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

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 and second-order linear differential equations with constant coefficients; matrices and determinants; algebra of complex numbers.

Newton’s laws and their applications; velocity and acceleration in Cartesian, polar, and cylindrical coordinate systems; uniformly rotating frame; centrifugal and Coriolis forces; motion under a central force; Kepler’s laws; gravitational law and field; conservative and non-conservative forces; system of particles; centre of mass; conservation of linear momentum, angular momentum, and energy; variable mass systems; elastic and inelastic collisions; rigid body motion; moments of inertia; parallel and perpendicular axes theorems; kinematics of moving fluids; equation of continuity; Euler’s equation; Bernoulli’s theorem.

Differential equation of simple harmonic oscillator; damped and forced oscillations; resonance; Lissajous figures; wave equation; travelling and stationary waves in one dimension; energy density and energy transmission in waves; group velocity and phase velocity; sound waves; Doppler effect; Fermat’s principle; thick and thin lens theory; interference of light; Fraunhofer diffraction; Rayleigh criterion and resolving power; diffraction gratings; polarization of light.

Coulomb’s law; Gauss’s law; electric field and potential; solution of Laplace’s equation for simple cases; conductors, capacitors, and dielectrics; electrostatic energy; Biot-Savart law; Ampere’s law; Faraday’s law of electromagnetic induction; self and mutual inductance; alternating currents; RL, RC, and LC circuits; AC generator and transformer; Maxwell’s equations; plane electromagnetic waves; Poynting vector; reflection and refraction at a dielectric interface.

Kinetic theory of gases; velocity distribution; equipartition of energy; specific heat of mono, di, and tri-atomic gases; ideal gas; van der Waals gas and equation of state; mean free path; Zeroth, First, and Second Laws of thermodynamics; isothermal and adiabatic processes; entropy; Carnot cycle; Maxwell’s thermodynamic relations; thermodynamic potentials; phase transitions; Clausius-Clapeyron equation; Maxwell-Boltzmann, Fermi-Dirac, and Bose-Einstein distributions.

Special theory of relativity; Lorentz transformations; length contraction; time dilation; relativistic velocity addition; mass-energy equivalence; blackbody radiation; photoelectric effect; Compton effect; Bohr’s atomic model; wave-particle duality; uncertainty principle; Schrödinger equation and solutions for one- and three-dimensional boxes; one-dimensional harmonic oscillator; reflection and transmission at a step potential; Pauli exclusion principle; nuclear structure; alpha, beta, and gamma decay; fission and fusion.

Crystal structure; Bravais lattices; Miller indices; X-ray diffraction and Bragg’s law; intrinsic and extrinsic semiconductors; Fermi level; p-n junction diode; I-V characteristics; Zener diode; BJT characteristics; MOSFET; operational amplifiers and applications; Boolean algebra; binary number systems; combinational and sequential digital circuits; cathode ray oscilloscope.

Functions and their properties; maxima and minima; integrals; ordinary differential equations; vectors and matrices; determinants; elementary statistics and probability theory.

Atomic and Molecular Structure: Hydrogen atom wave functions; orbital shapes and energies; Hückel’s molecular orbital theory for conjugated systems.

Theory of Gases: Equations of state for ideal and non-ideal gases (van der Waals); kinetic theory; Maxwell-Boltzmann distribution.

Chemical Thermodynamics: First, Second, and Third Laws; Gibbs free energy; chemical potential; Hess’s law; bond and resonance energies.

Chemical and Phase Equilibria: Law of mass action; Le Chatelier’s principle; activities; Gibbs phase rule; Clausius-Clapeyron equation.

Electrochemistry: Debye-Hückel theory; electrochemical cells; standard electrode potentials; Nernst equation; Faraday’s laws of electrolysis.

Chemical Kinetics: Reaction rate laws; integrated rate expressions; Arrhenius equation; collision theory; activation energy; enzyme kinetics basics.

Adsorption: Gibbs and Langmuir adsorption isotherms; surface phenomena; BET isotherm.

Spectroscopy: Beer-Lambert law; rotational and vibrational spectroscopy; UV-Vis spectroscopy; NMR basics — chemical shift and coupling constants.

Basic Concepts and Stereochemistry: Hybridization; electronic effects (inductive, resonance, hyperconjugation); aromaticity; optical and geometrical isomerism; conformational analysis of ethane and cyclohexane; chirotopic centers; R/S nomenclature.

Organic Reaction Mechanisms and Synthetic Applications: SN1, SN2, E1, E2 reactions; electrophilic and nucleophilic addition; Diels-Alder reaction; Aldol condensation; Claisen rearrangement; Mannich reaction; Grignard and organolithium reagents; retrosynthetic analysis.

Qualitative Organic Analysis: Detection of elements; detection and identification of functional groups — alcohols, aldehydes, ketones, amines, and carboxylic acids.

Aromatic and Heterocyclic Chemistry: Benzene and substituted benzenes; electrophilic aromatic substitution; Birch reduction; heterocyclic compounds — pyridine, pyrimidine, purine, furan, thiophene, pyrrole, indole, and quinoline.

Periodic Table: Effective nuclear charge; periodic trends in atomic radius, electronegativity, ionization energy, and electron affinity.

Chemical Bonding: Lewis structures; VSEPR theory; MO theory; hybridization; hydrogen bonding; van der Waals interactions.

Main Group Elements (s and p blocks): Hydrides, oxides, oxyacids, and halides of Groups 1, 2, 13–17; noble gas chemistry; pseudohalogens.

Transition Metals (d block): General properties; coordination chemistry; crystal field theory; color; magnetic properties; spectrochemical series; organometallic compounds.

Bioinorganic Chemistry: Metal ions in biology — haemoglobin, myoglobin, cytochrome, chlorophyll, carbonic anhydrase, and vitamin B12.

Instrumental Methods and Analytical Chemistry: UV-Visible, IR, NMR, and Mass Spectrometry basics; flame tests; gravimetric and volumetric analysis.

Convergence of sequences; bounded and monotone sequences; Cauchy sequences; subsequences; Bolzano-Weierstrass theorem; convergence criteria for series of real numbers; absolute and conditional convergence; comparison, ratio, root, and Leibniz tests; power series (radius and interval of convergence).

Limit; continuity; intermediate value property; differentiation; Rolle’s theorem; mean value theorem; L’Hôpital rule; Taylor’s theorem; maxima and minima; Riemann integration (Riemann sums; fundamental theorem of calculus; improper integrals).

Limit and continuity of functions of two and three variables; partial derivatives; total derivative; directional derivatives; maxima and minima; saddle points; Lagrange’s method of multipliers; double and triple integrals and their applications to area and volume.

Integration as inverse of differentiation; definite integrals and properties; fundamental theorem of integral calculus; double and triple integrals; change of order of integration; calculating surface areas and volumes using double integrals; calculating volumes using triple integrals.

ODEs of the first order — variable separable, homogeneous, exact, and Bernoulli’s forms; orthogonal trajectories; linear ODEs of second and higher order with constant coefficients; method of variation of parameters; Cauchy-Euler equation; systems of first-order linear ODEs.

Scalar and vector fields; gradient; divergence; curl; line integrals; surface integrals; Green’s theorem in the plane; Stokes’ theorem; Gauss’ divergence theorem and their applications.

Groups; subgroups and their examples; the order of a group; Lagrange’s theorem; normal subgroups; quotient groups; homomorphism and isomorphism of groups; cyclic groups; center of a group; product of two groups; permutation groups; Cayley’s theorem.

Finite-dimensional vector spaces over real or complex fields; linear independence; basis; dimension; linear transformations; matrix representation; range space; null space; rank-nullity theorem; rank and inverse of a matrix; determinant; systems of linear equations; consistency conditions; eigenvalues and eigenvectors; Cayley-Hamilton theorem; diagonalization.

Interior points; limit points; open sets; closed sets; bounded sets; connected sets; compact sets; completeness of the real line; power series (radius of convergence; term-by-term differentiation and integration); Fourier series; uniform convergence; Weierstrass M-test.

Sequences and series of real numbers; limits; continuity and differentiability; mean value theorems; Riemann integration; functions of two variables; partial derivatives; maxima and minima; matrices; determinants; eigenvalues and eigenvectors; systems of linear equations.

Probability: Axiomatic probability; conditional probability and independence; Bayes’ theorem; classical and frequency definitions.

Random Variables: Discrete and continuous random variables; expectation; variance; moments and moment generating functions; probability generating functions.

Standard Distributions: Bernoulli; binomial; Poisson; geometric; uniform; exponential; gamma; beta; normal distributions and their properties.

Sampling Distributions: Chi-square; t; F distributions and their uses; central limit theorem; law of large numbers.

Joint Distributions: Joint, marginal, and conditional distributions; covariance; correlation coefficient; bivariate normal distribution.

Estimation: Unbiasedness; consistency; efficiency; sufficiency; completeness; Maximum Likelihood Estimation (MLE) and method of moments; Cramer-Rao lower bound; interval estimation.

Testing of Hypotheses: Basic concepts; simple and composite hypotheses; Type I and Type II errors; Neyman-Pearson lemma; likelihood ratio tests; power of a test; UMP tests; p-value.

General Biology: Taxonomy; heredity; genetic variation; conservation principles; morphology of plants and animals.

Biochemistry and Physiology: Carbohydrates, proteins, lipids, and nucleic acids; enzyme kinetics (Michaelis-Menten); cofactors and coenzymes; respiration; photosynthesis; nitrogen fixation; plant and animal hormones; nervous and endocrine systems; immunity.

Molecular Biology: DNA structure, replication, and repair; RNA transcription and processing; protein translation; gene regulation in prokaryotes and eukaryotes; restriction mapping; recombinant DNA technology; PCR; DNA fingerprinting.

Cell Biology: Prokaryotic and eukaryotic cell structures; cell cycle; mitosis and meiosis; cell signaling; membrane structure and transport.

Microbiology: Classification of microorganisms; bacterial growth curves; aseptic techniques; culture media; viruses; prions.

Genetics: Mendelian genetics; linkage and recombination; gene mapping; chromosomal mutations; non-Mendelian inheritance.

Plant and Animal Biotechnology: Cloning vectors; gene expression systems; monoclonal antibodies; stem cell technology; transgenic animals and plants; CRISPR basics.

Food Biotechnology: Fermentation; probiotics; food safety standards; genetically modified organisms (GMOs).

Atomic structure and bonding; acids and bases (Brønsted-Lowry and Lewis); nucleophilic substitution and electrophilic addition mechanisms; stereochemistry; chemical equilibrium and thermodynamics; electrochemistry; coordination chemistry; carbohydrates, amino acids, peptides, and lipids from an organic chemistry perspective.

Sets, relations, and functions; mathematical induction; logarithms; complex numbers; linear and quadratic equations; sequences and series; trigonometry; two-dimensional coordinate geometry; limits; differential calculus (derivatives; tangents; maxima and minima); integral calculus (integration techniques; definite integrals; area under curves); differential equations; permutations and combinations; statistics (central tendency; dispersion; correlation); probability (classical, axiomatic; conditional; Bayes’ theorem; binomial and Poisson distributions).

Consumer theory — utility maximization; demand curves; elasticity; income and substitution effects; Slutsky equation; revealed preference; producer theory — production functions; cost curves; profit maximization; duality; market structures — perfect competition; monopoly; price discrimination; monopolistic competition; oligopoly (Cournot, Bertrand, and Stackelberg models); general equilibrium and welfare economics (Pareto efficiency; social welfare functions); externalities; public goods; game theory (Nash equilibrium; prisoner’s dilemma; mixed strategies).

National income accounting — GDP, GNP, NNP, NDP; circular flow; Keynesian income-expenditure model; IS-LM model; AD-AS framework; money supply and demand; monetary policy (tools and transmission); fiscal policy (multiplier effects; crowding out); inflation — types, causes, and measurement; Phillips curve; balance of payments; exchange rate systems; Mundell-Fleming model; growth models — Harrod-Domar; Solow growth model; golden rule of accumulation.

Probability theory; standard distributions — normal; binomial; Poisson; statistical inference — point and interval estimation; hypothesis testing; regression analysis — OLS estimation; R-squared; interpretation of coefficients; multicollinearity; heteroskedasticity; autocorrelation; time series — trend, seasonality, and stationarity basics.

Indian economy since independence; GDP growth and structural change; poverty measurement — headcount ratio; poverty line; alleviation programs; agriculture — green revolution; land reforms; MSP policy; industry — 1991 liberalization; industrial policy; trade policy and WTO; monetary policy in India (RBI and its tools); fiscal policy and government budget; HDI; demographic dividend and labor markets.

Differential calculus (single and multivariable); unconstrained and constrained optimization (Lagrange multipliers; Kuhn-Tucker conditions); integral calculus; linear algebra (matrices; determinants; Cramer’s rule; eigenvalues); difference equations; differential equations; input-output analysis; comparative statics.

Concepts of stress and strain in the crust; geological mapping and map interpretation; attitude of beds (strike, dip, and plunge); outcrop patterns; folds — types, geometry, and classification; faults — normal, reverse, strike-slip, and thrust; joints; foliations; lineations; unconformities and their recognition; stereographic projections and their use in structural analysis.

Crystal systems and symmetry; Miller indices; crystallographic notation; optical mineralogy — polarizing microscope; refractive index; birefringence; extinction angle; pleochroism; optic sign; silicate mineral groups — olivine, pyroxene, amphibole, feldspar, mica, quartz, garnet, and their distinguishing optical properties; non-silicate minerals — carbonates (calcite, dolomite), oxides (magnetite, hematite), and sulfides (pyrite, galena).

Igneous Petrology: Magma types and composition; Bowen’s reaction series; IUGS classification of igneous rocks; textures and structures; intrusive (plutonic) and extrusive (volcanic) bodies; magmatic differentiation; fractional crystallization; binary and ternary phase diagrams.

Sedimentary Petrology: Clastic and chemical sedimentary rocks; siliciclastic and carbonate sedimentology; diagenesis; sedimentary environments and facies; provenance analysis.

Metamorphic Petrology: Types of metamorphism (contact, regional, dynamic); metamorphic zones and grades; index minerals; P-T-t paths; metamorphic facies (greenschist, amphibolite, granulite, eclogite).