IIT JAM 2025 - Indian Institute of Technology Joint Admission Test : Application Form, Exam Date, Eligibility, Syllabus and Exam Pattern

And other Post-Bachelor’s Degree programmes at the IITs and to the Integrated PhD programmes at IISc. This year JAM 2025 is being conducted by the IIT Kharagpur. The participating IITs are-

Joint Admission Test 2025 Important Dates

Date of Notification & Start of Online Registration

• To be notified.

Last Date of Submission of Application Form

• To be notified.

Date of Entrance Exam

• To be notified.

Date of Declaration of Result

• To be notified. 

Joint Admission Test 2024 was held on-

• 11th February 2024

IIT JAM Entrance Exam 2025 Eligibility 

Educational Qualification

Aspiring Candidates should have a bachelor's degree from a recognised board. They should possess aggregate marks or CGPA/CPI without rounding off.

• 55% or 5.5 out of 10 for General/OBC (NCL) category candidates
• 50% or 5.0 out of 10 for SC/ST and PwD category candidates.

IIT JAM Exam 2025 Syllabus

For Biological Sciences

General Biology

• Taxonomy and physiology, Pro-and eukaryotic organisms; cell organelles and their function; multicellular organisation; energy transformations; internal transport systems of plants; respiration; regulation of body fluids and excretory mechanisms; cellular reproduction; Mendelian genetics and heredity; biology and populations and communities; evolution; genesis and diversity of organisms; animal behaviour, plant and animal diseases.

Basics of Biochemistry, Biophysics, Molecular Biology

• Buffers; trace elements in biological systems; enzymes and proteins; vitamins; biological oxidations, carbohydrates and lipids and their metabolisms; digestion and absorption; detoxifying mechanisms; plant and animal hormones and their action, nervous system, nucleic acids, nature of the gene and its function, Genetic code, synthesis of nucleic acids and proteins. Enzyme mechanisms and kinetics, nucleic acid metabolism, photosynthesis. Structure of biomolecules; intra and intermolecular forces; thermodynamics and kinetics of biological systems, principles of x-ray diffraction, IR and UV spectroscopy and hydrodynamic techniques.

Microbiology, Cell Biology and Immunology

• Classes of microorganisms and their characterization, nutrient requirement for growth; laboratory techniques in microbiology, pathogenic microorganisms and disease; applied microbiology; viruses, Microbial genetics. Innate and adaptive immunity, antigen antibodies. Cell theory; Cell architecture; methods of cell fractionation; cell division; types of chromosome structure; biochemical genetics- inborn errors of metabolisms; viruses and fungi; principles of processes of development.

Mathematical Sciences

• Mathematical functions (algebraic, exponential, trigonometric), their derivatives (derivatives and integrals of simple functions), permutations and combinations.

For Biotechnology

• The Biotechnology (BT) test paper comprises of Biology (44% weight-age), Chemistry (20% weight-age), Mathematics (18% weight-age) and Physics (18% weight-age). The question paper will be full of objective type. There will be negative marking (one third) for the wrong answer.

Biology (10+2+3 level)

• General Biology: Taxonomy; Heredity; Genetic variation; Conservation; Principles of ecology; Evolution; Techniques in modern biology. Biochemistry and Physiology: 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. Basic Biotechnology: Tissue culture; Application of enzymes; Antigen-antibody interaction; Antibody production; Diagnostic Aids. Molecular Biology: DNA; RNA; Replication; Transcription; Translation; Proteins; Lipids and Membranes; Operon model; Gene transfer. Cell Biology: Cell cycle; Cytoskeletal elements; Mitochondria; Endoplasmic reticulum; Chloroplast; Golgi apparatus; Signaling. Microbiology: Isolation; Cultivation; Structural features of the virus; Bacteria; Fungi; Protozoa; Pathogenic micro-organisms. 

Chemistry (10+2+3 level)

• Atomic Structure: 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.

Mathematics (10+2 level)

• 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. 

Physics (10+2 level)

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

For Chemistry

Physical Chemistry

• Basic Mathematical Concepts: Functions, maxima and minima, integrals, ordinary differential equations, vectors and matrices, determinants, elementary statistics and probability theory. Atomic and Molecular Structure: Fundamental particles, Bohr's theory of hydrogen-like atom; wave-particle duality; Uncertainty principle; Schrodinger's wave equation; Quantum numbers, shapes of orbitals; Hund's rule and Pauli's exclusion principle, electronic configuration of simple homonuclear diatomic molecules.
• Theory of Gases: Equation of state of ideal and non-ideal (van der Waals) gases, Kinetic theory of gases. Maxwell-Boltzmann distribution law; equipartition of energy. Solid-state: Crystals, crystal systems, X-rays, NaCl and Kcl structures, close packing, atomic and ionic radii, radius ratio rules, lattice energy, Born-Haber cycle, isomorphism, the heat capacity of solids. Chemical Thermodynamics: Reversible and irreversible processes; First law and its application to ideal and nonideal gases; Thermochemistry; Second law; Entropy and free energy, Criteria for spontaneity.
• Chemical and Phase Equilibria: 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. Electrochemistry: 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.
• Chemical Kinetics: Reactions of various order, Arrhenius equation, Collision theory; Theory of absolute reaction rate; Chain reactions - Normal and branched chain reactions; Enzyme kinetics; photochemical processes; Catalysis. Adsorption: Gibbs adsorption equation, adsorption isotherm, types of adsorption, the surface area of adsorbents, surface films on liquids.

Organic Chemistry

• Basic Concepts in Organic Chemistry and Stereochemistry: Electronic effect (resonance, inductive, hyperconjugation) and steric effects and its applications (acid/base property). Optical isomerism in compounds without any stereocenters (allenes, biphenyls), the confirmation of acyclic systems (substituted ethane/n-propane/n-butane) and cyclic systems (mono and disubstituted cyclohexanes).
• Organic Reaction Mechanism and Synthetic Applications: Chemistry reactive intermediates, carbine, nitrene, benzyne, Hofmann-Curtius-Lossen rearrangement, Wolf rearrangement, Simmons-Smith reaction, Reimer- Tiemann reaction, Michael reaction, Darzens reaction, Witting reaction, McMurry reaction. Pinacol-pinacolone, Favorskii, benzilic acid rearrangement, dienonc-phenol rearrangement, Bayer-Villager reaction). Oxidation and reduction reactions in organic chemistry. Organometallic reagents in organic synthesis (Grignard and organocopper). Diels-Alder reaction, Sigmatropic reactions.
• Qualitative Organic Analysis: Functional group interconversions, structural problems using chemical reactions, identification of functional groups by chemical tests, elementary 1H NMR and IR spectroscopy as a tool for structural elucidation. Natural Products Chemistry: Introductory chemistry of alkaloids, terpenes, carbohydrates, amino acids, peptides and nucleic acids. Heterocyclic Chemistry: Monocyclic compounds with one heteroatom.

Inorganic Chemistry

• Periodic Table: 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; the structure of NaCl, CsCl, diamond and graphite; lattice energy. Main Group Elements (s and p blocks): Chemistry with an emphasis on group relationship and gradation in properties; the structure of electron-deficient compounds of main group elements and application of main group elements.
• Transition Metals (d block): Characteristics of 3d elements; oxide, hydroxide and salts of first row metals; coordination complexes; VB and Crystal Field theoretical approaches for structure, colour and magnetic properties of metal complexes. Organometallic compounds, metal carbonyls, nitrosyls and metallocenes, ligands with back bonding capabilities; MO theory approaches to explain bonding in metal-carbonyl, metal-nitrosyl and metal phosphine complexes.
• Bioinorganic Chemistry: Essentials and trace elements of life, basic reactions in the biological systems and the role of metal ions especially Fe2+, Fe3+, Cu2+ and Zn2+, the function of haemoglobin and myoglobin. Instrumental Methods of Analysis: Basic principles, instrumentations and simple applications of conductometry, potentiometry, UV-vis spectrophotometry, analysis of water, air and soil samples. Analytical Chemistry: Principles of qualitative and quantitative analysis; acid-base, oxidation-reduction and EDTA and precipitation reactions; use of indicators; use of organic reagents in the inorganic analysis; radioactivity; nuclear reactions; applications of isotopes.

For Computer Applications

• The Computer Applications (CA) test paper comprises of Mathematics, Computer Awareness, and Analytical Ability and General Awareness and they will be in the ratio 4:2:1. The question paper will be full of objective type. There will be negative marking (one third) for the wrong answer.

Mathematics 

• Algebra: Set theory and its simple applications. Basic concepts of groups, fields and vector spaces. Matrices: Rank of a matrix. Existence and uniqueness of the solution of a system of linear equations. Eigenvalues and Eigenvectors. The inverse of a matrix by elementary transformations.
• Differential Calculus: Differentiation, Partial differentiation, Taylor series and approximate calculations. Maxima and minima of functions of one and two variables.
• Integral Calculus: Single and multiple integrations. Definite integrals, Change of order and change of variables. Applications to the evaluation of area, surface and volume.
• Differential Equations: First order differential equations, linear differential equations of higher order with constant coefficients.
• Vector Algebra: Addition, subtraction, dot product, cross product, triple product and their applications.
• Numerical Analysis: Solution of non-linear equations using iterative methods. Interpolation (Lagrange's formula and Newton's formula for equidistant points). Numerical differentiation and integration (Trapezoidal and Simpson's rules).
• Probability: Basic concepts of probability theory. Binomial and Poisson distributions.
• Linear Programming: Formulation and its graphical solution for two-variable problems.

Computer Awareness

• Elements of computers. Number systems. Basic electronic gates.  Boolean algebra. Flip-Flops. An algorithmic approach to solving problems.  Fundamentals of C  language.
• Analytical Ability and General Awareness: Simple questions will be asked to test the analytical ability and general awareness of candidates.

For Geology

• The Planet Earth: 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; Energy in the earth system; Volcanism and volcanic landforms; Interior of the earth; Earthquakes; Earth's magnetism and gravity, Isostasy; Elements of Plate tectonics; Orogenic cycles.
• Geomorphology: Weathering and erosion; Transportation and deposition due to the wind, ice, river, sea, and resulting landforms, Structurally controlled landforms.
• Structural Geology: Concept of stratum; Contour; Outcrop patterns; Maps and cross-sections; Dip and strike; Classification & origin of folds, faults, joints, foliation and lineation, unconformities; shear zones.
• Palaeontology: 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 vertebrate fossils in India.
• Stratigraphy: Principles of stratigraphy; Litho-, Chrono and biostratigraphic classification; distribution and classification of the stratigraphic horizons of India from Archaean to Recent.
• Mineralogy: 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.
• Petrology: 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, texture and properties.
• Economic Geology: 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.
• Applied Geology: Ground Water; Mineral exploration, elements of Mining Geology and Environmental Geology; Principles of Engineering Geology.

For Geophysics

• There will be Three Sections in the Geophysics (GP)test paper, namely, Geology, Mathematics and Physics, each with a weight age of 50%. A candidate has to attempt any Two Sections. The syllabi for the Geology, Mathematics and Physics Sections of the Geophysics (GP) test paper are given below:

Geology Section

• The Planet Earth: 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 the rocks and age of the Earth; Energy in the earth system; Volcanism and volcanic landforms; Interior of the earth; Earthquakes. Earth's magnetism and gravity, Elements of plate tectonics.
• Geomorphology: Weathering and erosion; transportation and deposition due to the wind, ice, river, sea, and resulting landforms, Structurally controlled landforms.
• Structural Geology: Concept of stratum; Contour; Outcrop patterns; Maps and cross-sections; Dip and strike; Classification and origin of folds, faults, joints, foliation and lineation, unconformities; shear zones.
• Mineralogy: 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 the rock. Transmitted polarized light microscopy and optical properties of uniaxial and biaxial minerals.
• Palaeontology: 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;
• Stratigraphy: Principles of Stratigraphy, Geological Time Scale and ages of major stratigraphic units of India.
• Petrology: Definition and classification of rocks; Igneous rock-forms of igneous bodies; Crystallisation from magma; classification, association and genesis of igneous rocks; Sedimentary rocks-classification, texture and structure; Metamorphic rocks-Classification, facies, texture and structure.
• Economic Geology: Physical properties of common ore minerals, General processes of formation of mineral deposits; Mode of occurrence of important metallic and nonmetallic deposits in India; Coal, petroleum and groundwater occurrences in India.

Mathematics Section

• Sequences, Series and Differential Calculus: Sequences of real numbers, Convergent sequences and series. Mean Value Theorem, Taylor's theorem, Maxima and Minima, functions of several variables.
• Integral Calculus: Fundamental theorem of calculus, Integration, Double and Triple integrals, change of order of integration, Surface Areas and Volumes.
• Differential Equations: Linear and Non-linear ODE, existence and uniqueness (without proof), Linear Differential Equations of second order with constant coefficients.
• Vector Calculus: Gradient, Divergence, Curl, Laplacian, Green's, Stokes and Gauss theorems and their Applications.
• Linear Algebra: System of Linear Equations, Matrices, Rank, Determinant, Inverse, eigenvalues and eigenvectors. Dimension, Linear transformations.
• Probability: Probability spaces, Conditional Probability, Independence, Bayes Theorem, Univariate and Bivariate Random Variables, Moment Generating and Characteristic Functions, Binomial, Poisson and Normal distributions.
• Statistics: Sampling Distributions of Sample Mean and Variance, Exact Sampling Distribution (Normal Population), Simple and Composite hypothesis, a Best critical region of a Test, Neyman-Pearson theorem, Likelihood Ratio Testing and its Application to Normal population, comparison of normal populations, large sample theory of test of hypothesis, approximate test on the parameter of a binomial population, comparison of two binomial populations.
• Numerical Analysis: Difference table, symbolic operators, differences of a factorial, representation of a polynomial by factorials. Forward, backward and central difference approximation formulae. Simpson's one-third rule, Newton- Raphson method for finding the solution of f(x)=0.

Physics Section

• Mechanics and General Properties of Matter: Newton's laws of motion and applications, Kepler's laws, Gravitational Law and field, Conservative and non-conservative forces. The system of particles, Centre of mass (CM), the equation of motion of the CM, conservation of linear and angular momentum, conservation of energy. Elastic and inelastic collisions. Rigid body motion, fixed axis rotations, rotation and translation, moments of Inertia and products of Inertia. Principal moments and axes. Elasticity, Hooke’s law and elastic constants of isotropic solid, stress energy. Kinematics of moving fluids, the equation of continuity, Euler's equation, Bernoulli's theorem, viscous fluids, surface tension and surface energy, capillarity.
• Oscillations, Waves and Optics: Differential equation for the simple harmonic oscillator and its general solution. Superposition of two or more simple harmonic oscillators. Lissajous figures. Damped and forced oscillators, resonance. Wave equation, travelling 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. The 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.
• Electricity and Magnetism: Coulomb's law, Gauss's law. The concept of Potential, Field and Boundary Conditions, Solution of Laplace's equation for simple cases. Conductors, capacitors, dielectrics, dielectric polarization, volume and surface charges, electrostatic energy. Magnetic susceptibility, a bar magnet, Earth's magnetic field and its elements. Biot-Savart law, Ampere's law, Lenz'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. Lorentz Force and motion of charged particles in electric and magnetic fields.
• Kinetic theory, Thermodynamics: Elements of the 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. Zeroeth law and the concept of thermal equilibrium. The first law of thermodynamics and its consequences. Isothermal and adiabatic processes. Reversible, irreversible and quasi-static processes. The second law of thermodynamics. Carnot cycle.
• Modern Physics: 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, Bohr's atomic model, X-rays. Wave-particle duality, Uncertainty principle, Pauli Exclusion Principle, Structure of atomic nucleus, mass and binding energy. Radioactivity and its applications. Laws of radioactive decay and half-life, Fission and fusion.
• Solid State Physics and Electronics: Crystal structure, Bravais lattices and basis. Miller indices. X-ray diffraction and Bragg's law, Origin of energy bands. The concept of holes. Intrinsic and extrinsic semiconductors. p-n junctions, transistors. Amplifier circuits with transistors.

For Mathematics

• Sequences, Series and Differential Calculus: Sequences and Series of real numbers: Sequences and series of real numbers. Convergent and divergent sequences bounded and monotone sequences, convergence criteria for sequences of real numbers, Cauchy sequences, absolute and conditional convergence; Tests of convergence for series of positive terms - comparison test, ratio test, root test, Leibnitz test for convergence of alternating series.
• Functions of one variable: limit, continuity, differentiation, Rolle's Theorem, Mean value theorem. Taylor's theorem. Maxima and minima.
• Functions of two real variables: limit, continuity, partial derivatives, differentiability, maxima and minima. Method of Lagrange multipliers, Homogeneous functions including Euler's theorem.
• Integral Calculus: Integration as the inverse process of differentiation, definite integrals and their properties, Fundamental theorem of integral calculus. Double and triple integrals, change of order of integration. Calculating surface areas and volumes using double integrals and applications. Calculating volumes using triple integrals and applications.
• Differential Equations: 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-separable solutions, Linear differential equations of second and higher-order with constant coefficients, the method of variation of parameters. Cauchy- Euler equation.
• Vector Calculus: Scalar and vector fields, gradient, divergence, curl and Laplacian. Scalar line integrals and vector line integrals, scalar surface integrals and vector surface integrals, Green's, Stokes and Gauss theorems and their applications.
• Group Theory: 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 (only group theory).
• Linear Algebra: Vector spaces, Linear dependence of vectors, basis, dimension, linear transformations, matrix representation with respect to an ordered basis, Range space and null space, rank-nullity theorem; Rank and inverse of a matrix, determinant, solutions of systems of linear equations, consistency conditions. Eigenvalues and eigenvectors. Cayley-Hamilton theorem. Symmetric, skew-symmetric, Hermitian, skew-hermitian, orthogonal and unitary matrices.
• Real Analysis: Interior points, limit points, open sets, closed sets, bounded sets, connected sets, compact sets; completeness of R, Power series (of the real variable) including Taylor's and Maclaurin's, domain of convergence, term-wise differentiation and integration of power series.

For Mathematical Statistics

• The Mathematical Statistics (MS) test paper comprises Mathematics (40% weight-age) and Statistics (60% weightage).
• Mathematics: Sequences and Series: Convergence of sequences of real numbers, Comparison, root and ratio tests for convergence of series of real numbers.
• Differential Calculus: 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.
• Integral Calculus: Fundamental theorems of integral calculus. Double and triple integrals, applications of definite integrals, arc lengths, areas and volumes. Matrices: Rank, the inverse of a matrix. systems of linear equations. Linear transformations, eigenvalues and eigenvectors. Cayley-Hamilton theorem, symmetric, skew-symmetric and orthogonal matrices.
• Differential Equations: Ordinary differential equations of the first order of the form y' = f(x,y). Linear differential equations of the second order with constant coefficients.
• Statistics Probability: Axiomatic definition of probability and properties, conditional probability, multiplication rule. The theorem of total probability. Bayes' theorem and independence of events.
• Random Variables: Probability mass function, probability density function and cumulative distribution functions, distribution of a function of a random variable. Mathematical expectation, moments and moment generating function. Chebyshev's inequality.
• Standard Distributions: Binomial, negative binomial, geometric, Poisson, hypergeometric, uniform, exponential, gamma, beta and normal distributions. Poisson and normal approximations of a binomial distribution.
• Joint Distributions: Joint, marginal and conditional distributions. Distribution of functions of random variables. Product moments, correlation, simple linear regression. Independence of random variables.
• Sampling distributions: Chi-square, t and F distributions, and their properties.
• Limit Theorems: the Weak law of large numbers. Central limit theorem (i.i.d.with finite variance case only).
• Estimation: Unbiasedness, consistency and efficiency of estimators, the method of moments and method of maximum likelihood. Sufficiency, factorization theorem. Completeness, Rao-Blackwell and Lehmann-Scheffe theorems, uniformly minimum variance unbiased estimators. Rao-Cramer inequality. Confidence intervals for the parameters of univariate normal, two independent normals, and one parameter exponential distributions.
• Testing of Hypotheses: Basic concepts, applications of Neyman-Pearson Lemma for testing simple and composite hypotheses. Likelihood ratio tests for parameters of the univariate normal distribution.

For Physics

• Mathematical Methods: 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.
• Mechanics and General Properties of Matter: Newton’s laws of motion and applications, Velocity and acceleration in Cartesian, polar and cylindrical coordinate systems, uniformly rotating the frame, centrifugal and Coriolis forces, Motion under a central force, Kepler’s laws, Gravitational Law and field, Conservative and non-conservative forces. The system of particles, Centre of mass, the 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, the equation of continuity, Euler’s equation, Bernoulli’s theorem.
• Oscillations, Waves and Optics: Differential equation for the simple harmonic oscillator and its general solution. Super-position of two or more simple harmonic oscillators. Lissajous figures. Damped and forced oscillators, resonance. Wave equation, travelling 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. The 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.
• Electricity and Magnetism: 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.
• Kinetic theory, Thermodynamics: Elements of the 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 the 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.
• Modern Physics: 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. The solution of the Schrodinger equation for the one-dimensional harmonic oscillator. Reflection and transmission at a step potential, Pauli exclusion principle. Structure of the atomic nucleus, mass and binding energy. Radioactivity and its applications. Laws of radioactive decay.
• Solid State Physics, Devices and Electronics: Crystal structure, Bravais lattices and basis. Miller indices. X-ray diffraction and Bragg’s law; Intrinsic and extrinsic semiconductors, the 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; the combination of gates; de Morgan’s theorem.

IIT JAM Exam 2025 Pattern

JAM will have seven test papers, namely

• Biological Sciences (BL)
• Biotechnology (BT)
• Chemistry (CY)
• Geology (GG)
• Mathematics (MA)
• Mathematical Statistics (MS) and
• Physics (PH), each of three hours duration.

Total Marks: The question paper contains a total of 100 marks.

Negative Marking: Negative marking will be only for section I.

The entire paper will be divided into three sections, A, B and C and all the sections are compulsory.

Important

• Use of a calculator (non-programmable) is permitted.
• The medium for all the test papers will be English only.

How to Apply for IIT JAM 2025?

Aspiring candidates can apply Online modes only. Candidates are required to visit the official website i.e., http://jam.iitkgp.ac.in. / and follow the instructions given there.

IIT JAM Exam 2025 Fee

The exam fee for various categories is as follows.

IIT JAM Exam 2025 Dates

JAM Exam will be held in the month of February.

IIT JAM Exam 2025 Test Centres

The exam will be conducted at various centres in all 8 selected zones throughout India.

• IISc Bangalore Zone
• IIT Bombay Zone
• IIT Delhi Zone
• IIT Guwahati Zone
• IIT Kharagpur Zone
• IIT Madras Zone
• IIT Roorkee Zone

IIT JAM 2025 Contact Details

Organizing Chairperson
GATE-JAM Office
Indian Institute of Technology Kharagpur
Kharagpur – 721302
West Bengal
Ph: 03222-282091/282095
Email: [email protected]
Web: http://www.iitkgp.ac.in/