WBJEE Syllabus 2027: Physics, Chemistry, Maths Topics, Weightage and PDF Download

Scope of physics; physical quantities; measurement; SI units; dimensional analysis; significant figures; orders of magnitude; error analysis.

Scalars and vectors; displacement, velocity and acceleration; motion in a straight line; projectile motion; uniform circular motion; relative velocity and acceleration.

Newton’s three laws; force and momentum; impulse; work-energy theorem; conservation of energy; power; elastic and inelastic collisions; coefficient of restitution.

Centre of mass; linear momentum conservation; recoil; Atwood machine; spring-mass system; static and kinetic friction; angle of repose.

Kepler’s three laws; Newton’s universal law of gravitation; variation of g with altitude and depth; gravitational potential energy; escape velocity; orbital speed; geostationary satellites.

Elasticity; Hooke’s law; stress-strain curve; Young’s, bulk and rigidity moduli; fluid pressure; Pascal’s law; Archimedes’ principle; surface tension; angle of contact; capillarity.

Coefficient of viscosity; Stokes’ law; terminal velocity; streamline vs turbulent flow; Reynolds’ number; equation of continuity; Bernoulli’s theorem and its applications.

Thermal equilibrium; zeroth law; first law (internal energy, heat, work); isothermal and adiabatic processes; second law; Carnot engine efficiency; refrigerator coefficient of performance; entropy.

Ideal gas equation; kinetic interpretation of temperature; RMS, mean and most probable speeds; equipartition of energy; degrees of freedom; mean free path.

Simple harmonic motion; energy in SHM; spring-mass system; simple pendulum; transverse and longitudinal waves; superposition; standing waves; beats; Doppler effect; harmonics and overtones.

Coulomb’s law; electric field lines; Gauss’s theorem and applications; electric potential; equipotential surfaces; capacitors (series and parallel); energy stored; polarisation of dielectrics.

Ohm’s law; resistivity and conductivity; temperature dependence; resistors in series and parallel; Kirchhoff’s laws; Wheatstone bridge; metre bridge; potentiometer; EMF and internal resistance.

Biot-Savart law; Ampere’s law and applications; Lorentz force; motion of charged particles in magnetic fields; cyclotron; moving coil galvanometer; conversion to ammeter and voltmeter.

Magnetic dipole moment; torque on a magnetic dipole; paramagnetic, diamagnetic and ferromagnetic materials; hysteresis loop; retentivity; coercivity; earth’s magnetic field.

Faraday’s laws; Lenz’s law; motional EMF; self-inductance; mutual inductance; energy stored in an inductor; AC generator; RMS values; impedance; RLC series circuit; resonance; quality factor; transformers.

Displacement current; Maxwell’s equations (conceptual); properties of EM waves (transverse, speed in vacuum); electromagnetic spectrum (radio, microwave, infrared, visible, UV, X-ray, gamma); uses of each band.

Laws of reflection and refraction; plane and spherical mirrors; lens formula; lens maker’s equation; combination of lenses; total internal reflection; optical fibre; prism (minimum deviation, dispersive power); microscope; astronomical telescope.

Huygens’ principle; coherent sources; Young’s double-slit experiment (fringe width, conditions for bright and dark fringes); diffraction at single slit; Rayleigh’s criterion; polarisation (Malus’ law, Brewster’s angle).

Photoelectric effect; Einstein’s photoelectric equation; threshold frequency; work function; stopping potential; de Broglie wavelength; Davisson-Germer experiment; X-rays (production, properties, Bragg’s law).

Thomson model; Rutherford model (alpha-particle scattering); Bohr’s atomic model; energy levels and spectral series of hydrogen (Lyman, Balmer, Paschen); quantum numbers (brief).

Nuclear composition; mass number; atomic number; isotopes; mass defect; binding energy per nucleon; radioactivity (alpha, beta, gamma); half-life; decay constant; radioactive equilibrium; fission; fusion; chain reaction.

Energy bands in solids; intrinsic and extrinsic semiconductors (p-type, n-type); p-n junction diode (I-V characteristics); rectification; Zener diode; LED; photodiode; solar cell; NPN/PNP transistor basic action; logic gates (AND, OR, NOT, NAND, NOR, XOR).

Dalton’s atomic theory; atomic and molecular mass; mole concept; Avogadro’s number; equivalent weight; stoichiometry; limiting reagent; percentage composition; empirical and molecular formulae.

Bohr model; quantum numbers (n, l, m, s); orbital shapes (s, p, d); Aufbau principle; Pauli exclusion principle; Hund’s rule; electronic configuration; Heisenberg’s uncertainty principle.

Natural and artificial radioactivity; alpha, beta and gamma decay; half-life; disintegration constant; radioactive equilibrium; nuclear reactions; fission and fusion.

Modern periodic law; s, p, d and f blocks; periodic trends (atomic radius, ionisation energy, electron affinity, electronegativity, oxidation states); anomalous behaviour of Period 2 elements.

Ionic, covalent and metallic bonds; VSEPR theory; molecular geometry; hybridisation (sp, sp², sp³, sp³d, sp³d²); bond order; resonance; hydrogen bonding; dipole moment; MO theory (H₂ and O₂).

Gas: Boyle’s and Charles’s laws; ideal gas equation; Graham’s law; kinetic theory; van der Waals equation. Liquid: Surface tension; viscosity; vapour pressure; Raoult’s law. Solid: Crystal systems; unit cell; close packing (hcp, ccp); point defects.

System, surroundings; zeroth and first law; internal energy; enthalpy; Hess’s law; bond enthalpy; Kirchhoff’s equation; Gibbs free energy (ΔG = ΔH – TΔS); spontaneity; entropy and second law.

Law of mass action; equilibrium constant (Kc and Kp); relation between Kc and Kp; Le Chatelier’s principle; factors affecting equilibrium; applications (Haber process, Contact process).

Brønsted-Lowry and Lewis acid-base concepts; strong and weak acids; pH and pOH; buffer solutions; common ion effect; solubility product (Ksp); oxidation states; balancing redox equations; standard electrode potential; EMF; Nernst equation; electrolysis (Faraday’s laws).

Rate of reaction; rate law; order and molecularity; integrated rate equations (zero and first order); half-life expressions; Arrhenius equation; activation energy; collision theory; effect of temperature; catalysis.

Isotopes of hydrogen; ortho and para hydrogen; hydrides (ionic, covalent, metallic); water (structure and properties); heavy water; hydrogen peroxide.

Group 1 and 2 general trends; important compounds (NaOH, Na₂CO₃, NaHCO₃, CaO, Ca(OH)₂, plaster of Paris); anomalous behaviour of Li and Be; diagonal relationship.

Groups 13–18: Boron family (borax, boric acid); Carbon group (allotropes of C, CO, CO₂, silicates); Nitrogen family (NH₃, HNO₃, oxides of nitrogen); Oxygen and sulphur group (SO₂, SO₃, H₂SO₄, ozone, H₂O₂); Halogens (HX, interhalogen compounds, oxoacids); Noble gases (properties and uses).

General properties of transition metals (variable oxidation states, catalytic activity, colour, magnetic behaviour, complex formation); K₂Cr₂O₇; KMnO₄; lanthanoid and actinoid contractions.

Werner’s theory; IUPAC nomenclature; ligands (mono-, bi-, polydentate); coordination number; isomerism (structural, geometrical, optical); valence bond theory; crystal field theory (octahedral and tetrahedral splitting); colour and magnetic behaviour.

Hybridisation; IUPAC nomenclature; structural and stereoisomerism (E/Z, optical); electronic effects (inductive, resonance, hyperconjugation); reaction mechanisms (SN1, SN2, E1, E2, electrophilic addition, electrophilic aromatic substitution).

Alkanes (combustion, halogenation); alkenes (addition reactions, Markovnikov rule, anti-Markovnikov); alkynes (acidic character, addition); haloalkanes (SN reactions, Grignard reagent); alcohols and phenols (dehydration, oxidation, esterification, acidity); ethers; aldehydes and ketones (Aldol, Cannizzaro, nucleophilic addition); carboxylic acids (esterification, relative acidic strength); acid derivatives; aliphatic amines.

Benzene structure and aromaticity (Hückel rule); electrophilic aromatic substitution (halogenation, nitration, sulphonation, Friedel-Crafts); directive effects; phenol reactions; aniline chemistry; diazonium salts (coupling reactions).

Polymers (addition: PVC, polythene; condensation: nylon, dacron, bakelite); surface chemistry (adsorption, colloids, Tyndall effect, coagulation); environmental chemistry (air, water, soil pollution, ozone depletion, acid rain); bio-molecules (carbohydrates, amino acids, proteins, nucleic acids); synthetic dyes.

Detection of anions: Cl⁻, Br⁻, I⁻, NO₃⁻, SO₄²⁻, CO₃²⁻, PO₄³⁻, S²⁻. Detection of cations by group tests: Na⁺, K⁺, Ca²⁺, Mg²⁺, Al³⁺, Fe²⁺/Fe³⁺, Cu²⁺, Zn²⁺, Pb²⁺. Salt analysis procedure.

A.P./G.P./H.P.: General term; sum formulae; AM-GM-HM inequality; infinite GP sum; arithmetico-geometric series.
Complex Numbers: Argand plane; polar form; De Moivre’s theorem; nth roots of unity; cube roots of unity; geometric applications.
Permutation and Combination: Fundamental counting principle; circular permutations; combinations with repetition; multinomial theorem.
Matrices and Determinants: Operations; transpose; adjoint; inverse; Cramer’s rule; rank; characteristic polynomial.
Sets, Relations and Mappings: Types of sets; Venn diagrams; equivalence relations; injective, surjective and bijective functions; composition and inverse of functions.

Radian measure; six trigonometric functions and graphs; basic identities; compound and multiple angle formulae; sub-multiple angles; product-to-sum and sum-to-product; conditional identities; general solutions; inverse trig functions (domain, range, principal values, standard identities); sine rule; cosine rule; area of a triangle; in-radius and circum-radius.

Straight Lines: Distance and section formulae; slope; various line forms; angle between lines; family of lines; locus problems.
Circles: Standard and general forms; tangent and normal; chord of contact; power of a point; radical axis.
Parabola: Standard parabola y² = 4ax; tangent; normal; chord properties.
Ellipse: Standard form; eccentricity; auxiliary circle; tangent and normal; conjugate diameters.
Hyperbola: Standard form; asymptotes; rectangular hyperbola xy = c²; tangent and normal.

Direction cosines and direction ratios; angle between two lines in 3D; Cartesian and vector equations of a line; Cartesian and vector equations of a plane; angle between planes; distance from a point to a plane; shortest distance between skew lines.

Differential Calculus: Limits (standard forms, L’Hôpital’s rule); continuity and differentiability; chain rule; implicit and parametric differentiation; higher-order derivatives.
Applications: Increasing and decreasing functions; maxima and minima; tangents and normals; Rolle’s theorem; Lagrange’s MVT; approximations.
Integral Calculus: Standard integrals; substitution; integration by parts; partial fractions; definite integrals and their properties; area under and between curves.
Differential Equations: Order and degree; variable separable; homogeneous equations; first-order linear ODE using integrating factor.

Vector representation; magnitude; unit vector; position vector; addition, subtraction and scalar multiplication; dot product and properties; cross product and properties; scalar triple product; vector triple product; area of triangle and parallelogram; coplanarity and collinearity conditions.

Statistics: Mean, median, mode, range, mean deviation, variance, standard deviation, coefficient of variation.
Probability: Classical and axiomatic definitions; mutually exclusive and independent events; addition theorem; multiplication theorem; conditional probability; Bayes’ theorem; random variables; expectation and variance; Binomial distribution; Poisson distribution.