nPr, nCr, applications, circular arrangements.

Mathematical Induction and Binomial Theorem

PMI, binomial expansion, general/middle term, applications.

Matrices and Determinants

Operations, transpose, inverse, properties of determinants, system of linear equations.

Linear Inequations

Algebraic and graphical solutions in one and two variables.

Trigonometric Functions and Identities

Trig identities, sum/difference and multiple-angle formulas, transformations.

Trigonometric Equations

General solutions of trigonometric equations.

Inverse Trigonometric Functions

Domain, range, principal value, properties.

Solutions of Triangles

Sine and cosine rules, area of triangle, properties, heights and distances.

Straight Lines

Slope, equations of lines, angle between lines, distance from a point.

Pair of Straight Lines

Homogeneous and general second-degree equation representing two lines.

Circles

Equation of circle, position of point, tangent, normal, family of circles.

Conic Sections

Parabola, ellipse, hyperbola — equations, properties, tangents and normals.

Three-Dimensional Geometry

Direction cosines, lines, planes, distance and angle formulas.

Vectors

Vector operations, dot and cross products, scalar triple product, projection.

Statistics

Measures of dispersion — mean deviation, variance, standard deviation, coefficient of variation.

Probability

Conditional probability, Bayes' theorem, random variables, binomial distribution.

Limits and Continuity

Limit definition, standard limits, continuity tests, types of discontinuities.

Differentiation

Differentiation rules, chain rule, implicit/parametric, higher order derivatives.

Applications of Derivatives

Rate of change, tangent/normal, monotonicity, maxima/minima, approximations.

Integration

Indefinite integrals, by substitution/parts/partial fractions, definite integrals, properties.

Applications of Integrals

Area under curves, area between curves and lines.

Differential Equations

Order, degree, formation, variable separable, linear and homogeneous DEs.

Linear Programming

LPP formulation, graphical solution, feasible region, optimal value.