**IIT JAM Syllabus 2021** will differ according to the courses chosen by the candidates. IIT Joint Admission Test (IIT JAM 2021) will be organized by the officials of IISC, Bangalore. The candidates will be offered admissions into MSc programmes through the entrance exam, a two-year program, and other post-bachelor programmes offered by the IITs. Those candidates who want to get access to integrated PhD courses offered by the IISc are also allowed to attend the examination. The article discusses the details regarding IIT JAM 2021 syllabus for every paper.

## IIT JAM Exam Pattern 2021

JAM 2021 entrance examination will be held online for all papers. JAM 2021 exam will be conducted for all seven papers. The test will be held for about three hours. The total number of questions asked in the entrance examination will be 60 questions. The full maximum marks will be of 100 marks. There will be three sections/ parts asked in the question paper: Section A, Section B, Section C. The Section A part and Section B parts will consist of multiple-choice objective type questions, and that of Section C will be of Numerical Answer type questions (NAT). Section A part will contain negative marking and that of Section B and Section C, there will be no negative markings for wrong responses or answers.

## IIT JAM Syllabus 2021

IIT JAM 2021 syllabus will be published by the authorities along with the release of the information bulletin. Candidates can go through and check the entire syllabus for JAM 2021 for all the seven papers. The seven papers are as mentioned below Biological Sciences, Biotechnology, Chemistry, Geology, Mathematics, Mathematical Statistics and Physics. Candidates can check the details of paper-wise syllabus through the article.

**Biological Sciences (BL) Syllabus**

**General Biology:** Topics includes Taxonomy of plants and animals; pro-and eukaryotic organisms; cell organelles and their function; multicellular organization; general physiology; energy transformations; internal transport systems of plants and animals; photosynthesis; respiration; regulation of body fluids and excretory mechanisms; reproductive biology; plant and animal hormones and their action; nervous systems; animal behaviour; plant and animal diseases; basics of developmental biology; biology of populations and communities; evolution; basic principles of ecology; genesis and diversity of organisms, Mendelian genetics and heredity.

**Basics of Biochemistry, Biophysics, Molecular Biology:** Includes Buffers; trace elements in biological systems; enzymes and proteins; vitamins; biological oxidations, photosynthesis; carbohydrates and lipids and their metabolism; digestion and absorption; detoxifying mechanisms; nucleic acids; nucleic acid metabolism; nature of the gene and its function, genetic code; synthesis of nucleic acids and proteins; regulation of gene expression, operons; enzyme mechanisms and kinetics. Structure of biomolecules; intra and intermolecular forces; thermodynamics and kinetics of biological systems; principles of X-ray diffraction; IR- and UV- spectroscopy; analytical and biochemical techniques

**Microbiology, Cell Biology and Immunology:** Includes classification of micro-organisms and their characterization; nutrient requirement for growth, viruses and fungi, laboratory techniques in microbiology; pathogenic micro-organisms and disease; applied microbiology, microbial genetics; cell theory, cell architecture; cell division; types of chromosome structure, biochemical genetics- inborn errors of metabolisms; innate and adaptive immunity, antigen antibodies, principles of processes of development.

**Mathematical Sciences:** Includes basic probability, Mathematical functions (algebraic, exponential, trigonometric) and their derivatives (derivatives and integrals of simple functions); permutations and combinations, volumetric calculations.

**Geology (GG) Syllabus**

**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, Elements of Plate tectonics, 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, Orogenic cycles.

**Geomorphology:** Includes Weathering and erosion, resulting in landforms, Transportation and deposition due to wind, ice, river, sea, Structurally controlled landforms.

**Structural Geology:** Includes stratum concept; Contour; Outcrop patterns, Maps and cross-sections, Dip and strike, classification and origin of folds, unconformities, faults, joints, foliations and lineation, shear zones. Stereographic and equal-area projections of planes and lines; computation of true thickness of beds from outcrops and bore-holes.

**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 standard crystal classes; Physical properties of minerals; Isomorphism and polymorphism, Mode of occurrence of minerals in rocks, Classification of minerals, Structure of silicates, Mineralogy of common rock-forming minerals. Transmitted polarized light microscopy and optical properties of uniaxial and biaxial minerals.

**Petrology:** Definition and classification of rocks; Igneous rocks-forms of igneous bodies, Sedimentary rocks – classification, texture and structure, size and shape of sedimentary bodies, Crystallization from magma, classification, association and genesis of igneous rocks. Metamorphic rocks – classification, facies, zones and texture. Characteristic mineral assemblages of pelites in the Barrovian zones and mafic rocks in common facies.

**Economic Geology:** Properties of common economic minerals, Physical characters, General processes of formation of mineral deposits, Mode of occurrence and distribution in India both metallic and non-metallic mineral deposits, Coal and petroleum occurrences in India.

**Applied Geology:** Involves Ground Water & Principles of Engineering Geology.

**Physics (PH) Syllabus**

**Mathematical Methods:** Calculus of single and multiple variables, Taylor expansion, Fourier series, partial derivatives, Jacobian, imperfect and perfect differentials. Vector algebra, Vector Calculus, Multiple integrals, Divergence theorem, Green’s theorem, Stokes’ theorem. Matrices and determinants, Algebra of complex numbers. First-order equations and linear second-order differential equations with constant coefficients.

**Mechanics and General Properties of Matter:** Includes topics on 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, Centre 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.

**Oscillations, Waves and Optics:** Includes 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. Double refraction and optical rotation. 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 & their lens combinations. Interference of light, optical path retardation. Fraunhofer diffraction. Rayleigh criterion and resolving power. Diffraction gratings. Polarization, linear, circular and elliptic polarization.

**Electricity and Magnetism:** Includes 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, Faraday’s law of electromagnetic induction, Self and mutual inductance volume and surface charges, electrostatic energy. Biot-Savart law, Ampere’s law. 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:** Includes 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 the concept of thermal equilibrium. Maxwell’s thermodynamic relations and simple applications. First law and its consequences. Isothermal and adiabatic processes. Reversible, irreversible and quasi-static processes. Second law and entropy. Carnot cycle. Thermodynamic potentials and their applications. Phase transitions and Clausius-Clapeyron equation. Bose-Einstein distributions, Ideas of ensembles, Maxwell-Boltzmann, Fermi-Dirac.

**Modern Physics:** Includes Inertial frames and Galilean invariance. Postulates of special relativity. Lorentz transformations. Relativistic velocity addition theorem, mass-energy equivalence. Black body radiation, photoelectric effect, Compton effect, Bohr’s atomic model, X-rays. Wave-particle duality, Length contraction, time dilation, Uncertainty principle, the superposition principle, calculation of expectation values, Schrödinger equation and its solution for one-, two three-dimensional boxes. The solution of the Schrödinger equation for the one-dimensional harmonic oscillator. Reflection and transmission at a step potential, Pauli exclusion principle. Radioactivity and its applications. Structure of the atomic nucleus, mass and binding energy. Laws of radioactive decay.

**Solid State Physics, Devices and Electronics:** Includes 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. Binary number systems; conversion from one system to another system; binary addition and subtraction. 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 stages R-C coupled amplifiers. Simple Oscillators: Barkhuizen condition, sinusoidal oscillators. OPAMP and applications: Inverting and non-inverting amplifier. Boolean algebra. Logic Gates AND, OR, NOT, NAND, NOR exclusive OR; Truth tables; the combination of gates; de Morgan’s theorem.

**Mathematical Statistics (MS) Syllabus**

Mathematics statistics paper, about 40% weightage is set from mathematics questions, and the rest of the 60% weightage is given to Statistics.

**Mathematics**

**Sequences and Series:**Includes 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, indeterminate forms, maxima and minima of functions of one and two variables, Taylor’s theorem.**Integral Calculus:**Fundamental theorems of integral calculus, arc lengths, areas and volumes. Double and triple integrals, applications of definite integrals.**Matrices:**Rank, the inverse of a matrix. Systems of linear equations. Linear transformations, eigenvalues and eigenvectors, symmetric, skew-symmetric, Cayley-Hamilton theorem and orthogonal matrices.

**Statistics**

**Probability:**Includes Axiomatic definition of probability and properties, conditional probability, multiplication rule. The theorem of total probability. Bayes’ theorem and independence of events.**Random Variables:**Includes Probability mass function, probability density function and cumulative distribution functions, Chebyshev’s inequality, distribution of a function of a random variable. Mathematical expectation, moments and moment generating function.**Standard Distributions:**Includes Binomial, negative binomial, geometric, Poisson, Poisson and normal approximations of a binomial distribution, hypergeometric, uniform, exponential, gamma, beta and normal distributions.**Joint Distributions:**Includes Joint, marginal and conditional distributions. Distribution of functions of random variables. Product moments, correlation, simple linear regression. Independence of random variables. Joint moment generating function.**Sampling distributions:**Chi-square, t and F distributions, and their properties.**Limit Theorems:**Includes Weak law of large numbers. Central limit theorem (i.i.d.with finite variance case only).**Estimation:**Includes Unbiasedness, consistency and efficiency of estimators, method of moments and method of maximum likelihood. Completeness, Rao-Blackwell and Lehmann-Scheffe theorems, uniformly minimum variance unbiased estimators. Rao-Cramer inequality. Sufficiency, factorization theorem. Confidence intervals for the parameters of univariate normal, two independents normal, and one exponential parameter distributions.**Testing of Hypotheses:**Includes Likelihood ratio tests for univariate normal distribution parameters: basic concepts, applications of Neyman-Pearson Lemma for testing simple and composite hypotheses.

**Biotechnology (BT) Syllabus**

The weightage of each subject in biotechnology syllabus are:

Biology (44% weightage), Chemistry (20% weightage), Mathematics (18% weightage) and Physics (18% weightage)

**Biology (10+2+3 level)**

**General Biology:**Includes Taxonomy; Heredity, Techniques in modern biology, Genetic variation; Conservation; Principles of ecology; Evolution.**Biochemistry and Physiology:**Includes Carbohydrates; Proteins; Lipids; Nucleic acids; Enzymes; Vitamins; Hormones; Metabolism – Glycolysis, TCA cycle, Oxidative Phosphorylation, Photosynthesis., Vascular system, Immune system, Nitrogen Fixation, Fertilization and Osmoregulation; Vertebrates-Nervous system; Endocrine system, Digestive system and Reproductive System.**Basic Biotechnology:**Tissue culture, Application of enzymes; Antigen-antibody interaction; Antibody production; Diagnostic aids, Cell Biology: Cell cycle, Cytoskeletal element, Mitochondria, Endoplasmic reticulum; Chloroplast; Golgi apparatus, Molecular Biology: DNA, RNA, Replication, Transcription, Translation, Proteins, Lipids and Membranes, Operon model; Gene transfer, Signalling, Microbiology: Isolation; Cultivation; Structural features of virus; Bacteria, Fungi, Protozoa, Pathogenic micro-organisms.

**Chemistry (10+2+3 level)**

Includes topics on 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), Hydrocarbons, alkyl halides, alcohols, aldehydes, ketones, carboxylic acids, amines and their derivatives, Photochemistry; Electrochemistry; Acid-base concepts; Stereochemistry of carbon compounds; Inductive, electrometric, conjugative effects and resonance; Chemistry of Functional Groups, Aromatic hydrocarbons, halides, nitro and amino compounds, phenols, diazonium salts, carboxylic and sulphonic acids; Mechanism of organic reactions, ) Instrumental techniques – chromatography (TLC, HPLC), electrophoresis, UV-Vis, IR and NMR spectroscopy, mass spectrometry, Soaps and detergents, Synthetic polymers; Biomolecules – amino acids, proteins, nucleic acids, lipids and carbohydrates (polysaccharides).

**Mathematics (10+2 level)**

Includes Sets, Relations and Functions, Mathematical Induction, Logarithms, Complex numbers, Linear and Quadratic Equations, Sequences and Series, Trigonometry, Cartesian System of Rectangular Coordinates, Application of Derivatives, Definite and Indefinite Integrals, Differential Equations, 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.

**Physics (10+2 level)**

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

**Chemistry (CY) Syllabus**

**Physical Chemistry**

**Fundamental Mathematical Concepts:** Includes Functions; maxima and minima, integrals, ordinary differential equations, probability theory, vectors and matrices, determinants, elementary statistics.

Atomic and Molecular Structure: Includes Fundamental particles; Bohr’s theory of hydrogen-like atom; wave-particle duality, uncertainty principle, electronic configuration of simple homonuclear diatomic molecules, Schrödinger’s wave equation; Quantum numbers, shapes of orbitals, Hund’s rule and Pauli’s exclusion principle.

**Theory of Gases:** Includes Equation of state for ideal and non-ideal (van der Waals) gases; Kinetic theory of gases; Maxwell-Boltzmann distribution law, Equipartition of energy.

**Solid-state:** Includes Crystals and crystal systems; X-rays, the heat capacity of solids, NaCl and KCl structures; close packing; atomic and ionic radii; radius ratio rules, lattice energy, Born-Haber cycle, isomorphism.

**Chemical Thermodynamics:** Includes 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.

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,; phase equilibria–phase rule and its Application to one-component and two-component systems, hydrolysis, solubility product, colligative properties.

**Electrochemistry:** Includes conductance and its applications, transport number, galvanic cells, concentration cells with and without transport; Debey-Huckel-Onsager theory of strong electrolytes, EMF and free energy, concentration cells with and without transport; polarography. Chemical Kinetics: Reactions of various order; Arrhenius equation; collision theory; transition state theory; chain reactions – normal and branched; enzyme kinetics; photochemical processes; catalysis.

**Adsorption:** Includes Gibbs adsorption equation, surface films on liquids, adsorption isotherm; types of adsorption; surface area of adsorbents.

**Spectroscopy:** Includes Beer-Lambert law, electronic and magnetic resonance spectroscopy, fundamental concepts of rotational, vibrational.

**Organic Chemistry**

**Basic Concepts in Organic Chemistry and Stereochemistry:** Includes Electronic effects (resonance, inductive, hyperconjugation) and steric effects and its applications (acid/base property); optical isomerism in compounds with and without any stereo enters (allenes, biphenyls); the conformation of acyclic systems (substituted ethane/n-propane/n-butane) and cyclic systems (mono- and di-substituted cyclohexenes).

**Organic Reaction Mechanism and Synthetic Applications:** Include, Michael reaction, Darzens 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.

**Qualitative Organic Analysis:** Includes functional groups’ Identification by chemical tests; elementary UV, IR and 1H NMR spectroscopic techniques as tools for structural elucidation.

Natural Products Chemistry: Includes Chemistry of alkaloids, peptides and nucleic acids steroids, terpenes, carbohydrates, amino acids.

**Aromatic and Heterocyclic Chemistry:** Includes Monocyclic, bicyclic and tricyclic aromatic hydrocarbons, and monocyclic compounds with one hetero atom: synthesis, reactivity and properties.

**Inorganic Chemistry**

**Periodic Table:** Includes Periodic classification of elements and periodicity in properties; general methods of isolation and purification of elements.

**Chemical Bonding and Shapes of Compounds:** Includes Types of bonding; VSEPR theory and shapes of molecules, dipole moment, ionic solids, the structure of NaCl, CsCl, diamond and graphite, hybridization, lattice energy.

**Main Group Elements (s and p blocks):** Includes General concepts on group relationships and gradation in properties; the structure of electron-deficient compounds involving main group elements.

**Transition Metals (d block):** Includes 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 metallocene; homogenous catalysis.

**Bioinorganic Chemistry:** Includes Essentials and trace elements of life; necessary reactions in the biological systems and structure and function of haemoglobin and myoglobin and carbonic anhydrase, the role of metal ions, especially Fe2+, Fe3+, Cu2+ and Zn2.

**Instrumental Methods of Analysis:** Includes Basic principles; instrumentations and simple conductometry applications, potentiometry and UV-vis spectrophotometry; analysis of water, air and soil samples.

**Analytical Chemistry:** Includes Principles of qualitative and quantitative analysis; acid-base, radioactivity, nuclear reactions, applications of isotopes, oxidation-reduction and complexometric titrations using EDTA; precipitation reactions; use of indicators; use of organic reagents in inorganic analysis.

**Mathematics (MA) Syllabus**

**Sequences and Series of Real Numbers:** Includes Sequence of real numbers, the 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 favourable terms – comparison test, ratio test, root test, Leibniz test for convergence of alternating series.

**Functions of One Variable:** Includes Limit, continuity, intermediate value property, differentiation, Rolle’s Theorem, mean value theorem, L’Hospital rule, Taylor’s theorem, maxima and minima.

Functions of Two or Three Real Variables: Includes Limit, continuity, maxima and minima, partial derivatives, differentiability.

**Integral Calculus:** Includes calculating volumes using triple integrals, 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.

**Differential Equations:** Includes 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, Stokes and Gauss theorems.

**Group Theory:** Includes Groups, subgroups, group homomorphisms and basic concepts of quotient groups, Abelian groups, non-Abelian groups, cyclic groups, permutation groups, normal subgroups, Lagrange’s Theorem for finite groups.

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

**Real Analysis:** Includes Interior points, limit points, open sets, closed sets, bounded sets, connected sets, compact sets, completeness of R. Power series (of a real variable), Taylor’s series, integration of power series, radius and interval of convergence, term-wise differentiation.

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