JEE Mains Syllabus 2027: Paper 1 & 2 Topics List, Important Chapters & Weightage

Unit 1: Sets, Relations and Functions

Sets and their representation; union, intersection and complement of sets and their algebraic properties; power set; relations, types of relations, equivalence relations, functions; one-one, into and onto functions; composition of functions

Unit 2: Complex Numbers and Quadratic Equations

Complex numbers as ordered pairs of reals; representation in the form a + ib and in a plane; Argand diagram; algebra of complex numbers; modulus and argument; quadratic equations in real and complex number systems; relations between roots and coefficients; nature of roots; formation of quadratic equations with given roots

Unit 3: Matrices and Determinants

Matrices, algebra of matrices, types of matrices; determinants and matrices of order two and three; evaluation of determinants; area of triangles using determinants; adjoint and inverse of a square matrix; test of consistency and solution of simultaneous linear equations using matrices

Unit 4: Permutations and Combinations

Fundamental principle of counting; permutations and combinations; meaning of P(n, r) and C(n, r); simple applications

Unit 5: Binomial Theorem and its Simple Applications

Binomial theorem for a positive integral index; general term and middle term; simple applications

Unit 6: Sequence and Series

Arithmetic and Geometric progressions; insertion of arithmetic and geometric means between two given numbers; relation between A.M. and G.M.

Unit 7: Limit, Continuity and Differentiability

Real-valued functions, algebra of functions (polynomial, rational, trigonometric, logarithmic, exponential); inverse functions; graphs of simple functions; limits, continuity, differentiability; differentiation of sum, difference, product, quotient; differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions; derivatives up to order two; applications of derivatives — rate of change, increasing/decreasing functions, maxima and minima

Unit 8: Integral Calculus

Integral as anti-derivative; fundamental integrals (algebraic, trigonometric, exponential, logarithmic); integration by substitution, by parts, by partial fractions; integration using trigonometric identities; standard integral forms (1/(x²+a²), 1/√(x²±a²), 1/(a²−x²), etc.); fundamental theorem of calculus; properties and evaluation of definite integrals; areas bounded by simple curves

Unit 9: Differential Equations

Ordinary differential equations, order and degree; solution by separation of variables; solution of homogeneous and linear differential equations of the type dy/dx + p(x)y = q(x)

Unit 10: Co-ordinate Geometry

Cartesian system, distance formula, section formula, locus and its equation; slope of a line, parallel and perpendicular lines, intercepts. Straight line: forms of equations, intersection of lines, angles between lines, concurrence of three lines, distance of a point from a line, centroid/orthocentre/circumcentre. Circle & Conic Sections: standard and general forms of a circle, radius and centre, circle with given diameter endpoints, intersection of line and circle, equations of parabola, ellipse and hyperbola in standard forms

Unit 11: Three Dimensional Geometry

Coordinates of a point in space, distance between two points, section formula, direction ratios and direction cosines, angle between two intersecting lines; equation of a line; skew lines and shortest distance between them

Unit 12: Vector Algebra

Vectors and scalars; addition of vectors; components of a vector in 2D and 3D; scalar and vector products

Unit 13: Statistics and Probability

Measures of dispersion; mean, median, mode of grouped/ungrouped data; standard deviation, variance, mean deviation. Probability: probability of an event, addition and multiplication theorems, Bayes' theorem, probability distribution of a random variable

Unit 14: Trigonometry

Trigonometric identities and functions; inverse trigonometric functions and their properties

Unit 1: Units and Measurements

Units of measurement, systems of units, SI units, fundamental and derived units, least count, significant figures, errors in measurement; dimensions, dimensional analysis and applications

Unit 2: Kinematics

Frame of reference, motion in a straight line, speed and velocity, uniform/non-uniform motion, average speed, instantaneous velocity, uniformly accelerated motion, velocity-time and position-time graphs, relative velocity; motion in a plane, projectile motion, uniform circular motion

Unit 3: Laws of Motion

Force and inertia, Newton's laws of motion, momentum, impulse; conservation of linear momentum and applications; equilibrium of concurrent forces; static and kinetic friction, laws of friction, rolling friction; dynamics of uniform circular motion — centripetal force, vehicle on level/banked road

Unit 4: Work, Energy and Power

Work by constant and variable force, kinetic and potential energy, work-energy theorem, power; potential energy of a spring, conservation of mechanical energy, conservative and non-conservative forces, motion in a vertical circle; elastic and inelastic collisions in one and two dimensions

Unit 5: Rotational Motion

Centre of mass of two-particle system and rigid body; torque, angular momentum, conservation of angular momentum; moment of inertia, radius of gyration, values for simple geometrical objects, parallel and perpendicular axes theorems; equilibrium of rigid bodies, rotational motion equations, comparison of linear and rotational motion

Unit 6: Gravitation

Universal law of gravitation; acceleration due to gravity and its variation with altitude/depth; Kepler's laws; gravitational potential energy and potential; escape velocity, satellite motion — orbital velocity, time period, energy

Unit 7: Properties of Solids and Liquids

Elastic behaviour, stress-strain, Hooke's law, Young's/bulk modulus, modulus of rigidity; fluid pressure, Pascal's law, viscosity, Stoke's law, terminal velocity, streamline/turbulent flow, critical velocity, Bernoulli's principle; surface energy and surface tension, angle of contact, drops/bubbles/capillary rise; heat, temperature, thermal expansion, specific heat, calorimetry, change of state, latent heat; conduction, convection, radiation

Unit 8: Thermodynamics

Thermal equilibrium, zeroth law, heat/work/internal energy; first law of thermodynamics, isothermal and adiabatic processes; second law of thermodynamics — reversible and irreversible processes

Unit 9: Kinetic Theory of Gases

Equation of state of a perfect gas, work done on compressing a gas; kinetic theory assumptions, concept of pressure, kinetic interpretation of temperature, RMS speed, degrees of freedom, law of equipartition of energy, specific heat capacities of gases, mean free path, Avogadro's number

Unit 10: Oscillations and Waves

Periodic motion, time period, frequency, displacement function, periodic functions; SHM and its equation, phase, spring oscillations, energy in SHM, simple pendulum; wave motion, longitudinal/transverse waves, wave speed, displacement relation, superposition, reflection, standing waves in strings/organ pipes, harmonics, beats

Unit 11: Electrostatics

Electric charges and conservation, Coulomb's law, superposition, continuous charge distribution; electric field, field lines, dipole, torque on dipole; electric flux, Gauss's law and applications (wire, sheet, shell); electric potential, potential energy, equipotential surfaces; conductors, insulators, dielectrics, polarization; capacitors, series/parallel combination, parallel plate capacitor, energy stored

Unit 12: Current Electricity

Drift velocity, mobility, Ohm's law, resistance, I-V characteristics; electrical energy and power, resistivity, conductivity, series/parallel resistors, temperature dependence; internal resistance, EMF, cells in series/parallel; Kirchhoff's laws, Wheatstone bridge, Metre bridge

Unit 13: Magnetic Effects of Current and Magnetism

Biot-Savart law, Ampere's law and applications (straight wire, solenoid); force on moving charge and current-carrying conductor, force between parallel currents, torque on current loop, moving coil galvanometer; magnetic dipole moment, bar magnet, magnetic field lines, dia/para/ferromagnetism, effect of temperature

Unit 14: Electromagnetic Induction and Alternating Currents

Faraday's law, induced EMF, Lenz's law, eddy currents, self/mutual inductance; AC peak/RMS values, reactance, impedance, LCR circuit, resonance, power in AC circuits, wattless current, AC generator, transformer

Unit 15: Electromagnetic Waves

Displacement current, characteristics of EM waves, transverse nature; electromagnetic spectrum and applications

Unit 16: Optics

Reflection, spherical mirrors, mirror formula; refraction, thin lens/lens maker formula, total internal reflection, magnification, power of lens, combination of lenses, refraction through prism, microscope and telescope; wave optics — Huygens' principle, interference (YDSE, fringe width), diffraction (single slit), polarization, Brewster's law, Polaroid

Unit 17: Dual Nature of Matter and Radiation

Photoelectric effect, Hertz and Lenard's observations, Einstein's photoelectric equation; de Broglie relation and matter waves

Unit 18: Atoms and Nuclei

Alpha-particle scattering, Rutherford's and Bohr's atomic models, energy levels, hydrogen spectrum; composition and size of nucleus, atomic masses, mass-energy relation, mass defect, binding energy per nucleon, nuclear fission and fusion

Unit 19: Electronic Devices

Semiconductors, p-n junction diode I-V characteristics, diode as rectifier, LED, photodiode, solar cell, Zener diode as voltage regulator; logic gates (OR, AND, NOT, NAND, NOR)

Unit 20: Experimental Skills

Vernier calipers, screw gauge, simple pendulum, metre scale, Young's modulus, surface tension, viscosity, speed of sound, specific heat, resistivity by metre bridge, Ohm's law, galvanometer figure of merit, focal length of mirrors/lens, prism deviation, refractive index, diode/Zener characteristics, component identification

Unit 1: Some Basic Concepts in Chemistry

Matter and its nature, Dalton's atomic theory, atom/molecule/element/compound; laws of chemical combination; atomic and molecular masses, mole concept, molar mass, percentage composition, empirical and molecular formulae; chemical equations and stoichiometry

Unit 2: Atomic Structure

Electromagnetic radiation, photoelectric effect, hydrogen spectrum; Bohr model — postulates, energy and radii of orbits, limitations; dual nature of matter, de Broglie relation, Heisenberg uncertainty principle; quantum mechanical model, atomic orbitals, quantum numbers, shapes of s/p/d orbitals, electron spin; Aufbau principle, Pauli's exclusion principle, Hund's rule, electronic configuration, stability of half-filled/filled orbitals

Unit 3: Chemical Bonding and Molecular Structure

Kossel-Lewis approach, ionic and covalent bonds; ionic bonding and lattice enthalpy; electronegativity, Fajan's rule, dipole moment, VSEPR theory and molecular shapes; valence bond theory, hybridization, resonance; molecular orbital theory, LCAO, bonding/antibonding orbitals, sigma/pi bonds, bond order/length/energy; metallic bonding, hydrogen bonding

Unit 4: Chemical Thermodynamics

System and surroundings, extensive/intensive properties, state functions, entropy, types of processes; first law — work, heat, internal energy, enthalpy, heat capacity, Hess's law, enthalpies of bond dissociation/combustion/formation/atomization/sublimation/phase transition/hydration/ionization/solution; second law — spontaneity, ΔS and ΔG as criteria; ΔG° and equilibrium constant

Unit 5: Solutions

Concentration expressions — molality, molarity, mole fraction, percentage; vapour pressure and Raoult's law, ideal/non-ideal solutions; colligative properties — relative lowering of vapour pressure, depression of freezing point, elevation of boiling point, osmotic pressure; molecular mass determination, abnormal molar mass, van't Hoff factor

Unit 6: Equilibrium

Concept of dynamic equilibrium; physical equilibria (solid-liquid, liquid-gas, gas-gas, solid-gas), Henry's law; chemical equilibrium — law of chemical equilibrium, Kp and Kc, ΔG and ΔG°, factors affecting equilibrium, Le Chatelier's principle; ionic equilibrium — weak/strong electrolytes, acid-base concepts (Arrhenius, Bronsted-Lowry, Lewis), ionization constants, pH scale, common ion effect, salt hydrolysis, solubility product, buffer solutions

Unit 7: Redox Reactions and Electrochemistry

Oxidation and reduction, redox reactions, oxidation number, balancing redox reactions; electrolytic and metallic conduction, molar conductivity, Kohlrausch's law; electrochemical cells — electrolytic and galvanic cells, electrode potentials, EMF, Nernst equation, cell potential and Gibbs energy, dry cell, lead accumulator, fuel cells

Unit 8: Chemical Kinetics

Rate of reaction, factors affecting rate; elementary and complex reactions, order and molecularity; rate law, rate constant; zero and first order reactions — differential/integral forms, half-life; effect of temperature, Arrhenius theory, activation energy; collision theory of bimolecular gaseous reactions

Unit 9: Classification of Elements and Periodicity in Properties

Modern periodic law, periodic table; s, p, d and f block elements; periodic trends — atomic/ionic radii, ionization enthalpy, electron gain enthalpy, valence, oxidation states, chemical reactivity

Unit 10: p-Block Elements

Group 13 to Group 18 — electronic configuration, periodic/group trends in physical and chemical properties, unique behaviour of the first element in each group

Unit 11: d- and f-Block Elements

Transition elements — configuration, occurrence, characteristics, physical properties, ionization enthalpy, oxidation states, atomic radii, colour, catalytic behaviour, magnetic properties, complex formation, interstitial compounds, alloy formation; preparation/properties/uses of K₂Cr₂O₇ and KMnO₄; lanthanoids and actinoids — configuration, oxidation states, lanthanoid contraction

Unit 12: Coordination Compounds

Introduction, Werner's theory, ligands, coordination number, denticity, chelation, IUPAC nomenclature, isomerism; valence bond approach, crystal field theory basics, colour and magnetic properties; importance in qualitative analysis, metal extraction, biological systems

Unit 13: Purification and Characterisation of Organic Compounds

Crystallization, sublimation, distillation, differential extraction, chromatography; qualitative detection of N, S, P, halogens; quantitative estimation of C, H, N, halogens, S, P; empirical and molecular formulae calculations

Unit 14: Some Basic Principles of Organic Chemistry

Tetravalency of carbon, shapes of molecules, hybridization; classification by functional groups; homologous series; structural and stereoisomerism; IUPAC/trivial nomenclature; covalent bond fission (homolytic/heterolytic), free radicals, carbocations, carbanions, electrophiles, nucleophiles; inductive effect, electromeric effect, resonance, hyperconjugation; substitution, addition, elimination, rearrangement reactions

Unit 15: Hydrocarbons

Classification, isomerism, IUPAC nomenclature, preparation, properties. Alkanes: conformations (Sawhorse, Newman), halogenation mechanism. Alkenes: geometrical isomerism, electrophilic addition mechanism, Markovnikov's/peroxide effect, ozonolysis, polymerization. Alkynes: acidic character, addition reactions, polymerization. Aromatic hydrocarbons: benzene structure and aromaticity, electrophilic substitution, halogenation, nitration, Friedel-Crafts alkylation/acylation, directive influence of substituents

Unit 16: Organic Compounds Containing Halogens

Preparation, properties, reactions; nature of C-X bond, substitution mechanisms; uses and environmental effects of chloroform, iodoform, freons, DDT

Unit 17: Organic Compounds Containing Oxygen

Alcohols, Phenols, Ethers: identification of 1°/2°/3° alcohols, dehydration mechanism; phenol acidity, electrophilic substitution, Reimer-Tiemann reaction; ether structure. Aldehydes and Ketones: carbonyl group nature, nucleophilic addition, reactivity comparison, HCN/NH₃ derivative addition, Grignard reagent, oxidation, reduction (Wolff-Kishner, Clemmensen), α-hydrogen acidity, aldol condensation, Cannizzaro reaction, haloform reaction, distinguishing tests. Carboxylic Acids: acidic strength and affecting factors

Unit 18: Organic Compounds Containing Nitrogen

Preparation, properties, reactions, uses. Amines: nomenclature, classification, structure, basic character, identification of 1°/2°/3° amines. Diazonium Salts: importance in synthetic organic chemistry

Unit 19: Biomolecules

Carbohydrates: classification, aldoses/ketoses, monosaccharides (glucose, fructose), constituent sugars of oligosaccharides. Proteins: α-amino acids, peptide bond, polypeptides, protein structure levels, denaturation, enzymes. Vitamins: classification and functions. Nucleic Acids: DNA/RNA constitution, biological functions. Hormones: general introduction

Unit 20: Principles Related to Practical Chemistry

Detection of extra elements (N, S, halogens); detection of functional groups (hydroxyl, carbonyl, carboxyl, amino); preparation of Mohr's salt, potash alum, acetanilide, p-nitro acetanilide, aniline yellow, iodoform; titrimetric exercises (acids, bases, indicators, oxalic acid vs KMnO₄, Mohr's salt vs KMnO₄); qualitative salt analysis (cations & anions); enthalpy of solution/neutralization, sol preparation, kinetics of iodide-peroxide reaction