JEE Advanced Syllabus 2027: Topic Wise Weightage, Subject Wise Topics and PDF Download

Units and dimensions; dimensional analysis; least count; significant figures. Methods of measurement and error analysis for physical quantities. Experiments: Vernier calipers (length/diameter), screw gauge (diameter/thickness), simple pendulum (g determination), Young’s modulus by wire, surface tension by capillary rise, resistance by metre bridge, refractive index of glass, focal length of concave mirror and convex lens, speed of sound using resonance column.

Kinematics in 1D and 2D; projectile motion; uniform circular motion. Newton’s laws of motion; frictional forces; inertial reference frames. Work and kinetic energy theorem; conservative forces; potential energy; power. Elastic and inelastic collisions; impulse; momentum conservation. System of particles; centre of mass motion. Rigid body dynamics: moment of inertia; torque; angular momentum; conservation of angular momentum; rolling without slipping. Fluid mechanics: pressure; Pascal’s law; Archimedes’ principle; viscosity (Stokes’ law); surface tension; capillarity. Gravitation: Newton’s law; gravitational potential energy; escape velocity; orbital velocity; Kepler’s laws. Simple harmonic motion: energy; damped oscillations. Wave motion: transverse and longitudinal waves; standing waves; resonance; Doppler effect.

Thermal expansion of solids, liquids, and gases. Calorimetry: specific heat; latent heat. Heat transfer: conduction; convection; radiation; Newton’s law of cooling; Stefan–Boltzmann law. Kinetic theory of gases: ideal gas equation; pressure; temperature; RMS speed; degrees of freedom; equipartition of energy. Thermodynamics: first and second laws; internal energy; work done; isothermal; adiabatic; isobaric; isochoric processes; Carnot cycle and efficiency; entropy (qualitative).

Electrostatics: Coulomb’s law; electric field lines; Gauss’s theorem; electric potential; work done; capacitors; dielectrics; energy stored. Current electricity: Ohm’s law; resistance; Kirchhoff’s laws; Wheatstone bridge; metre bridge; potentiometer. Magnetic field: Biot-Savart law; Ampere’s law; solenoid; toroid; magnetic force on moving charge and current-carrying wire. Electromagnetic induction: Faraday’s law; Lenz’s law; self and mutual inductance; LC oscillations. AC circuits: RMS values; LCR circuits; resonance; power factor; transformers. Electromagnetic waves: nature and spectrum (qualitative).

Ray optics: reflection at plane and curved surfaces; refraction; Snell’s law; total internal reflection; thin lens formula; lens-maker’s equation; combination of lenses and mirrors; prism; dispersion; angular dispersion. Wave optics: Huygens’ wave theory; Young’s double slit experiment; conditions for constructive and destructive interference; single slit diffraction; resolving power of telescope and microscope; polarisation by scattering and reflection.

Dual nature of matter and radiation: photoelectric effect; Einstein’s photoelectric equation; de Broglie wavelength. Bohr’s model of hydrogen atom; energy levels; quantisation condition; hydrogen spectrum. X-rays: Moseley’s law; characteristic and continuous X-ray spectra. Nuclear physics: radioactivity (alpha, beta, gamma); decay laws; half-life; mean life; binding energy per nucleon; mass defect; Q-value of nuclear reactions; fission; fusion.

Concept of atoms and molecules; Dalton’s atomic theory; mole concept; Avogadro’s number; empirical and molecular formula calculations; chemical equations; stoichiometry; concentration terms (mole fraction, molarity, molality, normality).

Bohr model; hydrogen atom spectrum; wave-particle duality; de Broglie wavelength; Heisenberg’s uncertainty principle; quantum numbers; orbital shapes (s, p, d); Aufbau principle; Pauli exclusion principle; Hund’s rule; electronic configurations of elements up to Z = 36.

Ionic bonding; Born-Haber cycle; covalent bonding; Lewis structures; VSEPR theory; valence bond theory; hybridisation (sp, sp2, sp3, sp3d, sp3d2); resonance; molecular orbital theory; bond order; dipole moments; hydrogen bonding.

First law of thermodynamics; internal energy; enthalpy; Hess’s law; bond enthalpies; enthalpy of formation, combustion, and atomisation. Second law; entropy; Gibbs free energy; spontaneity; the relationship ΔG = ΔH – TΔS.

Law of mass action; Kp and Kc; Le Chatelier’s principle; factors affecting equilibrium. Acids and bases: Arrhenius; Brønsted–Lowry; Lewis concepts; pH; buffers; hydrolysis of salts; solubility product (Ksp); common ion effect.

Electrolytic cells; Faraday’s laws of electrolysis. Galvanic cells; electrode potential; EMF; Nernst equation; standard electrode potentials; electrochemical series; relation between Gibbs energy and EMF; concentration cells.

Rate of reaction; factors affecting rate; rate law; order and molecularity; first-order reactions; half-life; Arrhenius equation; activation energy; collision theory (qualitative); catalysis types; enzyme kinetics (Michaelis-Menten, qualitative).

Solid State: types of solids; unit cells (cubic systems); packing efficiency; density calculation; crystal defects. Solutions: vapour pressure; Raoult’s law; colligative properties (elevation in boiling point, depression in freezing point, osmotic pressure); van’t Hoff factor. Nuclear Chemistry: radioactivity; types of decay; nuclear reactions; binding energy calculations. Surface Chemistry: adsorption isotherms; types of colloids; Tyndall effect; Brownian motion; coagulation; emulsions.

IUPAC nomenclature; structural and stereoisomerism (optical, geometrical); electronic effects (inductive, mesomeric, hyperconjugation); reactive intermediates — carbocations, carbanions, free radicals, carbenes; SN1, SN2, E1, E2 mechanisms; aromaticity; Hückel’s rule.

Alkanes: preparation; halogenation; combustion. Alkenes: preparation by elimination; addition reactions (Markovnikov; anti-Markovnikov with peroxide effect); oxidation; ozonolysis. Alkynes: preparation; acidic nature; addition of H2, HX, H2O. Benzene and substituted benzene: electrophilic aromatic substitution (halogenation, nitration, sulfonation, Friedel-Crafts); directing effects of substituents.

Haloalkanes: nucleophilic substitution; Grignard reagent preparation; reactions with metals. Haloarenes: nucleophilic aromatic substitution. Alcohols: preparation; oxidation; esterification; dehydration; reaction with HX. Phenols: acidity; electrophilic substitution; Kolbe reaction; Reimer-Tiemann reaction. Ethers: Williamson synthesis; reactions with HI and H2SO4.

Aldehydes and Ketones: preparation; nucleophilic addition (cyanohydrin, hydration, hemiacetal formation, reaction with alcohols); aldol condensation; Cannizzaro reaction; Wittig reaction; oxidation and reduction. Carboxylic Acids: preparation; acidity; reactions; derivatives (acid chlorides, anhydrides, esters, amides); Hell-Volhard-Zelinsky reaction.

Amines: classification; preparation; basicity; reactions (acylation, sulfonylation); diazonium salts; azo coupling reactions. Biomolecules: carbohydrates (classification, reducing sugars, mutarotation); amino acids and proteins (structure, peptide bond, denaturation); nucleic acids (DNA, RNA — basic structure). Polymers: addition and condensation polymers; natural rubber; vulcanisation; synthetic rubbers; plastics. Chemistry in Everyday Life: analgesics; antibiotics; antiseptics and disinfectants; soaps and detergents.

Classification of elements; Mendeleev and modern periodic law; periodic trends in atomic radius, ionic radius, ionisation enthalpy, electron affinity, and electronegativity; effective nuclear charge and shielding effects.

s-Block: Group 1 and 2 properties; important compounds of sodium (NaOH, Na2CO3, NaHCO3, NaCl) and calcium (CaO, Ca(OH)2, CaCO3, CaSO4). p-Block: Groups 13–18 — important compounds including borax, boric acid, silicones, phosphine, sulphuric acid, halogens, inter-halogen compounds, noble gases, ozone, sodium peroxide, bleaching powder.

d-Block: general properties of transition metals; oxidation states; colour; magnetic properties; catalytic behaviour; important compounds (K2Cr2O7, KMnO4). f-Block: lanthanides and actinides (general properties and contraction). Coordination Compounds: Werner’s theory; IUPAC nomenclature; isomerism (structural, stereochemical); bonding theories (VBT and CFT); stability constants; applications.

Occurrence and extraction of metals: iron (blast furnace), copper, silver, zinc, aluminium; carbon reduction; electrolytic reduction; aluminothermic process. Qualitative salt analysis: identification of cations (Pb2+, Cu2+, Fe3+, Zn2+, Ni2+, Co2+, Mn2+, Ca2+, Ba2+, NH4+, Na+, K+) and anions (CO32–, HCO3–, SO42–, Cl–, Br–, I–, NO3–, NO2–, CH3COO–).

Sets and their representations; union, intersection, complement, symmetric difference; power set; Venn diagrams. Relations: types (reflexive, symmetric, transitive, equivalence). Functions: domain, codomain, range; injective, surjective, bijective; composition; inverse functions; real-valued functions; even and odd functions; periodic functions; graphical transformations.

Algebra of complex numbers; modulus and argument; Argand plane; triangle inequality; square roots of complex numbers; polar form; cube roots of unity; nth roots of unity; de Moivre’s theorem and its applications in geometry and summation of series.

Quadratic equations in real and complex variables; relations between roots and coefficients; nature of roots; formation of equations. AP, GP, HP; AM-GM inequality; sum of finite AP and GP; infinite GP sum; sum of special series (Σn, Σn2, Σn3). Permutations and combinations; fundamental counting principle; circular permutations. Binomial theorem for positive integral index; general term; middle term; properties of binomial coefficients.

Matrix algebra; types; transpose; adjoint; inverse (using cofactors; Cayley-Hamilton theorem). Determinants: properties; expansion along rows and columns; Cramer’s rule for 2×2 and 3×3 systems; consistency of linear equations; homogeneous systems; rank of matrix.

Classical and axiomatic probability; addition rule; conditional probability; multiplication theorem; Bayes’ theorem; independence of events. Discrete random variable; mean and variance; binomial distribution. Measures of central tendency: mean, median, mode. Measures of dispersion: variance; standard deviation.

Trigonometric ratios and identities; addition formulae; multiple-angle and submultiple-angle formulae; product-to-sum formulae. Trigonometric equations: general solutions. Properties of triangles: sine rule; cosine rule; area formulae; incircle and circumradius. Inverse trigonometric functions: domains and ranges; principal values; identities and equations.

Cartesian coordinates; distance and section formulae; area of triangle. Straight lines: slope; intercept forms; angle between lines; distance from a point; concurrent lines; locus problems. Circles: standard and general equations; centre and radius; tangent and normal; chord of contact; power of a point; radical axis. Conics — Parabola, Ellipse, Hyperbola: standard equations; focus-directrix property; eccentricity; tangents; normals; chord of contact; pole and polar; parametric forms.

3D Geometry: direction cosines and direction ratios; equation of a line in space (symmetric and parametric forms); equation of a plane (intercept, normal, and general forms); angle between line and plane; distance of a point from a plane; coplanarity of lines; skew lines. Vectors: addition; scalar and vector products; scalar triple product; vector triple product; geometric applications (area of triangle and parallelogram; volume of parallelepiped).

Real-valued functions; limits; continuity; differentiability. Derivatives: chain rule; implicit differentiation; parametric differentiation; logarithmic differentiation; nth derivatives. Rolle’s theorem; Lagrange’s mean value theorem; Taylor and Maclaurin series (applications). Applications: increasing and decreasing functions; maxima and minima (first and second derivative tests); tangents and normals; rate of change; L’Hôpital’s rule.

Indefinite integration: standard forms; substitution; integration by parts; partial fractions; reduction formulae. Definite integrals: properties (King’s rule, symmetry, periodicity); Leibniz rule; limit of sum definition. Area under curves; area between two curves. Differential equations: order and degree; separation of variables; homogeneous equations; linear first-order equations (integrating factor method); applications in geometry and physical problems.