IIT JAM Syllabus 2025: Download Subject-wise Syllabus PDF

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,

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

Cytoskeleton elements

Mitochondria

Endoplasmic reticulum

Chloroplast

Golgi apparatus

Signalling

Microbiology

Isolation

Cultivation

Structural features of the virus

Bacteria

Fungi

Protozoa

Pathogenic micro-organisms

Physical

Basic Mathematical concepts

Atomic and Molecular Structure

Theory of gases

Solid state

Chemical Thermodynamics

Chemical & phase Equilibria

Electrochemistry

Chemical Kinetics

Adsorption

Spectroscopy

Organic

Basic concepts

Stereochemistry

Organic reaction mechanism

Synthetic applications

Qualitative organic Analysis

Natural products chemistry

Aromatic and Heterocyclic chemistry

Inorganic

Periodic table

Chemical bonding

Shapes of compounds

S and P block elements

Transition elements

Bio-inorganic chemistry

Instrumental Method of analysis

Analytical Chemistry

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 the age of the Earth

Volcanism and volcanic landforms

Interior of the Earth

Earthquakes

Earth’s magnetism and gravity

Isostasy

Elements of Plate tectonics

Orogenic cycles

Weathering and erosion

Transportation and deposition due to wind, ice, river, sea, and resulting landforms

Structurally controlled landforms

Concept of stratum

Contour

Outcrop patterns

Maps and cross-sections

Dip and strike

Classification and origin of folds, faults, joints, unconformities, foliations, lineations, shear zones

Stereographic and equal area projections of planes and lines

Computation of true thickness of beds from outcrops and boreholes

Major steps in the evolution of life forms

Fossils: preservation, utility, morphological characters

Major evolutionary trends and ages of important animal groups (Brachiopoda, Mollusca, Trilobita, Graptoloidea, Anthozoa, Echinodermata)

Gondwana plant fossils

Elementary idea of vertebrate fossils in India

Principles of stratigraphy

Litho-, chrono-, and biostratigraphic classification

Distribution and classification of stratigraphic horizons of India from Archaean to Recent

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

Definition and classification of rocks

Igneous rocks: forms of igneous bodies, crystallization from magma, classification, association, and genesis

Sedimentary rocks: classification, texture, structure, size and shape of sedimentary bodies

Metamorphic rocks: classification, facies, zones, texture, characteristic mineral assemblages

Properties of common economic minerals

General processes

Sequences and Series of Real Numbers

Sequence of real numbers

Convergence of sequence

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 a series of positive terms

Comparison test

Ratio test

Root test

Leibniz test for convergence of alternating series

Functions of Two or Three Real Variables

Limit

Continuity

Partial derivatives

Differentiability

Maxima and minima

Integral Calculus

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

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

Variable separable equations

Linear differential equations of second order with constant coefficients

Method of variation of parameters

Cauchy-Euler equation

Vector Calculus

Scalar and vector fields

Gradient

Divergence

Curl

Line integrals

Surface integrals

Green’s theorem

Stokes’ theorem

Gauss’ theorem

Group Theory

Groups

Subgroups

Abelian groups

Non-Abelian groups

Cyclic groups

Permutation groups

Normal subgroups

Lagrange’s Theorem for finite group

Group homomorphisms

Basic concepts of quotient groups

Linear Algebra

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

Real Analysis

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

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 a complex number

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 frame, centrifugal and Coriolis forces

Motion under a central force, Kepler’s laws

Gravitational Law and field, and Conservative and non-conservative forces

System of particles

Centre of mass

Equation of motion of the CM, conservation of linear and angular momentum

Conservation of energy and 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

Oscillations, Waves and Optics

The Differential equation for simple harmonic oscillator and its general Solution

Superposition of two or more a 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 the 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 Kinetic theory of gasses

Velocity distribution and Equipartition of energy

Specific heat of Mono-, di- and triatomic gasses

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

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

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

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, 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

OP AMP 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; a combination of gates; de Morgan’s theorem

Sequences and Series

Sequences and Series

Convergence of sequences of real numbers

Comparison, root, and ratio tests for convergence of a 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, inverse of a matrix

Systems of linear equations

Linear transformations, eigenvalues, and eigenvectors

Cayley-Hamilton theorem, symmetric, skew-symmetric, and orthogonal matrices

Probability

Axiomatic definition of probability and properties

Conditional probability, multiplication rule

Theorem of total probability, Bayes’ theorem, independence of events

Random Variables

The 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

Joint moment generating function

Product moments, correlation, simple linear regression

Independence of random variables

Sampling Distributions

Chi-square, t, and F distributions and their properties

Limit Theorems

Weak law of large numbers

Central limit theorem (i.i.d. with finite variance case only)

Estimation

Unbiasedness,

Consistency and efficiency of estimators

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 normal, 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 univariate normal distribution