The Joint Admission Test for MSc.

Admission to Integrated PhD Programmes at Indian Institute of Science Bangalore and

MSc (Two Years), Joint MSc-PhD, MSc-PhD Dual Degree, MSc-MTech, MSc-MS (Research) / PhD Dual Degree and other Post-Bachelor's Degree Programmes at

Indian Institute of Technology (Bhubaneswar, Bombay, Delhi, Gandhinagar, Guwahati, Hyderabad, Indore, Kanpur, Kharagpur, Madras, Roorkie, Ropar.

The entrance examination of JAM is conducted online all over India in subjects : Biological Sciences, Biotechnology, Chemistry, Geology, Mathematics, Mathematical Statistics, Physics.

**Visit IIT JAM Exam Books**

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In the JAM Exam, Indian nationals as well as foreign can apply. There is no age restriction.

## Exam Pattern: IIT JAM

Candidates applying for the IIT JAM Exam must go through the educational qualification eligibility. The exam pattern or say question paper pattern for the JAM is same for all the subjects (Biological Sciences, Biotechnology, Chemistry, Geology, Mathematics, Mathematical Statistics, Physics).

The IIT JAM exam will be held online Computer-based.

The duration of the exam is

__3 hour.__There will be 60 questions asked with 100 marks.

The question paper is divided into three sections : Section A, Section B and Section C.

All the sections are compulsory, no attempt of the answer will result in zero marks.

__About Section A__It consist of total 30

**Multiple Choice Questions (MCQs)**with one or two marks. Each question has four choices. Out of which only one choice is correct. Please note there is negative marking.

__About Section B__The Section B of the JAM exam is much similar to Section A, but with a difference. Here the answer to the question may be

**. There is no negative marking. There will be 10 questions with 2 marks each.**__one or more than one__

__About Section C__Here in this section, there is no answer or choices. Candidates have to enter the answer by using a virtual numeric keyboard. There will be 20 questions of one or two marks. There is no negative marking.

Also note that electronic gadgets like calculators are not allowed in the exam.

## IIT JAM Syllabus

Biological Science Syllabus IIT JAM

**Taxonomy and physiology, Pro-and eukaryotic organizms; cell organelles and their function; multicellular organization; 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 organizms; animal behaviour, plant and animal diseases.**

__General 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 gene and its function, Genetic code, synthesis of nucleic acids and proteins. Enzyme mechanisms and kinetics, nucleic acid metabolism, photo synthesis. 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.**

__Basics of Biochemistry, Biophysics, Molecular Biology:__**Classes of microorganizms 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.**

__Microbiology, Cell Biology and Immunology:__**Mathematical functions (algebraic, exponential, trigonometric), their derivatives (derivatives and integrals of simple functions), permutations and combinations.**

__Mathematical Sciences:__### Chemistry (CY) Syllabus IIT JAM

#### PHYSICAL CHEMISTRY

*Functions, maxima and minima, integrals, ordinary differential equations, vectors and matrices, determinants, elementary statistics and probability theory.*

**Basic Mathematical Concepts:****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.**

*Atomic and Molecular Structure:***Equation of state of ideal and non-ideal (van der Waals) gases, Kinetic theory of gases. Maxwell-Boltzmann distribution law; equipartition of energy.**

*Theory of Gases:***Crystals, 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.**

*Solid state:***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 Thermodynamics:***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.**

*Chemical and Phase Equilibria:***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.**

*Electrochemistry:***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.**

*Chemical Kinetics:***Gibbs adsorption equation, adsorption isotherm, types of adsorption, surface area of adsorbents, surface films on liquids.**

*Adsorption:*#### ORGANIC CHEMISTRY

*Electronic effect (resonance, inductive, hyperconjugation) and steric effects and its applications (acid/base property). Optical isomerism in compounds without any stereocenters (allenes, biphenyls), conformation of acyclic systems (substituted ethane/npropane/n-butane) and cyclic systems (mono and di substituted cyclohexanes).*

**Basic Concepts in Organic Chemistry and Stereochemistry:****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-Villeger reaction. Oxidation and reduction reactions in organic chemistry. Organometallic reagents in organic synthesis (Grignard and organocopper). Diels-Alder reaction, Sigmatropic reactions.**

*Organic Reaction Mechanism and Synthetic Applications:***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.**

*Qualitative Organic Analysis:***Introductory chemistry of alkaloids, terpenes, carbohydrates, amino acids, peptides and nucleic acids.**

*Natural Products Chemistry:***Monocyclic compounds with one hetero atom.**

*Heterocyclic Chemistry:*#### INORGANIC CHEMISTRY

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

*Periodic Table:***Types of bonding; VSEPR theory and shapes of molecules; hybridization; dipole moment; ionic solids; structure of NaCl, CsCl, diamond and graphite; lattice energy.**

*Chemical Bonding and Shapes of Compounds:***Chemistry with emphasis on group relationship and gradation in properties; structure of electron deficient compounds of main group elements and application of main group elements.**

*Main Group Elements (s and p blocks):***Characteristics of 3d elements; oxide, hydroxide and salts of first row metals; coordination complexes; VB and Crystal Field theoretical approaches for structure, color and magnetic properties of metal complexes. Organometallic compounds, metal carnonyls, nitrosyls and metallocenes, ligands with back bonding capabilities; MO theory approaches to explain bonding in metal-carbonyl, metal-nitrosyl and metalphosphine complexes.**

*Transition Metals (d block):***Essentials and trace elements of life, basic reactions in the biological systems and the role of metal ions especially Fe2+, Fe3+, Cu2+ and Zn2+, function of hemoglobin and myoglobin.**

*Bioinorganic Chemistry:***Basic principles, instrumentations and simple applications of conductometry, potentiometry, UV-vis spectrophotometry, analysis of water, air and soil samples.**

*Instrumental Methods of Analysis:***Principles of qualitative and quantitative analysis; acid-base, oxidation-reduction and EDTA and precipitation reactions; use of indicators; use of organic reagents in inorganic analysis; radioactivity; nuclear reactions; applications of isotopes.**

*Analytical Chemistry:*### Mathematical Statistics (MS) IIT JAM

The Mathematical Statistics (MS) test paper comprises of Mathematics (40% weightage) and Statistics (60%weightage).

#### Mathematics

**Convergence of sequences of real numbers, Comparison, root and ratio tests for convergence of series of real numbers.**

*Sequences and Series:***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.**

*Differential Calculus:***Fundamental theorems of integral calculus. Double and triple integrals, applications of definite integrals, arc lengths, areas and volumes.**

*Integral Calculus:***Rank, inverse of a matrix. Systems of linear equations. Linear transformations, eigenvalues and eigenvectors. Cayley-Hamilton theorem, symmetric, skew-symmetric and orthogonal matrices.**

*Matrices:***Ordinary differential equations of the first order of the form y' = f(x,y). Linear differential equations of the second order with constant coefficients.**

*Differential Equations:*#### Statistics

**Axiomatic definition of probability and properties, conditional probability, multiplication rule. Theorem of total probability. Bayes’ theorem and independence of events.**

*Probability:***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.**

*Random Variables:***Binomial, negative binomial, geometric, Poisson, hypergeometric, uniform, exponential, gamma, beta and normal distributions. Poisson and normal approximations of a binomial distribution.**

*Standard Distributions:***Joint, marginal and conditional distributions. Distribution of functions of random variables. Product moments, correlation, simple linear regression. Independence of random variables.**

*Joint Distributions:***Chi-square, t and F distributions, and their properties.**

*Sampling distributions:***Weak law of large numbers. Central limit theorem (i.i.d. with finite variance case only).**

*Limit Theorems:***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.**

*Estimation:***Basic concepts, applications of Neyman-Pearson Lemma for testing simple and composite hypotheses. Likelihood ratio tests for parameters of univariate normal distribution.**

*Testing of Hypotheses:*### Biotechnology (BT) Syllabus IIT JAM

The Biotechnology (BT) test paper comprises of Biology (44% weightage), Chemistry (20% weightage), Mathematics (18% weightage) and Physics (18% weightage).

#### BIOLOGY (10+2+3 level)

**Taxonomy; Heredity; Genetic variation; Conservation; Principles of ecology; Evolution; Techniques in modern biology.**

*General Biology:***Carbohydrates; Proteins; Lipids; Nucleic acids; Enzymes; Vitamins; Hormones; Metabolism – Glycolysis, TCA cycle, Oxidative Phosphoryation; Photosynthesis. Nitrogen Fixation, Fertilization and Osmoregulation; Vertebrates-Nervous system; Endocrine system; Vascular system; Immune system; Digestive system and Reproductive System.**

*Biochemistry and Physiology:***Tissue culture; Application of enzymes; Antigen-antibody interaction; Antibody production; Diagnostic aids.**

*Basic Biotechnology:***DNA; RNA; Replication; Transcription; Translation; Proteins; Lipids and Membranes; Operon model; Gene transfer.**

*Molecular Biology:***Cell cycle; Cytoskeletal elements; Mitochondria; Endoplasmic reticulum; Chloroplast; Golgi apparatus; Signaling.**

*Cell Biology:***Isolation; Cultivation; Structural features of virus; Bacteria; Fungi; Protozoa; Pathogenic micro-organizms.**

*Microbiology:*#### CHEMISTRY (10+2+3 level)

**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.**

*Atomic Structure:*#### 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.

### Mathematics (MA) Syllabus IIT JAM

**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.**

*Sequences and Series of Real Numbers:***limit, continuity, differentiation, Rolle’s Theorem, Mean value theorem. Taylor's theorem. Maxima and minima.**

*Functions of One Variable:***limit, continuity, partial derivatives, differentiability, maxima and minima. Method of Lagrange multipliers, Homogeneous functions including Euler’s theorem.**

*Functions of Two Real Variables:***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.**

*Integral Calculus:***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, method of variation of parameters. Cauchy-Euler equation.**

*Differential Equations:***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.**

*Vector Calculus:***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).**

*Group Theory:***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.**

*Linear Algebra:***Interior points, limit points, open sets, closed sets, bounded sets, connected sets, compact sets; completeness of R, Power series (of real variable) including Taylor’s and Maclaurin’s, domain of convergence, term-wise differentiation and integration of power series.**

*Real Analysis:*### Physics (PH) Syllabus IIT JAM

**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.**

*Mathematical Methods:***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, Center 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.**

*Mechanics and General Properties of Matter:***Differential equation for 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, traveling 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. 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.**

*Oscillations, Waves and Optics:***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.**

*Electricity and Magnetism:***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 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.**

*Kinetic theory, Thermodynamics:***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.**

*Modern Physics:***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. 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; combination of gates; de Morgan’s theorem.**

*Solid State Physics, Devices and Electronics:*## IIT JAM Previous Years Question Papers

Download IIT JAM previous year question papers arranged yearwise. The question papers are in the PDF format.

## IIT JAM Exam Books

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