IIT JAM 2027: Registration (September 5), Exam Date (Out), Admit Card, Syllabus & Pattern

Biology: Unit 01

• Taxonomy; heredity; genetic variation; conservation; principles of ecology; evolution; techniques in modern biology

Biology: Unit 02

• Carbohydrates; proteins; lipids; nucleic acids; enzymes; vitamins; hormones; metabolism-glycolysis, TCA cycle, oxidative phosphorylation; photosynthesis
• Nitrogen fixation, fertilization and osmoregulation; vertebrates-nervous system; endocrine system; vascular system; immune system; digestive system and reproductive system

Biology: Unit 03

• Tissue culture; application of enzymes; antigen-antibody interaction; antibody production; diagnostic aids

Biology: Unit 04

• DNA; RNA; replication; transcription; translation; proteins; lipids and membranes; operon model; gene transfer

Biology: Unit 05

• Cell cycle; cytoskeletal elements; mitochondria; endoplasmic reticulum; chloroplast; golgi apparatus; signaling

Biology: Unit 06

• Isolation; cultivation; structural features of virus; bacteria; fungi; protozoa; pathogenic micro-organisms

Chemistry-Physical chemistry: Unit 01

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

Chemistry-Physical chemistry: Unit 02

• Fundamental particles; Bohr's theory of hydrogen-like atom; wave-particle duality; uncertainty principle; Schrödinger's wave equation; quantum 'numbers; shapes of orbitals; Hund’s rule and Pauli’s exclusion principle
• Electronic configuration of simple homonuclear diatomic molecules

Chemistry-Physical chemistry: Unit 03

• Equation of state for ideal and non-ideal (Van der Waals) gases; kinetic theory of gases; Maxwell-Boltzmann distribution law; equipartition of energy

Chemistry-Physical chemistry: Unit 04

• Crystals and crystal systems; X-rays; NaCl and KCl structures; close packing; atomic and ionic radii; radius ratio rules; lattice energy; Born-Haber cycle; isomorphism; heat capacity of solids

Chemistry-Physical chemistry: Unit 05

• Reversible and irreversible processes; first law and its application to ideal and non-ideal gases; thermochemistry; second law; entropy and free energy; criteria for spontaneity

Chemistry-Physical chemistry: Unit 06

• Law of mass action; Kp, Kc, Kx and Kn; effect of temperature on K; ionic equilibria in solutions; pH and buffer solutions; hydrolysis; solubility product; phase equilibria-phase rule and its application to one-component and two-component systems
• Colligative properties

Chemistry-Physical chemistry: Unit 07

• Conductance and its applications; transport number; galvanic cells; EMF and free energy; concentration cells with and without transport; polarography; concentration cells with and without transport; Debey-Huckel-Onsager theory of strong electrolytes

Chemistry-Physical chemistry: Unit 08

• Reactions of various order; Arrhenius equation; collision theory; transition state theory; chain reactions-normal and branched; enzyme kinetics; photochemical processes; catalysis

Chemistry-Physical chemistry: Unit 09

• Gibbs adsorption equation; adsorption isotherm; types of adsorption; surface area of adsorbents; surface films on liquids

Chemistry-Physical chemistry: Unit 10

• Beer-Lambert law; fundamental concepts of rotational, vibrational, electronic and magnetic resonance spectroscopy

Geology: Unit 01

• Origin of the solar system and the Earth; geosphere and the composition of the Earth; shape and size of the earth; Earth-moon system; formation of continents and oceans; dating rocks and age of the Earth; volcanism and volcanic landforms
• Interior of earth; Earthquakes; Earth's magnetism and gravity, isostasy; elements of plate tectonics; orogenic cycles

Geology: Unit 02

• Weathering and erosion; transportation and deposition due to wind, ice, river, sea, and resulting landforms, structurally controlled landforms

Geology: Unit 03

• Concept of stratum; contour; outcrop patterns; maps and cross sections; dip and strike; classification and origin of folds, faults, joints, unconformities, foliations and lineations,; shear zones
• Stereographic and equal area projections of planes and lines; computation of true thickness of beds from outcrops and bore-holes

Geology: Unit 04

• Major steps in the evolution of life forms; fossils; their mode of preservation and utility; morphological characters, major evolutionary trends and ages of important groups of animals
• Brachiopoda, mollusca, trilobita, graptolitoidea, anthozoa, echinodermata; Gondwana plant fossils; elementary idea of verterbrate fossils in India

Geology: Unit 05

• Principles of stratigraphy; litho-, chrono-, and biostratigraphic classification; distribution and classification of the stratigraphic horizons of India from Archaean to recent

Geology: Unit 06

• Symmetry and forms in common crystal classes; physical properties of minerals; isomorphism and polymorphism, classification of minerals; structure of silicates; mineralogy of common rock-forming minerals; mode of occurrence of minerals in rocks
• Transmitted polarised light microscopy and optical properties of uniaxial and biaxial minerals

Geology: Unit 07

• Definition and classification of rocks; igneous rocks-forms of igneous bodies; crystallization from magma; classification, association and genesis of igneous rocks; sedimentary rocks-classification, texture and structure
• Size and shape of sedimentary bodies
• Metamorphic rocks-classification, facies, zones and texture
• Characteristic mineral assemblages of pelites in the barrovian zones and mafic rocks in common facies

Geology: Unit 08

• Properties of common economic minerals; general processes of formation of mineral deposits; physical characters; mode of occurrence and distribution in India both of metallic and non-metallic mineral deposits; coal and petroleum occurrences in India

Geology: Unit 09

• Ground water; principles of engineering geology

Mathematics: Unit 01

• Sequence of real numbers, convergence of sequences, bounded and monotone sequences, convergence criteria for sequences of real numbers, Cauchy sequences, subsequences, Bolzano-Weierstrass theorem
• Series of real numbers, absolute convergence, tests of convergence for series of positive terms-comparison test, ratio test, root test; Leibniz test for convergence of alternating series

Mathematics: Unit 02

• Limit, continuity, intermediate value property, differentiation, Rolle's theorem, mean value theorem, L' Hospital rule, Taylor's theorem, maxima and minima

Mathematics: Unit 03

• Limit, continuity, partial derivatives, differentiability, maxima and minima

Mathematics: Unit 04

• Integration as the inverse process of differentiation, definite integrals and their properties, fundamental theorem of calculus
• Double and triple integrals, change of order of integration, calculating surface areas and volumes using double integrals, calculating volumes using triple integrals

Mathematics: Unit 05

• Ordinary differential equations of the first order of the form y'=f(x,y), Bernoulli's equation, exact differential equations, integrating factor, orthogonal trajectories, homogeneous differential equations, variable separable equations
• Linear differential equations of second order with constant coefficients, method of variation of parameters, Cauchy-Euler equation

Mathematics: Unit 06

• Scalar and vector fields, gradient, divergence, curl, line integrals, surface integrals, Green, Stokes and Gauss theorems

Mathematics: Unit 07

• Groups, subgroups, Abelian groups, non-Abelian groups, cyclic groups, permutation groups, normal subgroups, Lagrange's Theorem for finite groups, group homomorphisms and basic concepts of quotient groups

Mathematics: Unit 08

• Finite dimensional vector spaces, linear independence of vectors, basis, dimension, linear transformations, matrix representation, range space, null space, rank-nullity theorem
• Rank and inverse of a matrix, determinant, solutions of systems of linear equations, consistency conditions, eigenvalues and eigenvectors for matrices, Cayley-Hamilton theorem

Mathematics: Unit 09

• 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

Mathematics: Unit 01

• Convergence of sequences of real numbers, comparison, root and ratio tests for convergence of series of real numbers

Mathematics: Unit 02

• Limits, continuity and differentiability of functions of one and two variables
• Rolle's theorem, mean value theorems, Taylor's theorem, indeterminate forms, maxima and minima of functions of one and two variables

Mathematics: Unit 03

• Fundamental theorems of integral calculus
• Double and triple integrals, applications of definite integrals, arc lengths, areas and volumes.

Mathematics: Unit 04

• Rank, inverse of a matrix
• Systems of linear equations
• Linear transformations, eigenvalues and eigenvectors
• Cayley-Hamilton theorem, symmetric, skew-symmetric and orthogonal matrices

Physics: Unit 01

• 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 and linear second order differential equations with constant coefficients
• Matrices and determinants, algebra of complex numbers

Physics: Unit 02

• Newton's laws of motion and 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, center of mass, equation of motion of the CM, conservation of linear and angular momentum, conservation of energy, variable mass systems
• Elastic and inelastic collisions
• Rigid body motion, fixed axis rotations, rotation and translation, moments of inertia and products of inertia, parallel and perpendicular axes theorem
• Principal moments and axes
• Kinematics of moving fluids, equation of continuity, Euler's equation, Bernoulli's theorem

Physics: Unit 03

• Differential equation for simple harmonic oscillator and its general solution
• Superposition of two or more simple harmonic oscillators
• Lissajous figures
• Damped and forced oscillators, resonance
• Wave equation, traveling and standing waves in one-dimension
• Energy density and energy transmission in waves
• Group velocity and phase velocity
• Sound waves in media
• Doppler effect
• Fermat's principle
• General theory of image formation
• Thick lens, thin lens and lens combinations
• Interference of light, optical path retardation
• Fraunhofer diffraction
• Rayleigh criterion and resolving power
• Diffraction gratings
• Polarization: Linear, circular and elliptic polarization
• Double refraction and optical rotation

Physics: Unit 04

• Coulomb's law, Gauss's law
• Electric field and potential
• Electrostatic boundary conditions, solution of Laplace's equation for simple cases
• Conductors, capacitors, dielectrics, dielectric polarization, volume and surface charges, electrostatic energy
• Biot-Savart law, Ampere's law, Faraday's law of electromagnetic induction, self and mutual inductance
• Alternating currents
• Simple DC and AC circuits with R, L, and C components
• Displacement current, Maxwell's equations and plane electromagnetic waves, Poynting's theorem, reflection and refraction at a dielectric interface, transmission and reflection coefficients (normal incidence only)
• Lorentz Force and motion of charged particles in electric and magnetic fields

Physics: Unit 05

• Elements of kinetic theory of gases
• Velocity distribution and 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
• Laws of thermodynamics
• Zeroth law and concept of thermal equilibrium
• First law and its consequences
• Isothermal and adiabatic processes
• Reversible, irreversible and quasi-static processes
• Second law and entropy
• Carnot cycle
• Maxwell's thermodynamic relations and simple applications
• Thermodynamic potentials and their applications
• Phase transitions and Clausius-Clapeyron equation
• Ideas of ensembles, Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein distributions

Physics: Unit 06

• Inertial frames and galilean invariance
• Postulates of special relativity
• Lorentz transformations
• Length contraction, time dilation
• Relativistic velocity addition theorem, mass energy equivalence
• Blackbody radiation, photoelectric effect, Compton effect, Bohr's atomic model, X-rays
• Wave-particle duality, uncertainty principle, the superposition principle, calculation of expectation values, Schrödinger equation and its solution for one, two, and three-dimensional boxes
• Solution of Schrödinger equation for the one-dimensional harmonic oscillator
• Reflection and transmission at a step potential, Pauli exclusion principle
• Structure of atomic nucleus, mass and binding energy
• Radioactivity and its applications
• Laws of radioactive decay

Physics: Unit 07

• Crystal structure, Bravais lattices and basis
• Miller indices
• X-ray diffraction and Bragg's law; intrinsic and extrinsic semiconductors, variation of resistivity with temperature
• Fermi level
• p-n junction diode, I-V characteristics, Zener diode and its applications, BJT: Characteristics in CB, CE, CC modes
• Single stage amplifier, two stage R-C coupled amplifiers
• Simple oscillators: Barkhausen condition, sinusoidal oscillators
• OPAMP and applications: Inverting and non-inverting amplifier
• Boolean algebra: Binary number systems; conversion from one system to another system; binary addition and subtraction
• Logic gates AND, OR, NOT, NAND, NOR exclusive OR; truth tables; combination of gates; De Morgan's theorem

Economics: Unit 01

• Consumer theory: Preference, utility and representation theorem, budget constraint, choice, demand (ordinary and compensated), Slutsky equations, choice under risk and uncertainty, revealed preference axioms
• Production, costs with perfectly competitive markets: Technology, isoquants, production with one and more variable inputs, returns to scale, short run and long run costs, cost curves in the short run and long run, perfect competition in markets
• General equilibrium and welfare: Equilibrium and efficiency under pure exchange and production, welfare economics, theorems of welfare economics
• Market structure: Monopoly, pricing with market power, price discrimination (first, second, and third), monopolistic competition and oligopoly
• Game theory: Strategic form games, Nash equilibrium, mixed extension and mixed strategy Nash equilibrium, iterated elimination of dominated strategies, examples: Cournot, Bertrand duopolies, Prisoner's dilemma
• Game theory: Cooperative game theory-Shapley value, Nash bargaining
• Public goods and market failure: Externalities, public goods and markets with asymmetric information (adverse selection and moral hazard), VCG mechanism and transfer rules

Economics: Unit 02

• National income accounting: Structure, key concepts, measurements, and circular flow of income-for closed and open economy, money, fiscal and foreign sector variables-concepts and measurements
• Behavioural and technological functions: Consumption functions-absolute income hypothesis, life-cycle and permanent income hypothesis, investment functions-Keynesian, money demand and supply functions, production function
• Business cycles and economic models: Business cycles-facts and features, the classical model of the business cycle. The Keynesian model of the business cycle,
• Business cycles and economic models: Simple Keynesian cross model of income and employment determination and the multiplier (in a closed economy), IS-LM Model, Hicks' S-LM synthesis, role of monetary and fiscal policy
• Business cycles and economic models (open economy): Open economy, Mundell-Fleming model, Keynesian flexible price (aggregate demand and aggregate supply) model, role of monetary and fiscal policy
• Inflation and unemployment: Inflation-theories, measurement, causes, and effects, unemployment-types, measurement, causes, and effects
• Growth models: Harrod-Domar, Solow and neo-classical growth models

Economics: Unit 03

• Probability theory, sample spaces and events, axioms of probability and their properties, conditional probability and Bayes' rule, independent events
• Random variables and probability distributions, probability distributions, expected values and functions of random variables, properties of commonly used discrete and continuous distributions
• Random sampling, density and distribution functions for jointly distributed random variables, computing expected values of jointly distributed random variables, covariance and correlation coefficients
• Point and interval estimation, estimation of population parameters using methods of moments and maximum likelihood procedures, properties of estimators, confidence intervals
• Hypothesis testing, distributions of test statistics, testing hypotheses related to population parameters, type I and type II errors, the power of a test, tests for comparing parameters from two samples

Economics: Unit 04

• Indian economy before 1950: Transfer of tribute, deindustrialization of India
• Planning and Indian development: Planning models, relation between agricultural and industrial growth, challenges faced by Indian planning
• Indian economy after 1991: Balance of payments crisis in 1991, major aspects of economic reforms in India after 1991, reforms in trade and foreign investment
• Banking, finance, and macroeconomic policies: Aspects of banking in India, CRR and SLR, financial sector reforms in India, fiscal deficit, savings and investment rates in India
• Inequalities in social development: India's achievements in health, education and other social sectors, disparities between Indian states in human development
• Poverty: Methodology of poverty estimation, issues in poverty estimation in India
• India's labour market: Unemployment, labour force participation rates

Economics: Unit 05

• Preliminaries and functions of one real variable: a) Set theory and number theory, graphs, elementary types of functions: Quadratic, polynomial, power, exponential, logarithmic, sequences and series: Convergence, algebraic properties and applications
• Preliminaries and functions of one real variable: b) Continuous functions-characterisations, properties with respect to various operations and applications
• Preliminaries and functions of one real variable: c) Differentiable functions: Characterisations, properties with respect to various operations and applications, d) second and higher order derivatives: Properties and applications
• Single-variable optimization: Geometric properties of functions-convex functions, their characterisations and applications, local and global optima: Geometric and calculus-based characterisations, and applications
• Linear algebra: Vector spaces-algebraic and geometric properties, scalar products, norms, orthogonality, linear transformations: Properties, matrix representations and elementary operations, systems of linear equations: Properties of their solution sets
• Linear algebra: Determinants-characterisation, properties and applications
• Functions of several real variables: Geometric representations-graphs and level curves, differentiable functions: Characterisations, properties with respect to various operations and applications
• Functions of several real variables: Second order derivatives-properties and applications, the implicit function theorem, and application to comparative statics problems, homogeneous and homothetic functions: Characterisations and applications
• Multivariate optimization: Convex sets, geometric properties of functions: Convex functions, their characterisations, properties and applications
• Multivariate optimization: Further geometric properties of functions-quasi-convex functions, their characterisations, properties and applications, unconstrained optimisation: Geometric characterisations, characterisations using calculus and applications
• Multivariate optimization: Constrained optimisation with equality constraints-geometric characterisations, Lagrange characterisation using calculus and applications, properties of value function: Envelope theorem and applications
• Linear programming: Graphical solution, matrix formulation, duality, economic interpretation
• Integration, differential equations, and difference equations: Definite integrals, indefinite integrals and economic applications, first order difference equations, equilibrium and its stability, first order differential equations
• Integration, differential equations, and difference equations: Phase diagrams and stability