JEE Main Class 12 Syllabus 2027 - Download Free PDF

Units

Topics Covered

Relations and Functions

Types of relations: Reflexive, symmetric, transitive, equivalence; one-to-one and onto functions, inverse functions.

Inverse Trigonometric Functions

Definitions, principal value branches, graphs, elementary properties.

Matrices

Types of matrices, operations, invertible matrices, row/column operations, uniqueness of inverse.

Determinants

Properties, minors, cofactors, adjoint, inverse, solving linear equations, area of a triangle.

Continuity and Differentiability

Continuity, differentiability, chain rule, derivatives of inverse trig. functions, logarithmic differentiation, parametric forms, second-order derivatives.

Applications of Derivatives

Rate of change, increasing/decreasing functions, tangents, normals, maxima/minima, approximation.

Integrals

Integration methods: substitution, by parts, partial fractions, definite integrals, properties, Fundamental Theorem of Calculus.

Applications of Integrals

Areas under curves (lines, circles, parabolas, ellipses), area between curves.

Differential Equations

Order and degree, formation and solution (separation of variables, homogeneous, linear differential equations).

Vectors

Magnitude, direction cosines/ratios, types of vectors, dot and cross products, scalar triple product.

Three-dimensional Geometry

Cartesian and vector equations of lines and planes, angles, distance between lines, point-plane distance.

Linear Programming

Formulation, graphical solutions, feasible/infeasible regions and solutions, optimization problems.

Probability

Conditional probability, Bayes’ theorem, random variables, probability distributions, mean, variance, Binomial distribution.

Units

Topics Covered

Units and Measurements

SI units, fundamental and derived units, dimensional analysis, significant figures

Kinematics

Motion in a straight line and plane, projectile motion, circular motion

Laws of Motion

Newton’s laws, friction (static, kinetic, rolling), conservation of momentum

Work, Energy, and Power

Work-energy theorem, kinetic and potential energy, mechanical energy conservation

Rotational Motion

Torque, angular momentum, conservation of angular momentum, moment of inertia

Gravitation

Universal law, satellite motion, escape velocity

Properties of Solids and Fluids

Stress-strain, Hooke's law, Bernoulli’s principle, viscosity, surface tension

Thermodynamics

Zeroth, First, and Second laws, heat, work, internal energy, entropy

Kinetic Theory of Gases

Perfect gas equation, degrees of freedom, law of equipartition

Oscillations and Waves

SHM (time period, energy), wave motion, standing waves, beats

Electrostatics

Coulomb’s law, electric field, potential, Gauss’s law, capacitors, dielectrics

Current Electricity

Ohm’s law, resistivity, conductivity, Kirchhoff’s laws, Wheatstone bridge

Magnetic Effects of Current and Magnetism

Biot-Savart law, Ampere’s law, force on conductors, Earth’s magnetic field

Electromagnetic Induction and Alternating Currents

Faraday’s and Lenz’s laws, AC circuits, transformers, generators

Electromagnetic Waves

Displacement current, electromagnetic spectrum

Optics

Reflection, refraction, interference, diffraction, polarization

Dual Nature of Matter and Radiation

Photoelectric effect, Einstein’s equation, de Broglie hypothesis

Atoms and Nuclei

Bohr’s model, energy levels, radioactivity, binding energy

Electronic Devices

Semiconductor diodes, I-V characteristics, logic gates

Unit

Topics Covered

Solid State

Types of solids, unit cell, packing efficiency, density, point defects, electrical/magnetic properties, band theory.

Solutions

Concentration, solubility of gases, Raoult’s law, colligative properties, abnormal molecular mass, Van’t Hoff factor.

Electrochemistry

Conductance, Kohlrausch’s law, EMF, Nernst equation, dry cell, fuel cells, corrosion, Gibbs energy relation.

Chemical Kinetics

Rate of reaction, factors affecting rate, order and molecularity, integrated rate equations (zero/first order).

Coordination Compounds

Ligands, IUPAC nomenclature, Werner’s theory, VBT, CFT, isomerism, applications in analysis and extraction.

Haloalkanes and Haloarenes

Nomenclature, reactions, uses, environmental impact of DDT, Freons, etc.

Alcohols, Phenols, and Ethers

Nomenclature, preparation, properties, dehydration, acidic nature of phenols, electrophilic substitution.

Aldehydes, Ketones, and Carboxylic Acids

Nomenclature, preparation, nucleophilic addition, alpha hydrogen reactivity, acidity, properties, and uses.

Organic Compounds Containing Nitrogen

Amines (classification, preparation, properties), diazonium salts, and their synthetic importance.

Biomolecules

Carbohydrates, proteins, nucleic acids, vitamins, enzymes, and their biological roles.

Chapters

Topics

Calculus

Integral Calculus: Definite integrals, applications of integrals.

Differential Equations: Formation and Solutions

Algebra

Matrices and Determinants: Solving systems of linear equations.

Probability: Bayes' theorem, binomial distribution

Vectors and 3D Geometry

Equations of lines and planes

Chapters

Topics

Electrostatics

Gauss's law, electric field and potential, capacitors.

Current Electricity

Ohm's law, Kirchhoff's laws, Wheatstone bridge.

Magnetic Effects of Current and Magnetism

Biot-Savart law, Ampere's law, magnetic force, Earth's magnetism.

Optics

Reflection, refraction, interference, diffraction, polarization.

Thermodynamics and Kinetic Theory

Laws of thermodynamics, specific heats, molecular speeds.

Modern Physics

Photoelectric effect, atomic models, nuclear reactions.

Chapters

Topics

Physical Chemistry

Electrochemistry: Nernst equation, galvanic cells.

Chemical Kinetics: Reaction order, rate constants.

Inorganic Chemistry

Coordination Compounds: VBT, CFT, and ligands.