The Indian Institute of Technology Delhi, IIT Delhi, conducts the Joint Admission Test for Masters, JAM 2025. It is an entrance examination for admission into various postgraduate programs across multiple institutes. The examination consists of seven test papers, which correspond to specific subject areas. The following are the test papers along with their syllabus:
IIT JAM 2025: Biotechnology (BT)
The syllabus for Biotechnology (BT) in the JAM 2025 exam is extensive and covers topics in Biology, Chemistry, Mathematics, and Physics. Below is a detailed breakdown of the syllabus:
| Subject | Topics |
|---|---|
| Biology | Cell Biology: Prokaryotic and eukaryotic cell structure, membrane structure, organelles, signaling pathways, cell cycle stages. |
| Biochemistry: Structure/function of macromolecules, enzyme mechanisms, bioenergetics, metabolism (glycolysis, TCA cycle, etc.). | |
| Genetics: Mendel’s laws, inheritance patterns, pedigree analysis, chromosomal inheritance, plant breeding. | |
| Molecular Biology: DNA as genetic material, replication, transcription, gene expression regulation in prokaryotes and eukaryotes. | |
| Evolution: Natural selection, population genetics, speciation, phylogenetic classification, origin of life. | |
| Microbiology: Microbe structures, pathogenic microorganisms, microbial metabolism, growth kinetics, microbial genetics. | |
| Plant Biology: Tissues, morphogenesis, transport, nutrition, plant hormones, photobiology, stress responses. | |
| Animal Biology: Digestive, respiratory, circulatory systems, immunology, animal development. | |
| Ecology: Biomes, environmental constraints, population density, ecosystems, community interactions. | |
| Biotechnology: Plant tissue culture, cloning, recombinant DNA technology applications. | |
| Methods in Biology: Microscopy, staining, spectroscopy, chromatography, DNA cloning, PCR, hybridization. | |
| Chemistry | Structure and Properties of Atoms: Bohr’s theory, periodicity. |
| Bonding in Molecules: Chemical bonding, molecular interactions, complex formation. | |
| Chemical Kinetics and Thermodynamics: Laws of thermodynamics, equilibrium, reaction kinetics. | |
| Physical and Chemical Properties: Acid-base concepts, pH, buffer systems, photochemistry, electrochemistry. | |
| Organic Chemistry: Hydrocarbons, functional groups, aromatic compounds, stereochemistry, soaps/detergents. | |
| Instrumental Techniques: Spectroscopy (UV-Vis, IR, NMR), mass spectrometry, crystallography, calorimetry. | |
| Mathematics | Topics Covered: Sets, relations, functions, complex numbers, trigonometry, straight lines, sequences, series, calculus, ODEs. |
| Linear Algebra: Matrices, determinants. | |
| Probability and Statistics: Distributions, Bernoulli trials, random variables. | |
| Physics | Core Topics: Units, measurements, motion, work, energy, thermodynamics, electricity, magnetism, optics, nuclear physics, semiconductors. |
IIT JAM 2025: Chemistry
Here’s a structured table based on the detailed content provided for JAM-2025 Chemistry:
| Topic | Subtopics |
|---|---|
| Basic Mathematical Concepts (10+2 Level) | Functions, maxima and minima, integrals, ordinary differential equations, vectors and matrices, determinants, elementary statistics. |
| Physical Chemistry | Atomic and Molecular Structure: Planck’s black body radiation, Photoelectric effect, Bohr’s theory, de Broglie postulate, Heisenberg’s Uncertainty Principle, Schrödinger’s wave equation, quantum mechanics postulates, normalized and orthogonal wave functions, operators, particle in one-dimension box, radial and angular wave functions, hydrogen atom energy spectrum, orbital shapes, Pauli’s Exclusion Principle, Hund’s rule. Gaseous State: Kinetic molecular model, Maxwell-Boltzmann distribution, ideal gas deviations, van der Waals equation, critical state. Liquid State: Vapour pressure, surface tension, viscosity, solute concentration effects. |
| Solid State: Unit cells, crystal systems, X-ray diffraction, Bragg’s Law, NaCl and CsCl structures, metal packing, semiconductors, crystal defects, lattice energy. Chemical Thermodynamics: Laws, thermodynamic functions, Gibbs free energy, partial molar quantities, chemical potential. Chemical and Phase Equilibria: Mass action law, equilibrium constants, ionic equilibria, buffer solutions, phase rule, phase diagrams. Electrochemistry: Conductivity, Nernst equation, electrochemical series, EMF applications. Chemical Kinetics: Reaction order, Arrhenius equation, catalysts, enzyme catalysis. | |
| Organic Chemistry | Basic Concepts and Stereochemistry: Electronic effects, optical isomerism, conformations of acyclic/cyclic systems. Organic Reaction Mechanism: Reactive intermediates, substitution and elimination reactions, specific organic reactions (e.g., Wittig, Michaelis-Menten, etc.), organometallic reagents, pericyclic reactions. Qualitative Organic Analysis: Functional group identification, spectroscopic techniques. Natural Products Chemistry: Chemistry of alkaloids, steroids, carbohydrates, nucleic acids. Aromatic and Heterocyclic Chemistry: Synthesis and reactivity, substitution reactions, aromaticity. |
| Inorganic Chemistry | Periodic Table: Periodicity, Aufbau’s principle, orbital energy variations. Extractions of Metals: Methods of isolation, Ellingham diagrams. Chemical Bonding: Ionic and covalent bonds, molecular orbital theory, hydrogen bonding, VSEPR theory. Main Group Elements: Reactions, properties, and structures (e.g., borazine, phosphazene). Transition Metals: d-block characteristics, coordination complexes, MO and crystal field theory, organometallic compounds. Bioinorganic Chemistry: Role of metal ions in biological systems, hemoglobin, carbonic anhydrase. |
| Instrumental Methods of Analysis | Basic principles, conductometry, potentiometry, UV-vis spectrophotometry, environmental sample analysis (water, air, soil). |
| Analytical Chemistry | Qualitative and quantitative analysis, titration principles, use of organic reagents, radioactivity, nuclear reactions, error analysis, statistics. |
IIT JAM 2025: Economics
The syllabus of JAM 2025 Economics (EN) consists of extensive and detailed curriculum and covers a variety of branches of economics and their mathematical foundations. Here is a summarized overview:
| Section | Topics |
|---|---|
| Microeconomics | Consumer Theory: Preferences, utility, Slutsky equation, demand functions, revealed preferences. |
| Production and Costs: Technology, returns to scale, cost curves (short- and long-run). | |
| General Equilibrium and Welfare: Pure exchange and production, welfare theorems. | |
| Market Structures: Perfect competition, monopoly, price discrimination, monopolistic competition, oligopoly. | |
| Game Theory: Strategic games, Nash equilibrium, Cournot/Bertrand models, Prisoner's dilemma. | |
| Market Failures: Public goods, externalities, asymmetric informationrmation (adverse selection, moral hazard). | |
| Macroeconomics | National Income Accounting: Closed and open economies, fiscal and foreign sector variables. |
| Economic Functions: Consumption (Keynesian models, life-cycle hypothesis), investment, money demand/supply. | |
| Business Cycles: Classical and Keynesian models, IS-LM framework, simple Keynesian cross model. | |
| Open Economy Models: Mundell-Fleming, monetary and fiscal policies. | |
| Inflation and Unemployment: Theories, measurement, causes, and effects. | |
| Growth Models: Harrod-Domar, Solow, AK model, Romer, Schumpeterian growth models. | |
| Statistics for Economics | Probability Theory: Concepts, distributions, random variables, Bayes’ rule. |
| Mathematical Statistics: Sampling, estimation (method of moments, maximum likelihood), properties of estimators, CLT. | |
| Hypothesis Testing: Errors, test statistics, population parameter tests. | |
| Regression and Correlation: OLS, assumptions, properties, goodness-of-fit. | |
| Indian Economy | Pre-1950s: Deindustrialization, transfer of tribute. |
| Post-Independence Planning: Models, agriculture-industry relations, challenges. | |
| Post-1991 Reforms: BoP crisis, trade and investment liberalization. | |
| Banking & Finance: CRR, SLR, fiscal and monetary policies. | |
| Development: Health, education disparities, poverty estimation. | |
| Labour Market: Unemployment, labour force participation rates. | |
| Mathematics for Economics | Functions and Preliminaries: Set theory, functions, sequences, and series. |
| Differential Calculus: Limits, differentiation, implicit function theorem, comparative statics. | |
| Integral Calculus: Definite/indefinite integrals, applications. | |
| Linear Algebra: Matrices, eigenvalues/eigenvectors, quadratic forms. | |
| Optimization: Constrained/unconstrained optimization, Lagrange multipliers, linear programming. |
IIT JAM 2025: GEOLOGY
| Section | Topics |
|---|---|
| The Planet Earth | Origin of the Solar System and Earth; Composition of the Earth; Shape and size; Earth-Moon system; Dating rocks and Earth's age; Volcanism and landforms; Earth's interior; Earthquakes; Magnetism; Gravity; Isostasy; Plate Tectonics; Orogenic cycles. |
| Geomorphology | Weathering, erosion; Soil formation; Transportation and deposition by wind, ice, rivers, sea; Resulting landforms. |
| Structural Geology | Orientation of planes/lines (dip, strike, rake, plunge); Contour lines; Rule of ‘V’s; Outcrop patterns; Geological maps and cross-sections; Folds, faults, joints, unconformities; Stereographic projections; Bore-hole data problems. |
| Paleontology | Evolution of life forms; Fossils: preservation, age determination, paleoenvironment; Morphology, trends, ages of Brachiopoda, Mollusca, Trilobita, Graptoloidea, Anthozoa, Echinodermata; Gondwana plants; Vertebrate fossils in India. |
| Stratigraphy | Principles: Litho-, Chrono-, Biostratigraphy; Correlation techniques; Archean cratons: Dharwar, Singhbhum, Aravalli; Proterozoic mobile belts; Stratigraphy: Cuddapah, Vindhyan basins, Paleozoic-Mesozoic sequences, Gondwana Supergroup, Siwaliks. |
| Mineralogy | Symmetry and crystal classes; Mineral physical properties; Isomorphism, polymorphism; Mineral classification; Silicate structures; Common rock-forming minerals; Optical properties; Elements of Optical Mineralogy. |
| Petrology | Rock classification; Igneous rocks: forms, magma evolution, common rock genesis; Sedimentary rocks: classification, texture, structure; Petrology of sandstone, limestone; Metamorphic rocks: classification, textures, controls, Barrovian zones. |
| Economic Geology | Properties of economic minerals; Mineral deposit formation; Metallic and non-metallic deposits in India; Reserve calculation; Coal and hydrocarbon geology; Indian coal and hydrocarbon occurrences. |
| Applied Geology | Groundwater and hydrological cycle; Aquifers, porosity, permeability; Engineering geology principles; Dams and tunnels: geological considerations. |
IIT JAM 2025: Mathematics
| Section | Topics |
|---|---|
| Real Analysis | Sequences and Series of Real Numbers: Convergence, bounded and monotone sequences, Cauchy sequences, Bolzano-Weierstrass theorem; Absolute convergence; Tests for series convergence (comparison, ratio, root); Power series, radius and interval of convergence, term-wise differentiation and integration. |
| Functions of One Real Variable: Limit, continuity, intermediate value property; Differentiation: Rolle’s Theorem, mean value theorem, L'Hospital rule, Taylor's theorem and series; Maxima and minima; Riemann integration: definite integrals, properties, fundamental theorem of calculus. | |
| Multivariable Calculus and Differential Equations | Functions of Two or Three Variables: Limit, continuity, partial derivatives, total derivative, maxima and minima. |
| Integral Calculus: Double and triple integrals, change of order of integration; Surface areas and volumes using double integrals; Volumes using triple integrals. | |
| Differential Equations: Bernoulli’s equation, exact differential equations, integrating factors; Orthogonal trajectories; Homogeneous differential equations; Separation of variables; Linear differential equations (2nd order, constant coefficients); Method of variation of parameters; Cauchy-Euler equation. | |
| Linear Algebra and Algebra | Matrices: Systems of linear equations, rank, ity, rank-ity theorem; Inverse, determinant; Eigenvalues and eigenvectors. |
| Finite Dimensional Vector Spaces: Linear independence, basis, dimension; Linear transformations, matrix representation, range space, space, rank-ity theorem. | |
| Groups: Cyclic, abelian, non-abelian groups; Permutation groups, normal subgroups, quotient groups; Lagrange's theorem for finite groups; Group homomorphisms. |
IIT JAM 2025: MATHEMATICAL STATISTICS (MS)
| Topic | Subtopics |
|---|---|
| Mathematics (30% Weight) | |
| Sequences and Series | - Convergence, limits, Cauchy sequences, monotonic sequences, power series (radius of convergence). - Tests: Comparison, Limit comparison, Ratio, Root, Cauchy condensation, Integral, Leibnitz for alternating series. |
| Differential Calculus | - One Variable: Limits, continuity, differentiability, Rolle's theorem, Taylor’s theorem, Maclaurin’s series, L’Hospital’s rule, maxima/minima. - Two Variables: Partial/total differentiation, Hessian matrix, constrained optimization. |
| Integral Calculus | - Fundamental theorems, differentiation under integral sign, improper integrals. - Beta and Gamma functions. - Applications: Arc lengths, areas, and volumes. |
| Matrices and Determinants | - Vector spaces: Subspaces, basis, dimension. - Matrix types: Symmetric, Hermitian, Orthogonal, Idempotent, Nilpotent. - Eigenvalues/vectors, rank, Cramer’s rule, Cayley-Hamilton theorem. |
| Statistics (70% Weight) | |
| Probability | - Sample space, axioms of probability, geometric probability. - Conditional probability, total probability theorem, Bayes’ theorem. - Independence (pairwise/mutual). |
| Univariate Distributions | - Definitions: c.d.f., p.m.f., p.d.f., moments, mean, variance, skewness, kurtosis, m.g.f. - Standard Distributions: Bernoulli, Binomial, Poisson, Uniform, Exponential, Gamma, Normal. |
| Multivariate Distributions | - Joint/marginal c.d.f., p.m.f., p.d.f., independence, covariance, correlation. - Additive properties (Binomial, Poisson, Gamma). - Standard Distributions: Multinomial, Bivariate Normal. |
| Limit Theorems | - Convergence in probability and distribution. - Weak Law of Large Numbers, Central Limit Theorem (i.i.d. case). |
| Sampling Distributions | - Definitions: Random sample, parameter, statistic. - Central distributions: Chi-square, t-distribution, F-distribution (properties and derivations). |
| Estimation | - Unbiasedness, sufficiency, consistency, UMVUE, Rao-Blackwell theorem, Cramer-Rao inequality. - Methods: Moments, MLE, least squares estimation, confidence intervals. |
| Hypothesis Testing | - /alternative hypotheses, Type I/II errors, p-value, Neyman-Pearson Lemma. - Tests: MP, UMP, likelihood ratio tests (univariate normal). |
IIT JAM 2025: PHYSICS (PH)
| Topic | Subtopics |
|---|---|
| Mathematical Methods | - Calculus: Single and multiple variables, partial derivatives, Jacobian. - Taylor expansion, Fourier series. - Vector algebra, Vector Calculus, Divergence, Green’s and Stokes’ theorems. - Differential equations. |
| Mechanics and General Properties of Matter | - Newton's laws of motion and applications. - Motion in Cartesian, polar, cylindrical coordinates, forces (centrifugal, Coriolis). - Kepler’s laws, Gravitational Law, conservative and non-conservative forces. - System of particles, energy, linear/angular momentum. - Elastic and inelastic collisions, rigid body motion, rotation, translation, moments of inertia, parallel/perpendicular axes theorem. |
| Oscillations, Waves, and Optics | - Simple harmonic oscillator, Lissajous figures, resonance. - Wave equation, traveling and standing waves, energy density, group and phase velocity. - Sound waves, Doppler effect, Fermat's principle, image formation. - Lens theory, diffraction, polarization (linear, circular, elliptic). |
| Electricity and Magnetism | - Coulomb’s law, Gauss’s law, electric field and potential. - Electrostatics: Boundary conditions, Laplace’s equation. - Conductors, capacitors, dielectric polarization. - Biot-Savart law, Ampere’s law, Faraday’s law. - Maxwell’s equations, electromagnetic waves, Poynting’s theorem, Lorentz force. |
| Kinetic Theory, Thermodynamics | - Kinetic theory of gases, velocity distribution, equipartition of energy. - Ideal and van-der-Waals gases, specific heat, mean free path. - Thermodynamic laws, Carnot cycle, entropy, Maxwell's relations, phase transitions. - Thermodynamic potentials, Clausius-Clapeyron equation. |
| Modern Physics | - Galilean invariance, special relativity, Lorentz transformations, length contraction, time dilation. - Blackbody radiation, photoelectric effect, Compton effect, Bohr’s atomic model. - Wave-particle duality, Schrödinger equation, Pauli exclusion principle. - Nuclear structure, radioactivity, decay laws. |
| Solid State Physics, Devices, and Electronics | - Crystal structure, Bravais lattices, Miller indices. - X-ray diffraction, Bragg’s law, semiconductors (intrinsic, extrinsic), resistivity variation, Fermi level. - Diodes, transistors (BJT), amplifiers, oscillators, OPAMP, Boolean algebra, logic gates. |
