JEE Main 2027 Syllabus

Sets, Relations and Functions

Sets and their algebra, power set · Types of relations, equivalence relations · One-one, into and onto functions, composition of functions

Complex Numbers and Quadratic Equations

Argand diagram, algebra of complex numbers, modulus and argument · Quadratic equations in real and complex systems · Roots and coefficients, nature of roots

Matrices and Determinants

Algebra and types of matrices · Determinants of order two and three, area of triangle · Adjoint and inverse, consistency and solution of linear equations

Permutations and Combinations

Fundamental principle of counting · P(n, r) and C(n, r), simple applications

Binomial Theorem and its Simple Applications

Positive integral index · General term and middle term

Sequence and Series

Arithmetic and geometric progressions · Insertion of means, relation between AM and GM

Limit, Continuity and Differentiability

Real-valued functions, inverse functions, graphs · Limits, continuity, differentiability · Differentiation rules, derivatives up to order two · Rate of change, monotonicity, maxima and minima

Integral Calculus

Anti-derivative, substitution, parts, partial fractions · Fundamental theorem and properties of definite integrals · Areas bounded by simple curves

Differential Equations

Order and degree · Separation of variables · Homogeneous and linear equations of first order

Co-ordinate Geometry

Distance and section formulae, locus, slope · Straight line forms, angle between lines, centroid, orthocentre, circumcentre · Circle and standard conics: parabola, ellipse, hyperbola

Three Dimensional Geometry

Points in space, distance, section formula · Direction ratios and cosines, angle between lines · Equation of a line, skew lines, shortest distance

Vector Algebra

Vectors and scalars, addition · Components in 2D and 3D · Scalar and vector products

Statistics and Probability

Mean, median, mode, variance, standard deviation, mean deviation · Addition and multiplication theorems, Bayes' theorem · Probability distribution of a random variable

Trigonometry

Trigonometrical identities and functions · Inverse trigonometrical functions and properties

Units and Measurements

SI units, fundamental and derived units · Least count, significant figures, errors · Dimensional analysis and applications

Kinematics

Motion in a straight line, graphs, relative velocity · Projectile and uniform circular motion

Laws of Motion

Newton's laws, momentum, impulse · Friction · Dynamics of circular motion, banked roads

Work, Energy and Power

Work-energy theorem, power · Spring energy, conservation of mechanical energy · Vertical circle, collisions in one and two dimensions

Rotational Motion

Centre of mass · Torque, angular momentum and conservation · Moment of inertia, parallel and perpendicular axes, rigid body equations

Gravitation

Universal law, variation of g · Kepler's laws · Potential, escape velocity, satellites

Properties of Solids and Liquids

Stress-strain, elastic moduli · Pascal's law, viscosity, Bernoulli's principle · Surface tension · Calorimetry, thermal expansion, heat transfer

Thermodynamics

Zeroth and first law · Isothermal and adiabatic processes · Second law, reversible and irreversible processes

Kinetic Theory of Gases

Gas equation, kinetic interpretation of temperature · RMS speed, degrees of freedom, equipartition · Mean free path

Oscillations and Waves

SHM, spring and simple pendulum · Wave motion, superposition, standing waves, beats

Electrostatics

Coulomb's law, electric field, dipole · Gauss's law and applications · Potential, equipotential surfaces · Dielectrics, capacitors

Current Electricity

Drift velocity, Ohm's law, resistivity · Cells, internal resistance · Kirchhoff's laws, Wheatstone bridge, metre bridge

Magnetic Effects of Current and Magnetism

Biot-Savart and Ampere's laws · Force on charges and conductors, galvanometer · Magnetic dipole, para-, dia- and ferromagnetism

Electromagnetic Induction and Alternating Currents

Faraday's and Lenz's laws, inductance · AC circuits, LCR, resonance · Generator and transformer

Electromagnetic Waves

Displacement current · Electromagnetic spectrum and applications

Optics

Mirrors, lenses, refraction, prism, total internal reflection · Microscope and telescope · Huygens principle, interference, diffraction, polarization

Dual Nature of Matter and Radiation

Photoelectric effect and Einstein's equation · de Broglie relation

Atoms and Nuclei

Rutherford and Bohr models, hydrogen spectrum · Mass defect, binding energy, fission and fusion

Electronic Devices

Semiconductor diode, LED, photodiode, solar cell, Zener diode · Logic gates: OR, AND, NOT, NAND, NOR

Experimental Skills

Vernier calipers, screw gauge, simple pendulum · Young's modulus, surface tension, viscosity · Meter bridge, Ohm's law, galvanometer · Focal length, prism deviation, refractive index · Diode and Zener characteristics

Some Basic Concepts in Chemistry

Laws of chemical combination, mole concept · Empirical and molecular formulae, stoichiometry

Atomic Structure

Bohr model, hydrogen spectrum, de Broglie, uncertainty principle · Quantum numbers, orbitals, Aufbau, Pauli, Hund

Chemical Bonding and Molecular Structure

Ionic and covalent bonding, VSEPR, hybridization · Molecular orbital theory, bond order · Hydrogen bonding

Chemical Thermodynamics

First law, enthalpy, Hess's law · Entropy, Gibbs energy and spontaneity

Solutions

Concentration terms, Raoult's law · Colligative properties, van't Hoff factor

Equilibrium

Physical and chemical equilibrium, Kp and Kc, Le Chatelier · Ionic equilibrium, pH, buffers, solubility product

Redox Reactions and Electrochemistry

Oxidation number, balancing redox · Conductance, Kohlrausch's law · Galvanic cells, Nernst equation, fuel cells

Chemical Kinetics

Rate law, order and molecularity · Zero and first-order reactions, Arrhenius theory

Classification of Elements and Periodicity in Properties

Periodic law and trends · Radii, ionization enthalpy, electron gain enthalpy

p-Block Elements

Group 13 to 18 general trends · Unique behaviour of first element in each group

d- and f-Block Elements

Transition element properties · K2Cr2O7 and KMnO4 · Lanthanoids and actinoids

Coordination Compounds

Werner's theory, nomenclature, isomerism · Valence bond and crystal field ideas, colour, magnetism

Purification and Characterisation of Organic Compounds

Crystallization, distillation, chromatography · Qualitative and quantitative analysis

Some Basic Principles of Organic Chemistry

Hybridization, isomerism, IUPAC nomenclature · Electronic effects, carbocations, reaction types

Hydrocarbons

Alkanes, alkenes, alkynes · Aromaticity, electrophilic substitution

Organic Compounds Containing Halogens

Preparation, properties, substitution mechanisms · Chloroform, iodoform, freons, DDT

Organic Compounds Containing Oxygen

Alcohols, phenols, ethers · Aldehydes and ketones, named reactions · Carboxylic acids

Organic Compounds Containing Nitrogen

Amines and basic character · Diazonium salts

Biomolecules

Carbohydrates, proteins, vitamins · Nucleic acids, hormones

Principles Related to Practical Chemistry

Detection of elements and functional groups · Mohr's salt, potash alum, acetanilide preparation · Titrations and salt analysis of listed ions · Enthalpy and kinetic experiments