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

Taxonomy of plants and animals; Prokaryotic and eukaryotic organisms; Cell organelles and their function; Biological macromolecules — carbohydrates, lipids, proteins, nucleic acids; Mendel’s laws and their extensions; Cell division — mitosis and meiosis; Fundamentals of genetics (linkage, crossing over, gene mapping); Basic plant physiology; Basic animal physiology; Origin of life and fundamentals of evolutionary biology.

Carbohydrates, lipids, proteins, and nucleic acids — structure and function; Enzyme kinetics — Michaelis-Menten equation, enzyme inhibition (competitive, non-competitive, uncompetitive), allosteric regulation; Vitamins and coenzymes; Bioenergetics; Metabolic pathways — glycolysis, TCA cycle, oxidative phosphorylation, pentose phosphate pathway, fatty acid metabolism; Hormones and their mechanisms of action; Homeostasis; pH and temperature regulation.

Tissue culture — plant and animal cell culture; Vaccines — types and production; Antibody production and hybridoma technology; Recombinant DNA technology — restriction enzymes, vectors (plasmids, bacteriophages, cosmids, BAC, YAC), cloning strategies; PCR — standard, RT-PCR, qPCR; ELISA — direct, indirect, sandwich; Gel electrophoresis; Southern, Northern, and Western blotting; Applications in health, agriculture, and environment; Biosensors.

DNA replication — prokaryotic and eukaryotic mechanisms; Transcription — prokaryotic and eukaryotic; Translation — ribosomes, tRNA, genetic code properties; DNA repair mechanisms (excision repair, mismatch repair); Post-translational modifications; Regulation of gene expression — lac operon, trp operon, eukaryotic transcription factors; Chromatin structure and epigenetics; RNA processing — splicing, 5’ capping, 3’ polyadenylation; Signal transduction pathways (cAMP, IP3, MAPK).

Cell cycle — G1, S, G2, M phases; Checkpoints (G1/S, G2/M, spindle assembly); Cyclins and cyclin-dependent kinases (CDKs); Apoptosis — intrinsic and extrinsic pathways; Intracellular transport — ER to Golgi, vesicular trafficking; Cell signalling — receptor tyrosine kinases, GPCRs; Membrane structure — fluid mosaic model, lipid bilayer; Cytoskeleton — actin filaments, microtubules, intermediate filaments; Cell adhesion molecules; Cancer biology — oncogenes, tumour suppressors; Stem cells.

Microbial diversity — bacteria, fungi, viruses, protozoa; Microbial nutrition and growth kinetics — growth curve (lag, log, stationary, death phases); Sterilisation and disinfection methods; Microbial genetics — transformation, conjugation, transduction, transposons, plasmids; Antimicrobial agents and resistance mechanisms; Industrial microbiology — fermentation, bioreactors; Environmental microbiology — nitrogen and carbon cycling; Pathogen-host interactions.

Sets, functions, and relations; Differential calculus — limits, continuity, derivatives, application to maxima/minima; Integral calculus — definite and indefinite integrals; First-order differential equations; Matrices and determinants; Probability theory — basic rules, conditional probability, Bayes’ theorem; Descriptive statistics — mean, median, mode, standard deviation, variance; Statistical distributions — Binomial, Poisson, Normal; Hypothesis testing — t-test, chi-square test; Regression and correlation.

Quantum mechanics fundamentals; Particle in a box; Harmonic oscillator; Hydrogen atom wave functions; Many-electron atoms (Slater’s rules); Molecular orbital theory (LCAO-MO); Hybridisation; Hückel molecular orbital theory; Aromaticity; Molecular symmetry (point groups, character tables, selection rules).

Kinetic theory of gases; Ideal gas law; Real gases — van der Waals equation, Boyle temperature; Maxwell-Boltzmann distribution; Critical constants and critical phenomena; Effusion and diffusion (Graham’s law); Virial equation of state; Liquefaction of gases.

First, second, and third laws of thermodynamics; State functions; Gibbs and Helmholtz free energy; Chemical potential; Gibbs-Duhem equation; Phase rule (Gibbs) and phase diagrams; Colligative properties; Chemical equilibrium — Le Chatelier’s principle, Kp, Kc; Thermodynamics of solutions and mixing.

Rate laws; Order and molecularity; Integrated rate equations; Arrhenius equation; Activation energy; Collision theory; Transition state theory; Enzyme kinetics (Michaelis-Menten); Chain reactions; Photochemical reactions; Homogeneous and heterogeneous catalysis.

Ionic conduction; Debye-Hückel theory; Electrolytic and galvanic cells; Nernst equation; Standard electrode potentials; Electrochemical series; Basics of UV-Vis spectroscopy (Beer-Lambert law); IR spectroscopy — functional group identification; ¹H NMR spectroscopy — chemical shift, spin-spin coupling, multiplicity; Mass spectrometry — molecular ion peak, fragmentation patterns.

IUPAC naming of all organic compound classes; Optical isomerism — chirality, enantiomers, diastereomers, R/S nomenclature, optical rotation; Geometric isomerism — E/Z; Conformational analysis — Newman projections, chair and boat conformations; Relative and absolute configuration; Racemic mixtures and resolution.

SN1 and SN2 reactions; E1 and E2 reactions; Electrophilic aromatic substitution — nitration, sulfonation, halogenation, Friedel-Crafts; Nucleophilic aromatic substitution; Electrophilic addition to alkenes and alkynes; Carbonyl chemistry — nucleophilic addition, acyl substitution; Rearrangement reactions (Baeyer-Villiger, Beckmann, Pinacol, Fries); Free radical reactions.

Alkanes, alkenes, alkynes — preparation and reactions; Arenes and aromatic compounds; Alcohols and phenols — acidity, reactions; Ethers and epoxides; Aldehydes and ketones — Aldol condensation, Cannizzaro, Wittig; Carboxylic acids and derivatives (esters, amides, acid chlorides, anhydrides); Amines — basicity, reactions; Heterocyclic chemistry (pyridine, pyrrole, furan, thiophene).

Carbohydrates — classification (aldoses, ketoses), ring structures (Haworth projections), reactions; Amino acids — classification, isoelectric point, peptide bonds; Proteins — primary to quaternary structure; Nucleic acids — DNA and RNA structure; Vitamins; Terpenes and steroids; Basics of polymers and dyes.

Periodic trends — atomic radii, ionisation energies, electron affinities, electronegativity; Chemistry of s-block elements (Groups 1 and 2); p-block elements — Groups 13–18 including boranes, silicones, phosphazenes, interhalogen compounds; Hydrogen and its compounds; Lewis and Brønsted acid-base theories; HSAB principle; Noble gas chemistry.

d-block element properties — variable oxidation states, colour, magnetism; Coordination compounds — IUPAC nomenclature, coordination number, isomerism (geometric, optical, linkage, ionisation); Bonding theories — VBT, Crystal Field Theory (CFT), Molecular Orbital Theory; Crystal field splitting — high spin vs low spin; Organometallics — 18-electron rule, sandwich compounds; Catalytic applications.

Radioactivity — alpha, beta, gamma decay; Radioactive decay series; Nuclear reactions; Binding energy and mass defect; Fission and fusion; Biologically important metal ions (Fe, Cu, Zn, Mo, Co); Metalloporphyrins — haemoglobin, myoglobin, chlorophyll; Metal-enzyme systems; Bioinorganic aspects of nitrogen fixation.

Consumer preferences and utility; Budget constraints; Utility maximisation; Slutsky equation; Revealed preference; Production functions (Cobb-Douglas, CES); Cost and revenue concepts; Market structures — perfect competition, monopoly, oligopoly (Cournot, Bertrand), monopolistic competition; Game theory — Nash equilibrium, dominant strategies, mixed strategies; General equilibrium; Welfare economics (Pareto optimality, social welfare functions); Externalities and public goods; Asymmetric information (adverse selection, moral hazard).

National income accounting (GDP, GNP, NNP); Keynesian theory of income and employment; IS-LM model; AD-AS framework; Phillips curve; Consumption theories (Keynesian, Permanent Income Hypothesis, Life Cycle Hypothesis); Investment theories; Money supply and banking (money multiplier); Monetary policy — instruments and transmission; Fiscal policy and multiplier; Open economy (Mundell-Fleming model); Balance of payments; Exchange rate systems; Solow growth model; Endogenous growth.

Probability theory — axioms, conditional probability, Bayes’ theorem; Random variables — discrete and continuous; Distributions — Binomial, Poisson, Normal; Sampling theory; OLS estimation — BLUE properties (Gauss-Markov theorem); Hypothesis testing — t-test, F-test, chi-square test; Index numbers; Time series — components and decomposition; Correlation coefficient; Simple and multiple regression.

Economic history post-Independence; Five-year plans and NITI Aayog; Poverty and inequality measurement; Agriculture in India — Green Revolution, land reforms; Industrial policy evolution; Economic reforms of 1991; Banking and financial sector; GST and fiscal federalism; HDI and human development; Recent government economic schemes and flagship programmes.

Functions — domain, range, continuity, differentiability; Differential calculus — single and multivariable derivatives; Integration and economic applications; Unconstrained optimisation — second-order conditions; Constrained optimisation — Lagrange multiplier method; Matrix algebra — rank, determinants, eigenvalues; Linear programming — graphical and simplex; Differential equations; Difference equations — economic dynamics.

Origin and interior structure of the Earth — crust, mantle, core; Plate tectonics — sea-floor spreading, continental drift, convergent and divergent margins, subduction zones, hot spots; Earthquakes — types of seismic waves, Richter scale, seismicity patterns; Volcanism — types of volcanoes and volcanic rocks; Geomorphic processes; Hydrological cycle; Geologic time scale; Geochronology — radiometric dating methods (U-Pb, K-Ar, Rb-Sr).

Weathering — physical, chemical, and biological; Mass wasting; Erosion and deposition processes; Fluvial landforms (flood plains, terraces, alluvial fans, deltas); Glacial landforms (moraines, drumlins, eskers); Aeolian landforms (dunes, loess); Coastal landforms; Drainage patterns and basin morphometry; Basics of remote sensing — electromagnetic spectrum, resolution types; GIS applications in geological mapping.

Stress and strain — principal stresses, strain ellipsoid, brittle and ductile deformation; Folds — classification (anticline, syncline, isoclinal, overturned), nomenclature, fold mechanisms; Faults — normal, reverse, thrust, strike-slip — recognition in field and maps; Joints and fractures; Cleavage — slaty, crenulation, fracture; Geological map reading and construction; Strike and dip measurement; Stereographic projections (equal-angle, Wulff net); Kinematic indicators.

Fossils and fossilisation processes; Morphology and classification of major invertebrate groups — Brachiopoda, Mollusca (Bivalvia, Gastropoda, Cephalopoda), Echinodermata, Coelenterata; Vertebrate fossil groups; Plant fossils (leaf impressions, coal balls, spores, pollen); Microfossils (Foraminifera, Ostracoda, Conodonts); Index fossils and their stratigraphic importance; Biostratigraphy; Evolutionary trends in geological time.

Laws of stratigraphy — superposition, original horizontality, lateral continuity, cross-cutting relationships; Indian stratigraphic column — Archaean to Quaternary; Sedimentary processes — transportation and deposition; Sedimentary structures — cross-bedding, graded bedding, ripple marks, bioturbation; Classification of sedimentary rocks; Facies and facies models; Diagenesis; Gondwana sequence; Deccan Traps; Flysch and Molasse.

Crystallography — seven crystal systems, symmetry elements (axes, planes, centres), crystal forms and habits; Optical mineralogy — isotropic vs anisotropic minerals, refractive index (RI), birefringence, extinction angle, pleochroism; Physical properties — hardness (Mohs scale), cleavage, lustre, colour, streak; Silicate classification (nesosilicates to tectosilicates); Major rock-forming minerals — feldspar, pyroxene, amphibole, mica, olivine, quartz, calcite; Common ore minerals.

Igneous petrology — IUGS classification, textures (phaneritic, aphanitic, porphyritic, glassy), structures, Bowen’s reaction series, crystallisation order, plutonic and volcanic rock types; Sedimentary petrology — clastic and non-clastic classification and description; Metamorphic petrology — types of metamorphism (contact, regional, dynamic), Barrovian metamorphic zones, facies concept (P-T fields), metamorphic textures (foliation, lineation, porphyroblasts); P-T-t paths.

Mineral deposit classification — magmatic, hydrothermal, sedimentary, residual, placer; Important metallic deposits of India — iron ore (Bailadila), copper (Khetri), bauxite, manganese, gold, uranium; Non-metallic deposits — limestone, rock phosphate, mica; Groundwater geology — aquifer types, Darcy’s law, water table; Engineering geology basics — site investigation, rock mechanics; Coal types and formation; Petroleum geology — source rock, reservoir, traps; Environmental geology and geohazards.

Sequences — convergence and divergence; Bounded and monotone sequences; Cauchy criterion; Subsequences and Bolzano-Weierstrass theorem; Limit superior and limit inferior; Series of real numbers — absolute and conditional convergence; Tests of convergence — comparison, limit comparison, ratio, root, Dirichlet, Abel; Power series — radius of convergence, interval of convergence, term-by-term differentiation and integration.

Limits and continuity; Intermediate value theorem; Uniform continuity; Differentiability; Rolle’s theorem; Mean value theorems (Lagrange and Cauchy); Taylor’s theorem with Lagrange remainder; L’Hôpital’s rule; Monotone functions and inverse functions; Maxima and minima; Riemann integration — definition and properties; Fundamental theorem of calculus; Improper integrals — convergence tests.

Limits and continuity of multivariable functions; Partial derivatives; Differentiability and total derivative; Directional derivatives; Gradient vector; Chain rule for composite functions; Taylor’s theorem in two variables; Maxima, minima, and saddle points — second derivative test; Lagrange multipliers for constrained optimisation; Double and triple integrals — Fubini’s theorem; Change of variables and Jacobians.

Techniques of integration — substitution, integration by parts, trigonometric substitution, partial fractions; Beta function — properties, relation to Gamma function; Gamma function — properties and recurrence relation; Line integrals — scalar and vector line integrals; Surface integrals; Volume integrals; Green’s theorem in the plane; Divergence theorem (Gauss); Stokes’ theorem; Applications to area, volume, and flux calculations.

First-order ODEs — separable, homogeneous, exact, linear (integrating factor); Bernoulli’s equation; Second-order linear ODEs with constant coefficients — complementary function and particular integral (methods of undetermined coefficients and variation of parameters); Cauchy-Euler equations; Systems of linear ODEs; Power series solutions near ordinary and regular singular points (Frobenius method).

Scalar and vector fields; Gradient, divergence, and curl; Laplacian operator; Line integrals and independence of path; Surface integrals — flux; Green’s, Gauss’s, and Stokes’ theorems; Conservative fields and potential functions; Irrotational and solenoidal fields; Curvilinear coordinates — cylindrical and spherical.

Groups — definition, examples (integers mod n, symmetric group, dihedral group, matrix groups); Subgroups and their properties; Cosets; Lagrange’s theorem; Normal subgroups; Quotient groups; Group homomorphisms and isomorphisms; First isomorphism theorem; Cyclic groups and their properties; Permutation groups — cycle notation, alternating group; Sylow’s first, second, and third theorems with applications; Classification of finitely generated abelian groups.

Vector spaces and subspaces over R and C; Linear independence, span, basis, and dimension; Linear transformations — kernel, image, rank-nullity theorem; Matrix representation of linear transformations; Eigenvalues and eigenvectors; Characteristic and minimal polynomials; Diagonalisation — conditions and procedure; Cayley-Hamilton theorem; Inner product spaces; Gram-Schmidt orthonormalisation; Unitary and orthogonal matrices; Symmetric, Hermitian, and skew-Hermitian matrices; Quadratic forms — classification (positive definite, etc.).

Metric spaces — definition, open and closed sets, interior, boundary, closure; Compactness — Heine-Borel theorem, sequential compactness; Connectedness; Completeness — Cauchy sequences in metric spaces, Banach fixed-point theorem; Sequences and series of functions — pointwise and uniform convergence; Weierstrass M-test; Uniform convergence and continuity/differentiability/integrability; Power series; Functions of bounded variation; Riemann-Stieltjes integral.

Sequences and series — convergence and tests; Differential calculus — Rolle’s theorem, MVT, Taylor’s theorem, L’Hôpital’s rule; Riemann integration — Fundamental theorem of calculus; Multiple integrals — double and triple; Beta and Gamma functions — properties and evaluation; Improper integrals.

Matrices and determinants; Rank of a matrix; System of linear equations — consistency; Eigenvalues and eigenvectors; Orthogonality and orthonormal bases; Quadratic forms; Positive semi-definite matrices; Vector spaces and subspaces.

First-order ODEs — separable, linear, Bernoulli; Second-order linear ODEs with constant coefficients — complementary function and particular integral; Method of undetermined coefficients; Variation of parameters; Cauchy-Euler equations.

Axiomatic probability; Conditional probability and independence; Bayes’ theorem; Random variables — discrete and continuous; CDF, PMF, and PDF; Expectation, variance, and higher moments; Moment generating functions; Characteristic functions; Chebyshev inequality; Markov inequality; Jensen’s inequality; Convergence in probability; Weak law of large numbers; Central Limit Theorem (Lindeberg-Lévy).

Discrete distributions — Uniform, Bernoulli, Binomial, Poisson, Geometric, Negative Binomial, Hypergeometric; Continuous distributions — Uniform, Normal, Exponential, Gamma, Beta, Cauchy, Lognormal; Bivariate Normal distribution; Marginal and conditional distributions; Transformations of random variables (univariate and bivariate); Sampling distributions — chi-square, t (Student’s), F.

Point estimation — unbiasedness, consistency, efficiency; Sufficiency — Factorisation theorem, minimal sufficient statistics; Completeness; MVUE — Rao-Blackwell theorem; Cramér-Rao lower bound; Methods of estimation — Maximum Likelihood Estimation (MLE), method of moments; Interval estimation — confidence intervals for normal population parameters; Hypothesis testing — simple and composite hypotheses, Neyman-Pearson lemma, UMP tests, likelihood ratio tests; Chi-square test for goodness of fit and independence; t-test and F-test; Non-parametric tests — sign test, Wilcoxon signed-rank test, Mann-Whitney U test, run test.

Simple random sampling — with and without replacement; Stratified random sampling — proportional and Neyman allocation; Systematic sampling; Cluster sampling; One-way and two-way ANOVA — assumptions, F-test, multiple comparison tests; Design of experiments — CRD, RBD, LSD — efficiency comparisons; Factorial designs (2² and 2³); Simple linear regression — OLS, testing, confidence intervals; Multiple linear regression; Gauss-Markov theorem; Regression diagnostics.

Vector calculus — gradient, divergence, curl; Stokes’ and Gauss’ (divergence) theorems; Curvilinear coordinates — spherical and cylindrical; Linear algebra — matrices, eigenvalues, eigenvectors; Partial differential equations — Laplace, diffusion, wave equation; Special functions — Legendre polynomials, Bessel functions, Hermite polynomials; Fourier series and Fourier transforms; Laplace transforms; Complex analysis — analytic functions, Cauchy’s integral theorem, residue theorem, contour integration.

Newton’s laws; Conservation of energy and linear momentum; Elastic and inelastic collisions; Centre of mass frame; Rigid body dynamics — moment of inertia tensor, parallel and perpendicular axes theorems; Euler’s equations; Non-inertial frames — pseudo forces, rotating frames, Coriolis force; Central force problem — effective potential, Kepler’s laws; Gravitational potential energy; Elasticity — Young’s modulus, bulk modulus; Viscosity — Stokes’ law; Surface tension; Fluid dynamics — Bernoulli’s equation, Poiseuille flow.

Damped harmonic oscillator; Forced oscillations; Resonance and Q-factor; Coupled oscillators — normal modes; Wave equation and its solutions; Group velocity and phase velocity; Standing waves; Doppler effect; Diffraction — single slit, double slit, diffraction grating; Interference — Young’s double slit, Lloyd’s mirror, Fabry-Perot etalon, Michelson interferometer; Polarisation — Malus’ law, Brewster’s angle, wave plates; Geometric optics — reflection, refraction, thin lenses, mirror equation.

Electrostatics — Coulomb’s law, Gauss’s law (differential and integral form), electric potential; Conductors and dielectrics — polarisation, displacement field D; Laplace and Poisson equations; Method of images; Magnetostatics — Biot-Savart law, Ampere’s law, magnetic vector potential; Faraday’s law and Lenz’s law; Maxwell’s equations — in free space and in matter; Electromagnetic waves — wave equation, Poynting vector, radiation pressure; Boundary conditions at interfaces; AC circuits — RC, RL, LC; LCR resonance — series and parallel.

Kinetic theory — Maxwell-Boltzmann speed distribution, equipartition theorem, mean free path, transport phenomena; Zeroth, first, second, and third laws of thermodynamics; Carnot cycle and efficiency; Entropy — definition, properties, and increase in irreversible processes; Thermodynamic potentials — internal energy (U), enthalpy (H), Helmholtz free energy (F), Gibbs free energy (G); Maxwell’s thermodynamic relations; Phase transitions — Clausius-Clapeyron equation; van der Waals gas; Statistical mechanics basics — Boltzmann distribution, partition function, free energy.

Special Theory of Relativity — postulates, Lorentz transformations, time dilation, length contraction, relativistic momentum and energy, mass-energy equivalence (E = mc²); Photoelectric effect; Compton effect; de Broglie hypothesis; Davisson-Germer experiment; Bohr model of the hydrogen atom — energy levels and spectral series; Characteristic and continuous X-rays; Radioactivity — alpha, beta, gamma decay; Half-life and decay law; Nuclear reactions; Liquid drop model; Nuclear fission and fusion; Elementary particles and basic conservation laws.

Wave-particle duality; Schrödinger equation — time-dependent and time-independent; Wave functions — normalisation and Born interpretation; Operators and observables; Commutation relations; Heisenberg uncertainty principle; Particle in a box (1D and 3D); Quantum harmonic oscillator — ladder operators, energy levels; Hydrogen atom — energy levels, quantum numbers (n, l, m, s), radial wave functions; Angular momentum operator and spherical harmonics; Spin — Pauli matrices; Addition of angular momenta; Time-independent perturbation theory (first and second order); Variational method; Identical particles — bosons and fermions, Pauli exclusion principle.

Crystal structure — Bravais lattices, basis, Miller indices, reciprocal lattice; X-ray diffraction — Bragg’s law, powder method; Free electron theory — Drude model, Sommerfeld model, Fermi energy; Band theory — energy bands, Bloch’s theorem, Brillouin zones; Metals, insulators, and semiconductors; Intrinsic and extrinsic semiconductors — carrier concentration, Fermi level; p-n junction — I-V characteristics, Zener breakdown; Bipolar junction transistor (BJT) basics; Op-amp — inverting and non-inverting amplifier; Boolean algebra; Logic gates (AND, OR, NOT, NAND, NOR, XOR, XNOR); Flip-flops; Superconductivity — Meissner effect, Type I and Type II superconductors, BCS theory (qualitative).