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

Convergence of sequences; bounded and monotone sequences; Cauchy sequences; Bolzano-Weierstrass theorem; absolute and conditional convergence; tests of convergence for series of positive terms — ratio test, root test, comparison test, integral test; alternating series test; power series.

Limit, continuity, intermediate value property; differentiation; Rolle’s theorem; mean value theorem; L’Hôpital rule; maxima and minima; Taylor’s theorem and Taylor series; Riemann integration — definition, properties, fundamental theorem of calculus.

Limit, continuity, partial derivatives, differentiability; maxima and minima; method of Lagrange multipliers; double and triple integrals; change of order of integration; surface areas and volumes using multiple integrals.

First-order ODEs — exact, linear, Bernoulli, separable; orthogonal trajectories; homogeneous equations; second-order linear ODEs with constant coefficients; variation of parameters; Cauchy-Euler equations.

Scalar and vector fields; gradient, divergence, curl; directional derivative; line integrals; surface integrals; flux; Green’s theorem; Gauss divergence theorem; Stokes’ theorem.

Groups, subgroups, cyclic groups; Abelian and non-Abelian groups; permutation groups; normal subgroups; quotient groups; cosets and Lagrange’s theorem; group homomorphisms and isomorphisms; isomorphism theorems; symmetric group S_n.

Systems of linear equations; rank and nullity; rank-nullity theorem; inverse of a matrix; determinant; eigenvalues and eigenvectors; Cayley-Hamilton theorem; diagonalization; inner product spaces; orthogonality and Gram-Schmidt process.

Interior points, limit points, open sets, closed sets; bounded sets; connected sets; compact sets; completeness of ℝ; power series of real variable; Taylor’s series; radius and interval of convergence; term-wise differentiation and integration of power series; Weierstrass approximation theorem.

Vector algebra and calculus; linear algebra; matrices; eigenvalues; Fourier series and transforms; Laplace transforms; elements of complex analysis; first- and second-order ODEs; partial differential equations.

Newton’s laws; energy-momentum conservation; elastic and inelastic collisions; rigid body motion; moment of inertia; fluid dynamics; non-inertial frames and pseudo forces; special theory of relativity; Lorentz transformations; mass-energy equivalence.

Simple, damped, and forced harmonic oscillations; resonance; transverse and longitudinal waves; wave equation; superposition; interference; single-slit and double-slit diffraction; diffraction grating; polarization; Brewster’s angle; optical instruments.

Coulomb’s law; Gauss’s law; electric potential; dielectrics and capacitance; current electricity; Biot-Savart law; Ampere’s law; Faraday’s law; Lenz’s law; Maxwell’s equations; electromagnetic waves; Poynting vector; energy in electromagnetic fields.

Kinetic theory of gases; Maxwell-Boltzmann distribution; specific heats; zeroth, first, and second laws of thermodynamics; Carnot cycle and efficiency; entropy; Helmholtz and Gibbs free energies; phase transitions.

Blackbody radiation; photoelectric effect; Compton scattering; Bohr model of hydrogen; de Broglie hypothesis; wave-particle duality; Heisenberg uncertainty principle; Schrödinger equation — particle in a box, harmonic oscillator, hydrogen atom; nuclear physics basics; radioactive decay.

Crystal structure; Bravais lattices; X-ray diffraction; band theory of solids; semiconductors; p-n junction; transistor basics; operational amplifiers; Boolean algebra; digital circuits (logic gates, flip-flops).

Quantum mechanical model of hydrogen atom; atomic orbitals; orbital quantum numbers; wave functions; molecular orbital theory; VBT; hybridization; VSEPR theory.

Ideal and real gases; van der Waals equation; kinetic theory; Maxwell distribution; viscosity; mean free path; Joule-Thomson effect.

Laws of thermodynamics; enthalpy; entropy; Gibbs and Helmholtz free energy; chemical potential; equilibrium constant and its temperature dependence; Clausius-Clapeyron equation.

Law of mass action; K_p, K_c, K_x; Le Chatelier’s principle; phase rule; one- and two-component systems; Raoult’s law; colligative properties.

Electrochemical cells; Nernst equation; Kohlrausch law; rate laws; order of reactions; activation energy; Arrhenius equation; catalysis; Michaelis-Menten kinetics.

IUPAC nomenclature; resonance; aromaticity; inductive and mesomeric effects; reaction intermediates (carbocations, carbanions, radicals, carbenes); chirality; enantiomers; diastereomers; optical activity; conformational analysis of cyclohexane.

Substitution (SN1, SN2), addition, elimination (E1, E2), and rearrangement reactions; alkanes, alkenes, alkynes, halides, alcohols, ethers, aldehydes, ketones, carboxylic acids and derivatives, amines, aromatic compounds; named reactions: Aldol, Claisen, Diels-Alder, Wittig, Grignard.

UV-Vis spectroscopy; IR spectroscopy; ¹H and ¹³C NMR spectroscopy; mass spectrometry; structure determination from combined spectral data.

Periodic trends; effective nuclear charge; Lewis structures; VSEPR; crystal field theory; spectrochemical series; coordination chemistry — naming, isomerism, stability constants; s-, p-, d-, f-block element chemistry.

Hydrides, halides, and oxides of s- and p-block elements; transition metal properties — oxidation states, colour, magnetic behaviour; bioinorganic chemistry basics.

Cell biology (structure, organelles, cell division); genetics and Mendelian inheritance; molecular biology (DNA structure, replication, transcription, translation, gene regulation); microbiology (bacteria, viruses, fungi, culture techniques); biochemistry (biomolecules — carbohydrates, proteins, lipids, nucleic acids; enzyme kinetics; metabolic pathways — glycolysis, TCA cycle, oxidative phosphorylation); immunology (antibodies, antigens, immune response, vaccines); ecology and evolution; plant physiology; animal physiology; biotechnology applications — recombinant DNA technology, PCR, ELISA, blotting techniques, plant tissue culture, bioreactors.

Atomic structure; chemical bonding; solutions; chemical equilibrium; electrochemistry; thermodynamics basics; organic chemistry fundamentals; biomolecule chemistry — structures of amino acids, monosaccharides, fatty acids, and nucleotides.

Sets, relations, and functions; logarithms; sequences and series; limits, derivatives, and integrals; vectors; statistics (mean, median, standard deviation, correlation); permutations and combinations; basic probability.

Physical world and measurement; kinematics; Newton’s laws; work, energy, and power; electrostatics; current electricity; electromagnetic induction; optics; modern physics basics — photoelectric effect, nuclear structure.

Sequences and series of real numbers; convergence; functions of one and two real variables; continuity; differentiation; integration; double integrals; matrices; rank; eigenvalues; linear systems of equations.

Axiomatic definition; conditional probability and independence; Bayes’ theorem; discrete and continuous random variables; PMF, PDF, CDF; expectation; variance; covariance; correlation; Markov inequality; Chebyshev’s inequality.

Binomial; Poisson; geometric; negative binomial; uniform; exponential; normal; gamma; beta; bivariate normal; chi-square, t, and F distributions and their properties.

Estimation — unbiasedness, consistency, MLE, method of moments; confidence intervals; hypothesis testing — Neyman-Pearson lemma, likelihood ratio tests; z-test; t-test; chi-square test; F-test; one-way ANOVA.

Simple and multiple linear regression; correlation; goodness-of-fit tests; non-parametric tests (sign test, Wilcoxon tests, Kruskal-Wallis test); order statistics; Law of Large Numbers; Central Limit Theorem.

Origin of the solar system and Earth; Earth’s internal structure; geophysical methods; isostasy; plate tectonics; seafloor spreading; ocean floor features; volcanism; earthquakes and seismicity.

Weathering and erosion; drainage patterns; fluvial geomorphology; coastal features; glacial landforms; remote sensing basics; photo interpretation for geological mapping.

Stress and strain; fold types and classification; fault types (normal, reverse, strike-slip, thrust); joints; unconformities; stereographic projections; geological map interpretation.

Stratigraphic principles; index fossils; geological time scale; Gondwana flora and fauna; evolution of life; stratigraphy of India — Precambrian Basement, Gondwana basins, Deccan Traps, Himalayan sequences.

Crystallography (symmetry elements; crystal systems); optical mineralogy; common rock-forming minerals (silicates, carbonates, oxides); igneous petrology — classification, textures, Bowen’s reaction series; sedimentary petrology — classification, diagenesis; metamorphic petrology — grades, facies, textures.

Ore deposit genesis and classification; coal and petroleum geology; groundwater occurrence and movement; engineering geology basics; natural hazards (landslides, floods, earthquakes) and mitigation strategies.

Utility and preference; budget constraint; demand; revealed preference; Slutsky equation; elasticity; production function; cost curves; profit maximization; market structures — perfect competition, monopoly, oligopoly, monopolistic competition; game theory basics; welfare economics.

National income accounting; Keynesian models; IS-LM model; AD-AS framework; money demand and supply; inflation; unemployment; open economy macroeconomics; exchange rates; balance of payments.

Measures of central tendency and dispersion; probability basics; discrete and continuous distributions (Binomial, Poisson, Normal); hypothesis testing; simple regression and correlation.

Differential and integral calculus; unconstrained and constrained optimization; matrix algebra; differential equations; set theory; linear programming.

Economic development since Independence; poverty, inequality, and human development; agriculture, industry, and services sectors; fiscal and monetary policy; economic reforms post-1991; international trade; HDI and social indicators.