APPENDIX - I

SYLLABUS FOR PAPER - I (Section A)

1. General information on science and its interface with society to test the candidate’s awareness of

science, aptitude of scientific and quantitative reasoning. 2. COMMON ELEMENTRY COMPUTER SCIENCE (Applicable to all candidates offering subject areas). (i) History of development of computers, Mainframe, mini, micro and Super Computer Systems. (ii) General awareness of computer Hardware i.e. CPU and other peripheral devices (input/output and

auxiliary storage devices). (iii) Basic knowledge of computer systems software and programming language i.e. Machine language.

Assembly language and higher level language. (iv) General awareness of popular commercial software packages like LOTUS, DBASE, WordStar, other

scientific application packages.

SYLLABUS FOR PAPER - I (SECTION - B) AND PAPER - II

(1) CHEMICAL SCIENCES

PAPER I - SECTION B (1) Structure and Bonding: Atomic orbitals, electronic configuration of atoms (L-S coupling) and the

periodic properties of elements; ionic radii, ionisation potential, electron affinity, electronegativity; concept of hybridization. Molecular orbitals and electronic configuration of homonuclear and heteronuclear diatomic molecules. Shapes of polyatomic molecules; VSEPR, theory. Symmetry elements and point groups for simple molecules. Bond lengths, bond angles, bond order and bond energies. Types of Chemical Bond (weak and strong) intermolecular forces, structure of simple ionic and covalent solids, lattice energy.

(2) Acids and Bases: Bronsted and Lewis acids and bases, pH and pKa, acid-based concept in non-

aqueous media; HSAB concept. Buffer solution. (3) Redox Reactions: Oxidation numbers. Redox potential. Electrochemical series. Redox indicators. (4) Energetics and Dynamics of Chemical Reactions: Law of conservation of energy. Energy and

enthalpy of reactions. Entropy, free-energy, relationship between free energy change and equilibrium. Rates of chemical reactions (first-and second - order reactions). Arrhenius equation and concept of transition state. Mechanisms, including SN1 and SN2 reactions, electron transfer reactions, catalysis. Colligative properties of solutions.

(5) Aspects of s.p.d.f. Block Elements: General characteristics of each block. Chemical principles

involved in extractions and purification of iron, copper, lead, zinc and aluminium. Coordination chemistry: structural aspects, isomerism, octahedral and tetrahedral crystal - field splitting of dorbitals. CFSE, magnetism and colour of transition metal ions. Sandwich compounds, metal carbonyls and metal clusters. Rare gas compounds, non-stoichiometric oxides. Radio activity and transmutation of elements. Isotopes and their applications.

(6) IUPAC Nomenclature of Simple Organic and Inorganic Compounds. (7) Concept of Chirality: Recognition of symmetry elements and chiral structures; R-S nomenclature,

diastereoisomerism in acyclic and cyclic systems; E-Z isomerisms. Conformational analysis of simple cyclic (chair and boat cyclo hexanes) and acyclic systems. Interconversion of Fischer, Newman and Sawhorse projections.

(8) Common Organic Reactions and Mechanisms: Reactive intermediates. Formation and stability of

carbonium ions, carbanians, carbenes, nitrenes, radicals and arynes. Nucleophilic, electrophilic, radical substitution, addition and elimination reactions. Familiar name reactions: Aldol, Perkin, Stobbe, Dieckmann condensations; Hofmann, Schmidt, Lossen, Curtius, Beckmann and Fries rearrangements; Reimer - Tiemann, Reformatsky and Grignard reactions. Diels - Alder reactions; Clasien rearrangements; Friedeal - Crafts reactions; Wittig reactions; and Robinson annulation. Routine functional group transformations and interconversions of simple functionalities. Hydroboration, Oppenaur oxidations; Clemmensen, Wolff- Kishner, Meerwein-Ponndorf-Verley and Birch reductions.

(9) Elementary principles and applications of electronic, vibrational, NMR, EPR and Mass Spectral

techniques to simple structural problems. (10) Data Analysis: Types of errors, propagation of errors, accuracy and precision, least-squares

analysis, average standard deviation.

PAPER II

1. Quantum Chemistry: Planck’s quantum theory, wave-particle duality. Uncertainty Principle, operators and commutation relations: postulates of quantum mechanics and Schrodinger equation: free particle, particle in a box, degeneracy, harmonic oscillator, rigid rotator and the hydrogen atom. Angular momentum, including spin; coupling of angular momenta including spin-orbit coupling.

2. The variation method and perturbation theory. Application to the helium atom; antisymmetry and

Exclusion Principle, Slater determinantal wave functions. Terms symbols and spectroscopic states. 3. Born-Oppenheimer approximation. Hydrogen molecule ion. LCAO-MO and VB treatments of the

hydrogen molecule; electron density, forces and their role in chemical binding. Hybridization and valence MOs of H2O, NH3 and CH4. Huckel pi-electron theory and its applications to ethylene, butadiene and benzene. Idea of self-consistent fields.

4. Group theoretical representations and quantum mechanics: vanishing of integrals; spectroscopic

selection rules for vibrational, electronic, vibronic and Raman spectroscopy. MO treatment of large molecules with symmetry.

5. Spectroscopy: Theoretical treatment of rotational, vibrational and electronic spectroscopy. Principles

of magnetic resonance, Mossbauer and photoelectron spectroscopy. 6. Thermodynamics: First law of thermodynamics, relation between Cp. and CV; enthalpies of physical

and chemical changes; temperature dependence of enthalpies. Second law of thermodynamics, entropy, Gibbs-Helmoholtz equation. Third law of thermodynamics and calculation of entropy.

7. Chemical Equilibrium: Free energy and entropy of mixing, partial molar quantities, Gibbs-Duhem

equation. Equilibrium constant, temperature-dependence of equilibrium constant, phase diagram of one-and two-component systems, phase rule.

8. Ideal and Non-ideal solutions. Excess functions, activities, concept of hydration number: activities

in electrolytic solutions; mean ionic activity coefficient; Debye-Huckel treatment of dilute electrolyte solutions.

9. Electrochemistry: Electrochemical cell reactions, Nernst equation, Electrode Kinetics, electrical

double layer, electode/electrolyte interface, Batteries, primary & secondary Fuel Cells, corrosion and corrosion prevention.

10. Surface Phenomena: Surface tension, adsorption on solids, electrical phenomena at interfaces,

including electrokinetic, micelles and reverse micelles: solubilization, micro-emulsions. Application of photoelectron spectroscopy. ESCA and Auger spectroscopy to the study of surfaces.

11. Statistical Thermodynamics: Thermodynamic probability and entropy; Maxwell-Boltzmann, Bose-

Einstein and Fermi-Dirac statistics. Partition function: rotational translational, vibrational and electronic partition functions for diatomic molecules; calculations of thermodynamic functions and equilibrium constants. Theories of specific heat for solids.

12. Non-equilibrium Thermodynamics: Postulates and methodologies, linear laws, Gibbs equation,

Onsager reciprocal theory. 13. Reaction Kinetics: Methods of determining rate laws. Mechanisms of photochemical, chain and

oscillatory reactions. Collision theory of reaction rates; steric factor, treatment of unimolecular reactions. Theory of absolute reaction rates, comparison of results with Eyring and Arrhenius equations. Ionic reactions: salt effect. Homogeneous catalysis and Michaelis-Menten kinetics; heterogeneous catalysis.

14. Fast Reaction: Luminescence and Energy transfer processes. Study of kinetics by stoppedflow

technique, relazation method, flash photolysis and magnetic resonance method. 15. Macromolecules: Number-average and weight average molecular weights; determination of

molecular weights. Kinetics of polymerization. Stereochemistry and mechanism of polymerization. 16. Solids: Dislocation in solids, Schottky and Frenkel defects, Electrical properties; Insulators and

semiconductors; superconductors; band theory of solids, Solid-state reactions. 17. Nuclear Chemistry: Radioactive decay and equilibrium. Nuclear reactions; Q value, cross sections,

types of reactions, Chemical effects of nuclear transformations; fission and fusion, fission products and fission yields. Radioactive techniques; tracer technique, neutron activation analysis, counting techniques such as G.M. ionization and proportional counter.

18. Chemistry of Non-transition Elements: General discussion on the properties of the nontransition

elements; special features of individual elements; synthesis, properties and structure of their halides and oxides, polymorphism of carbon, phosphorus and sulphur. Synthesis, properties and structure of boranes, carboranes, borazines, silicates carbides, silicones, phosphazenes, sulphur -nitrogen compounds: peroxo compounds of boron, carbon and sulphur; oxy acids of nitrogen, phosphorus, sulphur and halogens, interhalogens pseudohalides and noble gas compounds.

19. Chemistry of Transition Elements: Coordination chemistry of transition metal ions; Stability

constants of complexes and their determination; stabilization of unusual oxidation states. Stereochemistry of coordination compounds. Ligandfield theory, splitting of d-orbitals in low-symmetry environments. Jahn-Teller effect; interpretation of electronic spectra including charge transfer spectra; spectrochemical series, nephelauxetic series Magnetism: Dia-, para-, ferro- and antiferromagnetism, quenching of orbital angular moment, spinorbit coupling, inorganic reaction mechanisms; substitution reactions, trans effect and electron transfer reactions, photochemical reaction of chromium and ruthenium complexes. Fluxional molecules iso-and heteropolyacids; metal clusters. Spin crossover in coordination compounds.

20. Chemistry of Lanthanides and Actinides: Spectral and magnetic properties; Use of lanthanide

compounds as shift reagents. 21. Organometallic Chemistry of Transition Elements: Synthesis, structure and bonding,

organometallic reagents in organic synthesis and in homogeneous catalytic reactions (hydrogenation, hydroformaylation, isomerisation and polymerization); pi-acid metal complexes, activation of small molecules by coordination.

22. Topics in Analytical Chemistry: Adsorption partition, exclusion electrochromatography, Solvent

extraction and ion exchange, methods. Application of atomic and molecular absorption and emission spectroscopy in quantitative analysis Light scattering techniques including nephelometry and Raman spectroscopy. Electronalytical techniques: voltammetry, cyclic, voltammetry, polarography,

amperometry, coulometry and conductometry ion-elective electrodes. Annodic stripping voltammetry; TGA, DTA, DSC and online analyzers.

23. Bioinorganic Chemistry: Metal ions in Biology, Molecular mechanism of ion transport across

membranes; ionophores. Photosynthesis, PSL, PSH; nitrogen fixation, oxygen uptake proteins, cytochromes and ferrodoxins.

24. Aromaticity: Huckel’s rule and concept of aromaticty (n) annulenes and heteroannulenes, fullerenes

(C60) 25. Stereochemistry and conformational Analysis: Nwere method of asymmetric synthesis (including

enzymatic and catalytic nexus), enantio and diastereo selective synthesis. Effects of conformation on reactivity in acyclic compounds and cyclohexanes.

26. Selective Organic Name Reactions: Favorskli reaction; Stork enamine reaction; Michael addition,

Mannich Reaction; Sharpless asymmetric epoxidation; Ene reaction, Barton reaction, Hofmann-Loffler-Freytag reaction, Shapiro reaction, Baeyer-Villiger reaction, Chichibabin reaction.

27. Mechanisms of Organic Reactions: Labelling and Kinetic isotope effects, Hamett equation, (sigma-

rho) relationship, non-classical carbonium ions, neighbouring group participation. 28. Pericyclic Reactions: Selection rules and stereochemistry of electrocyclic reactions, cycloaddition

and sigmatropic shifts, Sommelet, Hauser, Cope and Claisen rearrangements. 29. Heterocyclic Chemistry: Synthesis and reactivity of furan, thiophene, pyrrole, pyridine, quinoline,

isoquinoline and indole; Skraup synthesis, Fischer indole synthesis. 30. Reagents in Organic Synthesis: Use of the following reagents in organic synthesis and functional

group transformations; Complex metal hydrides, Gilman’s reagent, lithium dimethylcuprate, lithium disopropylamide (LDA) dicyclohexylcarbodimide. 1,3-Dithiane (reactivity umpolung), trimethylsilyl iodide, tri-n-butyltin hybride, Woodward and prevost hydroxylation, osmium tetroxide, DDQ, selenium dioxide, phase transfer catalysts, crown ethers and Merrifield resin, Peterson’s synthesis, Wilkinson's catalyst, Baker yeast.

31. Chemistry of Natural Products: Familiarity with methods of structure elucidation and biosynthesis of

alkaloids, terponoids, steroids, carbohydrates and proteins. 32. Bioorganic Chemistry: Elementary structure and function of biopolymers such as proteins and

nucleic acids. 33. Photochemistry: Cis-trans isomeriation, Paterno-Buchi reaction, Norrish Type I and II reactions,

photoreduction of ketones, di-pimethane rearrangement, photochemistry of areanes. 34. Spectroscopy: Applications of mass, UV-VIS, IR and NMR spectroscopy for structural elucidation of

compound.

(2) EARTH, ATMOSPHERIC, OCEAN AND PLANETARY SCIENCES

PAPER I -- SECTION B

1. About the Earth: The earth and the solar system; important physical parameters and properties of the

planet earth; abundance of elements in the earth; primary differentiation of the earth and composition of its various zones; composition of meteorites and the solar photosphere; shape and internal structure of the earth. Uniformitarianism; geological time scale; use of fossils and nuclear clocks in the subdivision of geological time.

2. Materials of the Earth: Gross composition and physical properties of important rocks and minerals; properties and processes responsible for mineral concentrations; nature and distribution of rocks and minerals in different units of the earth; deformation of rocks; folds and faults and their surface expressions.

3. Surface Features and Processes: Physiography of the earth; landscape and seafloor; weathering,

erosion, transportation and deposition of earth’s material; formation of soil, sediments and sedimentary rocks; energy balance of the earth’s surface processes.

4. Internal Features and Processes: Elastic waves and fine structure of the earth: crust, mantle and

core; thermal, gravitational and magnetic fields of the earth; origin of the main geomagnetic field; mantle convection and plate tectonics; earthquakes and volcanoes; Isostasy.

5. The Atmosphere: Composition of the atmosphere and its internal structure; prevailing and adiabatic

lapse rates; instability of dry and moist air; geopotential; cloud classification; condensation nucleii; artificial precipitation. Fundamental forces in the atmosphere; Coriolis force and the geostrophic wind; basic structure and mechanism of atmospheric general circulation; monsoon systems; cyclones, anticyclones and tornadoes; jet streams; climate and climatic changes: natural and human induced factors.

6. The Hydrosphere: The hydrological cycle; inter-relationship of surface and ground water; seafloor

spreading and hydrothermal vents; marine sediments, their composition and uses; distribution of temperature and salinity in the ocean; surface circulation, causes of ocean currents and important current systems; deep circulation. Water masses - their formation and characteristics; convergence and upwelling of ocean waters; sea level changes; waves and tides; chemistry of sea water; biological controls on the composition of the oceans; oceanic modulation of climatic changes; estuary, bay and marine pollution.

7. Geology and Geography of India: Land, biotic and mineral resources and their role in development;

salient aspects of plant zoogeography; geologic setting; location and approximate reserves of minerals, fuel and water resources of the Indian territory. Important geological features of the Precambrian shield, the Gondwanas, the Deccan Trap, Indo-Gangetic Plains, the Himalaya - their physiography, landforms, drainage systems. Soils; their characteristics and distribution; climate and population; location of important natural resources and renewable sources of energy in relation to industrial centres.

8. Man and Environment: Ecology, ecosystem and biotic communities; carbon and nutrient cycling and

food-chain; human impact on air, land, soil, water, climate and forest resources; conservation of resources; coping with natural hazards; problems of pollution and waste; application of engineering geology to development without destruction; optimum use of energy alternatives.

PAPER II 1. GEOLOGY :

(i) Geomorphology: Landforms - their types and development; weathering, transport and erosion;

landforms in relation to rock type, structure and tectonics. Soils - their development and types. Geomorphic processes and their impact on various landforms and associated dynamics - slope, channel, coastline, glacial and aeolian; evolution of major geomorphological features of the Indian sub-continent; geomorphometric analysis and modelling.

(ii) Sedimentology: Classification of sedimentary rocks; petrography of rocks of clastic, chemical and

biochemical origin. Sedimentary textures and structures. Diagenesis; marine, non- marine and mixed depositional environments. Facies association, sedimentation and tectonics; basin analysis; Reconstruction of palaeoenvironments using radioactive and stable isotopes.

(iii) Paleontology: Origin and evolution of life; fossils and their uses; species concept; functional

morphology, classification and evolution of important invertebrate, vertebrate and plant fossils; biomineralisation and trace fossils; types of microfossils and their applications; palaeobiogeography and palaeoecology; evolution of man. Oxygen and carbon isotopic studies on fossils; analysis of palaeontological record for tracing plate tectonics processes.

(iv) Stratigraphy: Recent developments in stratigraphic classification: Litho bio- and chrono

stratigraphic units and their interrelationships; modern methods of stratigraphic correlation; steps in stratigraphic studies; approaches to palaeogeography; Earth’s climatic history. Rocks of Phanerozoic Eon in India - their intercontinental correlations with special reference to type localities; boundary problems in stratigraphy; geodynamic evolution of the Indian subcontinent through the Phanerozoic.

(v) Structural Geology and Geotectonics: Concepts of stress and strain: strain analysis using

deformed objects; geometric classification of folds; mechanics of folding; folding in shear zones; geometry of superposed folding; structural analysis in terrains with multiple deformation; foliation and lineation; geometry and mechanics of shear zones; brittle-ductile and ductile structures in shear zones; geometry of thrust sheets. Classification of unconformities; map patterns and their uses in the determination of large-scale structures. Isostasy; seismicity; sea-floor spreading and plate tectonics; orogenesis; orogenic belts of India; Evolution of the Himalaya and Himalayan tectonics.

(vi) Mineralogy: Concept of symmetry, point group, lattice and space group; principles of crystal

chemistry; principles of optical and X-ray mineralogy. Structural classification of minerals; structure and its interrelation with physical and chemical properties of minerals; important phase diagrams of major rockforming minerals and ore minerals; principles of geothermo-barometry.

(vii) Geochemistry: Abundances of elements; structure and atomic properties of elements; the

Periodic Table; geochemical classification and distribution of elements in the earth; principles of geochemical cycling; principles of ionic substitution in minerals; laws of thermodynamics; concepts of free energy, activity, fugacity and equilibrium constant; thermodynamics of ideal, nonideal and dilute solutions; element partitioning in minerals/rock formation and concept of distribution coefficients; concept of P-T-X, Eh-pH diagrams and mineral stabilities; radioactive decay schemes, growth of daughter isotopes and radiometrics dating; stable isotopes and their fractionation. Mineral/Mineral assemblages as ‘sensors’ of ambient environments.

(viii)Petrology: Phase equilibria studies of single, binary, ternary and quaternary silicate systems with

reference to petrogenesis; magmas, their generation in the crust and mantle, their emplacement and their relation to plate tectonics; magmatic crystallization, differentiation and assimilation; classification of igneous rocks; major and trace elements and isotopic composition of igneous rocks in the context of petrogenesis; petrogenesis of important types of igneous rocks; volatile components in petrogenesis. Physical and rheological properties of silicate melts - Bingham liquid; partial melting and fractional crystallization in closed and open system models. Role of T, P and fluids in metamorphism; metamorphic facies; mineral assemblages and important reactions in different facies; types of metamorphism and metamorphic - belts; relationship among metamorphism, anatexis and grantization. Petrogenetic aspects of important rocks of India such as the Deccan Trap, the Layered intrusions, charnockites, khondalites and ‘gondites’.

(ix) Ore Geology: Physico-chemical controls of deposition and of post-depositional changes in ores:

geological processes of formation of economic mineral deposits: global metallogeny as related to crustal evolution; metallogenesis in space and time. Elements of ore petrology; mineral assemblages and fluid inclusions as ‘sensors’ of ore-forming environments; Live ore- forming systems. Geological setting, characteristics features and genesis of ferrous and non-ferrous ore deposits of India. Metallogenic history of India.

(x) Marine Geology: Morphological and tectonic domains of the ocean floor; midocean ridge systems;

seawater-basalt interaction and hydrothermal vents; models and rates of ocean circulation and of sedimentation in the oceans; diagenetic changes in oxic and anoxic environments; mobility of redox metals; major components of marine sediments and processes regulating sediment composition; geochronology of marine sediments from radioactivity measurements; sedimentary markers of palaeoenvironmental conditions; mineral resources of the oceans and factors controlling their distribution. Ocean margins; nature of deep-sea sediments, their chronology and correlation; tectonic history of the oceans.

(xi) Petroleum and Coal Geology: Origin, migration and entrapment of petroleum; properties of source and reservoir rocks; structural, stratigraphic and combinations traps. Techniques of

exploration. Petroliferous basins of India. Origin of peat, lignite, bitumen and anthracite. Classification, rank and grading of coal; coal petrography, coal measures of India.

(xii) Precambrian Geology and Crustal Evolution: Evolution of the early crust, early Precambrian life, lithological, geochemical and stratigraphic characteristics of granite- greenstone and granulite belts. Stratigraphy and geochronology of the Precambrian terrains of India.

(xiii)Applied Geology:

(a) Photogeology and Remote Sensing: Elements of photogrammetry; elements of photo interpretation; electromagnetic spectrum, emission range, film and imagery; multispectral sensors; geological interpretation of air-photos and imagery.

(b) Engineering Geology: Mechanical properties of rocks; geological investigations for the

construction of dams, bridges, highways and tunnels. (c) Mineral Exploration: Geological and geophysical methods of surface and subsurface

exploration on different scales, sampling, assaying and evaluation of mineral deposits; geochemical and geobotanical surveys in exploration.

(d) Hydrogeology: Ground water, Darcy’s law; hydrological characteristics of aquifers;

hydrological cycle; precipitation, evapotranspiration and infiltration processes; hydrological classification of water-bearing formations; fresh and salt water relationship in coastal and inland areas; ground water exploration and management, water pollution; ground water regimes in India.

2. PHYSICAL GEOGRAPHY:

(i) Geomorphology: Landforms - their types and developments; weathering, transport and erosion;

landforms in relation to rock type, structure and tectonics. Soils - their development and types. Geomorphic processes and their impact on various landforms and associated dynamics - slope, channel coastline, glacial and aeolian; evolution of major geomorphological features of the Indian subcontinent. Geomorphometric analysis and modelling.

(ii) Climatology: Fundamental principles of climatology; Earth- sun relationship: earth’s radiation

balance, latitudinal and seasonal variation of insolation, temperature humidity, wind and precipitation. Indian climatology with special reference to seasonal distribution and variations of temperature, humidity, wind and precipitation: air masses notably monsoons, and jet streams, tropical cyclones, and cloud formation, classification of climates: Koppen’s and Thornthwaite’s scheme as applicable to India. Climate zones of India. Hydrological cycle and water balance. Climate change: green house warming, stratospheric ozone depletion. Palaeoclimatology.

(iii) Geohydrology: Ground water as part of the hydrological cycle; precipitation and

evapotranspiration and infiltration processes; rainfall-run off analysis: stream flow, stage- discharge relationship: hydrograph and flood frequency analysis. Hydrological classification of water-bearing formations, fresh and salt-water relationship in coastal and inland areas; ground water regimes in India. Principles of management of water resources; concept of safe yield; water balance studies and conjunctive use of surface and ground water; ground water problems and their management in India.

(iv) Biogeography: Elements of biogeography with special reference to India; environment, habitat

and plant-animal association; zoogeography of India; distribution of major animal groupings; elements of plant geography, distribution of forests and major plant communities. National forest policy, conservation of forests; afforestation, social forestry; ecology and man in India. Ecological balance, environmental pollution and deterioration.

(v) Oceanography: Submarine relief, continental shelf, continental slope, ocean deeps; temperature

of ocean water; salinity in the coastal open and enclosed seas; movement of ocean waters; waves, tides, currents; island arcs and coral reefs; and atolls; oceanic deposits.

3. GEOPHYSICS:

(i) Geophysical Fields: Concept of fields; scalar, vector and tensor; conservation laws; mass,

momentum, energy and charge; constitutive relations: and dynamical equations: elastic, viscous,

electro-magnetic, and thermal; Laws of thermodynamics and entropy; Partial differential equations of physics: wave, diffusion, potential and Schrodinger; analytical (Green’s functions and integral transforms) and numerical (Spectral, finite difference and finite element) methods for solving initial value and boundary value problems of geophysics. Linear instability theory and onset of convection; Benard Cells; Elements of nonlinear instability in fluids; Theory of Attractors; phase space, critical points, limit cycles and bifurcation of nonlinear systems.

(ii) Signal Processing: Continuous and discrete signals; Fourier analysis; linear time-invariant systems with deterministic and random inputs; bandlimited signals and sampling theorem; Z- transform, discrete and Fast Fourier transforms; filters: discrete and continuous, recursive and non-recursive, optimal, inverse filters, deconvolution. Estimation of signal parameters, system identification. Hypothesis testing.

(iii) Solid Earth: Gravity and figure of the Earth: spheroid and geoid; mass inhomogenetics and

associated gravity anomalies; geoidal undulations and deflection of the vertical; isostasy: local and regional compensation mechanisms. Seismology: causes and space distribution of earthquakes; theory of seismic waves; (body and surface waves), free oscillations, application for estimating earth structure and earthquake source parameters; earthquake hazard assessment. Geomagnetism; main field, its secular variation and reversals; remnant magnetization, paleomagnetism and lithospheric movements; geodynamo theory and hydromagnetic waves; magnetosphere and geomagnetic storms. Electrical structure of the earth; geomagnetic and magnetotelluric depth sounding. Plate tectonics theory: kinematics, dynamics and evolution of plates; types of boundaries, processes and corresponding geophysical and geological signatures. Heat flow: thermal and mechanical structure of continental and oceanic lithosphere; role of fluids in crustal processes; mantle convection. Mineral physics; constraints on earth structure from seismological and petrological investigations.

(iv) Geophysical Exploration: Basic principles: various methods, their distincitve features, scope,

limitations and prospects of conjuctive use. Geophysical exploration from the air, on the ground, in bore holes, across drill holes, in underground mines and in the oceans. Instruments used: theory, behaviour and precision of spring-mass systems, magnetometers (suspended magnet type, nuclear precession, nuclear resonance, flux gate and superconducting), Gravimeters (land, shipborne, spaceborne and borehole), wide band seismograph and geophone systems. Electrical systems, (resistivity, IP, MT, EM, TEM), Well logging units (caliper, electrical, radiation, acoustic, dipmeter, televiewer, induction, nuclear magnetism log) and seismic sources.

Principles of measuring complex signals; measurements in time and frequency domain. Pseudorandom sources for electrical and seismic exploration.

Signal Analysis: Gravity (free air, Bouguer, terrain, drift and Eotvos corrections) and magnetic (diurnal) and latitude (corrections) data reduction; regional and residual separation; derivatives, continuation and reduction to pole of potential field data. Electrical/EM data processing, Seismic (velocity analysis, signal enhancement, deconvolution, migration and time to depth conversion), Shear wave, VSP, 2-D/3D multifold and marine data processing. Numerical experiments for computer aided design of high-resolution field measurements; sensitivity analysis of various control parameters for maximum information/uncertainty ratio.

(v) Geophysical Inversion and Interpretation: Distinction between well-posed and ill-posed problems. Generalized inversion techniques: error analysis and the study of resolution and uniqueness in geophysical interpretation; Backus-Gilbert inversion method: linear and non-linear programming methods; Joint inversion of geophysical data and effective strategies for integrated geophysical exploration from a system’s viewpoint. Interpretation for average value of physical properties of rocks and minerals and their structure; direct detection of hydrocarbons (fluid content); lithostratigraphy, ground water, ore deposit, engineering sites, environmental parameters.

4. OCEANOGRAPHY:

(i) Physical Oceanography: Equation of State of seawater, current system including under current,

their formation and theories, oceanic fronts. Subtropical current system - Western and Eastern boundary currents Somali current thermohaline

and abyssal circulation; formation of water masses mixing and double diffusion. TSV diagrams; computation of divergence and estimation of vertical velocity; acoustics and optics.

(ii) Dynamical Oceanography: Equations of motion of frictionless ocean currents; scale analysis; barotropic and baroclinic approximation; geostrophic currents in a stratified ocean, the 2- layer approximation, and White-Margules equation; gradient currents and mass stratification; relative currents and slope currents; Ekman’s theory, Sverdrup, Stommel and Munk’s theories; Upwelling and sinking with special reference to the Indian ocean.

(iii) Ocean Waves and Tides: Small amplitude ocean waves; wave celerity; wave energy and group

velocity. Finite amplitude waves, long waves and internal wave; wind waves, their origin, growth, propagation and decay; significant wave height and period. Waves spectrum, Principles of wave forecasting SMB and PNJ methods; tides, their causes, variation and types; tidal currents; harmonic analysis, finite difference method and prediction of tides.

(iv) Air-Sea Interaction: Laminar and turbulent flows; Reynolds stresses; Richardson’s criterion for

turbulence; principles of Prandtl’s mixing length theory; Taylor’s statistical theory and Kolmogoroffs similarity theory; Air Sea interaction at various scales; planetary and laminar boundary layer, surface layer and spiral layer; Sea surface as a lower boundary of air-flow, and its geometry; wind field in the first few meters of the sea surface, wind structure in the maritime frictional layer; transfer of heat and water vapour, determination of air-sea fluxes; energy exchange and global heat and water budgets, convection and its role in tropical circulations, effects of upwelling and sinking on the ocean-atmosphere system.

(v) Coastal and Estuarine Oceanography: Factors influencing coastal processes; transformation of

waves in shallow water; Effects of stratification; effect of bottom friction, phenomena of wave reflection, refraction and diffraction; breakers and surf; littoral currents; wave action on sediments - movement to beach material; rip currents; beach stability ocean beach nourishment; harbour resonance; seiches; Tsunamis; Interaction of waves and structure. Sea Walls, groynes, revetments, etc. Estuaries: classification and nomenclature; tides in estuaries; estuarine circulation and mixing; depth - averaged and breadth - averaged models; sedimentation in estuaries; salinity intrusion in estuaries; Effect of stratification; coastal pollution; mixing and diffusion dispersal of pollutants in estuaries and nearshore areas; standing concentration; coastal zone management.

(vi) Chemical Oceanography: Major and minor constituents of sea- water and their residence times;

processes controlling the composition of sea-water; Dissolved gases in sea-water; their sources and sinks. Carbondioxide system, distribution of alkalinity; Physical chemistry of seawater; dynamic equilibrium in chemical composition of the ocean including trace metals, organic materials. Biogeochemical cycling and its effect on atmospheric composition and climate. Inter-relationships between ocean circulation, primary productivity and chemical composition of the atmosphere and ocean.

Stable and radioactive isotopes; chemistry of interstitial waters and transfer of solutes across the sediment- water interface; marine pollution, pathways of transfer of various pollutants (petroleum hydrocarbons, pesticides, trace metals etc.) and their fates in the sea.

Chemistry of marine natural products; biomedical potential of marine biota: remote sensing of the oceans.

(vii) Marine Geology: Morphological and tectonic domains of the ocean floor. Mid-oceanic ridge

systems, hydrothermal vents and sea-water basalt interaction; modes and rates of sedimentation in the oceans; diagenetic changes in oxic and anoxic environments, mobility of redoxmetals; nature of deep sea sediments and processes and regulating sedimentary composition; geochronology of marine sediments, sedimentary markers (biological and chemical) of paleoenvironmental conditions. Mineral resources of the ocean - phosphorites, manganese and other deposits and the factors controlling their distribution.

(viii)Marine Biology: Sea as a biological environment; divisions of the marine environment and their

characteristics fauna and flora and their adaptations. Marine ecosystems: rocky shores, sandy shores, estuarine, mangroves and coral reefs; description of communities, community structure and function: plankton, nekton and benthos; primary, secondary and tertiary production; food web and trophic structure; living resources of the Indian seas; mariculture: culture of molluses, crustacean, fishes and seaweeds.

5. METEOROLOGY:

(i) Climatology: Fundamental principles of climatology; Earth- sun relationship: earth’s radiation balance, latitudinal and seasonal variation of insolation, temperature, humidity, wind and precipitation. Indian climatology with special reference to seasonal distribution and variations of temperature, humidity, wind and precipitation: air masses notably monsoons, and jet streams, tropical cyclones, and cloud formation, classification of climates: Koppen’s and Thornthwaite’s schemes as applicable to India. Climatic zones of India. Hydrological cycle and water balance. Climate change: green house warming, stratospheric ozone depletion. Palaeoclimatology.

(ii) Physical Meteorology: Layered structure of the atmosphere and its composition. Radiation: basic

Laws - Raleigh and Mie scattering, multiple scattering, radiation from the sun, solar constant, effect of clouds, surface and planetary albedo. Emission and absorption of terrestrial radiation, radiation windows, radiative transfer, Greenhouse effect, net radiation budget; Derivation of radiance parameters from satellite observations. Thermodynamics of dry and moist air: specific gas constant, Adiabatic and Non adiabatic processes, entropy and enthalphy, Moisture variables, virtual Temperature; Clausius - Clapeyron equation, adiabatic process of a moist air; thermodynamic diagram: Emagram, tephigram, skew T-log p and Stuve diagrams. Hydrostatic equilibrium: Hydrostatic equation, variation of pressure with height, geopotential, standard atmosphere, altimetry. Vertical stability of the atmosphere: Dry and moist air parcel and slice methods, Entrainment, Bubble theory, Diurnal variation of lapse rate, convection in the atmosphere.

(iii) Atmospheric Electricity: Fair weather electric field in the atmosphere and potential gradients,

ionisation in the atmosphere, conduction currents, air-earth currents, point discharge currents. Electrical fields in thunderstorms, theories of thunderstorm electrification, lightning discharges.

(iv) Cloud Physics: Cloud classification, condensation nuclie, growth of cloud drops and ice-crystals,

precipitation mechanisms: Bergeron, Findeisen process, coalescence process - Precipitation of warm and mixed clouds, artificial precipitation, hail supression, fog and cloud - dissipation, radar observation of clouds and precipitation, radar equation, rain-drop spectra, radar echoes of hail and tornadoes, radar observation of hurricanes, measurements of rainfall by radar.

(v) Dynamical Meteorology: Basic equations and fundamental forces: Pressure gravity, centripetal and

coriolis forces, continuity equation in Cartesian and isobaric coordinates. A momentum equation in rotating, cartesian, and spherical coordinates; scale analysis, Inertial flow, Geostrophic and gradient winds, thermal wind. Divergence and vertical motion, Rossby, Richardson, Reynolds and Froude numbers. Circulation vorticity and divergence: Bjerknese circulation theorem and applications, Vorticity and divergence equations, Scale analysis, Potential vorticity, Stream function, velocity potential. Atmospheric turbulence: Mixing length theory, planetary boundary layer equations, surface layer, Ekmann layer, eddy transport of heat, water vapour and momentum, Richardson criterion. Linear perturbation theory: Internal and external gravity waves, Inertia waves, gravity waves, Rossby waves, wave motion in the tropics, barotropic and baroclinic instabilities; Taylor - Goldstein instability; theorems of Mines, Fjortozt, Howard and Pedlosky. Atmospheric energetics: Kinetic, potential and internal energies - Conversion of potential and internal energies into Kinetic energy, available potential energy.

(vi) Numerical Weather Prediction: Computational instability, filtering of sound and gravity waves, filtered

forecast equations, barotropic and equivalent barotropic models, two parameter baroclinic model, relaxation method, Two layer primitive equation model; short, medium and long range weather prediction models; objective analysis; Initialisation of the data for use in weather prediction models; data assimilation techniques.

(vii) General Circulation and Climate Modelling: Observed zonally symmetric circulations, meridional

circulation models, mean meridional and eddy transport of momentum and energy, angular momentum and energy budgets; zonally asymmetric features of general circulation; standing eddies; east-west circulations in tropics; climate variability and forcings; feedback processes, low frequency variability, ENSO, QBO and sunspot cycles. Basic principles of general circulation modelling; Grid-point and spectral GCMs; role of the ocean in climate modelling; interannual variability of ocean fields (SST, winds, circulation, etc.) and its relationship with monsoon, concepts of ocean - atmosphere coupled models.

(viii)Synoptic Meteorology: Synoptic charts, Weather observations, and transmission. Analysis of surface,

upper air and other derivative charts; Stream lines, isotachs and countour analysis; tilt and slope of pressure/weather systems with height. Synoptic weather forecasting, Prediction of Weather elements such as rain, maximum and minimum temperature and fog; hazardous weather elements like

thundestorms, duststorms, tornadoes, dates of onset, and withdrawal of monsoons, break monsoon; formation and movement of western disturbances, depressions and tropical cyclones; intensification, weakening, deepening and filling of surface pressure systems. Air masses and fronts: Sources, origin and classification of air masses; classification of fronts, frontogenesis and frontolysis; structure of cold and warm fronts; Weather systems associated with fronts. Extra-tropical synoptic scale features: jet streams, extratropical cyclones; anticyclones and blockings. Tropical synoptic meteorology: Trade wind inversion; ITCZ; monsoon trough; Tropical cyclones, their structure and development theory; Monsoon depressions; tropical easterly jet stream; Somali Jet; Waves in easterlies; western disturbances; SW and NE Monsoons; synoptic features associated with onset, withdrawal, break, active and weak monsoons.

(ix) Aviation Meteorology: Meteorological hazards to aviation; take-off, landing, inflight-icing, turbulence,

visibility, fog, clouds, rain, gusts, wind shear and thunderstorms. (x) Satellite Meteorology: Meteorological satellites: Polar orbitting and geostationary satellites, Visible and

infrared radiometers, multiscanner ratiometers; identification of synoptic systems, fog and sandstorms, detection of cyclones, estimation of SST and cloud top temperatures, winds, and rainfall; temperature and humidity soundings.

(3) LIFE SCIENCES

PAPER I - SECTION B

1. Cell Biology : Structure and function of cells and intracellular organelles (of both prokaryotes and eukaryotes) : mechanism of cell division including (mitosis and meiosis) and cell differentiation: Cell-cell interaction; Malignant growth; Immune response: Dosage compensation and mechanism of sex determination.

2. Biochemistry: Structure of atoms, molecules and chemical bonds; Principles of physical chemistry:

Thermodynamics, Kinetics, dissociation and association constants; Nucleic acid structure, genetic code, replication, transcription and translation: Structure, function and metabolism of carbohydrates, lipids and proteins; Enzymes and coenzyme; Respiration and photosynthesis.

3. Physiology: Response to stress: Active transport across membranes; Plant and animal hormones:

Nutrition (including vitamins); Reproduction in plants, microbes and animals. 4. Genetics: Principles of Mendelian inheritance, chromosome structure and function; Gene Structure

and regulation of gene expression: Linkage and genetic mapping; Extrachromosomal inheritance (episomes, mitochondria and chloraplasts); Mutation: DNA damage and repair, chromosome aberration: Transposons; Sex-linked inheritance and genetic disorders; Somatic cell genetics; Genome organisation (in both prokaryotes and eukaryotes).

5. Evolutionary Biology: Origin of life (including aspects of prebiotic environment and molecular

evolution); Concepts of evolution; Theories of organic evolution; Mechanisms of speciation; Hardyweinberg genetic equilibrium, genetic polymorphism and selection; Origin and evolution of economically important microbes, plants and animals.

6. Environmental Biology: Concept and dynamics or ecosystem, components, food chain and energy

flow, productivity and biogeochemical cycles; Types of ecosystems, Population ecology and biological control; Community structure and organisation; Environmental pollution; Sustainable development; Economic importance of microbes, plants and animals.

7. Biodiversity and Taxonomy: Species concept; Biological nomenclature theories of biological

classification, Structural biochemical and molecular systematics; DNA finger printing, numerical taxonomy, Biodiversity, characterization, generation maintenance and loss; Magnitude and distribution of biodiversity, economic value, wildlife biology, conservation strategies, cryopreservation.

PAPER II

1. Principles of Taxonomy as applied to the systamics and Classification of Plant Kingdom: Taxonomic

structure; Biosystematics; Plant geography; Floristics. 2. Patterns of variation in morphology and life history in plants; Broad outlines of classification AND

evolutionary trends among algae, fungi,bryophytes and pteridophytes; Principles of palaeobotany; Economic importance of algae, fungi and lichens.

3. Comparative anatomy and developmental morphology of gymnosperms and angiosperms;

Histochemical and ultrastructural aspects of development; Differentiation and morphogenesis. 4. Androgensis and gynogenesis; Breeding system; Pollination biology; structural and functional aspects

of pollen and pistil; Male sterility; Self and inter-specific incompatibility; Fertilization; Embryo and seed development.

5. Plants and civilization; Centres of origin and gene diversity; Botany, utilization, cultivation and

improvement of plants of food, drug, fibre and industrial values, Unexploited plants of potential economic value; Plants as a source of renewable energy; Genetic resources and their conservation.

6. Water Relation; Mineral nutrition; Photosynthesis and photorespiration; Nitrogen, Phosphorous and

Sulphur metabolism; Stomatal physiology; Source and sink relationship. 7. Physiology and biochemistry and seed dormancy and germination; Hormonal regulation of growth

and development; Photoregulation: Growth responses, Physiology of flowering: Senescence. 8. Principles of plant breeding; Important conventional methods of breeding self and cross-pollinated

and vegetatively propagated crops; Non conventional methods; Polyploidy: Genetic variability; Plant diseases and defensive mechanisms.

9. Principles of taxonomy as applied to the systematics and classification of the animal kingdom;

Classification and interrelationship amongst the major invertebrate phyla; Minor invertebrate phyla, Functional anatomy of the nonchordates; Larval forms and their evolutionary significance.

10. Classification and comparative anatomy of protochordates and chordates; Origin, evolution and

distribution of chordates groups: Adaptive radiation. 11. Histology of mammalian organ systems, nutrition, digestion and absorption; Circulation (open and

closed circular, lymphatic systems, blood composition and function); Muscular contraction and electric organs; Excretion and osmoregulation: Nerve conduction and neurotransmitters; major sense organs and receptors; Homeostatis (neural and hormonal); Bioluminiscence; Reproduction.

12. Gametogenesis in animals: Molecular events during fertilization, Cleavage patterns and fate maps,

Concepts of determination, competence and induction, totipotency and nuclear transfer experiments: Cell differentiation and differential gene activity: Morphogenetic determinants in egg cytoplasm; Role of maternal contributions in early embryonic development; Genetic regulations of early embryonic development in Drosophila; Homeotic genes.

13. Feeding, learning, social and sexual behavior of animals; Parental care; Circadian rhythms; Mimicry;

Migration of fishes and birds; Sociobiology; Physiological adaptation at high altitude. 14. Important human and veterinary parasites (protozoans and helminths); Life cycle and biology of

Plasmodium, Trypanosoma, Ascaris, Wuchereria, Fasciola, Schistosoma and Leishmania; Molecular, cellular and physiological basis of host - parasite interactions.

15. Arthropods and vectors of human diseases (mosquitoes, lice, flies and ticks); Mode of transmission of

pathogens by vectors,; Chemical, biological and environmental control of anthropoid vectors; Biology and control of chief insect pests of agricultural importance; Plant host-insect interaction, insect pest management; useful insects: Silkworm

16. The law of DNA constancy and C-value paradox; Numerical, and structural changes in chromosomes; Molecular basis of spontaneous and induced mutations and their role in evolution; Environmental mutagenesis and toxicity testing; Population genetics.

17. Structure of pro-and eukaryotic cells; membrane structure and function; Intracellular compartments,

proteinsorting, secretory and endocytic pathways; Cytoskeleton; Nucleus; Mitochondria and chloroplasts and their genetic organisation; cell cycle; Structure and organisation of chromatin, polytene and lamphrush chromosomes; Dosage compensation and sex determination and sex-linked inheritance.

18. Interactions between environment and biota; Concept of habitat and ecological niches; Limiting factor;

Energy flow, food chain, food web and tropic levels; Ecological pyramids and recycling, biotic community-concept, structure, dominance, fluctuation and succession; N.P.C. and S cycles in nature.

19. Ecosystem dynamics and management; Stability and complexity of ecosystems; Speciation and

extinctions; environmental impact assessment; Principles of conservation; Conservation strategies; sustainable development.

20. Physico-chemical properties of water; Kinds of aquatic habitats (fresh water and marine); Distribution

of and impact of environmental factors on the aquatic biota; Productivity, mineral cycles and biodegradation in different aquatic ecosystems; Fish and Fisheries of India with respect to the management of estuarine, coastal water systems and man-made reservoirs; Biology and ecology of reservoirs.

21. Structure, classification, genetics, reproduction and physiology of bacteria and viruses (of bacteria,

plants and animals); Mycoplasma protozoa and yeast (a general accounts). 22. Microbial fermentation; Antibiotics, organic acids and vitamins; Microbes in decomposition and

recycling processes; Symbiotic and asymbiotic N2-fixation; Microbiology of water, air, soil and sewage: Microbes as pathological agents in plants, animals and man; General design and applications of a biofermenter, Biofertilizer.

23. Antigen; Structure and functions of different clauses of immunoglobulins; Primary and secondary

immune response; Lymphocytes and accessory cells; Humoral and cell mediated immunity; MHC; Mechanism of immune response and generation of immunological diversity; Genetic control of immune response, Effector mechanisms; Applications of immunological techniques.

24. Enzyme Kinetics (negative and positive cooperativity); Regulation of enzymatic activity; Active sites;

Coenzymes : Activators and inhibitors, isoenzymes, allosteric enzymes; Ribozyme and abzyme. 25. Van der Waal’s, electrostatic, hydrogen bonding and hydrophobic interaction; Primary structure and

proteins and nucleic acids; Conformation of proteins and polypeptides (secondary, Tertiary, quaternary and domain structure); Reverse turns and Ramachandran plot; Structural polymorphism of DNA, RNA and three dimensional structure of tRNA; Structure of carbohydrates, polysaccharides, glycoproteins and peptido-glycans; Helixcoil transition; Energy terms in biopolymer conformational calculation.

26. Glycolysis and TCA cycle; Glycogen breakdown and synthesis; Gluconeogenesis; Interconversion of

hexoses and pentoses; Amino acid metabolism; Coordinated control of metabolism; Biosynthesis of purines and pyrimidines; Oxidation of lipids; Biosynthesis of fatty acids; Triglycerides; Phospholipids; Sterols.

27. Energy metabolism (concept of free energy); Thermodynamic principles in biology; Energy rich

bonds; Weak interactions; Coupled reactions and oxidative phosphorylations; Group transfer; Biological energy transducers; Bioenergietics.

28. Fine structure of gene, Eukaryotic genome organisation (structure of chromatin, coding and non-

coding sequences, satellite DNA); DNA damage and repair, DNA replication, amplification and rearrangements.

29. Organization of transcriptional units; Mechanism of transcription of prokaryotes and eukaryotes; RNA processing (capping, polyadenylation, splicing, introns and exons); Ribonucleoproteins, structure of mRNA; Genetic code and protein synthesis.

30. Regulation of gene expression in pro and eukaryotes; Attenuation and antitermination; Operon

concept; DNA methylation; Heterochromatization; Transposition; Regulatory sequences and transacting factors; Environmental regulation of gene expression.

31. Biochemistry and molecular biology of cancer; Oncogenes; Chemical carcinogenesis; Genetic and

metabolic disorders; Hormonal imbalances; Drug metabolism and detoxification; Genetic load and genetic counseling.

32. Lysogeny and lytic cycle in bacteriophages; Bacterial transformation; Host cell restriction;

Transduction; Complementation; Molecular recombination; DNA ligases; Topoisomerases; Gyrases; Methylases; Nucleases; Restriction endonucleases; Plasmids and bacteriophage base vectors for cDNA and genomic libraries.

33. Principles and methods of genetic engineering and Gene targeting; Applications in agriculture, health

and industry. 34. Cell and tissue culture in plants and animals; Primary culture; Cell line; Cell clones; Callus cultures;

Somaclonal variation; Micropropagation; Somatic embryogenesis; Haploidy; Protoplast fusion and somatic hybridization; Cybrides; Genetransfer methods in plants and in animals; Transgenic biology; Allopheny; Artificial seeds; Hybridoma technology.

35. Structure and organisation of membranes; Glycoconjugates and proteins in membrane systems; Ion

transport, Na+/K+ATPase; Molecular basis of signal transduction in bacteria, plants and animals; Model membranes; Liposomes.

36. Principles and application of light phase contrast, fluorescence, scanning and transmission electron

microscopy, Cytophotometry and flow cytometry, fixation and staining. 37. Principles and applications of gel-filtration, ion-exchange and affinity chromatography; Thin layer and

gas chromatography; High pressure liquid (HPLC) chromatography; Electrophoresis and electrofocussing; Ultracentrifugation (velocity and buoyant density).

38. Principles and techniques of nucleic acid hybridization and Cot curves; Sequencing of Proteins and

nucleic acids; Southern, Northern and South-Western blotting techniques; Polymerase chain reaction; Methods for measuring nucleic acid and protein interactions.

39. Principles of biophysical methods used for analysis of biopolymer structure, X-ray diffraction,

fluorescence, UV, ORD/CD, Visible, NMR and ESR spectroscopy; Hydrodynamic methods; Atomic absorption and plasma emission spectorocopy.

40. Principles and applications of tracer techniques in biology; Radiation dosimetry; Radioactive isotopes

and half life of isotopes; Effect of radiation on biological system; Autoradiography; Cerenkov radiation; Liquid scintillation spectrometry.

41. Principles and practice of statistical methods in biological research, samples and populations; Basic

statistics-average, statistics of dispersion, coefficient of variation; Standard error; Confidence limits; Probability distributions (biomial, Poisson and normal; Tests of statistical significance; Simple correlation of regression; Analysis of variance.

(4) MATHEMATICAL SCIENCES

PAPER I -SECTION B

General Information: Units 1, 2, 3 and 4 are compulsory for all candidates. Candidates with Mathematics background may omit units 10-14 and units 17, 18. Candidates with Statistics background may omit units 6,7,9,15 and 16. Adequate alternatives would be given for candidates with O.R. Background. 1. Basic concepts of Real and Complex analysis: Sequences and series, continuity, uniform

continuity, Differentiability, Mean Value Theorem, sequences and series of functions, uniform convergence, Riemann integral - definition and simple properties. Algebra of Complex numbers, Analytic functions, Cauchy's Theorem and integral formula, Power series, Taylor's and Laurent's series, Residues, Contour integration.

2. Basic Concepts of Linear Algebra: Space of n-vectors, Linear dependence, Basis, Linear

transformation, Algebra of matrices, Rank of a matrix, Determinants, Linear equations, Quadratic forms. Characteristic roots and vectors.

3. Basic concepts of probability: Sample space, discrete probability, simple theorems on probability,

independence of events, Bayes Theorem. Discrete and continuous random variables, Binomial, Poisson and Normal distributions; Expectation and moments, independence of random variables, Chebyshev's inequality.

4. Linear Programming Basic Concepts: Convex sets. Linear Programming Problem (LPP).

Examples of LPP. Hyperplane, open and closed half-spaces. Feasible, basic feasible and optimal solutions. Extreme point and graphical method.

5. Real Analysis: Finite, countable and uncountable sets, Bounded and unbounded sets, Archimedean

property, ordered field, completeness of R, Extended real number system, limsup and liminf of a sequence, the epsilon-delta definition of continuity and convergence, the algebra of continuous functions, monotonic functions, types of discontinuities, infinite limits and limits at infinity, functions of bounded variation, elements of metric spaces.

6. Complex Analysis: Riemann Sphere and Stereographic projection. Lines, Circles, crossratio. Mobius

transformations, Analytic functions, Cauchy - Riemann equations, line integrals, Cauchy's theorem, Morera's theorem, Liouville's theorem, integral formula, zero-sets of analytic functions, exponential, sine and cosine functions, Power series representation, Classification of singularities, Conformal Mapping.

7. Algebra: Group, subgroups, Normal subgroups, Quotient Groups, Homomorphisms, Cyclic Groups,

permutation Groups, Cayley's Theorem, Rings, Ideals, Integral Domains, Fields, Polynomial Rings. 8. Linear Algebra: Vector spaces, subspaces, quotient spaces, Linear independence, Bases,

Dimension. The algebra of linear Transformations, kernel, range, isomorphism, Matrix Representation of a linear transformation, change of bases, Linear functionals, dual space, projection, determinant function, eigenvalues and eigen vectors, Cayley-Hamilton Theorem, Invariant Sub-spaces, Canonical Forms: diagonal form, Triangular form, Jordan Form, Inner product spaces.

9. Differential Equations: First order ODE, singular solutions, initial value Problems of First Order ODE,

General theory of homogeneous and non-homogeneous Linear ODE, Variation of Parameters. Lagrange's and Charpit's methods of solving first order Partial Differential Equations. PDE's of higher order with constant coefficients.

10. Data Analysis Basic Concepts: Graphical representation, measures of central tendency and

dispersion. Bivariate data, correlation and regression. Least squares - polynomial regression, Applications of normal distribution.

11. Probability: Axiomatic definition of probability. Random variables and distribution functions

(univariate and multivariate); expectation and moments; independent events and independent random variables; Bayes' theorem; marginal and conditional distribution in the multivariate case, covariance matrix and correlation coefficients (product moment, partial and multiple), regression.

Moment generating functions, characteristic functions; probability inequalities (Tchebyshef, Markov, Jensen). Convergence in probability and in distribution; weak law of large numbers and central limit theorem for independent identically distributed random variables with finite variance.

12. Probability Distribution: Bernoulli, Binomial, Multinomial, Hypergeomatric, Poisson, Geometric and Negative binomial distributions, Uniform, exponential, Cauchy, Beta, Gamma, and normal (univariate and multivariate) distributions Transformations of random variables; sampling distributions. t, F and chi-square distributions as sampling distributions, Standard errors and large sample distributions. Distribution of order statistics and range.

13. Theory of Statistics: Methods of estimation: maximum likelihood method, method of moments,

minimum chi-square method, least-squares method. Unbiasedness, efficiency, consistency. Cramer-Rao inequality. Sufficient Statistics. Rao-Blackwell Theorem. Uniformly minimum variance unbiased estimators. Estimation by confidence intervals. Tests of hypotheses: Simple and composite hypotheses, two types of errors, critical region, randomized test, power function, most powerful and uniformly most powerful tests. Likelihood-ratio tests. Wald's sequential probability ratio test.

14. Statistical methods and Data Analysis: Tests for mean and variance in the normal distribution: one-

population and two- population cases; related confidence intervals. Tests for product moment, partial and multiple correlation coefficients; comparison of k linear regressions. Fitting polynomial regression; related test. Analysis of discrete data: chi-square test of goodness of fit, contingency tables. Analysis of variance: one-way and two-way classification (equal number of observations per cell). Large-sample tests through normal approximation. Nonparametric tests: sign test, median test, Mann-Whitney test, Wilcoxon test for one and two-samples, rank correlation and test of independence.

15. Operational Research Modelling: Definition and scope of Operational Research. Different types of

models. Replacement models and sequencing theory, Inventory problems and their analytical structure. Simple deterministic and stochastic models of inventory control. Basic characteristics of queueing system, different performance measures. Steady state solution of Markovian queueing models: M/M/1, M/M/1 with limited waiting space M/M/C, M/M/C with limited waiting space.

16. Linear Programming: Linear Programming, Simplex method, Duality in linear programming.

Transformation and assignment problems. Two person-zero sum games. Equivalence of rectangular game and linear programming.

17. Finite Population: Sampling Techniques and Estimation: Simple random sampling with and without

replacement. Stratified sampling; allocation problem; systematic sampling. Two stage sampling. Related estimation problems in the above cases.

18. Design of Experiments: Basic principles of experimental design. Randomisation structure and

analysis of completely randomised, randomised blocks and Latin-square designs. Factorial experiments. Analysis of 2n factorial experiments in randomised blocks.

PAPER II 1. Real Analysis: Riemann integrable functions; improper integrals, their convergence and uniform

convergence. Eulidean space R", Bolzano-Weierstrass theorem, compact Subsets of R", Heine-Borel theorem, Fourier series.

Continuity of functions on R", Differentiability of F: R"-> Rm, Properties of differential, partial and directional derivatives, continuously differentiable functions. Taylor's series. Inverse function theorem, Implicit function theorem.

Integral functions, line and surface integrals, Green's theorem, Stoke's theorem. 2. Complex Analysis: Cauchy's theorem for convex regions, Power series representation of Analytic

functions. Liouville's theorem, Fundamental theorem of algebra, Riemann's theorem on removable singularities, maximum modulus principle, Schwarz lemma, Open Mapping theorem, Casoratti-Weierstrass-theorem, Weierstrass's theorem on uniform convergence on compact sets, Bilinear transformations, Multivalued Analytic Functions, Riemann Surfaces.

3. Algebra: Symmetric groups, alternating groups, Simple groups, Rings, Maximal Ideals, Prime Ideals,

Integral domains, Euclidean domains, principal Ideal domains, Unique Factorisation domains, quotient fields, Finite fields, Algebra of Linear Transformations, Reduction of matrices to Canonical Forms, Inner Product Spaces, Orthogonality, quadratic Forms, Reduction of quadratic forms.

4. Advanced Analysis: Elements of Metric Spaces, Convergence, continuity, compactness, Connectedness, Weierstrass's approximation Theorem, Completeness, Bare category theorem, Labesgue measure, Labesgue Integral, Differentiation and Integration.

5. Advanced Algebra: Conjugate elements and class equations of finite groups, Sylow theorems,

solvable groups, Jordan Holder Theorem, Direct Products, Structure Theorem for finite abelian groups, Chain conditions on Rings; Characteristic of Field, Field extensions, Elements of Galois theory, solvability by Radicals, Ruler and compass construction.

6. Functional Analysis: Banach Spaces, Hahn-Banach Theorem, Open mapping and closed Graph

Theorems. Principle of Uniform boundedness, Boundedness and continuity of Linear Transformations, Dual Space, Embedding in the second dual, Hilbert Spaces, Projections. Orthonormal Basis, Riesz-representation theorem, Bessel's Inequality, parsaval's identity, self-adjoined operators, Normal Operators.

7. Topology: Elements of Topological Spaces, Continuity, Convergence, Homeomorphism,

Compactness, Connectedness, Separation Axioms, First and Second Countability, Separability, Subspaces, Product Spaces, quotient spaces. Tychonoff's Theorem, Urysohn's Metrization theorem, Homotopy and Fundamental Group.

8. Discrete Mathematics: Partially ordered sets, Lattices, Complete Lattices, Distributive lattices,

Complements, Boolean Algebra, Boolean Expressions, Application to switching circuits, Elements of Graph Theory, Eulerian and Hamiltonian graphs, planar Graphs, Directed Graphs, Trees, Permutations and Combinations, Pigeonhole principle, principle of Inclusion and Exclusion, Derangements.

9. Ordinary and Partial Differential Equations: Existence and Uniqueness of solution dy/dx =f(x,y)

Green's function, sturm Liouville Boundary Value Problems, Cauchy Problems and Characteristics, Classification of Second Order PDE, Separation of Variables for heat equation, wave equation and Laplace equation, Special functions.

10. Number Theory: Divisibility; Linear diophantine equations. Congruences. Quadratic residues; Sums

of two squares, Arithmetic functions Mu, Tau, Phi and Sigma ( and ). 11. Mechanics: Generalised coordinates; Lagranges equation; Hamilton's cononical equations;

Variational principles - Hamilton's principles and principles of least action; Two dimensional motion of rigid bodies; Euler's dynamical equations for the motion of rigid body; Motion of a rigid body about an axis; Motion about revolving axes.

12. Elasticity: Analysis of strain and stress, strain and stress tensors; Geometrical representation;

Compatibility conditions; Strain energy function; Constitutive relations; Elastic solids Hookes law; Saint-Venant's principle, Equations of equilibrium; Plane problems - Airy's stress function, vibrations of elastic, cylindrical and spherical media.

13. Fluid Mechanics: Equation of continuity in fluid motion; Euler's equations of motion for perfect fluids;

Two dimensional motion complex potential; Motion of sphere in perfect liquid and motion of liquid past a sphere; vorticity; Navier-Stokes's equations for viscous flows-some exact solutions.

14. Differetial Geometry: Space curves - their curvature and torsion; Serret Frehat Formula;

Fundamental theorem of space curves; Curves on surfaces; First and second fundamental form; Gaussian curvatures; Principal directions and principal curvatures; Goedesics, Fundamental equations of surface theory.

15. Calculus of Variations: Linear functionals, minimal functional theorem, general variation of a

functional, Euler- Lagrange equation; Variational methods of boundary value problems in ordinary and partial differential equations.

16. Linear Integral Equations: Linear Integral Equations of the first and second kind of Fredholm and

Volterra type; solution by successive substitutions and successive approximations; Solution of equations with separable kernels; The Fredholm Alternative; Holbert-Schmidt theory for symmetric kernels.

17. Numerical analysis: Finite differences, Interpolation; Numerical solution of algebraic equation; Iteration; Newton- Raphson method; Solution on linear system; Direct method; Gauss elimination method; Matrix - Inversion, eigenvalue problems; Numerical differentiation and integration.

Numerical solution of ordinary differential equation; iteration method, Picard's method, Euler's method and improved Euler's method.

18. Integral Transform: Laplace transform; Transform of elementary functions, Transform of Derivatives,

Inverse Transform, Convolution Theorem, Applications, Ordinary and Partial differential equations; Fourier transforms; sine and cosine transform, Inverse Fourier Transform, Application to ordinary and partial differential equations.

19. Mathematical Programming: Revised simplex method, Dual simplex method, Sensitivity analysis and

parametric linear programming. Kuhn-Tucker conditions of optimality. Quadratic programming; methods due to Beale, Wofle and Vandepanne, Duality in quadratic programming, self-duality, Integer programming.

20. Measure Theory: Measurable and measure spaces; Extension of measures, signed measures,

Jordan-Hahn decomposition theorems. Integration, monotone convergence theorem, Fatou's lemma, dominated convergence theorem. Absolute continuity, Radon Nikodym theorem, Product measures, Fubini's theorem.

21. Probability: Sequences of events and random variables; Zero- one laws of Borel and Kolmogorov.

Almost sure convergence, convergence in mean square, Khintchine's weak law of large numbers; Kolmogorov's inequality, strong law of large numbers.

Convergence of series of random variables, three-series criterion. Central limit theorems of Liapounov and Lindeberg- Feller. Conditional expectation, martingales.

22. Distribution Theory: Properties of distribution functions and characteristic functions; continuity

theorem, inversion formula, Representation of distribution function as a mixture of discrete and continuous distribution functions; Convolutions, marginal and conditional distributions of bivariate discrete and continuous distributions.

Relations between characteristic functions and moments; Moment inequalities of Holder and Minkowski.

23. Statistical Inference and Decision Theory: Statistical decision problem: non-randomized, mixed and randomized decision rules; risk function,

admissibility, Bayes' rules, minimax rules, least favourable distributions, complete class, and minimal complete class. Decision problem for finite parameter space. Convex loss function. Role of sufficiency. Admissible, Bayes and minimax estimators; illustrations. Unbiasedness. UMVU estimators. Families of distributions with monotone likelihood property, exponential family of distributions. Test of a simple hypothesis against a simple alternative from decision-theoretic viewpoint. Tests with Neyman structure. Uniformly most powerful unbiased tests. Locally most powerful tests. Inference on location and scale parameters; estimation and tests. Equivariant estimators. Invariance in hypothesis testing.

24. Large sample statistical methods: Various modes of convergence. Op and op, CLT, Sheffe's

theorem, Polya's theorem and Slutsky's theorem. Transformation and variance stabilizing formula. Asymptotic distribution of function of sample moments. Sample quantiles. Order statistics and their functions. Tests on correlations, coefficients of variation, skewness and kurtosis. Pearson Chi-square, contingency Chi-square and likelihood ratio statistics. U-statistics. Consistency of Tests. Asymptotic relative efficiency.

25. Multivariate Statistical Analysis: Singular and non-singular multivariate distributions. Characteristics

functions. Multivariate normal distribution; marginal and conditional distribution, distribution of linear forms, and quadratic forms, Cochran's theorem.

Inference on parameters of multivariate normal distributions: one-population and two-population cases. Wishart distribution. Hotellings T2, Mahalanobis D2. Discrimination analysis, Principal components, Canonical correlations, Cluster analysis.

26. Linear Models and Regression: Standard Gauss-Markov models; Estimability of parameters; best

linear unbiased estimates (BLUE); Method of least squares and Gauss-Markov theorem; Variance-covariance matrix of BLUES.

Tests of linear hypothesis; One-way and two-way classifications. Fixed, random and mixed effects models (two-way classifications only); variance components, Bivariate and multiple linear regression; Polynomial regression; use of orthogonal polynomials. Analysis of covariance. Linear and nonlinear regression. Outliers.

27. Sample Surveys: Sampling with varying probability of selection, Hurwitz-Thompson estimator; PPS

sampling; Double sampling. Cluster sampling. Non-sampling errors: Interpenetrating samples. Multiphase sampling. Ratio and regression methods of estimation.

28. Design of Experiments: Factorial experiments, confounding and fractional replication. Split and

strip plot designs; Quasi-Latin square designs; Youden square. Design for study of response surfaces; first and second order designs. Incomplete block designs; Balanced, connectedness and orthogonality, BIBD with recovery of inter-block information; PBIBD with 2 associate classes. Analysis of series of experiments, estimation of residual effects. Construction of orthogonal-Latin squares, BIB designs, and confounded factorial designs. Optimality criteria for experimental designs.

29. Time-Series Analysis: Discrete-parameter stochastic processes; strong and weak stationarity;

autocovariance and autocorrelation. Moving average, autoregressive, autoregressive moving average and autoregressive integrated moving average processes. Box-Jenkins models. Estimation of the parameters in ARIMA models; forecasting. Periodogram and correlogram analysis.

30. Stochastic Processes: Markov chains with finite and countable state space, classification of states,

limiting behaviour of n-step transition probabilities, stationary distribution; branching processes; Random walk; Gambler's ruin. Markov processes in continuous time; Poisson processes, birth and death processes, Wiener process.

31. Demography and Vital Statistics: Measures of fertility and mortality, period and Cohort measures.

Life tables and its applications; Methods of construction of abridged life tables. Application of stable population theory to estimate vital rates. Population projections. Stochastic models of fertility and reproduction.

32. Industrial Statistics: Control charts for variables and attributes; Acceptance sampling by attributes;

single, double and sequential sampling plans; OC and ASN functions, AOQL and ATI; Acceptance sampling by varieties. Tolerance limits. Reliability analysis: Hazard function, distribution with DFR and IFR; Series and parallel systems. Life testing experiments.

33. Inventory and Queueing theory: Inventory (S,s) policy, periodic review models with stochastic

demand. Dynamic inventory models. Probabilistic re-order point, lot size inventory system with and without lead-time. Distribution free analysis. Solution of inventory problem with unknown density function. Warehousing problem. Queues: Imbedded markov chain method to obtain steady state solution of M/G/1, G/M/1 AND M/D/C, Network models. Machine maintenance models. Design and control of queueing systems.

34. Dynamic Programming and Marketing: Nature of dynamic programming, Deterministic processes,

Non-sequential discrete optimisation-allocation problems, assortment problems. Sequential discrete optimisation long-term planning problems, multi stage production processes. Functional approximations. Marketing systems, application of dynamic programming to marketing problems. Introduction of new product, objective in setting market price and its policies, purchasing under fluctuating prices, Advertising and promotional decisions, Brands switching analysis, Distribution, decisions.

(5) PHYSICAL SCIENCES

PAPER I --SECTION - B

1. Basic Mathematical Methods: Calculus: Vector algebra and vector calculus. Linear algebra, matrices. Linear differential equations. Fourier series, Elementary complex analysis.

2. Classical Dynamics: Basic principles of classical dynamics. Lagrangian and Hamiltonian formalisms.

Symmetries and conservation laws. Motion in the central field of force. Collisions and scattering. Mechanics of a system of particles. Small oscillations and normal modes. Wave motion - wave equation, phase velocity, group velocity, dispersion. Special theory of relativity - Lorentz transformations, addition of velocities, mass-energy equivalence.

3. Electromagnetics: Electrostatics - Laplace and Poisson equations, boundary value problems.

Magnetostatics - Ampere's theorem, Biot-Savart law, electromagnetic induction. Maxwell's equations in free space and in linear isotropic media. Boundary conditions on the fields at interfaces. Scalar and vector potentials. Gauge invariance. Electromagnetic waves - reflection and refraction, dispersion, interference, coherence, diffraction, polarization. Electrodynamics of a charged particle in electric and magnetic fields. Radiation from moving charges radiation from a dipole. Retarded potential.

4. Quantum Physics and Applications: Wave-particle duality. Heisenberg's uncertainty Principle. The

Schrodinger equation Particle in a box, Harmonic Oscillator, Tunnelling through a barrier. Motion in a central potential, Orbital angular momentum. Angular momentum algebra, spin. Addition of angular momenta. Time-independent perturbation theory. Fermi's Golden Rule. Elementary theory of scattering in a central potential. Phase shifts, partial wave analysis, Born approximation, Identical particles, spin-statistics connection.

5. Thermodynamic and Statistical Physics: Laws of thermodynamics and their consequences,

Thermodynamic potentials and Maxwell's relations. Chemical potential, phase equilibria. Phase space, microstates and macrostates. Partition function. Free Energy and connection with thermodynamic quantities. Classical and quantum statistics, Degenerate electron gas. Blackbody radiation and Planck's distribution law, Bose-Einstein condensation. Einstein and Debye models for lattice specific heat.

6. Experimental Design: Measurement of fundamental constants: e, h, c. Measurement of High & Low

Resistances, L and C. Detection of X-rays, Gamma rays, charged particles, neutrons etc: Ionization chamber, proportional counter, GM counter, Scintillation detectors, Solid State detectors. Emission and Absorption Spectroscopy. Measurement of Magnetic field, Hall effect, magnetoresistance. X-ray and neutron Diffraction. Vacuum Techniques: basic idea of conductance, pumping speed etc. Pumps: Mechanical Pump, Diffusion pump; Gauges: Thermocouple, Penning, Pirani, Hot Cathode. Low Temperature: Cooling a sample over a range upto 4 K and measurement of temperature.

Measurement of Energy and Time using electronic signals from the detectors and associated instrumentation: Signal processing, A/D conversion & multichannel analyzers, Time-of-flight technique; Coincidence Measurements: true to chance ratio, correlation studies. Error Analysis and Hypothesis testing: Propagation of errors, Plotting of Graph, Distributions, Least squares fitting, criteria for goodness of fits - chi square test.

PAPER - II Part 'A' ( Weightage 50%) SYLLABUS SAME AS FOR PAPER - I (SECTION - B)

Part 'B' Weightage 50%

1. Electronics : Physics of p-n junction. Diode as a circuit element; clipping, clamping; Rectification, Zener regulated power supply: Transistor as a circuit element: CC, CB and CE configuration. Transistor as a switch, OR, AND, NOT gates. Feed back in Amplifiers.

Operational amplifier and its applications: inverting, non - inverting amplifier, adder, integrator, differentiator, wave form generator, comparator & Schmidt trigger.

Digital integrated circuits - NAND & NOR gates as building blocks, X-OR Gate, simple combinational circuits, Half & Full adder, Flip-flop, shift register, counters Basic principles of A/D & D/A converters; Simple applications of A/D & D/A converters.

2. Atomic & Molecular Physics: Quantum states of an electron in an atom. Hydrogen atom spectrum. Electron spin. Stern- Gerlach experiment. Spin-orbit coupling, fine structure, relativistic correction, spectroscopic terms and selection rules, hyperfine structure. Exchange symmetry of wave functions. Pauli's exclusion principle, periodic table alkali - type spectra, LS & JJ coupling, Zeeman, Paschen-Back and Stark effects.

X-Rays and Auger transitions, Compton effect. Principles of ESR, NMR ; Molecular Physics: Convalent, ionic and Van der Waal's interaction. Rotation/Vibration spectra. Raman Spectra, selection rules, nuclear spin and intensity alternation,

isotope effects, electronic states of diatomic molecules, Frank-Condon principle. Lasers-spontaneous and stimulated emission, optical pumping, population inversion, coherence (temporal and spatial) simple description of Ammonia maser, CO2 and He-Ne Lasers.

3. Condensed Matter Physics: Crystal classes and systems, 2d & 3d lattices, Bonding of common

crystal structures, reciprocal lattice, diffraction and structure factor, elementary ideas about point defects and dislocations.

Lattice vibrations, Phonons, specific heat of solids, free electron theory-Fermi statistics; heat capacity. Electron motion in periodic potential, energy bands in metals, insulators and semi-conductors; tight

binding approximation; impurity levels in doped semi-conductors. Electronic transport from classical kinetic theory, electrical and thermal conductivity. Hall effect and thermo-electric power transport in semi-conductors.

Di-electrics-Polarization mechanisms, Clausius-Mossotti equation, Piezo, Pyro and ferro electricity. Dia and Para magnetism; exchange interactions, magnetic order, ferro, anti-ferro and ferrimagnetism. Super conductivity-basic phenomenology; Meissner effect, Type-1 & Type-2 Super conductors, BCS

Pairing mechanism. 3. Nuclear and Particle Physics: Basic nuclear properties - size, shape, charge distribution, spin &

parity, binding, empirical mass formula, liquid drop model. 4. Nature of nuclear force, elements of two-body problem, charge independence and charge symmetry of

nuclear forces. Evidence for nuclear shell structure. Single particle shell model-its validity and limitations, collective model. Interactions of charged particles and e.m. rays with matter. Basic principles of particle detectors-ionization chamber; gas proportional counter and GM counter, scintillation and semiconductor detectors.

Radioactive decays, basic theoretical understanding. Nuclear reactions, elementary ideas of reaction mechanisms, compound nucleus and direct reactions, elementary ideas of fission and fusion.

Particle Physics: Symmetrics an conservation laws, classification of fundamental forces and elementary particles, iso-spin, strangeness, Gell-Mann Nishijima formula, Quark model. C,P,T, invariance in different interactions, parity-nonconservation in weak interaction.

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