JEE Main Syllabus 2027: Subject-Wise Topics, Chapter-Wise Weightage and PDF Download

SI units and fundamental quantities; dimensional analysis and applications; significant figures; errors in measurement (absolute, mean absolute, relative, percentage error); instruments — Vernier callipers, screw gauge; order-of-magnitude estimation.

Frame of reference; position, displacement, velocity, acceleration; equations of uniformly accelerated motion in 1D; motion graphs; relative velocity; projectile motion; uniform circular motion; scalars and vectors — addition, subtraction, resolution; dot and cross products (basic).

Newton’s first, second, and third laws; inertia; impulse and momentum; conservation of linear momentum; static and kinetic friction; laws of friction; angle of friction and angle of repose; circular motion dynamics; banking of roads; conical pendulum; Atwood machine.

Work done by constant and variable force; work-energy theorem; kinetic energy; potential energy (gravitational and spring); conservative and non-conservative forces; conservation of mechanical energy; power; elastic and perfectly inelastic collisions in 1D and 2D; coefficient of restitution.

Centre of mass and its motion; angular displacement, velocity, acceleration; moment of inertia (for standard rigid bodies); parallel and perpendicular axis theorems; radius of gyration; torque; angular momentum; conservation of angular momentum; rolling motion without slipping.

Kepler’s three laws of planetary motion; Newton’s universal law of gravitation; variation of g with altitude, depth, and latitude; gravitational field and potential; gravitational potential energy; escape velocity; orbital velocity of satellites; geostationary and polar satellites.

Hooke’s law; Young’s modulus, Bulk modulus, Shear modulus; Poisson’s ratio; pressure in fluids; Pascal’s law; buoyancy (Archimedes’ principle); Bernoulli’s theorem and applications; viscosity; Stokes’ law; terminal velocity; Reynold’s number; surface tension; capillarity; heat transfer (conduction, convection, radiation); Newton’s law of cooling; Wien’s law; Stefan-Boltzmann law.

Thermal equilibrium; zeroth law; heat, work, and internal energy; first law of thermodynamics; specific heat capacities of gases (Cv, Cp, and γ); isothermal, adiabatic, isobaric, and isochoric processes; second law; heat engines; Carnot cycle and efficiency; refrigerators and heat pumps.

Kinetic-molecular theory assumptions; pressure exerted by an ideal gas; RMS, average, and most probable speeds; degrees of freedom; law of equipartition of energy; specific heat capacity derivation; mean free path; ideal gas equation; real gas deviations (brief).

Periodic motion; simple harmonic motion (SHM) — displacement, velocity, acceleration, energy; spring-mass system; simple pendulum; damped and forced oscillations; resonance; wave motion (transverse and longitudinal); wave equation; speed of transverse waves; superposition principle; standing waves; beats; Doppler effect in sound.

Coulomb’s law; superposition principle; electric field lines; electric dipole; Gauss’s law and applications (spherical, cylindrical, planar symmetry); electric potential and potential energy; relation between E and V; conductors in electrostatic field; dielectrics; capacitors (parallel plate, spherical, cylindrical); series and parallel combinations; energy stored in a capacitor; effect of dielectric.

Electric current and drift velocity; mobility; Ohm’s law; resistivity and conductivity; temperature dependence of resistance; EMF and internal resistance; terminal voltage; Kirchhoff’s current and voltage laws; Wheatstone bridge; metre bridge; potentiometer (applications: comparison of EMF and internal resistance).

Biot-Savart law; Ampere’s circuital law; force on a moving charge (Lorentz force); cyclotron; force on current-carrying conductor; torque on current loop; magnetic dipole moment; moving coil galvanometer (conversion to ammeter and voltmeter); bar magnet; Earth’s magnetic field; diamagnetic, paramagnetic, and ferromagnetic materials; Curie’s law; hysteresis.

Faraday’s law of induction; Lenz’s law; motional EMF; self-inductance and mutual inductance; energy stored in an inductor; AC generator principle; peak and RMS values; phasor diagram; inductive and capacitive reactance; series LCR circuit; resonance; power factor; wattless current; transformers (step-up, step-down).

Displacement current; Maxwell’s equations (qualitative); transverse nature of EM waves; speed of light; electromagnetic spectrum (radio waves → gamma rays) — wavelength ranges, properties, and applications of each; intensity of EM waves.

Ray Optics: reflection at curved mirrors (mirror formula, magnification); refraction (Snell’s law, refractive index); total internal reflection and critical angle; refraction at spherical surfaces; thin lens formula; lens maker’s equation; power of a lens; lens combinations; optical instruments (simple and compound microscope, astronomical telescope). Wave Optics: Huygens’ principle; Young’s double slit experiment (fringe width, intensity distribution); single-slit diffraction; polarisation (plane, Brewster’s law, Malus’s law).

Photoelectric effect; Hertz and Lenard observations; Einstein’s photoelectric equation; work function; threshold frequency and wavelength; stopping potential; de Broglie hypothesis; de Broglie wavelength for electrons and particles; Davisson-Germer experiment.

Rutherford’s alpha-scattering experiment; Bohr model of hydrogen atom; energy levels; hydrogen spectrum (series); nuclear composition; atomic mass unit; mass defect; binding energy per nucleon; nuclear stability; radioactivity — alpha, beta, gamma decays; half-life; decay law; nuclear fission; nuclear fusion; Q-value.

Energy bands in solids; intrinsic and extrinsic semiconductors (n-type, p-type); p-n junction (forward and reverse bias); I-V characteristics; half-wave and full-wave rectifiers; Zener diode (voltage regulator); LED; photodiode; solar cell; transistor (CE configuration — characteristics, gain, amplifier, switch); logic gates (AND, OR, NOT, NAND, NOR) — truth tables and universal gates.

Matter classification; laws of chemical combination; mole concept; Avogadro number; empirical and molecular formulae; stoichiometry; limiting reagent; concentration terms (molarity, molality, normality, mole fraction, mass percentage).

Thomson and Rutherford models; Bohr’s model for hydrogen-like atoms; quantum numbers (n, l, m, s); shapes of s, p, d orbitals; Aufbau principle; Pauli’s exclusion principle; Hund’s rule; electronic configuration; de Broglie’s relation; Heisenberg’s uncertainty principle.

Lewis dot structures; VSEPR theory (geometry prediction); hybridisation (sp, sp², sp³, sp³d, sp³d²); sigma and pi bonds; bond parameters (order, length, energy, angle); dipole moment; resonance; molecular orbital theory — bond order, magnetic properties of homonuclear diatomic molecules; hydrogen bonding.

System and surroundings; extensive and intensive properties; heat (q) and work (w); internal energy (U); enthalpy (H); Hess’s law; standard enthalpies (formation, combustion, neutralisation); bond enthalpy; entropy (S); Gibbs energy (G = H − TS); spontaneity criteria; ΔG and equilibrium constant.

Types of solutions; expressing concentration; Raoult’s law (ideal and non-ideal solutions); Henry’s law; colligative properties — relative lowering of vapour pressure, boiling point elevation (Tb), freezing point depression (Tf), osmotic pressure (π); van ’t Hoff factor; abnormal molar masses.

Law of mass action; Kc and Kp; Kp-Kc relationship; Le Chatelier’s principle; ionic equilibrium; strong and weak acids; acids and bases (Arrhenius, Brønsted-Lowry, Lewis); Ka, Kb; pH scale; buffer solutions; hydrolysis of salts; solubility product (Ksp); common ion effect.

Oxidation number; balancing redox equations (half-reaction method); galvanic cells; standard electrode potential (E°); Nernst equation; relationship between ΔG° and E°cell; electrolytic cells; Faraday’s first and second laws; molar conductivity; Kohlrausch’s law; batteries and fuel cells.

Rate of reaction; factors affecting rate (concentration, temperature, catalyst, surface area); rate law and rate constant; order and molecularity; integrated rate equations (zero and first order); half-life; Arrhenius equation; activation energy (Ea); collision theory; homogeneous and heterogeneous catalysis; enzyme catalysis.

Modern periodic law and periodic table structure; s, p, d, f blocks; groups and periods; periodic trends — atomic and ionic radius, ionisation enthalpy, electron gain enthalpy, electronegativity, valence electrons, metallic character; anomalous behaviour of elements.

Group 15 (N family): N₂, NH₃, HNO₂, HNO₃; phosphorus allotropes; PCl₃, PCl₅, P₄O₁₀. Group 16 (O family): ozone; H₂S; H₂SO₄ (preparation and properties); SO₂, SO₃. Group 17 (Halogens): halide compounds; oxoacids of halogens; interhalogen compounds; bleaching powder. Group 18 (Noble Gases): properties and selected compounds.

Electronic configuration of first row transition metals; general properties — variable oxidation states, coloured ions, catalytic behaviour, magnetic properties, interstitial compounds, alloy formation; important compounds of Cr (K₂Cr₂O₇) and Mn (KMnO₄); lanthanoids — lanthanoid contraction; actinoids — key oxidation states.

Werner’s theory; terminology (ligand, coordination number, coordination sphere); types of ligands (monodentate, polydentate, ambidentate, chelating); IUPAC nomenclature of coordination compounds; isomerism (structural: ionisation, linkage, solvate/hydrate; stereoisomerism: geometric, optical); valence bond theory; crystal field theory — splitting patterns, colour, magnetic properties; stability constants; biological importance (haemoglobin, chlorophyll) and industrial applications (EDTA).

IUPAC nomenclature; structural and stereoisomerism; inductive effect; resonance (mesomeric effect); hyperconjugation; electromeric effect; types of reaction intermediates (carbocations, carbanions, free radicals, carbenes); electrophiles and nucleophiles; SN1 vs SN2; E1 vs E2 elimination.

Alkanes: conformations, free-radical halogenation, combustion. Alkenes: Markovnikov’s rule, anti-Markovnikov (peroxide effect), hydration, ozonolysis, oxidation with KMnO₄. Alkynes: acidity, reduction (Lindlar’s catalyst vs Na/liquid NH₃), hydration. Aromatic hydrocarbons: Hückel’s rule; EAS — nitration, halogenation, sulphonation, Friedel-Crafts alkylation and acylation; directive effects.

Haloalkanes: preparation, SN1 and SN2 mechanisms, stereochemistry, E1 and E2 elimination; Grignard reagent formation; Wurtz reaction. Haloarenes: nucleophilic aromatic substitution (lower reactivity); preparation; uses and environmental effects of DDT and BHC.

Preparation and physical properties of aldehydes and ketones; nucleophilic addition (HCN, NaBH₄, LiAlH₄, Grignard); Aldol condensation; Cannizzaro reaction; oxidation tests (Tollens’, Fehling’s); carboxylic acids — acidity, preparation, reactions (esterification, RCOX, RCONH₂, RCOO⁻); Hell-Volhard-Zelinsky reaction.

Classification (1°, 2°, 3°); preparation (reduction, Gabriel synthesis, Hofmann bromamide rearrangement); basicity order (comparison with ammonia and aniline); reactions of amines; diazotisation; Sandmeyer and coupling reactions; cyanides and isocyanides; nitrobenzene (preparation and reduction); carbylamine test.

Carbohydrates — classification (mono, di, polysaccharides); open-chain and Haworth structures of glucose; reducing vs non-reducing sugars; sucrose, starch, cellulose. Proteins — amino acids; peptide bond; primary to quaternary structure; denaturation; enzymes. Vitamins — classification and deficiency diseases. Nucleic acids — DNA double helix (brief) and RNA types.

Detection of N, S, and halogens (Lassaigne’s test); qualitative analysis of organic compounds (detection of functional groups — hydroxyl, carbonyl, carboxyl, amino, nitro, halide); principles of acid-base and redox titrations relevant to organic compounds.

Sets (types, operations — union, intersection, difference, complement); Venn diagrams; Cartesian product; types of relations (reflexive, symmetric, transitive, equivalence); types of functions (injective, surjective, bijective); composition of functions; inverse functions; binary operations.

Complex number algebra (addition, multiplication, conjugate, modulus); Argand plane; polar form (r, θ); De Moivre’s theorem; nth roots of unity; quadratic equations — discriminant, nature of roots, Vieta’s formulas; equations reducible to quadratic; common roots.

Types of matrices; addition, subtraction, multiplication, scalar multiplication; transpose; symmetric and skew-symmetric; determinants — expansion, properties (row/column operations); minor and cofactor; adjoint and inverse; solving 2×2 and 3×3 linear systems (matrix method, Cramer’s rule).

Fundamental counting principle; factorial notation; permutations nPr (with and without repetition); circular permutations; combinations nCr; selection problems; distribution of objects into groups.

Binomial expansion for positive integral exponent; general term (Tr+1); middle term; numerically greatest term; coefficient of xr; multinomial expansion (basic applications); binomial approximation for small values.

Arithmetic progression (AP) — nth term, sum of n terms; geometric progression (GP) — nth term, sum, infinite GP; harmonic progression (HP); arithmetic-geometric progression (AGP); AM-GM-HM inequality; sum of special series (Σn, Σn², Σn³).

Limits — algebraic, trigonometric, exponential, logarithmic standard forms; L’Hôpital’s rule; left and right limits; continuity at a point and on an interval; differentiability; chain rule; derivatives of standard functions; product and quotient rules; implicit differentiation; parametric differentiation; higher-order derivatives; applications — monotonicity, maxima and minima.

Indefinite integration — standard forms; substitution; integration by parts; partial fractions; trigonometric substitution. Definite integrals — properties (symmetry, periodicity, odd/even); limit-as-sum definition. Applications — area under a curve; area between two curves.

Order and degree; general, particular, and singular solutions; formation of differential equations; methods of solving — variable separable; homogeneous; linear first-order ODE (integrating factor method); applications (growth and decay, Newton’s law of cooling).

Straight Lines: slope; various forms of equations (slope-point, two-point, intercept, normal); angle between lines; distance from point to line; pair of straight lines. Circles: standard and general equations; tangent and normal; chord of contact; family of circles. Parabola, Ellipse, Hyperbola: standard equations; eccentricity; focus-directrix; tangent and normal; chord properties; conjugate hyperbola.

Direction cosines and direction ratios; angle between two lines; skew lines and shortest distance; equations of a line in 3D (symmetric, vector, parametric forms); equations of a plane (normal, intercept, vector forms); angle between planes; distance from a point to a plane; line-plane intersection; coplanarity of lines.

Types of vectors (equal, unit, zero, collinear, coplanar); position vectors; addition, subtraction, and scalar multiplication; dot product (properties, angle, projection); cross product (magnitude, direction, area); scalar triple product; vector triple product; applications to 3D geometry.

Statistics: mean, median, mode for grouped and ungrouped data; mean deviation; variance and standard deviation. Probability: random experiments; sample space; events (simple, compound, mutually exclusive); addition theorem; conditional probability; multiplication theorem; independent events; Bayes’ theorem; total probability theorem; random variable and expectation.

Trigonometric functions — domain, range, graphs, periodicity; identities (compound angle, multiple angle, sub-multiple angle, sum-to-product, product-to-sum); trigonometric equations — general solutions; inverse trigonometric functions (domain, range, principal values, properties, identities); properties of triangles (sine rule, cosine rule, projection formula, area); heights and distances.

Awareness of persons, places, buildings, and materials in the built environment; objects, textures, and architectural elements; visualising three-dimensional objects from two-dimensional drawings; visualising different sides of 3D objects (top, front, side views); analytical reasoning; mental ability — visual, numerical, and verbal.

Understanding and appreciation of scale and proportions of objects, buildings, and urban spaces; colour, texture, harmony, and contrast; design and drawing of geometrical or abstract shapes and patterns in pencil; transformation of forms — 2D and 3D (union, subtraction, rotation); development of surfaces and volumes; generation of plans, elevations, and 3D views of objects; creating 2D and 3D compositions using given shapes and forms.

Urban dynamics — rural-urban migration; urban sprawl; concept of urbanisation; slums and informal settlements; smart cities initiative; AMRUT; PMAY (Pradhan Mantri Awas Yojana); housing policies; concept of master plan, development plan, zonal plan; land use planning; types of land use; floor space index (FSI) and ground coverage.

Poverty and inequality in cities; basic services and infrastructure; water supply and sanitation; transportation and mobility (public transport, non-motorised transport); green and open spaces; urban heat island effect; environmental degradation linked to rapid urbanisation.

Land economics — demand and supply of land; property tax; urban local bodies (ULBs) and their functions; municipal finance; public-private partnerships in infrastructure; concepts of SEZs, industrial townships, and new towns.

74th Constitutional Amendment (Nagarpalika Act) — key provisions; role of planning authorities; Town and Country Planning Acts (overview); Environmental Impact Assessment (EIA) — basics; Heritage conservation acts and listed buildings.

Recent urban development schemes in India (Smart Cities Mission, HRIDAY, RERA); sustainable development goals (SDGs) related to cities (SDG 11); National Urban Transport Policy; climate-resilient city planning; regional planning organisations in India (NITI Aayog, Regional Plan 2041 for NCR).