IIT JAM Syllabus 2024 (Out): Download Syllabus PDF (Free) for Mathematics, Biotechnology, Physics, Chemistry

11th February

IIT Madras

Biotechnology (BL), Economics (EN), Chemistry (CY), Physics (PH), Mathematical Statistics(MS), Mathematics (MA), and Geology (GG)

• Section A – 30 MCQs
• Section B – 10 MCQs
• Section C – 20 Numerical answer type questions

3 hours

60

https://jam.iitm.ac.in/

Modern Physics, Solid State Physics, Kinetic Theory and Thermodynamics, Mathematical Methods, Mechanics and General Properties of Matter, Electricity and Magnetism, Oscillations, Waves and Optics, Devices and Electronics, Simple Oscillators

Physical Chemistry, Organic Chemistry, Inorganic Chemistry

Biology, Physics, Chemistry and Mathematics

National Income Accounting, Consumer Theory, Market Structure, Production, Costs With Perfectly Competitive Markets, Behavioural and Technological Functions, General equilibrium and welfare, Game theory, Public goods and market failure, Business Cycles and Economic Models

Mathematics and Statistics

Sequences and Series of Real Numbers, Linear Algebra, Functions of Two Real Variables, Real Analysis, Differential Equations, Vector Calculus, Group Theory

The Planet Earth, Applied Geology, Geomorphology, Structural Geology, Economic Geology, Palaeontology, Stratigraphy and Mineralogy, Petrology.

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Bohr’s Atomic Model, Postulates of Special Relativity, Lorentz Transformations, Inertial Frames and Galilean Invariance, Time Dilation, X-rays, Length Contraction, Relativistic Velocity Addition Theorem, Mass Energy Equivalence, Blackbody Radiation, Photoelectric Effect, Compton Effect.

Elements of Kinetic Theory of Gases, Van-Der-Waals Gas and Equation of State, Specific Heat of Mono-, Di- and Triatomic Gases, First Law and its Consequences, Second Law and Entropy, Laws of Thermodynamics, Velocity Distribution and Equipartition of Energy, Ideal Gas, Mean Free Path, Carnot Cycle, Zeroth Law and Concept of Thermal Equilibrium, Reversible, Irreversible and Quasi-Static Processes, Isothermal and Adiabatic Processes

Calculus of Single and Multiple Variables, Vector Calculus, Vector Algebra, Algebra of Complex Numbers, Fourier Series, First Order Equations and Linear Second Order Differential Equations with Constant Coefficients, Stoke’s Theorem, Taylor Expansion, Partial Derivatives, Jacobian, Fourier Series, Imperfect and Perfect Differentials, Multiple Integrals, Green’s Theorem, Divergence Theorem, Matrices and Determinants.

Doppler Effect, Wave Equation, Superposition of two or more Simple Harmonic Oscillators, Differential Equation for Simple Harmonic Oscillator and its General Solution, Travelling and Standing Waves in One-Dimension, Lissajous Figures, Damped and Forced Oscillators, Resonance, Energy Density and Energy Transmission in Waves, Fermat’s Principle, Group Velocity and Phase Velocity. Sound Waves in Media.

Crystal Structure, Zener Diode and its Applications, Miller Indices. X-ray diffraction and Bragg’s Law, Variation of Resistivity with Temperature, Bravais Lattices and Basis, Intrinsic and Extrinsic Semiconductors, Fermi Level, P-N Junction Diode, I-V Characteristics, BJT, Characteristics in CB, CE and CC Modes.

Kepler’s Law, Velocity and Acceleration in Cartesian, Centrifugal and Coriolis Forces, Newton’s Laws of Motion and Applications, Uniformly Rotating Frame, Motion under a Central Force, Equation of Motion of the CM System of Particles, Polar and Cylindrical Coordinate Systems, Gravitational Law and Field, Conservative and Non-Conservative Forces, Conservation of Energy, Center of Mass, Conservation of Linear and Angular Momentum, Elastic and Inelastic Collisions, Variable Mass Systems.

Physical World and Measurement, Laws of Motion, Elementary Statics and Dynamics, Kinematics, Laws of Motion, Oscillations, Waves, Work, Energy and Power, Gravitation, Electrostatics, Current electricity, Solids and Semiconductor Devices, Magnetic Effects of Current and Magnetism, Principles of Communication, Electromagnetic Induction and Alternating Current, Electromagnetic waves, Optics, Dual Nature of Matter and Radiations, Atomic Nucleus, Motion of System of Particles and Rigid Body, Mechanics of Solids and Fluids, Heat and Thermodynamics.

Atomic Structure

• Chemical Bonding, Bohr’s theory and Schrodinger wave equation, Chemical equilibrium, Periodicity in properties, Properties of s, p, d and f block elements, Complex formation, Coordination compounds, Photochemistry, Electrochemistry, Acid-base concepts, Inductive, Electrometric, Conjugative Effects and Resonance, Chemical thermodynamics (first and second law); Chemical kinetics (zero, first, second and third-order reactions) and Stereochemistry of Carbon Compounds.

Chemistry of Functional Groups

• Mechanisms of Organic Reactions, Aromatic hydrocarbons, halides, nitro and amino compounds, phenols, diazonium salts, carboxylic and sulphonic acids.
• Hydrocarbons, alkyl halides, alcohols, aldehydes, ketones, carboxylic acids, amines and their derivatives.

Synthetic Polymers

• Instrumental techniques – chromatography, electrophoresis, UV-Vis, IR and NMR spectroscopy and mass spectrometry.
• Biomolecules, amino acids, proteins, nucleic acids, lipids and carbohydrates (polysaccharides),

Basic Biotechnology

• Tissue culture, Application of enzymes, Antigen-antibody interaction, Antibody production, Diagnostic aids.

General Biology

• Evolution, Taxonomy, Heredity, Genetic variation, Conservation, Principles of ecology and Techniques in modern biology.

Cell Biology

• Mitochondria, Golgi Apparatus, Endoplasmic Reticulum, Cell cycle, Cytoskeletal elements, Chloroplast and Signalling.

Molecular Biology

• DNA, RNA, Replication, Transcription, Translation, Proteins, Lipids and Membranes, Operon model, and Gene transfer.

BiochemistryQuadratic and Physiology

• Carbohydrates, Proteins, Lipids, Nucleic acids, Enzymes, Vitamins, Hormones, Metabolism (Glycolysis, TCA cycle and Photosynthesis), Nitrogen Fixation, Fertilization and Osmoregulation, Vertebrates-Nervous system, Endocrine system, Vascular system, Immune system, Digestive system and Reproductive System.

Microbiology

• Isolation, Cultivation, Structural features of virus, Bacteria, Fungi, Protozoa, Pathogenic microorganisms.

Mathematical Induction, Sets, Relations and Functions, Logarithms, Linear and Quadratic Equations, Complex Numbers, Sequences and Series, Trigonometry, Cartesian System of Rectangular Coordinates, Binomial theory, Straight lines and Family, Circles, Conic Sections, Permutations and Combinations, Boolean Algebra, Exponential and Logarithmic Series, Mathematical Logic, Statistics, Three Dimensional, Application of Derivatives, Geometry, Vectors, Matrices and Determinants, Probability, Functions, limits and Continuity, Differentiation, Definite and Indefinite Integrals, Differential Equations.

Sequences and Series of Real Numbers

• Convergence of sequences, bounded and monotone sequences, Cauchy sequences, Bolzano-Weierstrass theorem.
• Absolute convergence, tests of convergence for series – comparison test, ratio test, root test; Power series (of one real variable), radius and interval of convergence, term-wise differentiation and integration of power series.

Functions of One Real Variable

• Limit, continuity, intermediate value property, differentiation, Rolle’s Theorem, mean value theorem, L’Hospital rule, Taylor’s theorem, Taylor’s series, maxima and minima, Riemann integration (definite integrals and their properties), fundamental theorem of calculus.

Multivariable Calculus and Differential Equations

• Functions of Two or Three Real Variables: limit, continuity, partial derivatives, total derivative, maxima and minima.

Integral Calculus

• Double and triple integrals, change of order of integration, calculating surface areas and volumes using double integrals, calculating volumes using triple integrals.

Differential Equations

• Bernoulli’s equation, exact differential equations, integrating factors, orthogonal trajectories, homogeneous differential equations, method of separation of variables, linear differential equations of second order with constant coefficients, method of variation of parameters, Cauchy-Euler equation.

Matrices

• Systems of linear equations, rank, nullity, rank-nullity theorem, inverse, determinant, eigenvalues, eigenvectors.

Finite Dimensional Vector Spaces

• Linear independence of vectors, basis, dimension, linear transformations, matrix representation, range space, null space, rank-nullity theorem.

Groups

• Cyclic groups, abelian groups, non-abelian groups, permutation groups, normal subgroups, quotient groups, Lagrange’s theorem for finite groups, group homomorphisms.

• Sequences and Series of real numbers
• Differential Calculus of one and two real variables
• Matrics and Determinants
• Integral Calculus

• Probability
• Univariate Distributions
• Limit Theorem
• Standard Multivariate Distributions
• Sampling Distributions
• Estimation
• Testing of Hypothesis

Atomic and Molecular Structure

• Bohr’s Theory of Hydrogen-like Atoms, Fundamental Particles, Wave-Particle Duality, Uncertainty Principle, Shapes of Orbitals, Schrödinger’s Wave Equation, Electronic Configuration of Simple Homonuclear Diatomic Molecules, Quantum Numbers, Hund’s Rule and Pauli’s Exclusion Principle.

Solid State

• X-rays, Crystals and Crystal Systems, NaCl and KCl Structures, Close Packing, Lattice Energy, Atomic and Ionic Radii, Radius Ratio Rules, Born-Haber Cycle, Isomorphism and Heat Capacity of Solids.

Electrochemistry

• Concentration cells with and without transport, Conductance and its Applications, Transport Number, Galvanic cells, Chemical Kinetics, EMF and Free Energy, Polarography, Concentration cells with and without Transport, Debye-Huckel-Onsager Theory of Strong Electrolytes, Chain Reactions – Normal and Branched, Reactions of Various Order, Arrhenius Equation, Collision Theory, Transition State Theory, Enzyme Kinetics, Photochemical Processes, Catalysis.

Theory of Gases

• Kinetic Theory of Gases, Equation of State for Ideal and Non-Ideal (Van Der Waals) Gases, Maxwell-Boltzmann Distribution Law and Equipartition of Energy.

Basic Mathematical Concepts

• Elementary Statistics and Probability Theory, Functions, Maxima and Minima, Vectors and Matrices Determinants, Integrals and Ordinary Differential Equations.

Chemical Thermodynamics

• First Law and Its Application to Ideal and Nonideal Gases, Thermochemistry, Second Law, Reversible and Irreversible Processes, Entropy and Free Energy and Criteria for Spontaneity.

Absorption

• Absorption Isotherm, Gibbs Adsorption Equation, Types of Adsorption, Surface Area of Adsorbents, Surface Films on Liquids.

Spectroscopy

• Fundamental Concepts of Rotational, Vibrational, Electronic and Magnetic Resonance Spectroscopy, Beer-Lambert Law.

Chemical and Phase Equilibria

• Ionic Equilibria in Solutions, PH and Buffer Solutions, Law of Mass Action, Kp, Kc, Kx and Kn, Effect of Temperature on K, Hydrolysis, Solubility Product.
• Phase Equilibria–Phase Rule and its Application to One-Component and Two-Component Systems, Colligative Properties.

Aromatic and Heterocyclic Chemistry

• Monocyclic Compounds with One Hetero Atom, Synthesis, Reactivity, and Properties.
• Monocyclic, Bicyclic and Tricyclic Aromatic Hydrocarbons.

Basic Concepts in Organic Chemistry and Stereochemistry

• Electronic Effects (Resonance, Inductive, Hyperconjugation) and Steric Effects and its Applications (Acid/Base Property).
• Cyclic Systems (Mono- and Di-Substituted Cyclohexanes).
• Optical Isomerism in Compounds with and without any Stereocenters (Allenes, Biphenyls).
• Conformation of Acyclic Systems (Substituted Ethane/n-Propane/n-Butane).

Natural Products Chemistry

• Chemistry of Alkaloids, Amino Acids, steroids, Terpenes, Carbohydrates, Peptides and Nucleic Acids.

Organic Reaction Mechanism and Synthetic Applications

• Oxidation and Reduction Reactions in Organic Chemistry, Dozens Reaction, Wittig Reaction and McMurry Reaction, Pinacol-Pinacolone, Favorskii, Benzilic Acid Rearrangement, Dienone-Phenol Rearrangement, Baeyer-Villiger Reaction, Organometallic Reagents in Organic Synthesis (Grignard, Organolithium and Organocopper), Diels-Alder, Electrocyclic and Sigmatropic Reactions.
• Functional Group Interconversions and Structural Problems using Chemical Reactions, Chemistry of Reactive Intermediates (Carbocations, Carbanions, Free Radicals, Carbenes, Nitrenes, Benzynes etc…), Hofmann-Curtius-Lossen Rearrangement, Wolff Rearrangement, Simmons-Smith Reaction, Reimer-Tiemann Reaction, Michael Reaction.

Qualitative Organic Analysis

• Identification of Functional Groups by Chemical Tests.
• Elementary UV, IR and 1H NMR Spectroscopic Techniques as Tools for Structural Elucidation.

Periodic Table

• Periodic Classification of Elements and Periodicity in Properties, Chemical Bonding and Shapes of Compounds.
• General Methods of Isolation and Purification of Elements, Types of Bonding, VSEPR Theory and Shapes of Molecules
• Hybridization, Dipole Moment, Structure of NaCl, CsCl, Diamond and Graphite, Ionic Solids, Lattice Energy.

Bioinorganic Chemistry

• Basic reactions in Biological Systems and the Role of Metal Ions (Fe2+, Fe3+, Cu2+ and Zn3+), Essentials and Trace Elements of Life, Structure and Function of Hemoglobin and Myoglobin and Carbonic Anhydrase.

Main Group Elements (s and p blocks)

• Structure of Electron Deficient Compounds (Main Group Elements), General Concepts on Group Relationships and Gradation in Properties.

Analytical Chemistry

• Acid-base, Oxidation-Reduction and Complexometric Titrations (using EDTA), Principles of Qualitative and Quantitative Analysis, Precipitation Reactions, Use of Indicators and Organic Reagents in Inorganic Analysis, Radioactivity, Nuclear Reactions, Applications of Isotopes.

Instrumental Methods of Analysis

• Basic principles; instrumentations and simple applications of conductometry, potentiometry and
• UV-vis spectrophotometry; analyses of water, air and soil samples.

Transition Metals (d block)

• Oxide, Hydroxide and Salts of First Row Metals, Characteristics of 3d Elements.
• Coordination Complexes, Structure, Isomerism, Reaction Mechanism and Electronic Spectra, Color and Magnetic Properties of Metal Complexes.
• VB, MO and Crystal Field Theoretical Approaches for Structure, Organometallic Compounds having Ligands with Back Bonding Capabilities.

Consumer Theory

• Preference, utility and representation theorem, budget constraint, choice, demand (ordinary and compensated), Slutsky equation, revealed preference axioms.

Theory of Production and Cost

• Production technology, isoquants, production function with one or more inputs, returns to scale, short-run and long-run costs, cost curves in the short run and long run

General Equilibrium and Welfare

• Equilibrium and efficiency under pure exchange and production, welfare economics, theorems of welfare economics

Market structure

• Perfect competition, monopoly, pricing with market power, price discrimination (first, second and third), monopolistic competition and oligopoly

Game theory

• Strategic form games, iterated elimination of dominated strategies, Nash equilibrium, mixed extension and mixed strategy Nash equilibrium, examples: Cournot, Bertrand duopolies, Prisoner’s dilemma.

Public goods and market failure

• Externalities, public goods and markets with asymmetric information (adverse selection and moral hazard).

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, random walk model of consumption, Investment functions – Keynesian, money demand and supply functions, production function

Business cycles and economic models (closed economy)

• Business cycles-facts and features, the Classical model of the business cycle, the Keynesian model of the business cycle, simple Keynesian cross model of income and employment determination and the multiplier (in a closed economy), IS-LM Model, Hicks’ IS-LM synthesis, role of monetary and fiscal policies

Business cycles and economic models (open economy)

• Open economy, MundellFleming model, Keynesian flexible price (aggregate demand and aggregate supply) model, role of monetary and fiscal policies

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 (AK model, Romer model and Schumpeterian growth model).

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 and monetary policy, 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.

Preliminaries and Functions

• Set theory and number theory.
• Elementary functions: quadratic, polynomial, power, exponential, logarithmic.
• Functions of several variables, graphs and level curves, convex set, concavity and quasiconcavity of function.
• Convexity and quasi-convexity of functions, sequences and series: convergence, algebraic properties and applications.

Differential Calculus

• Limits, continuity and differentiability, mean value theorems.
• Taylor’s theorem, partial differentiation, gradient, chain rule, second and higher order derivatives: properties and applications.
• Implicit function theorem, and application to comparative statics problems.
• Homogeneous and homothetic functions: characterisations and applications.

Integral calculus

• Definite integrals, fundamental theorems, indefinite integrals and applications.

Differential Equations and Difference Equations

• First-order difference equations, first-order differential equations and applications

Linear Algebra

• Matrix representations and Elementary operations

• Systems of linear equations: properties of their solution, linear independence and dependence.

• Eank, determinants, eigenvectors and eigenvalues of square matrices, symmetric matrices and quadratic forms, definiteness and semidefiniteness of quadratic forms.

Optimization

• Local and global optima: geometric and calculus-based characterisations, and applications.
• Multivariate optimization, constrained optimization and method of Lagrange multiplier.
• Second order condition of optima, definiteness and optimality, properties of value function: envelope theorem and applications.
• Linear programming: graphical solution, matrix formulation, duality, economic interpretation.

Probability Theory

• Sample space and events, axioms of probability and their properties, conditional probability and Bayes’ rule, independent events, random variables and probability distributions.
• Expectation, variance and higher order moments, functions of random variables, properties of commonly used discrete and continuous distributions.
• Density and distribution functions for jointly distributed random variables mean and variance of jointly distributed random variables, covariance and correlation coefficients.

Mathematical statistics

• Random sampling, types of sampling, point and interval estimation, estimation of population parameters using methods of moments and maximum likelihood procedures.
• Properties of estimators, sampling distribution, confidence intervals, central limit theorem, law of large number

Hypothesis testing

• Distributions of test statistics, testing hypotheses related to population parameters, Type I and Type II errors, the power of a test, and tests for comparing parameters from two samples.

Correlation and regression

• Correlation and types of correlation, the nature of regression analysis, method of Ordinary Least Squares (OLS), CLR.

• Origin of the Solar System and the Earth
• Isostasy
• Geosphere and the composition of the Earth
• Shape and size of the Earth
• Interior of the Earth
• Earthquakes
• Earth-Moon system
• Dating rocks and the age of the Earth
• Volcanism and volcanic landforms
• Earth’s magnetism and gravity
• Basic elements of Plate Tectonics and Orogenic cycles

• Soil formation
• Weathering and erosion
• Transportation and deposition of Soil by wind, ice, river, sea and resulting landforms.

• Contour lines; Rule of ‘V’s and outcrop patterns; Interpretation of geological maps and cross-section construction
• Orientation of planes and lines in space – the concept of dip, strike, rake and plunge
• Numerical problems related to outcrop and borehole data
• Classification and origin of folds, faults and joints.
• Stereographic and equal-area projections of planes and lines

• Major evolutions of life forms;
• Fossils; Modes of preservation, utility in age determination and paleoenvironmental interpretations
• Elementary idea of vertebrate fossils in India.
• Morphology, ages of important groups of animals – Mollusca, Brachiopoda, Trilobita, Graptolitoidea, Anthozoa, Echinodermata; Gondwana plant fossils
• Elementary idea of vertebrate fossils in India.

• Symmetry and forms in common crystal classes
• Physical properties of minerals
• Isomorphism, polymorphism, solid solution and exsolution
• Classification of minerals; Structure of silicates; Mineralogy of common rock-forming minerals
• Elements of Optical Mineralogy, Optical properties of common rock-forming minerals.

• Principles of stratigraphy; Litho-, Chrono- and biostratigraphic classification;
• Stratigraphic correlation techniques; Archaean cratons of Peninsular India (Dharwar, Singhbhum and Aravalli)
• Proterozoic mobile belts; Stratigraphy of Cuddapah and Vindhyan basins;
• Stratigraphy of Paleozoic – Mesozoic of Spiti and Kashmir, Gondwana Supergroup, Jurassic of Kutch, Cretaceous of Trichinopoly, Tertiary and Quaternary sequences of Assam, Bengal and Siwaliks.

• Physical properties of common economic minerals; General processes of formation of mineral deposits
• Mode of occurrence and distribution of metallic and non-metallic mineral deposits in India
• Fundamentals of reserve calculation; Elements of coal and hydrocarbon geology, Coal and hydrocarbon occurrences in India.

• Groundwater and hydrological cycle, Types of aquifers, porosity and permeability
• Principles of engineering geology
• Geological considerations in the construction of dams and tunnels.

• Definition and classification of rocks; Igneous rocks – forms of igneous bodies
• Processes of evolution and diversification of magma; Classification, association, and genesis of common igneous rocks. Sedimentary rocks – classification, texture, and structure
• Petrology of sandstone and limestone; Elements of sedimentary environments and facies
• Metamorphic rocks – classification and texture; Types of metamorphism; Controls on metamorphism – pressure, temperature and fluids
• Concept of projections – ACF, AKF and AFM diagrams; Phase Rule and its applications; Concepts of zones and facies, Characteristic mineral assemblages of pelites in the Barrovian zones and mafic rocks in common facies.