IIT JAM Syllabus 2027: 7 Subject Papers, Subject-Wise PDF Download and Topic-Wise Weightage

Calculus of single and multiple variables; partial derivatives; Jacobian; imperfect and perfect differentials; Taylor expansion; Fourier series; vector algebra; vector calculus; multiple integrals; Divergence theorem; Green’s theorem; Stokes’ theorem; first-order equations; linear second-order ODEs with constant coefficients; matrices and determinants; algebra of complex numbers.

Newton’s laws of motion; velocity and acceleration in Cartesian, Polar, and cylindrical coordinates; uniformly rotating frame; centrifugal and Coriolis forces; motion under central force; Kepler’s laws; gravitational law and Poisson’s equation; tidal force; conservation laws (energy, linear and angular momentum); centre of mass; elastic and inelastic collisions; rigid body motion; moment of inertia tensor; special relativity — Lorentz transformations, length contraction, time dilation, relativistic kinematics, mass-energy equivalence.

Differential equation of simple harmonic oscillator; damped and forced oscillators; resonance; Lissajous figures; wave equation; travelling and standing waves in 1D; sound waves; superposition; beats; phase and group velocity; interference; Fraunhofer diffraction (single and double slit); polarization (linear, circular, elliptic); Brewster’s angle; optical instruments.

Coulomb’s law; Gauss’s law; electric field and potential; electrostatic boundary conditions; Laplace’s equation (spherical symmetry); conductors, capacitors, dielectrics; Biot-Savart law; Ampere’s law; Faraday’s law; Lenz’s law; self and mutual inductance; alternating currents; LCR circuits; Maxwell’s equations; electromagnetic waves; Poynting vector; reflection and refraction at conducting and dielectric interfaces.

Kinetic theory of gases; Maxwell-Boltzmann velocity distribution; equipartition of energy; specific heat of mono-, di-, and tri-atomic gases; ideal gas; Van der Waals gas; zeroth and first laws of thermodynamics; second law and entropy; Carnot cycle; heat engines and refrigerators; thermodynamic potentials; Maxwell’s thermodynamic relations; phase transitions; Clausius-Clapeyron equation.

Postulates of special relativity; relativistic velocity addition; energy-momentum relation; photoelectric effect; Compton effect; de Broglie wavelength; Bohr’s quantization; hydrogen atom spectrum; wave-particle duality; Heisenberg uncertainty principle; Schrödinger equation; particle in a box; harmonic oscillator; hydrogen atom (orbital and spin angular momentum, spin-orbit coupling); nuclear stability; radioactive decay; nuclear reactions.

Crystal structure; Bravais lattices; X-ray diffraction (Bragg’s law); free electron theory; energy bands; semiconductors (intrinsic and extrinsic); p-n junction; transistors (BJT and FET); amplifier circuits; oscillators; operational amplifier circuits; Boolean algebra; logic gates; combinational and sequential circuits.

Fundamental particles; Bohr’s theory; wave-particle duality; uncertainty principle; quantum numbers; shapes of orbitals; Aufbau principle; Hund’s rule; electronic configuration; molecular orbital theory for diatomics; hybridization.

Equation of state for real gases; Van der Waals equation; critical constants; law of corresponding states; Maxwell-Boltzmann velocity distribution; average, root mean square, and most probable velocities; mean free path; collision frequency; viscosity; thermal conductivity.

Laws of thermodynamics; state and path functions; enthalpy; entropy; Gibbs and Helmholtz free energy; chemical potential; Kirchhoff’s law; Hess’s law; chemical equilibrium (Kp, Kc, Kx); Le Chatelier’s principle; van’t Hoff equation.

Phase rule; Raoult’s law; colligative properties; Nernst equation; electrode potentials; standard reduction potentials; EMF of galvanic cells; electrolysis; Faraday’s laws; conductance of electrolytic solutions; Kohlrausch’s law; Debye-Hückel limiting law.

Rate of reaction; order and molecularity; integrated rate laws; half-life; Arrhenius equation; collision theory; transition state theory; enzyme kinetics (Michaelis-Menten equation); photochemistry (Stark-Einstein law); adsorption isotherms (Langmuir and Freundlich); BET surface area.

Crystal systems; Bravais lattices; Miller indices; X-ray diffraction (Bragg’s law); close packing; radius ratio rules; ionic crystals; defects in crystals (Schottky and Frenkel); semiconductors; band theory basics.

Hybridization; inductive, mesomeric, resonance, and hyperconjugation effects; IUPAC nomenclature; chirality; optical activity; R/S and E/Z configurations; conformational analysis (Newman projections); ring strain; cis-trans isomerism.

SN1/SN2 and E1/E2 reactions; electrophilic addition to alkenes and alkynes; electrophilic aromatic substitution; nucleophilic addition to carbonyls; aldol condensation; Claisen condensation; Michael addition; Diels-Alder reaction; named reactions (Grignard, Wittig, Reformatsky, Cannizzaro, Baeyer-Villiger); reactive intermediates (carbocations, carbanions, free radicals, carbenes).

Aromaticity (Hückel’s rule); EAS reactions and directing effects; nucleophilic aromatic substitution; heterocycles — pyridine, pyrimidine, furan, thiophene, pyrrole, imidazole, indole; nucleic acid bases.

Grignard and organolithium reagents; amino acids and peptides; carbohydrates (monosaccharides, glycosidic bond); polymers (condensation and addition types); dyes and pharmaceutical chemistry basics.

UV-Visible spectroscopy (chromophores, auxochromes, Beer-Lambert law); IR spectroscopy (group frequencies, fingerprint region); 1H NMR (chemical shift, spin-spin coupling, coupling constant); mass spectrometry (molecular ion peak, fragmentation patterns).

Periodic trends (atomic and ionic radii, electron affinity, ionization energy, electronegativity); VSEPR theory; molecular orbital theory; ionic and covalent bonding; Born-Haber cycle; lattice energy.

Properties of alkali and alkaline earth metals; hydrides, oxides, oxyacids, and halides; anomalous behaviour of Li and Be; diagonal relationship; boron (borax, diborane, boranes); carbon group; nitrogen group (oxides, oxyacids); oxygen group; halogen group; noble gases.

Electronic configuration of transition metals; oxidation states; colour and magnetic properties; Crystal Field Theory (octahedral, tetrahedral, and square planar complexes); spectrochemical series; coordination compounds — IUPAC nomenclature, isomerism (geometric, optical, linkage, ionization), stability constants; organometallic compounds; bioinorganic chemistry (haemoglobin, chlorophyll, vitamin B12).

Principles of UV-Vis, IR, NMR, and mass spectrometry; flame photometry; atomic absorption spectroscopy; chromatography (TLC, column, HPLC, GC); gravimetric and volumetric analysis; errors in analytical measurements.

Convergence of sequences; bounded and monotone sequences; Cauchy sequences; Bolzano-Weierstrass theorem; absolute and conditional convergence of series; tests of convergence (ratio, root, comparison, Raabe’s, Leibnitz’s); power series and radius of convergence.

Limit, continuity, and differentiability; mean value theorem; Taylor’s theorem; maxima and minima (single variable); functions of two real variables — limit, continuity, partial derivatives, total differentiability; maxima and minima; method of Lagrange multipliers; Euler’s theorem for homogeneous functions.

Fundamental theorem of calculus; definite integrals and their properties; double and triple integrals; change of order of integration; Jacobian; surface and volume integrals; Green’s theorem; Stokes’ theorem; Gauss’s divergence theorem.

First-order ODEs (exact, linear, Bernoulli, separable); Euler’s method; homogeneous and non-homogeneous ODEs with constant coefficients; variation of parameters; Cauchy-Euler equation; power series solutions; Legendre polynomials and Bessel functions (basics).

Scalar and vector fields; gradient, divergence, and curl; line integrals; surface integrals; volume integrals; applications of Green’s, Stokes’, and Gauss’s theorems.

Groups; subgroups; Abelian and non-Abelian groups; cyclic groups; permutation groups; cosets and normal subgroups; quotient groups; homomorphisms and isomorphisms; Lagrange’s theorem; Cayley’s theorem; Sylow’s theorem.

Finite-dimensional vector spaces; linear independence; basis and dimension; linear transformations; matrix representation; range space and null space; rank-nullity theorem; eigenvalues and eigenvectors; Cayley-Hamilton theorem; diagonalization; symmetric, skew-symmetric, Hermitian, skew-Hermitian, orthogonal, and unitary matrices; inner product spaces; Gram-Schmidt orthogonalization.

Open sets, closed sets, compact sets, and connected sets in ℝ; Bolzano-Weierstrass theorem; uniform continuity; sequences and series of functions; uniform convergence; Riemann integration; improper integrals; Weierstrass approximation theorem.

Origin of solar system and Earth; Earth’s internal structure and composition; geophysical methods (gravity, seismics, magnetic); plate tectonics; continental drift; sea-floor spreading; geomorphic processes; weathering; erosion; drainage patterns and landforms.

Stress and strain in the crust; folds (geometry, classification, and terminology); faults (types, nomenclature, and kinematics); joints; unconformities; geological map reading and cross-section construction; stereographic projection basics.

Major fossil groups (invertebrate — Brachiopoda, Mollusca, Echinodermata, Trilobita; plant fossils; vertebrate fossils); index fossils and stratigraphic utility; modes of preservation; evolution and extinction events.

Principles of stratigraphy (Steno’s laws, uniformitarianism); geological time scale; stratigraphic codes and nomenclature; Indian stratigraphy — Archaean, Proterozoic, Palaeozoic, Mesozoic, Cenozoic (Gondwana, Vindhyan, Deccan Traps).

Crystallography (crystal systems, symmetry elements, crystal forms); physical properties of minerals (hardness, cleavage, fracture, colour, lustre); silicate structures (nesosilicate to tectosilicate); common rock-forming minerals (feldspars, pyroxenes, amphiboles, micas, olivine, quartz, carbonates); optical properties under polarized light (birefringence, extinction angle, pleochroism).

Igneous rocks (classification, textures, intrusive and extrusive types, Bowen’s reaction series, magmatic differentiation); sedimentary rocks (textures, classification, diagenesis, depositional environments); metamorphic rocks (types, grades, P-T conditions, metamorphic zones, contact and regional metamorphism).

Ore deposits (types, classification, formation processes); mineral resources of India (coal, iron ore, bauxite, petroleum); groundwater hydrology (aquifer types, Darcy’s law); natural hazards (earthquakes, volcanoes, landslides, floods); remote sensing basics; GIS and GPS applications in geology.

Cell Biology: structure of prokaryotic and eukaryotic cells; cell cycle; mitosis and meiosis; cell signalling; membrane transport. Molecular Biology: DNA structure and replication; transcription and translation; gene regulation (operon model); recombinant DNA technology (restriction enzymes, PCR, cloning vectors, blotting techniques). Genetics: Mendelian inheritance; linkage and recombination; mutation types; chromosomal aberrations. Microbiology: bacterial growth; viruses; antibiotics and resistance mechanisms. Immunology: innate and adaptive immunity; antigens and antibodies; complement system; vaccines. Biochemistry: amino acids, proteins, enzyme kinetics; carbohydrates and metabolic pathways (glycolysis, TCA cycle, electron transport chain); lipids and lipid metabolism; nucleic acid structure. Ecology and Evolution: population ecology; biodiversity; natural selection; speciation.

Atomic structure; chemical bonding; periodic table trends; chemical thermodynamics (entropy, enthalpy, Gibbs free energy); chemical kinetics; basic organic chemistry (functional groups, isomerism, reactions); coordination chemistry basics; pH and buffer systems; spectroscopy basics.

Sets and functions; matrices and determinants; system of linear equations; differential calculus (limits, derivatives, applications); integral calculus (definite and indefinite); probability and statistics (mean, median, mode, standard deviation, basic probability, Poisson and normal distributions).

Units and dimensions; motion and Newton’s laws; work, energy, and power; properties of matter (viscosity, surface tension, elasticity); heat and thermodynamics (laws, specific heat, heat transfer); electrostatics and current electricity; magnetic effects; electromagnetic induction; optics (reflection, refraction, lenses); modern physics (photoelectric effect, radioactivity).

Sequences and Series: convergence, tests of convergence. Differential Calculus: continuity; differentiability; mean value theorems; Taylor series; maxima-minima. Integral Calculus: fundamental theorem; integration techniques; double integrals. Matrices: rank; inverse; eigenvalues and eigenvectors; systems of linear equations; Cayley-Hamilton theorem.

Axiomatic probability; conditional probability; Bayes’ theorem; independence; random variables (discrete and continuous); probability mass and density functions; expectation; moments; moment generating functions; characteristic functions.

Discrete: Binomial, Negative Binomial, Geometric, Poisson, Hypergeometric. Continuous: Uniform, Exponential, Gamma, Beta, Normal, Lognormal, Cauchy, Pareto. Joint Distributions: marginal and conditional distributions; covariance and correlation; functions of random variables; order statistics.

Convergence in probability; Central Limit Theorem; law of large numbers; sampling distributions (chi-square, t, F); point estimation (MLE, method of moments; unbiasedness, consistency, sufficiency, completeness, UMVUE); confidence intervals; hypothesis testing (z, t, chi-square, F tests); Neyman-Pearson lemma; likelihood ratio test; non-parametric tests (sign test, Wilcoxon signed-rank, Mann-Whitney, Kruskal-Wallis); simple linear regression (OLS, inference).

Consumer Theory: preference relations and utility; budget constraints; utility maximisation and demand; expenditure minimisation; Slutsky equation; income and substitution effects; demand elasticity (price, income, cross); revealed preference theory. Producer Theory: production functions (Cobb-Douglas, CES, Leontief); isoquants; cost minimisation and cost curves; profit maximisation; factor demands. Market Structures: perfect competition; monopoly (price discrimination); monopolistic competition; oligopoly (Cournot, Stackelberg, and Bertrand models). General Equilibrium: exchange economy; Walrasian equilibrium; Edgeworth box; Pareto optimality; First and Second Welfare Theorems. Market Failure: externalities and Pigouvian tax; public goods; information asymmetry (adverse selection, moral hazard, signalling). Game Theory: strategic form games; dominant strategies; Nash equilibrium; mixed strategy equilibrium; extensive form games; backward induction; subgame perfect Nash equilibrium.

National Income Accounting: GDP, GNP, NNP; measurement methods (expenditure, income, value added); nominal vs real GDP; GDP deflator. IS-LM Framework: consumption function; investment function; IS curve derivation; money demand and supply; LM curve derivation; simultaneous equilibrium; fiscal and monetary policy multipliers; crowding-out effect. AD-AS Model: aggregate demand; short-run and long-run aggregate supply; price level and output determination; stagflation. Inflation and Unemployment: types of unemployment; natural rate of unemployment; Phillips curve (short-run and long-run); adaptive and rational expectations. Open Economy: balance of payments (current and capital account); exchange rate systems; purchasing power parity; Mundell-Fleming model. Economic Growth: Harrod-Domar model; Solow growth model (steady-state, golden rule of capital accumulation, convergence); endogenous growth basics (AK model).

Descriptive statistics (central tendency, dispersion, skewness, kurtosis); probability theory (sample space, events, Bayes’ theorem); probability distributions (binomial, Poisson, normal); sampling methods and sampling distributions; point and interval estimation; hypothesis testing (z-test, t-test, chi-square test, F-test); simple and multiple linear regression (OLS assumptions, R-squared, F-test, multicollinearity basics); index numbers (Laspeyres, Paasche, Fisher); time series basics (trend, seasonality).

Economic planning in India (Five-Year Plans, NITI Aayog); poverty (measurement, trends, anti-poverty programmes); inequality (Gini coefficient, Lorenz curve); agriculture sector (land reforms, Green Revolution, agricultural marketing, food security); industrial sector (industrial policy, public sector, 1991 liberalisation); foreign trade and balance of payments; monetary policy and RBI functions; fiscal policy (Union Budget, FRBM Act); banking sector reform; inflation trends; unemployment types; human development indicators (HDI, education, health).

Linear Algebra: matrix operations (addition, multiplication, transpose); determinants; rank; inverse; system of linear equations (Cramer’s rule, Gauss elimination); eigenvalues and eigenvectors. Calculus: univariate and multivariate functions; derivatives (chain rule, product rule); partial derivatives; total differential; implicit differentiation; Euler’s theorem for homogeneous functions. Optimisation: unconstrained optimisation (first and second order conditions, Hessian matrix); constrained optimisation (Lagrange multipliers, bordered Hessian; Kuhn-Tucker conditions); Envelope theorem. Differential Equations: first-order linear differential equations; stability analysis of equilibria.