IIT JAM Syllabus 2027- Check the syllabus

• Limit, 
• Intermediate Value Property, 
• Continuity, 
• Differentiation, 
• Rolle’s Theorem, 
• Mean Value Theorem Taylor’s Theorem, 
• L’Hospital Rule, 
• Maxima and Minima.

• Bolzano-Weierstrass Theorem, 
• Cauchy Sequences, 
• Subsequences. Absolute Convergence, 
• Series of Real Numbers, 
• Tests of Convergence for Series of Positive Terms – Comparison Test, 
• Ratio Test, Root test, 
• Convergence of Sequences, 
• Convergence Criteria for Sequences of Real Numbers,
• Bounded and Monotone Sequences, 
• The sequence of Real Numbers, 
• Leibniz Test for Convergence of Alternating Series.

• Limit, 
• Continuity, 
• Partial Derivatives, 
• Differentiability, 
• Maxima, and Minima.

• Orthogonal Trajectories, 
• Homogeneous Differential Equations, 
• Linear Differential Equations of Second Order with Constant Coefficients, Variable Separable Equations, Method of Variation of Parameters, Cauchy-Euler Equation, Ordinary Differential Equations of the First Order of the Form y’=f(xy), Bernoulli’s Equation, Integrating Factor, Exact Differential Equations

• Integration as an Inverse Process of Differentiation, Fundamental Theorem of Calculus, 
• Definite Integrals and their Properties. Double and Triple Integrals, 
• Calculating Surface Areas and Volumes using Double Integrals, Change of Order of Integration, 
• Calculating Volumes using Triple Integrals.

• Groups, 
• Subgroups, 
• Non-Abelian Groups, 
• Abelian Groups, 
• Cyclic Groups, 
• Permutation Groups, 
• Normal Subgroups, 
• Group Homomorphisms and Basic Concepts of Quotient Groups, 
• Lagrange’s Theorem for Finite Groups.

• Scalar and Vector Fields, 
• Divergence, 
• Gradient, 
• Curl, 
• Line Integrals, 
• Green, 
• Stokes and Gauss Theorems, 
• Surface Integrals.

• Interior Points, 
• Closed sets, 
• Limit Points, 
• Open Sets, 
• Bounded Sets, Connected Sets, 
• Compact Sets, Completeness of R. Power Series (of Real Variable), 
• Radius and Interval of Convergence, 
• Taylor’s Series, 
• Term-Wise Differentiation and Integration of Power Series.

• Matrix Representation, 
• Rank-Nullity Theorem. Rank and Inverse of a Matrix,
• Determinant, Consistency Conditions, 
• Solutions of Systems of Linear Equations,
• Eigenvalues, and Eigenvectors for Matrices,
• Finite-Dimensional Vector Spaces, 
• Linear Independence of Vectors, 
• Basis, Dimension, 
• Linear Transformations, 
• Range Space, Null Space, 
• Cayley-Hamilton Theorem.

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

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

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

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

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

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

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

• 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.

• Major Steps in the Evolution of Life Forms, 
• Fossils and their mode of Preservation and Utility, Morphological Characters, 
• Major Evolutionary Trends and Ages of Important Groups of Animals – Brachiopoda, 
• Mollusca, Trilobita, Grapto litoidea, Anthozoa, Echinodermata; Gondwana Plant Fossils, 
• Elementary Idea of Vertebrate Fossils in India.

• 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, Geomorphology, 
• Weathering and Erosion, 
• Transportation and Deposition due to Wind, 
• Ice, River, Sea, and Resulting Landforms,
• Structurally Controlled Landforms.

• Principles of Stratigraphy, Litho-, Chrono- and Biostratigraphic Classification, 
• Distribution and Classification of the Stratigraphic Horizons of India from Archaean to Recent.

• 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, Characteristics Mineral Assemblages of Pelites in the Barrovian Zones and Mafic Rocks in Common Facies

• 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 Polarized Light Microscopy and Optical Properties of Uniaxial and Biaxial Minerals.

• 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.

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

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

• 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

• 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.

• 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

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

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

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

• 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-Onsagar Theory of Strong Electrolytes, 
• Chemical Kinetics, Reactions of Various Order, Arrhenius Equation, 
• Collision Theory, Transition State Theory, Chain Reactions – Normal and Branched, 
• Enzyme Kinetics, 
• Photochemical Processes, Catalysis.

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

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

• Dozens Reaction, Wittig Reaction and McMurry Reaction, Pinacol-Pinacolone, 
• Favorskii, Benzilic Acid Rearrangement, Dienone-Phenol Rearrangement, 
• Baeyer-Villeger Reaction, Oxidation and Reduction Reactions in Organic Chemistry, Organometallic Reagents in Organic Synthesis (Grignard, Organolithium and Organocopper),
• Diels-Alder, Electrocyclic and Sigmatropic Reactions, Functional Group Inter-Conversions 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.

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

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

• General concepts on Group Relationships and Gradation in Properties, 
• Structure of Electron Deficient Compounds involving Main Group Elements

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

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

• Essentials and Trace Elements of Life, 
• Basic Reactions in Biological Systems and the Role of Metal Ions, especially Fe2+, Fe3+, Cu2+ and Zn2+, 
• Structure and Function of Haemoglobin and Myoglobin and Carbonic Anhydrase.

• Essentials and Trace Elements of Life, Basic Reactions in Biological Systems and the Role of Metal Ions, especially Fe2+, Fe3+, Cu2+ and Zn2+, 
• Structure and Function of Haemoglobin and Myoglobin and Carbonic Anhydrase.

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

• Taxonomy, Heredity, Genetic Variation, Conservation, 
• Principles of Ecology, 
• Evolution, 
• Techniques in Modern Biology.

• Tissue Culture, Application of Enzymes, Antigen-Antibody Interaction, 
• Antibody Production, 
• Diagnostic Aids

• DNA, RNA, Replication, 
• Transcription, Translation, 
• Proteins, Lipids and Membranes, 
• Operon Model, Gene Transfer

• 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.

• Cell Cycle, Cytoskeletal Elements, 
• Mitochondria, Endoplasmic Reticulum, Chloroplast, 
• Golgi apparatus, Signaling,

• Bohr’s Theory and Schrodinger Wave Equation, Periodicity in Properties, 
• Chemical Bonding, Properties of s, p, d and f block elements, Complex Formation, Coordination Compounds, 
• Chemical Equilibria, Chemical Thermodynamics (First and Second Law), 
• Chemical Kinetics (Zero, First, Second and Third Order Reactions), 
• Photochemistry, Electrochemistry, 
• Acid-Base Concepts, Stereochemistry of Carbon Compounds, Inductive, 
• Electromeric, Conjugative Effects and Resonance, 
• Chemistry of Functional Groups, Hydrocarbons, Alkyl Halides, 
• Alcohols, Aldehydes, Ketones, Carboxylic Acids, Amines and their Derivatives, Aromatic Hydrocarbons, 
• Halides, Nitro and Amino Compounds, Phenols, Diazonium Salts, 
• Carboxylic and Sulphonic Acids, Mechanism of Organic Reactions, Soaps and Detergents, Synthetic Polymers, Biomolecules – Amino Acids, Proteins, 
• Nucleic Acids, Lipids and Carbohydrates (Polysaccharides); 
• Instrumental Techniques – Chromatography (TLC, HPLC), Electrophoresis, 
• UV-Vis, IR and NMR Spectroscopy, Mass Spectrometry.

• Isolation, Cultivation, 
• Structural features of Virus, Bacteria, 
• Fungi, Protozoa, 
• Pathogenic Microorganisms

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

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

Mathematics 

• Limits, Continuity and Differentiability of Functions of One and Two Variables. 
• Rolle’s Theorem, Mean Value Theorems, 
• Indeterminate Forms, Taylor’s Theorem, 
• Maxima and Minima of Functions of One and Two Variables.

• Fundamental Theorems of Integral Calculus, Applications of Definite Integrals, 
• Arc Lengths, Double and Triple Integrals, 
• Areas and Volumes.

• Comparison, Root and Ratio Tests for Convergence of Series of Real Numbers, 
• Convergence of Sequences of Real Numbers.

• Rank, Inverse of a Matrix, Systems of Linear Equations, 
• Eigenvalues and Eigenvectors, Linear Transformations, 
• Symmetric, Cayley-Hamilton Theorem,
• Skew-Symmetric and Orthogonal Matrices.

IIT JAM Syllabus 2027 for Statistics

• Probability Mass Function, 
• Distribution of a Function of a Random Variable, 
• Mathematical Expectation, Probability Density Function and Cumulative Distribution Functions,
• Moments and Moment Generating Function,
• Chebyshev’s Inequality.

• Geometric, Binomial, Negative Binomial, 
• Poisson, Hypergeometric, 
• Uniform, Beta and Normal Distributions, Exponential, 
• Gamma. Poisson and Normal Approximations of a Binomial Distribution.

• Axiomatic Definition of Probability and Properties, Multiplication Rule, 
• The theorem of Total Probability, 
• Conditional probability, 
• Bayes’ Theorem and Independence of Events

• Joint, Marginal and Conditional Distributions,
• Distribution of Functions of Random Variables,
• Joint Moment Generating Function, Correlation, Simple Linear Regression, 
• Product Moments, 
• Independence of Random Variables.

• Basic Concepts, Applications of Neyman-Pearson Lemma for Testing Simple and Composite Hypotheses, 
• Likelihood Ratio Tests for Parameters of Univariate Normal Distribution.

• Unbiasedness, Method of Moments and Method of Maximum Likelihood, 
• Consistency and Efficiency of Estimators. Sufficiency, Factorization Theorem, 
• Rao-Blackwell and Lehmann-Scheffe Theorems, Completeness, 
• Uniformly Minimum Variance Unbiased Estimators, Confidence Intervals for the Parameters of Univariate Normal, 
• Two Independent Normal, and one Parameter Exponential Distributions. Rao-Cramer Inequality

• Weak Law of Large Numbers, 
• Central Limit Theorem.