

IIT JAM Exam 
Subject 
Syllabus 
Syllabus  Biological Sciences (BL) 
Syllabus  Biological Sciences (BL)
SYLLABUS
BIOLOGICAL SCIENCES (BL)
General Biology: Taxonomy of plants and animals; proand 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 behavior; plant and animal diseases; Mendelian genetics and heredity; basics of developmental biology; biology of populations and communities; evolution; basic principles of ecology; genesis and diversity of organisms.
Basics of Biochemistry, Molecular Biology, Biophysics:
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 gene and its function; genetic code; synthesis of nucleic acids and proteins; regulation of gene expression; operons.
Structure of biomolecules; intra and intermolecular forces; thermodynamics and kinetics of biological systems; enzyme mechanisms and kinetics;principles of Xray diffraction; IR and UV spectroscopy; analytical and biochemical techniques
Microbiology, Cell Biology and Immunology: Classification of microorganisms and their characterization; nutrient requirement for growth; laboratory techniques in microbiology; pathogenic microorganisms and disease; applied microbiology; viruses and fungi; 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: Mathematical functions (algebraic, exponential, trigonometric) and their derivatives (derivatives and integrals of simple functions); permutations and combinations; basic probability and volumetric calculations.

Geology 
Geology
SYLLABUS
GEOLOGY (GG)
Test Paper
(Test paper code) 
Academic Programme(s) 
Institute(s) 
Minimum Educational Qualification(s) for Admission 
Essential subjects in Bachelor's Degree along with minimum duration 
Essential subjects at (10+2) level 
Geology
(GG)

M.Sc. Applied Geology 
IITB, IITR 
Geology for three years/six semesters and any two subjects among Mathematics, Physics, Chemistry and Biological Science 
Mathematics 
Joint M.Sc. Ph.D. in Geophysics 
IITKGP 
Geology as a subject for three years/six semesters and any two subjects among Mathematics, Physics and Chemistry 
Joint M.Sc. Ph.D. in Geology 
IITKGP, IITBBS 
Joint M.Sc. Ph.D. in Atmosphere and Ocean Sciences 
IITBBS 
Mathematics and Physics and any one of these subjects among Chemistry, Computer Science, Computer Application, Geology and Statistics 
No Restrictions 
M.Sc.(Tech) in
Applied Geology * 
IITISM 
B.Sc degree (3 year) with Geology as Honours/ Major/ Main/Equivalent
subject and any 2 subsidiary subjects from Mathematics, Physics and Chemistry. 
Mathematics 
The Planet Earth: Origin of the Solar System and the Earth; Geosphere and the composition of the Earth; Shape and size of the earth; Earthmoon system; Formation of continents and oceans; Dating rocks and age of the Earth; Volcanism and volcanic landforms; Interior of earth; Earthquakes; Earth's magnetism and gravity, Isostasy; Elements of Plate tectonics; Orogenic cycles.
Geomorphology: Weathering and erosion; Transportation and deposition due to wind, ice, river, sea, and resulting landforms, Structurally controlled landforms.
Structural Geology: Concept of stratum; Contour; Outcrop patterns; Maps and cross sections; Dip and strike; Classification and origin of folds, faults, joints, unconformities, foliations and lineations,; shear zones. Stereographic and equal area projections of planes and lines; computation of true thickness of beds from outcrops and boreholes.
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 verterbrate 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 rockforming minerals; Mode of occurrence of minerals in rocks. Transmitted polarised light microscopy and optical properties of uniaxial and biaxial minerals.
Petrology: Definition and classification of rocks; Igneous rocksforms of igneous bodies; Crystallization from magma; classification, association and genesis of igneous rocks; Sedimentary rocks  classification, texture and structure; size and shape of sedimentary bodies. Metamorphic rocks  classification, facies, zones and texture. Characteristic mineral assemblages of pelites in the Barrovian zones and mafic rocks in common facies.
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 nonmetallic mineral deposits; Coal and petroleum occurrences in India.
Applied Geology: Ground Water; Principles of Engineering Geology.

Syllabus  Physics (PH) 
Syllabus  Physics (PH)
SYLLABUS
PHYSICS (PH)
Test Paper
(Test paper code) 
Academic Programme(s) 
Institute(s) 
Minimum Educational Qualification(s) for Admission 
Essential subjects in Bachelor's Degree along with minimum duration 
Essential subjects at (10+2) level 
Physics
(PH) 
M.Sc. Physics 
IITB, IITD, IITG, IITGN, IITH, IITI, IITJ,IITK, IITM, IITP, IITR, IITRPR, IITISM 
Physics for at least two years/four semesters and Mathematics for at least one year/two semesters 
No Restrictions 
Joint M.Sc. Ph.D. in Physics 
IITBBS, IITKGP 
M.Sc. Ph.D. Dual Degree in Physics 
IITK 
M.Sc. Applied Geophysics 
IITB 
Physics and Mathematics/Mathematical Physics for two years/four semesters and at least one of them as subject for three years/six semesters 
M.Sc. Astronomy 
IITI 
Physics/ Mathematics / Computer Science Engineering, Electrical Engineering/ Mechanical Engineering 
Joint M.Sc. Ph.D. in Atmosphere and Ocean Sciences 
IITBBS 
Mathematics and Physics and any one of these subjects among Chemistry, Computer Science, Computer Application, Geology and Statistics 
Joint M.Sc. Ph.D. in Geophysics 
IITKGP 
Geology as a subject for three years/six semesters and any two subjects among Mathematics, Physics and Chemistry 
Mathematics 
M.Sc. Ph.D. Dual Degree in Environmental Science and
Engineering 
IITB 
Any one of Biology, Biotechnology, Chemistry, Mathematics and Physics for two years/four semesters, and any one of the other four subjects for at least one year/two semesters 
M.Sc.(Tech) in Applied Geophysics 
IITISM 
B.Sc Degree (3 yr.) with Physics as Honours/ Major/ Main/ Equivalent subject, Mathematics as a subsidiary subject for 2 years/4 semesters and another subsidiary subject from Chemistry, Geology, Electronics, and Statistics for 1 year/ 2 semesters. 
No Restriction 
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 frame, centrifugal and Coriolis forces, Motion under a central force, Kepler's laws, Gravitational Law and field, Conservative and nonconservative 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.
Oscillations, Waves and Optics: 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. Wave equation, traveling and standing waves in onedimension. 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.
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. BiotSavart 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, Maxwelll'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 gases. Velocity distribution and Equipartition of energy. Specific heat of Mono, di and triatomic gases. Ideal gas, vanderWaals 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 quasistatic processes. Second law and entropy. Carnot cycle. Maxwell's thermodynamic relations and simple applications. Thermodynamic potentials and their applications. Phase transitions and ClausiusClapeyron equation. Ideas of ensembles, MaxwellBoltzmann, FermiDirac and BoseEinstein 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, Xrays. Waveparticle duality, Uncertainty principle, the superposition principle, calculation of expectation values, Schrodinger equation and its solution for one, two and three dimensional boxes. Solution of Schrodinger 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. Xray diffraction and Bragg's law; Intrinsic and extrinsic semiconductors, variation of resistivity with temperature. Fermi level. pn junction diode, IV characteristics, Zener diode and its applications, BJT: characteristics in CB, CE, CC modes. Single stage amplifier, two stage RC coupled amplifiers. Simple Oscillators: Barkhausen condition, sinusoidal oscillators. OPAMP and applications: Inverting and noninverting 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.

Syllabus  Mathematical Statistics (MS) 
Syllabus  Mathematical Statistics (MS)
SYLLABUS
MATHEMATICAL STATISTICS (MS)
Test Paper
(Test paper code) 
Academic Programme(s) 
Institute(s) 
Minimum Educational Qualification(s) for Admission 
Essential subjects in Bachelor's Degree along with minimum duration 
Essential subjects at (10+2) level 
Mathematical Statistics
(MS) 
M.Sc. Applied Statistics and Informatics 
IITB 
Mathematics or Statistics for at least two years/ four semesters 
No Restrictions 
M.Sc. Ph.D. Dual Degree in Operations Research 
IITB 
M.Sc. Statistics 
IITK 
Statistics for at least two years/ four semesters 
Joint M.Sc. Ph.D. in Atmosphere and Ocean Sciences 
IITBBS 
Mathematics and Physics and any one of these subjects among Chemistry, Computer Science, Computer Application, Geology and Statistics 
The Mathematical Statistics (MS) test paper comprises of Mathematics (40% weightage) 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, inverse of a matrix. Systems of linear equations. Linear transformations, eigenvalues and eigenvectors. CayleyHamilton theorem, symmetric, skewsymmetric and orthogonal matrices.
Statistics
Probability: Axiomatic definition of probability and properties, conditional probability, multiplication rule. 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. Joint moment generating function. Product moments, correlation, simple linear regression. Independence of random variables.
Sampling distributions: Chisquare, 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, RaoBlackwell and LehmannScheffe theorems, uniformly minimum variance unbiased estimators. RaoCramer inequality. Confidence intervals for the parameters of univariate normal, two independent normal, and one parameter exponential distributions.
Testing of Hypotheses:Basic concepts, applications of NeymanPearson Lemma for testing simple and composite hypotheses. Likelihood ratio tests for parameters of univariate normal distribution.

Biotechnology (BT) 
SYLLABUS
BIOTECHNOLOGY (BT)
Test Paper
(Test paper code) 
Academic Programme(s) 
Institute(s) 
Minimum Educational Qualification(s) for Admission 
Essential subjects in Bachelor's Degree along with minimum duration 
Essential subjects at (10+2) level 
Biotechnology
(BT) 
M.Sc. Biotechnology 
IITB, IITI, IITR 
Any Branch/ Subject 
Mathematics 
M.Sc. Ph.D. Dual Degree in Environmental Science and Engineering 
IITB 
Any one of Biology, Biotechnology, Chemistry, Mathematics and Physics for two years/four semesters, and any one of the other four subjects for at least one year/two semesters 
The Biotechnology (BT) test paper comprises of Biology, Chemistry, Mathematics and Physics.
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 Phosphoryation; Photosynthesis. Nitrogen Fixation, Fertilization and Osmoregulation; VertebratesNervous system; Endocrine system; Vascular system; Immune system; Digestive system and Reproductive System.
Basic Biotechnology: Tissue culture; Application of enzymes; Antigenantibody 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 virus; Bacteria; Fungi; Protozoa; Pathogenic microorganizms.
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; Acidbase 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, UVVis, 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.

Syllabus  Chemistry (CY) 
Syllabus  Chemistry (CY)
Test Paper
(Test paper code) 
Academic Programme(s) 
Institute(s) 
Minimum Educational Qualification(s) for Admission 
Essential subjects in Bachelor's Degree along with minimum duration 
Essential subjects at (10+2) level 
Chemistry
(CY) 
M.Sc. Chemistry 
IITB, IITD, IITG, IITGN, IITH, IITI, IITJ, IITK, IITM, IITP, IITR, IITRPR, IITISM 
Chemistry for three years/six semesters 
Mathematics 
Joint M.Sc. Ph.D. in Chemistry 
IITBBS, IITKGP 
M.Sc. Ph.D. Dual Degree in Environmental Science and Engineering 
IITB 
Any one of Biology, Biotechnology, Chemistry, Mathematics and Physics for two years/four semesters, and any one of the other four subjects for at least one year/two semesters 
Mathematics 
Joint M.Sc. Ph.D. in Atmosphere and Ocean Sciences 
IITBBS 
Mathematics and Physics with any one of these subjects among Chemistry, Computer Science, Computer Application, Geology and Statistics 
No Restrictions 
SYLLABUS
CHEMISTRY (CY)
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 hydrogenlike atom; waveparticle 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 for ideal and nonideal (van der Waals) gases; Kinetic theory of gases; MaxwellBoltzmann distribution law; equipartition of energy.
Solid state: Crystals and crystal systems; Xrays; NaCl and KCl structures; close packing; atomic and ionic radii; radius ratio rules; lattice energy; BornHaber cycle; isomorphism; 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 equilibriaphase rule and its application to onecomponent and twocomponent 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; DebeyHuckelOnsagar theory of strong electrolytes.
Chemical Kinetics: Reactions of various order; Arrhenius equation; collision theory; transition state theory; chain reactions  normal and branched; enzyme kinetics; photochemical processes; catalysis.
Adsorption: Gibbs adsorption equation; adsorption isotherm; types of adsorption; surface area of adsorbents; surface films on liquids.
Spectroscopy: BeerLambert law; fundamental concepts of rotational, vibrational, electronic and magnetic resonance spectroscopy.
ORGANIC CHEMISTRY
Basic Concepts in Organic Chemistry and Stereochemistry: Electronic effects (resonance, inductive, hyperconjugation) and steric effects and its applications (acid/base property); optical isomerism in compounds with and without any stereocenters (allenes, biphenyls); conformation of acyclic systems (substituted ethane/npropane/nbutane) and cyclic systems (mono and disubstituted cyclohexanes).
Organic Reaction Mechanism and Synthetic Applications: Chemistry of reactive intermediates (carbocations, carbanions, free radicals, carbenes, nitrenes, benzynes etc ...); HofmannCurtiusLossen rearrangement, Wolff rearrangement, SimmonsSmith reaction, ReimerTiemann reaction, Michael reaction, Darzens reaction, Wittig reaction and McMurry reaction; Pinacolpinacolone, Favorskii, benzilic acid rearrangement, dienonephenol rearrangement, BaeyerVilleger reaction; oxidation and reduction reactions in organic chemistry; organometallic reagents in organic synthesis (Grignard, organolithium and organocopper); DielsAlder, electrocyclic and sigmatropic reactions; functional group interconversions and structural problems using chemical reactions.
Qualitative Organic Analysis: Identification of functional groups by chemical tests; elementary UV, IR and ^{1}H NMR spectroscopic techniques as tools for structural elucidation.
Natural Products Chemistry: Chemistry of alkaloids, steroids, terpenes, carbohydrates, amino acids, peptides and nucleic acids.
Aromatic and Heterocyclic Chemistry: Monocyclic, bicyclic and tricyclic aromatic hydrocarbons, and monocyclic compounds with one hetero atom: synthesis, reactivity and properties.
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; structure of NaCl, CsCl, diamond and graphite; lattice energy.
Main Group Elements (s and p blocks): General concepts on group relationships and gradation in properties; structure of electron deficient compounds involving main group elements.
Transition Metals (d block): 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, color and magnetic properties of metal complexes; organometallic compounds having ligands with back bonding capabilities such as metal carbonyls, carbenes, nitrosyls and metallocenes; homogenous catalysis.
Bioinorganic Chemistry: Essentials and trace elements of life; basic reactions in the biological systems and the role of metal ions, especially Fe^{2+}, Fe^{3+}, Cu^{2+} and Zn^{2+}; structure and function of hemoglobin and myoglobin and carbonic anhydrase.
Instrumental Methods of Analysis: Basic principles; instrumentations and simple applications of conductometry, potentiometry and UVvis spectrophotometry; analysis of water, air and soil samples.
Analytical Chemistry: Principles of qualitative and quantitative analysis; acidbase, oxidationreduction and complexometric titrations using EDTA; precipitation reactions; use of indicators; use of organic reagents in inorganic analysis; radioactivity; nuclear reactions; applications of isotopes.

Mathematics 
Mathematics
SYLLABUS
MATHEMATICS (MA)
Test Paper
(Test paper code) 
Academic Programme(s) 
Institute(s) 
Minimum Educational Qualification(s) for Admission 
Essential subjects in Bachelor's Degree along with minimum duration 
Essential subjects at (10+2) level 
Mathematics
(MA) 
M.Sc. in Economics 
IITR 
Mathematics as one of the core subjects 
No Restrictions 
M.Sc. Mathematics 
IITB, IITD, IITGN, IITI, IITJ,IITK, IITM, IITP, IITR, IITRPR 
Mathematics for at least two years/four semesters 
M.Sc. Mathematics/ Mathematics and Computing 
IITH, IITISM 
M.Sc. Mathematics and Computing 
IITG 
Joint M.Sc. Ph.D. in Mathematics 
IITBBS, IITKGP 
Mathematics/ Statistics as a subject for at least two years/four semesters. 
M.Sc. Ph.D. Dual Degree in Operations Research 
IITB 
M.Sc. Ph.D. Dual Degree in Environmental Science and Engineering 
IITB 
Any one of Biology, Biotechnology, Chemistry, Mathematics and Physics for two years/four semesters, and any one of the other four subjects for at least one year/two semesters. 
Mathematics 
Joint M.Sc. Ph.D. in Atmosphere and Ocean Sciences 
IITBBS 
Mathematics and Physics and any one of these subjects among Chemistry, Computer Science, Computer Application, Geology and Statistics 
No Restrictions 
Sequences and Series of Real Numbers: Sequence of real numbers, convergence of sequences, bounded and monotone sequences, convergence criteria for sequences of real numbers, Cauchy sequences,subsequences, BolzanoWeierstrass theorem. Series of real numbers, absolute convergence, tests of convergence for series of positive terms  comparison test, ratio test, root test; Leibniz test for convergence of alternating series.
Functions of One Real Variable: 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: 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, CauchyEuler equation.
Vector Calculus: Scalar and vector fields, gradient, divergence, curl, line integrals, surface integrals, Green, Stokes and Gauss theorems.
Group Theory: Groups, subgroups, Abelian groups, nonAbelian groups, cyclic groups, permutation groups, normal subgroups, Lagrange's Theorem for finite groups, group homomorphisms and 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, ranknullity theorem. Rank and inverse of a matrix,determinant, solutions of systems of linear equations, consistency conditions, eigenvalues and eigenvectors for matrices,CayleyHamilton 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, termwise differentiation and integration of power series.



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