Chemical sciences: Unit 01

• Chemical periodicity
• Structure and bonding in homo and heteronuclear molecules, including shapes of molecules (VSEPR Theory)
• Concepts of acids and bases, hard-soft acid base concept, non-aqueous solvents
• Main group elements and their compounds: allotropy, synthesis, structure and bonding, industrial importance of the compounds
• Transition elements and coordination compounds: structure, bonding theories, spectral and magnetic properties, reaction mechanisms
• Inner transition elements: spectral and magnetic properties, redox chemistry, analytical applications
• Organometallic compounds: Synthesis, bonding and structure, and reactivity. Organometallics in homogeneous catalysis
• Cages and metal clusters
• Analytical chemistry-separation, spectroscopic, electro and thermoanalytical methods
• Bioinorganic chemistry: Photosystems, porphyrins, metalloenzymes, oxygen transport, electron transfer reactions; nitrogen fixation, metal complexes in medicine
• Characterisation of inorganic compounds by ir, raman, nmr, epr, mössbauer, uv-vis, nqr, ms, electron spectroscopy and microscopic techniques
• Nuclear chemistry: nuclear reactions, fission and fusion, radio-analytical techniques and activation analysis

Chemical sciences: Unit 02

• Basic principles of quantum mechanics: Postulates; operator algebra; exactly-solvable systems: Particle-in-a-box, harmonic oscillator and the hydrogen atom, including shapes of atomic orbitals; orbital and spin angular momenta; tunneling
• Approximate methods of quantum mechanics: Variational principle; perturbation theory up to second order in energy; applications
• Atomic structure and spectroscopy; term symbols; many-electron systems and antisymmetry principle
• Chemical bonding in diatomics; elementary concepts of MO and VB theories; Huckel theory for conjugated π-electron systems
• Chemical applications of group theory; symmetry elements; point groups; character tables; selection rules
• Molecular spectroscopy: Rotational and vibrational spectra of diatomic molecules; electronic spectra; IR and Raman activities-selection rules; basic principles of magnetic resonance
• Chemical thermodynamics: Laws, state and path functions and their applications; thermodynamic description of various types of processes; Maxwell’s relations; spontaneity and equilibria; temperature and pressure dependence of thermodynamic quantities
• Chemical thermodynamics: Le Chatelier principle; elementary description of phase transitions; phase equilibria and phase rule; thermodynamics of ideal and non-ideal gases, and solutions
• Statistical thermodynamics: Boltzmann distribution; kinetic theory of gases; partition functions and their relation to thermodynamic quantities-calculations for model systems
• Electrochemistry: Nernst equation, redox systems, electrochemical cells; Debye-Huckel theory; electrolytic conductance-Kohlrausch’s law and its applications; ionic equilibria; conductometric and potentiometric titrations
• Chemical kinetics: Empirical rate laws and temperature dependence; complex reactions; steady state approximation; determination of reaction mechanisms; collision and transition state theories of rate constants; unimolecular reactions
• Chemical kinetics: Enzyme kinetics; salt effects; homogeneous catalysis; photochemical reactions
• Colloids and surfaces: Stability and properties of colloids; isotherms and surface area; heterogeneous catalysis
• Solid state: Crystal structures; Bragg’s law and applications; band structure of solids
• Polymer chemistry: Molar masses; kinetics of polymerization
• Data analysis: Mean and standard deviation; absolute and relative errors; linear regression; covariance and correlation coefficient

Chemical sciences: Unit 03

• Iupac nomenclature of organic molecules including regio and stereoisomers
• Principles of stereochemistry: Configurational and conformational isomerism in acyclic and cyclic compounds; stereogenicity, stereoselectivity, enantioselectivity, diastereoselectivity and asymmetric induction
• Aromaticity: Benzenoid and non-benzenoid compounds-generation and reactions
• Organic reactive intermediates: Generation, stability and reactivity of carbocations, carbanions, free radicals, carbenes, benzynes and nitrene
• Organic reaction mechanisms involving addition, elimination and substitution reactions with electrophilic, nucleophilic or radical species
• Determination of reaction pathways
• Common named reactions and rearrangements-applications in organic synthesis
• Organic transformations and reagents: Functional group interconversion including oxidations and reductions; common catalysts and reagents (organic, inorganic, organometallic and enzymatic). Chemo, regio, and stereoselective transformations
• Concepts in organic synthesis: retrosynthesis, disconnection, synthons, linear and convergent synthesis, umpolung of reactivity and protecting groups
• Asymmetric synthesis: Chiral auxiliaries, methods of asymmetric induction-substrate, reagent and catalyst controlled reactions; determination of enantiomeric and diastereomeric excess; enantio-discrimination. Resolution-optical and kinetic
• Pericyclic reactions: Electrocyclization, cycloaddition, sigmatropic rearrangements and other related concerted reactions. Principles and applications of photochemical reactions in organic chemistry
• Synthesis and reactivity of common heterocyclic compounds containing one or two heteroatoms (o, n, s)
• Chemistry of natural products: Carbohydrates, proteins and peptides, fatty acids, nucleic acids, terpenes, steroids and alkaloids. Biogenesis of terpenoids and alkaloids
• Structure determination of organic compounds by IR, UV-Vis, ¹H and ¹³C NMR and mass spectroscopic techniques

Chemical sciences: Unit 04

• Chemistry in Nanoscience and Technology
• Catalysis and Green Chemistry
• Medicinal chemistry
• Supramolecular Chemistry
• Environmental chemistry

Earth, atmospheric, ocean and planetary sciences-paper-I (part-B): Unit 01

• Milky way and the solar system
• Modern theories on the origin of the earth and other planetary bodies
• Earth’s orbital parameters , Kepler’s laws of planetary motion, geological time scale; space and time scales of processes in the solid earth, atmosphere and oceans
• Radioactive isotopes and their applications
• Meteorite s chemical composition and the primary differentiation of the earth
• Basic principles of stratigraphy
• Theories about the origin of life and the nature of fossil record
• Earth’s gravity and magnetic fields and its thermal structure: Concept of geoid and, spheroid; isostasy

Earth, atmospheric, ocean and planetary sciences-paper-I (part-B): Unit 02

• Gross composition and physical properties of important minerals and rocks; properties and processes responsible for mineral concentrations; nature and distribution of rocks and minerals in different units of the earth and different parts of India
• Physiography of the earth; weathering, erosion, transportation and deposition of earth’s material; formation of soil, sediments and sedimentary rocks; energy balance of the earth’s surface processes; physiographic features and river basins in India

Earth, atmospheric, ocean and planetary sciences-paper-I (part-B): Unit 03

• Basic concepts of seismology and internal structure of the earth
• Physico-chemical and seismic properties of earth’s interior
• Concepts of stress and strain
• Behaviour of rocks under stress; folds, joints and faults
• Earthquakes-their causes and measurement
• Interplate and intraplate seismicity
• Paleomagnetism, sea floor spreading and plate tectonics

Earth, atmospheric, ocean and planetary sciences-paper-I (part-B): Unit 04

• Hypsography of the continents and ocean floor-continental shelf, slope, rise and abyssal plains
• Physical and chemical properties of sea water and their spatial variations
• Residence times of elements in seawater
• Ocean currents, waves and tides, important current systems, thermohaline circulation and the oceanic conveyor belt
• Major water masses of the world’s oceans
• Biological productivity in the oceans
• Motion of fluids, waves in atmospheric and oceanic systems
• Atmospheric turbulence and boundary layer
• Structure and chemical composition of the atmosphere, lapse rate and stability, scale height, geopotential, greenhouse gases and global warming
• Cloud formation and precipitation processes, air-sea interactions on different space and time scales
• Insolation and heat budget, radiation balance, general circulation of the atmosphere and ocean
• Climatic and sea level changes on different time scales
• Coupled ocean-atmosphere system, El Nino Southern Oscillation (ENSO)
• General weather systems of India, monsoon system, cyclone and jet stream, western disturbances and severe local convective systems, distribution of precipitation over India
• Marine and atmospheric pollution, ozone depletion

Earth, atmospheric, ocean and planetary sciences-paper-I (part-B): Unit 05

• Properties of water; hydrological cycle; water resources and management
• Energy resources, uses, degradation, alternatives and management; ecology and biodiversity
• Impact of use of energy and land on the environment
• Exploitation and conservation of mineral and other natural resources
• Natural hazards
• Elements of remote sensing

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-geology: Unit 01

• Concept of point group, space group, reciprocal lattice, diffraction and imaging
• Concepts of crystal field theory and mineralogical spectroscopy
• Lattice defects (point, line and planar)
• Electrical, magnetic and optical properties of minerals
• Bonding and crystal structures of common oxides, sulphides, and silicates
• Transformation of minerals-polymorphism, polytypism, and polysomatism
• Solid solution and exsolution
• Steady-state geotherms
• Genesis, properties, emplacement and crystallization of magmas
• Phase equilibrium studies of simple systems, effect of volatiles on melt equilibria
• Magma-mixing, mingling and immiscibility
• Metamorphic structures and textures; isograds and facies
• Mineral reactions with condensed phases, solid solutions, mixed volatile equilibria and thermobarometry
• Metamorphism of pelites, mafic-ultramafic rocks and siliceous dolomites
• Material transport during metamorphism
• P-T-t path in regional metamorphic terrains, plate tectonics and metamorphism
• Petrogenetic aspects of important rock suites of India, such as the Deccan traps, layered intrusive complexes, anorthosites, carbonatites, charnockites, alkaline rocks , Kimberlites, ophiolites and granitoid

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-geology: Unit 02

• Theory of stress and strain
• Behaviour of rocks under stress
• Mohr circle
• Various states of stress and their representation by mohr circles
• Different types of failure and sliding criteria
• Geometry and mechanics of fracturing and conditions for reactivation of pre-existing discontinuities
• Common types of finite strain ellipsoids
• L-, l-s-, and s-tectonic fabrics
• Techniques of strain analysis
• Particle paths and flow patterns
• Progressive strain history
• Introduction to deformation mechanisms
• Role of fluids in deformation processes
• Geometry and analyses of brittle-ductile and ductile shear zones
• Sheath folds
• Geometry and mechanics of development of folds, boudins, foliations and lineations
• Interference patterns of superposed fold
• Fault-related folding
• Gravity induced structures
• Tectonic features of extensional, compressional, and strike-slip-terrains and relevance to plate boundaries
• Mantle plumes
• Himalayan Orogeny; concept of supercontinent, their assembly and breakup

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-geology: Unit 03

• Theories on origin of life
• Organic evolution-punctuated equilibrium and phyletic gradualism models
• Mass extinctions and their causes
• Application of fossils in age determination and correlation
• Paleoecology, life habitats and various ecosystems, paleobiogeography
• Modes of preservation of fossils and taphonomic considerations
• Types of microfossils
• Environmental significance of fossils and trace fossils
• Use of microfossils in interpretation of seafloor tectonism
• Application of micropaleontology in hydrocarbon exploration
• Oxygen and carbon isotope studies of microfossils and their use in paleoceanographic and paleoclimatic interpretation
• Important invertebrate fossils, vertebrate fossils, plant fossils and microfossils in Indian stratigraphy

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-geology: Unit 04

• Classification of sediments and sedimentary rocks; elastic, volcaniclastic and chemical
• Classification of elastic rocks
• Flow regimes and processes of sediment transport
• Sedimentary textures and structures
• Sedimentary facies and environments, reconstruction of paleoenvironments
• Formation and evolution of sedimentary basins
• Diagenesis of siliciclastic and carbonate rocks
• Recent developments in stratigraphic classification
• Code of stratigraphic nomenclature-stratotypes, global boundary stratotype sections and points (GSSP)
• Lithostratigraphic, chronostratigraphic and biostratigraphic subdivisions
• Methods of stratigraphic correlation including Shaw’s graphic correlation
• Concept of sequence stratigraphy
• Rates of sediment accumulation, unconformities
• Facies concept in stratigraphy-Walther‟s law
• Methods for paleogeographic reconstruction
• Earth’s climatic history
• Phanerozoic stratigraphy of India with reference to the type areas-their correlation with equivalent formations in other regions
• Boundary problems in indian phanerozoic stratigraphy

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-geology: Unit 05

• Morphologic and tectonic domains of the ocean floor
• Structure, composition, and mechanism of the formation of oceanic crust
• Hydrothermal vents
• Ocean margins and their significance
• Ocean circulation, Coriolis effect and Ekman spiral, convergence, divergence and upwelling, El Nino
• Indian ocean dipole thermohaline circulation and oceanic conveyor belt
• Formation of bottom waters; major water masses of the world’s oceans
• Oceanic sediments: Factors controlling the deposition and distribution of oceanic sediments; geochronology of oceanic sediments, diagenetic changes in oxic and anoxic environments
• Tectonic evolution of the ocean basins
• Mineral resources
• Paleoceanography-approaches to paleoceanographic reconstructions; various proxy indicators for paleoceanographic interpretation
• Reconstruction of monsoon variability by using marine proxy records opening and closing of ocean gateways and their effect on circulation and climate during the cenozoic
• Sea level processes and sea level changes
• Methods of paleo sea surface temperature
• Quantifications

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-geology: Unit 06

• Atomic structure and properties of elements, the periodic table; ionic substitution in minerals; phase rule and its applications in petrology, thermodynamics of reactions involving pure phases, ideal and non-ideal solutions, and fluids
• Equilibrium and distribution coefficients
• Nucleation and diffusion processes in igneous, metamorphic and sedimentary environments, redox reactions and Eh-pH diagrams and their applications
• Mineral/ mineral assemblages as, sensors of ambient environments
• Geochemical studies of aerosols, surface, marine, and ground waters
• Radioactive decay schemes and their application to geochronology and petrogenesis
• Stable isotopes and their application to earth system processes; geochemical differentiation of the earth; geochemical cycles

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-geology: Unit 07

• Magmatic, hydrothermal and surface processes of ore formation
• Metallogeny and its relation to crustal evolution; active ore-forming systems, methods of mineral deposit studies including ore microscopy, fluid inclusions and isotopic systematics; ores and metamorphism-cause and effect relationships
• Geological setting, characteristics, and genesis of ferrous, base and noble metals
• Origin, migration and entrapment of petroleum; properties of source and reservoir rocks; structural, stratigraphic and combination traps
• Methods of petroleum exploration
• Concepts of petrophysics, petroliferous basins of India
• Origin of peat, lignite, bitumen and anthracite
• Classification, rank and grading of coal; coal petrography, coal resources of India
• Gas hydrates and coal bed methane
• Nuclear and non-conventional energy resources

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-geology: Unit 08

• Evolution of lithosphere, hydrosphere, atmosphere, biosphere, and cryosphere; lithological, geochemical and stratigraphic characteristics of granite-greenstone and granulite belts
• Stratigraphy and geochronology of the cratonic nuclei, mobile belts and proterozoic sedimentary basins of India
• Life in precambrian
• Precambrian-cambrian boundary with special reference to India

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-geology: Unit 09

• Definition of quaternary
• Quaternary stratigraphy-oxygen isotope stratigraphy, biostratigraphy and magnetostratigraphy
• Quaternary climates-glacial-interglacial cycles, eustatic changes, proxy indicators of paleoenvironmental/ paleoclimatic changes, land, ocean and cryosphere (ice core studies)
• Responses of geomorphic systems to climate, sea level and tectonics on variable time scales in the quaternary, quaternary dating methods, radiocarbon, uranium series, luminescence, amino-acid
• Quaternary stratigraphy of India-continental records (fluvial, glacial, aeolian, paleosols and duricrust); marine records; continental-marine correlation of quaternary record
• Evolution of man and stone age cultures
• Plant and animal life in relation to glacial and interglacial cycles during quaternary
• Tectonic geomorphology, neo tectonics, active tectonics and their applications to natural hazard assessment

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-geology: Unit 10

• Remote sensing and GIS: Elements of photogrammetry, elements of photo-interpretation, electromagnetic spectrum, emission range, film and imagery, sensors, geological interpretations of air photos and imageries. Global positioning systems
• Remote sensing and GIS: GIS-data structure, attribute data, thematic layers and query analysis
• Engineering geology: Engineering properties of rocks and physical characteristics of building stones, concretes and other aggregates. Geological investigations for construction of dams, bridges, highways and tunnels. Remedial measures
• Engineering geology: Mass movements with special emphasis on landslides and causes of hill slope instability. Seismic design of buildings
• Mineral exploration: Geological, geophysical, geochemical and geobotanical methods of surface and subsurface exploration on different scales. Sampling, assaying and evaluation of mineral deposits
• Hydrogeology: Groundwater, Darcy’s law, hydrological characteristics of aquifers, hydrological cycle. Precipitation, evapotranspiration and infiltration processes. Hydrological classification of water-bearing formations
• Hydrogeology: Fresh and salt-water relationships in coastal and inland areas. Groundwater exploration and water pollution. Groundwater regimes in India

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-physical geography: Unit 01

• Concepts in geomorphology
• Historical and process geomorphology
• Landforms in relation to climate, rock type , structure and tectonics
• Processes-weathering , pedogenesis, mass movement, erosion, transportation and deposition
• Geomorphic processes and landforms-fluvial, glacial, eolian, coastal and karst
• River forms and processes-stream flow, stage discharge relationship; hydrographs and flood frequency analysis
• Submarine relief
• Geomorphology and topographic analysis including DEM, environmental change-causes, effects on processes and landforms
• Extra-terrestrial geomorphology

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-physical geography: Unit 02

• Fundamental principles of climatology
• Earth’s radiation balance; latitudinal and seasonal variation of insolation, temperature, pressure, wind belts, humidity, cloud formation and precipitation, water balance
• Air masses, monsoon, jet streams, tropical cyclones, and enso
• Classification of climates-Koppen‟s and Thornthwaite’s scheme of classification
• Climate change

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-physical geography: Unit 03

• Elements of biogeography with special reference to India; environment, habitat, plant-animal association; zoo-geography of India; biomes, elements of plant geography, distribution of forests and major plant communities
• Distribution of major animal communities
• Conservation of forests
• Wildlife sanctuaries and parks

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-physical geography: Unit 04

• Manland relationship
• Resources-renewable and non-renewable
• Natural and man-made hazards-droughts, floods, cyclones, earthquakes, landslides, tsunamis
• Ecological balance, environmental pollution and deterioration

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-physical geography: Unit 05

• Physiography, drainage, climate, soils and natural resources-the Himalaya, Ganga-Brahmaputra plains , and peninsular India Precambrian shield, the Gondwana rift basins, Deccan plateau
• Indian climatology with special reference to seasonal distribution and variation of temperature, humidity, wind and precipitation; climate zones of India
• Agricultural geography of india
• Population-its distribution and characteristics
• Urbanization and migration
• Environmental problems and issues

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-geophysics: Unit 01

• Continuous and discrete signals; Fourier series; auto and cross correlations, linear time invariant systems with deterministic and random inputs; band limited signal and sampling theorem; Fourier and fast Fourier transforms; Z-transform; convolution
• Filters: Discrete and continuous, recursive, non-recursive, optimal and inverse filters; deconvolution; fractal analysis

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-geophysics: Unit 02

• Newtonian potential; Laplace and Poisson’s equations; Green’s theorem; Gauss’ law; continuation integral; equivalent stratum; Maxwell’s equations and electromagnetic theory; displacement potential, Helmholtz’s theorem and seismic wave propagation

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-geophysics: Unit 03

• Numerical differentiation and integration, finite element, and finite difference techniques; Simpson’s rules; Gauss’ quadrature formula; initial value problems; pattern recognition in geophysics
• Well posed and ill-posed problems; method of least squares; direct search and gradient methods; generalized inversion techniques; singular value decomposition; global optimization

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-geophysics: Unit 04

• Normal gravity field; Clairaut’s theorem; shape of the earth; deflection of the vertical, geoid, free-air, Bouguer and isostatic anomalies, isostatic models for local and regional compensation
• Geomagnetic field, secular and transient variations and their theories; palaeomagnetism, construction of polar wandering curves

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-geophysics: Unit 05

• Marine magnetic anomalies, sea floor spreading; mid-oceanic ridges and geodynamics; plate tectonics hypothesis; plate boundaries and seismicity
• Heat flow mechanisms, thermal modeling of earth, core-mantle convection and mantle plume

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-geophysics: Unit 06

• Seismometry: Short period, long period, broadband and strong motion; elements of earthquake seismology; seismic sources: Faulting source, double couple hypothesis, seismic moment tensor, focal mechanism and fault plane solutions; seismic gaps
• Seismotectonics and structure of the earth; Himalayan and stable continental region earthquakes, reservoir induced seismicity; seismic hazards; earthquake prediction, travel time residuals, velocity anomalies, seismic tomography

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-geophysics: Unit 07

• Gravimeters and magnetometers; data acquisition from land, air and ship; corrections and reduction of anomalies; ambiguity; regional and residual separation; continuation and derivative calculations; interpretation of anomalies of simple geometric bodies
• Single pole, sphere, horizontal cylinder, sheet, dyke and fault
• Forward modelling and inversion of arbitrary shaped bodies and 2D, 3D interfaces
• Interpretations in frequency domain

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-geophysics: Unit 08

• Electrical profiling and sounding, typical sounding curves, pseudo-sections; resistivity transform and direct interpretation; induced polarization methods
• Electromagnetic field techniques; elliptic polarization, in-phase and out of phase components, horizontal and vertical loop methods; interpretation; VLF (very low frequency); AFMAG (audio frequency magnetic ) methods; and central frequency sounding
• Transient electromagnetic methods; magneto-telluric method; geomagnetic depth sounding

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-geophysics: Unit 09

• Generalized Snell’s law; Ray theory; reflection, refraction, diffraction; Zoeppritz equation; seismic energy sources; detectors; seismic noises and noise profile analysis; seismic data recording, reduction to a datum and weathering corrections
• Interpretation of refraction and reflection data; CDP/CMP; velocity analysis, F-K filtering, stacking, deconvolution, migration before and after stack; bright spot analysis; wavelet processing; attenuation studies, shear waves, AVO; VSP
• Introduction to 3D seismics; seismic stratigraphy

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-geophysics: Unit 10

• Open hole, cased hole and production logging; electrical logs; lateral, latero, induction, temperature, S.P; porosity logs; sonic, density, neutron; natural gamma; determination of formation factor, porosity, permeability, density, water saturation
• Lithology; logging while drilling

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-meteorology: Unit 01

• Fundamental principles of climatology
• Earth’s radiation balance; latitudinal and seasonal variation of insolation, temperature, pressure, wind belts, humidity, cloud formation and precipitation, water balance
• Air masses, monsoon, jet streams, tropical cyclones, and enso
• Classification of climates-Koppen‟s and Thornthwaite’s scheme of classification
• Climate change

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-meteorology: Unit 02

• Thermal structure of the atmosphere and its composition
• Radiation: Basic laws-Rayleigh 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; thermodynamics of dry and moist air: Specific gas constant, adiabatic and isoentropic processes, entropy and enthalpy
• Thermodynamics of dry and moist air: Moisture variables, virtual temperature; Clausius-Clapeyron equation, adiabatic process of moist air; thermodynamic diagrams: Hydrostatic equilibrium-hydrostatic equation
• Hydrostatic equilibrium-variation of pressure with height, geopotential, standard atmosphere, altimetry
• Vertical stability of the atmosphere: Dry and moist air parcel and slice methods. Tropical convection. Atmospheric optics-visibility, optical phenomenon-rainbows, haloes, corona, glarg, mirage

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-meteorology: Unit 03

• Fair weather electric field in the atmosphere and potential gradients, ionization in the atmosphere
• Electrical fields in thunderstorms, theories of thunderstorm electrification-structure of lightning flash-mechanism of earth-atmospheric change balance-role of thunderstorm

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-meteorology: Unit 04

• Cloud classification, condensation nuclei, growth of cloud drops and ice-crystals, precipitation mechanisms: Bergeron, Findeisen process, coalescence process-precipitation of warm and mixed clouds, artificial precipitation, hail suppression
• Fog and cloud-dissipation, radar observation of clouds and precipitation, radar equation, raindrop spectra, radar echoes of hail storm and tornadoes, radar observation of hurricanes, measurements of rainfall by radar

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-meteorology: Unit 05

• Basic equations and fundamental forces: Pressure, gravity, centripetal and Coriolis forces, continuity equation in Cartesian and isobaric coordinates
• Momentum equation 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; Bjerknes circulation theorem and applications, vorticity and divergence equations, scale analysis, potential vorticity, stream function and velocity potential
• Atmospheric turbulence: Mixing length theory, planetary boundary layer equations, surface layer, Ekman layer, Eddy transport of heat, moisture and momentum, Richardson criterion; linear perturbation theory: Internal and external gravity waves
• Linear perturbation theory: Inertia waves, gravity waves, Rossby waves, wave motion in the tropics, barotropic and baroclinic instabilities
• Atmospheric energetics: Kinetic, potential and internal energies-conversion of potential and internal energies into kinetic energy, available potential energy

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-meteorology: Unit 06

• Computational instability, filtering of sound and gravity waves, filtered forecast equations, barotropic and equivalent barotropic models, two parameter baroclinic model, relaxation method
• Multi-layer primitive equation models
• Short, medium, and long range weather prediction
• Objective analysis; initialization of the data for use in weather prediction models; data assimilation techniques, application of satellite in NWP (numerical weather prediction) and remotely sensed data

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-meteorology: Unit 07

• 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, MJO Madden-Julian oscillation), ENSO, QBO (quasi-biennial oscillation) 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

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-meteorology: Unit 08

• Weather observations and transmission, synoptic charts, analysis of surface, upper air another derivative chart , stream-lines, isotachs and contour 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 thunderstorms, dust storms, tornadoes
• Tropical meteorology: Trade wind inversion, ITCZ; monsoon trough tropical cyclones, their structure and development theory; monsoon depressions; tropical easterly jet stream; low level jets, Somali jet, waves in easterlies; western disturbances
• Tropical meteorology: SW and NE monsoons; synoptic features associated with onset, withdrawal, break active and weak monsoons and their prediction
• Air masses and fronts: Sources, origin, and classification of air masses; and fronts, frontogenesis and frontolysis; structure of cold and warm fronts; weather systems associated with fronts
• Extra-tropical synoptic scale features: Jet streams, extratropical cyclones and anticyclones

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-meteorology: Unit 09

• Role of meteorology in aviation, weather hazards associated with take off cruising and landing, inflight-icing, turbulence, visibility, fog, clouds, rain, gusts, wind shear and thunderstorms, nowcasting and very short range forecasting

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-meteorology: Unit 10

• Meteorological satellites-polar orbiting and geostationary satellites, visible and infrared radiometers, multiscanner radiometers; identification of synoptic systems, fog and sandstorms, detection of cyclones, estimation of SST, cloud top temperatures
• Winds and rainfall: Temperature and humidity soundings

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-ocean sciences: Unit 01

• T-S diagrams; mixing processes in the oceans; characteristics of important water masses
• Wind generated waves in the oceans; their characteristics; shallow and deep water waves
• Propagation, refraction, and reflection of waves
• Wave spectrum, principles of wave forecasting
• Tide-producing forces and their magnitudes; prediction of tides by the harmonic method; tides and tidal currents in shallow seas, estuaries and rivers
• 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; tsunami; interaction of waves and structure
• 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
• Estuaries: Mixing and dispersal of pollutants in estuaries and near-shore areas; coastal zone management
• The global wind system; action of wind on ocean surface; Ekman’s theory; Sverdrup, Stommel and Munk’s theories; upwelling and sinking with special reference to the Indian ocean
• Inertial currents; divergences and convergences; geostrophic motion; barotropic and baroclinic conditions; oceanic eddies, relationship between density, pressure and dynamic topography; relative and slope currents
• Wind driven coastal currents; typical scales of motion in the ocean
• Characteristics of the global conveyor belt circulation and its causes
• Formation of subtropical gyres; western boundary currents; equatorial current systems; El Nino; monsoonal winds and currents over the north Indian ocean; Somali current; southern ocean
• Upwelling process in the arabian sea

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-ocean sciences: Unit 02

• Composition of seawater-classification of elements based on their distribution; major and minor elements, their behaviour and chemical exchanges across interfaces and residence times in seawater
• Element chemistry in a typical conditions-estuaries, hydrothermal vents, anoxic basins, HNLC waters, sediment pore fluid and anthropogenic inputs
• Chemical and biological interactions-ionic interactions; biogeochemical cycling of nutrients, trace metals and organic matter
• Air-sea exchange of important biogenic dissolved gases; carbon dioxide-carbonate system; alkalinity and control of pH; biological pump
• Factors affecting sedimentary deposits-CaCO₃, Silicate, manganese nodules, phosphorites and massive single deposits

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-ocean sciences: Unit 03

• Morphologic and tectonic domains of the ocean floor
• Structure, composition, and mechanism of the formation of oceanic crust
• Hydrothermal vents
• Ocean margins and their significance
• Ocean circulation, Coriolis effect and Ekman spiral, convergence, divergence and upwelling, El Nino
• Indian ocean dipole thermohaline circulation and oceanic conveyor belt
• Formation of bottom waters; major water masses of the world’s oceans
• Oceanic sediments: Factors controlling the deposition and distribution of oceanic sediments; geochronology of oceanic sediments, diagenetic changes in oxic and anoxic environments
• Tectonic evolution of the ocean basins
• Mineral resources
• Paleoceanography-approaches to paleoceanographic reconstructions; various proxy indicators for paleoceanographic interpretation
• Reconstruction of monsoon variability by using marine proxy records opening and closing of ocean gateways and their effect on circulation and climate during the cenozoic
• Sea level processes and sea level changes
• Methods of paleo sea surface temperature
• Quantifications

Earth, atmospheric, ocean and planetary sciences-paper-I (part-c)-ocean sciences: Unit 04

• Classification of the marine environment and marine organisms
• Physicochemical factors affecting marine life-light, temperature, salinity, pressure, nutrients, dissolved gases; adaptation and biological processes
• Primary and secondary production; factors controlling phytoplankton and zooplankton abundance and diversity; nekton and fisheries oceanography; benthic organisms; coastal marine communities and community ecology-estuaries
• Coral reefs and mangrove communities, deep-sea ecology including hydrothermal vent communities
• Energy flow and mineral cycling-energy transfer and transfer efficiencies through different trophic levels; food webs including the microbial loop
• Human impacts on marine communities; impacts of climate change on marine biodiversity
• Impact of pollution on marine environments including fisheries

Life sciences: Unit 01

• Structure of atoms, molecules and chemical bonds
• Composition, structure, and function of biomolecules (carbohydrates, lipids, proteins, nucleic acids, and vitamins)
• Stabilizing interactions (Van der Waals, electrostatic, hydrogen bonding, hydrophobic interaction, etc.)
• Principles of biophysical chemistry (pH, buffer, reaction kinetics, thermodynamics, colligative properties)
• Bioenergetics, glycolysis, oxidative phosphorylation, coupled reaction, group transfer, biological energy transducers
• Principles of catalysis, enzymes and enzyme kinetics, enzyme regulation, mechanism of enzyme catalysis, isozymes
• Conformation of proteins (Ramachandran plot, secondary structure, domains, motif and folds)
• Conformation of nucleic acids [helix (A, B, Z), t-RNA, micro-RNA]
• Stability of proteins and nucleic acids
• Metabolism of carbohydrates, lipids, amino acids nucleotides and vitamins

Life sciences: Unit 02

• Membrane structure and function: Structure of model membrane, lipid bilayer and membrane protein diffusion, osmosis, ion channels, active transport, membrane pumps, mechanism of sorting and regulation of intracellular transport
• Membrane structure and function: Electrical properties of membranes
• Structural organization and function of intracellular organelles: Cell wall, nucleus, mitochondria, golgi bodies, lysosomes, endoplasmic reticulum, peroxisomes, plastids, vacuoles, chloroplast
• Structural organization and function of intracellular organelles: Structure and function of cytoskeleton and its role in motility
• Organization of genes and chromosomes: Operon, unique and repetitive DNA, interrupted genes, gene families, structure of chromatin and chromosomes, heterochromatin, euchromatin, transposons
• Cell division and cell cycle: Mitosis and meiosis, their regulation, steps in cell cycle, regulation and control of cell cycle
• Microbial physiology: Growth yield and characteristics, strategies of cell division, stress response

Life sciences: Unit 03

• DNA replication, repair and recombination: Unit of replication, enzymes involved, replication origin and replication fork, fidelity of replication, extrachromosomal replicons, DNA damage and repair mechanisms, homologous and site-specific recombination
• RNA synthesis and processing: Transcription factors and machinery, formation of initiation complex, transcription activator and repressor, RNA polymerases, capping, elongation, and termination, RNA processing, RNA editing, splicing, and polyadenylation
• RNA synthesis and processing: Structure and function of different types of RNA, RNA transport
• Protein synthesis and processing: Ribosome, formation of initiation complex, initiation factors and their regulation, elongation and elongation factors, termination, genetic code, aminoacylation of tRNA, tRNA-identity
• Protein synthesis and processing: Aminoacyl tRNA synthetase, and translational proofreading, translational inhibitors, post-translational modification of proteins
• Control of gene expression at transcription and translation level: Regulating the expression of phages, viruses, prokaryotic and eukaryotic genes, role of chromatin in gene expression and gene silencing

Life sciences: Unit 04

• Host parasite interaction: Recognition and entry processes of different pathogens like bacteria, viruses into animal and plant host cells, alteration of host cell behaviour by pathogens, virus-induced cell transformation
• Host parasite interaction: Pathogen-induced diseases in animals and plants, cell-cell fusion in both normal and abnormal cells
• Cell signaling: Hormones and their receptors, cell surface receptor, signaling through G-protein coupled receptors, signal transduction pathways, second messengers, regulation of signaling pathways, bacterial and plant two-component systems
• Cell signaling: Light signaling in plants, bacterial chemotaxis and quorum sensing
• Cellular communication: Regulation of hematopoiesis, general principles of cell communication, cell adhesion and roles of different adhesion molecules, gap junctions, extracellular matrix, integrins, neurotransmission and its regulation
• Cancer: Genetic rearrangements in progenitor cells, oncogenes, tumor suppressor genes, cancer and the cell cycle, virus-induced cancer, metastasis, interaction of cancer cells with normal cells, apoptosis
• Cancer: Therapeutic interventions of uncontrolled cell growth
• Innate and adaptive immune system: Cells and molecules involved in innate and adaptive immunity, antigens, antigenicity and immunogenicity. B and T cell epitopes, structure and function of antibody molecules. Generation of antibody diversity
• Innate and adaptive immune system: Monoclonal antibodies, antibody engineering, antigen-antibody interactions, MHC molecules, antigen processing and presentation, activation and differentiation of B and T cells, B and T cell receptors
• Innate and adaptive immune system: Humoral and cell-mediated immune responses, primary and secondary immune modulation, the complement system, toll-like receptors, cell-mediated effector functions inflammation, hypersensitivity and autoimmunity
• Innate and adaptive immune system: Immune response during bacterial (tuberculosis), parasitic (malaria) and viral (HIV) infections, congenital and acquired immunodeficiencies, vaccines

Life sciences: Unit 05

• Basic concepts of development: Potency, commitment, specification, induction, competence, determination and differentiation; morphogenetic gradients; cell fate and cell lineages; stem cells; genomic equivalence and the cytoplasmic determinants; imprinting
• Basic concepts of development: Mutants and transgenics in analysis of development
• Gametogenesis, fertilization and early development: Production of gametes, cell surface molecules in sperm-egg recognition in animals; embryo sac development and double fertilization in plants; zygote formation, cleavage, blastula formation
• Gametogenesis, fertilization and early development: Embryonic fields, gastrulation and formation of germ layers in animals; embryogenesis, establishment of symmetry in plants; seed formation and germination
• Morphogenesis and organogenesis in animals: Cell aggregation and differentiation in dictyostelium; axes and pattern formation in drosophila, amphibia and chick; organogenesis-vulva formation in caenorhabditis elegans, eye lens induction
• Morphogenesis and organogenesis in animals: Organogenesis-limb development and regeneration in vertebrates; differentiation of neurons, post embryonic development-larval formation, metamorphosis; environmental regulation of normal development
• Morphogenesis and organogenesis in plants: Sex determination, organization of shoot and root apical meristem; shoot and root development; leaf development and phyllotaxy; transition to flowering
• Morphogenesis and organogenesis in plants: Floral meristems and floral development in Arabidopsis and Antirrhinum
• Programmed cell death, aging and senescence

Life sciences: Unit 06

• Photosynthesis: Light harvesting complexes; mechanisms of electron transport; photoprotective mechanisms; CO fixation-C₃, C₄, and CAM pathways
• Respiration and photorespiration: Citric acid cycle; plant mitochondrial electron transport and ATP synthesis; alternate oxidase; photorespiratory pathway
• Nitrogen metabolism: Nitrate and ammonium assimilation; amino acid biosynthesis
• Plant hormones: Biosynthesis, storage, breakdown and transport; physiological effects and mechanisms of action
• Sensory photobiology: Structure, function, and mechanisms of action of phytochromes, cryptochromes and phototropins; stomatal movement; photoperiodism and biological clocks
• Solute transport and photoassimilate translocation: Uptake, transport and translocation of water, ions, solutes and macromolecules from soil, through cells, across membranes, through xylem and phloem; transpiration
• Solute transport and photoassimilate translocation: Mechanisms of loading and unloading of photoassimilates
• Secondary metabolites: Biosynthesis of terpenes, phenols and nitrogenous compounds and their roles
• Stress physiology: Responses of plants to biotic (pathogen and insects) and abiotic (water, temperature and salt) stresses

Life sciences: Unit 07

• Blood and circulation: Blood corpuscles, haemopoiesis and formed elements, plasma function, blood volume, blood volume regulation, blood groups, haemoglobin, immunity, haemostasis
• Cardiovascular system: Comparative anatomy of heart structure, myogenic heart, specialized tissue, ECG-its principle and significance, cardiac cycle, heart as a pump, blood pressure, neural and chemical regulation of all above
• Respiratory system: Comparison of respiration in different species, anatomical considerations, transport of gases, exchange of gases, waste elimination, neural and chemical regulation of respiration
• Nervous system: Neurons, action potential, gross neuroanatomy of the brain and spinal cord, central and peripheral nervous system, neural control of muscle tone and posture
• Sense organs: Vision, hearing and tactile response
• Excretory system: Comparative physiology of excretion, kidney, urine formation, urine concentration, waste elimination, micturition, regulation of water balance, blood volume, blood pressure, electrolyte balance, acid-base balance
• Thermoregulation: Comfort zone, body temperature-physical, chemical, neural regulation, acclimatization
• Stress and adaptation
• Digestive system: Digestion, absorption, energy balance, BMR
• Endocrinology and reproduction: Endocrine glands, basic mechanism of hormone action, hormones and diseases; reproductive processes, gametogenesis, ovulation, neuroendocrine regulation

Life sciences: Unit 08

• Mendelian principles: Dominance, segregation, independent assortment
• Concept of gene: Allele, multiple alleles, pseudoallele, complementation tests
• Extensions of Mendelian principles: Codominance, incomplete dominance, gene interactions, pleiotropy, genomic imprinting, penetrance and expressivity, phenocopy, linkage and crossing over, sex linkage, sex limited and sex influenced characters
• Gene mapping methods: Linkage maps, tetrad analysis, mapping with molecular markers, mapping by using somatic cell hybrids, development of mapping population in plants
• Extra chromosomal inheritance: Inheritance of mitochondrial and chloroplast genes, maternal inheritance
• Microbial genetics: Methods of genetic transfers-transformation, conjugation, transduction and sex-duction, mapping genes by interrupted mating, fine structure analysis of genes
• Human genetics: Pedigree analysis, LOD score for linkage testing, karyotypes, genetic disorders
• Quantitative genetics: Polygenic inheritance, heritability and its measurements, QTL mapping
• Mutation: Types, causes, and detection, mutant types-lethal, conditional, biochemical, loss of function, gain of function, germinal vs somatic mutants, insertional mutagenesis
• Structural and numerical alterations of chromosomes: Deletion, duplication, inversion, translocation, ploidy and their genetic implications
• Recombination: Homologous and non-homologous recombination including transposition

Life sciences: Unit 09

• Principles and methods of taxonomy: Concepts of species and hierarchical taxa, biological nomenclature, classical and quantitative methods of taxonomy of plants, animals and microorganisms
• Levels of structural organization: Unicellular, colonial and multicellular forms. Levels of organization of tissues, organs and systems. Comparative anatomy, adaptive radiation, adaptive modifications
• Outline classification of plants, animals and microorganisms: Important criteria used for classification in each taxon. Classification of plants, animals and microorganisms. Evolutionary relationships among taxa
• Natural history of Indian subcontinent: Major habitat types of the subcontinent, geographic origins and migrations of species. Common Indian mammals, birds. Seasonality and phenology of the subcontinent
• Organisms of health and agricultural importance: Common parasites and pathogens of humans, domestic animals and crops
• Organisms of conservation concern: Rare, endangered species. Conservation strategies

Life sciences: Unit 10

• The Environment: Physical environment; biotic environment; biotic and abiotic interactions
• Habitat and niche: Concept of habitat and niche; niche width and overlap; fundamental and realized niche; resource partitioning; character displacement
• Population ecology: Characteristics of a population; population growth curves; population regulation; life history strategies (R and K selection); concept of metapopulation-demes and dispersal, interdemic extinctions, age structured populations
• Species interactions: Types of interactions, interspecific competition, herbivory, carnivory, pollination, symbiosis
• Community ecology: Nature of communities; community structure and attributes; levels of species diversity and its measurement; edges and ecotone
• Ecological succession: Types; mechanisms; changes involved in succession; concept of climax
• Ecosystem ecology: Ecosystem structure; ecosystem function; energy flow and mineral cycling (C,N,P); primary production and decomposition; structure and function of some Indian ecosystems
• Ecosystem ecology: Terrestrial (forest, grassland) and aquatic (fresh water, marine, estuarine)
• Biogeography: Major terrestrial biomes; theory of island biogeography; biogeographical zones of India
• Applied ecology: Environmental pollution; global environmental change; biodiversity: Status, monitoring and documentation; major drivers of biodiversity change; biodiversity management approaches
• Conservation biology: Principles of conservation, major approaches to management, Indian case studies on conservation/ management strategy (project tiger, biosphere reserves)

Life sciences: Unit 11

• Emergence of evolutionary thoughts: Lamarck; Darwin-concepts of variation, adaptation, struggle, fitness and natural selection; Mendelism; spontaneity of mutations; the evolutionary synthesis
• Origin of cells and unicellular evolution: Origin of basic biological molecules; abiotic synthesis of organic monomers and polymers; concept of Oparin and Haldane; experiment of Miller (1953); the first cell; evolution of prokaryotes
• Origin of cells and unicellular evolution: Origin of eukaryotic cells; evolution of unicellular eukaryotes; anaerobic metabolism, photosynthesis and aerobic metabolism
• Molecular evolution: Concepts of neutral evolution, molecular divergence and molecular clocks; molecular tools in phylogeny, classification and identification; protein and nucleotide sequence analysis; origin of new genes and proteins
• Molecular evolution: Gene duplication and divergence
• The mechanisms: Population genetics-populations, gene pool, gene frequency; Hardy-Weinberg law; concepts and rate of change in gene frequency through natural selection, migration and random genetic drift; adaptive radiation; isolating mechanisms
• The mechanisms: Speciation; allopatricity and sympatricity; convergent evolution; sexual selection; coevolution
• Brain, behaviour, and evolution: Approaches and methods in study of behavior; proximate and ultimate causation; altruism and evolution-group selection, kin selection, reciprocal altruism; neural basis of learning, memory, cognition, sleep and arousal
• Brain, behaviour, and evolution: Biological clocks; development of behaviour; social communication; social dominance; use of space and territoriality; mating systems, parental investment and reproductive success; parental care; aggressive behaviour
• Brain, behaviour, and evolution: Habitat selection and optimality in foraging; migration, orientation and navigation; domestication and behavioral change

Life sciences: Unit 12

• Microbial fermentation and production of small and macromolecules
• Application of immunological principles, vaccines, diagnostics
• Tissue and cell culture methods for plants and animals
• Transgenic animals and plants, molecular approaches to diagnosis and strain identification
• Genomics and its application to health and agriculture, including gene therapy
• Bioresource and uses of biodiversity
• Breeding in plants and animals, including marker-assisted selection
• Bioremediation and phytoremediation
• Biosensors

Life sciences: Unit 13

• Molecular biology and recombinant DNA methods: Isolation and purification of RNA, DNA (genomic and plasmid) and proteins, different separation methods. Analysis of RNA, DNA and proteins by one and two dimensional gel electrophoresis
• Molecular biology and recombinant DNA methods: Isoelectric focusing gels. Molecular cloning of DNA or RNA fragments in bacterial and eukaryotic systems. Expression of recombinant proteins using bacterial, animal and plant vectors
• Molecular biology and recombinant DNA methods: Isolation of specific nucleic acid sequences. Generation of genomic and cDNA libraries in plasmid, phage, cosmid, BAC and YAC vectors. In-vitro mutagenesis and deletion techniques
• Molecular biology and recombinant DNA methods: Gene knockout in bacterial and eukaryotic organisms. Protein sequencing methods, detection of post translational modification of proteins. DNA sequencing methods, strategies for genome sequencing
• Molecular biology and recombinant DNA methods: Methods for analysis of gene expression at RNA and protein level, large scale expression, such as microarray based techniques. Isolation, separation and analysis of carbohydrate and lipid molecules
• Molecular biology and recombinant DNA methods: RFLP, RAPD and AFLP techniques
• Histochemical and immunotechniques: Antibody generation, detection of molecules using ELISA, RIA, western blot, immunoprecipitation, flow cytometry and immunofluorescence microscopy, detection of molecules in living cells
• Histochemical and Immunotechniques: In-situ localization by techniques such as FISH and GISH
• Biophysical method: Molecular analysis using UV/ visible, fluorescence, circular dichroism, NMR and ESR spectroscopy molecular structure determination using X-ray diffraction and NMR, molecular analysis using light scattering
• Biophysical method: Different types of mass spectrometry and surface plasmon resonance method
• Statistical methods: Measures of central tendency and dispersal; probability distributions (binomial, Poisson and normal); sampling distribution; difference between parametric and non-parametric statistics; confidence interval; errors
• Statistical methods: Levels of significance; regression and correlation; t-test; analysis of variance; X2 test; basic introduction to multivariate statistics, etc
• Radiolabeling techniques: Detection and measurement of different types of radioisotopes normally used in biology, incorporation of radioisotopes in biological tissues and cells, molecular imaging of radioactive material, safety guideline
• Microscopic techniques: Visualization of cells and subcellular components by light microscopy, resolving powers of different microscopes, microscopy of living cells, scanning and transmission microscopes
• Microscopic techniques: Different fixation and staining techniques for EM, freeze-etch and freeze-fracture methods for EM, image processing methods in microscopy
• Electrophysiological methods: Single neuron recording, patch-clamp recording, ECG, brain activity recording, lesion and stimulation of brain, pharmacological testing, PET, MRI, fMRI, CAT
• Methods in field biology: Methods of estimating population density of animals and plants, ranging patterns through direct, indirect and remote observations, sampling methods in the study of behaviour
• Methods in field biology: Habitat characterization-ground and remote sensing methods

Mathematical sciences: Unit 01

• Elementary set theory, finite, countable and uncountable sets, real number system as a complete ordered field, Archimedean property, supremum, infimum
• Sequences and series, convergence, limsup, liminf
• Bolzano Weierstrass theorem, Heine Borel theorem
• Continuity, uniform continuity, differentiability, mean value theorem
• Sequences and series of functions, uniform convergence
• Riemann sums and riemann integral, improper integrals
• Monotonic functions, types of discontinuity, functions of bounded variation, Lebesgue measure, Lebesgue integral
• Functions of several variables, directional derivative, partial derivative, derivative as a linear transformation, inverse and implicit function theorems
• Metric spaces, compactness, connectedness
• Normed linear spaces
• Spaces of continuous functions as examples

Mathematical sciences: Unit 02

• Vector spaces, subspaces, linear dependence, basis, dimension, algebra of linear transformations
• Algebra of matrices, rank and determinant of matrices, linear equations
• Eigenvalues and eigenvectors, Cayley-Hamilton theorem
• Matrix representation of linear transformations
• Change of basis, canonical forms, diagonal forms, triangular forms, jordan forms
• Inner product spaces, orthonormal basis
• Quadratic forms, reduction and classification of quadratic forms

Mathematical sciences: Unit 03

• Algebra of complex numbers, the complex plane , polynomials, power series, transcendental functions such as exponential, trigonometric and hyperbolic functions
• Analytic functions, Cauchy-Riemann equations
• Contour integral, Cauchy’s theorem, Cauchy’s integral formula, Liouville’s theorem, maximum modulus principle, Schwarz lemma, open mapping theorem
• Taylor series, Laurent series, calculus of residues
• Conformal mappings, Mobius transformations

Mathematical sciences: Unit 04

• Permutations, combinations, pigeonhole principle, inclusion-exclusion principle, derangements
• Fundamental theorem of arithmetic, divisibility in Z, congruences, Chinese remainder theorem, Euler’s ø- function, primitive roots
• Groups, subgroups, normal subgroups, quotient groups, homomorphisms, cyclic groups, permutation groups, cayley’s theorem, class equations, sylow theorems
• Rings, ideals, prime and maximal ideals, quotient rings, unique factorization domain, principal ideal domain, Euclidean domain
• Polynomial rings and irreducibility criteria
• Fields, finite fields, field extensions, galois theory

Mathematical sciences: Unit 05

• Basis, dense sets, subspace and product topology, separation axioms, connectedness and compactness

Mathematical sciences: Unit 06

• Existence and uniqueness of solutions of initial value problems for first order ordinary differential equations, singular solutions of first order ODEs, system of first order ODEs
• General theory of homogeneous and nonhomogeneous linear ODEs, variation of parameters, Sturm-Liouville boundary value problem, green’s function

Mathematical sciences: Unit 07

• Lagrange and Charpit methods for solving first order PDEs, Cauchy problem for first order PDEs
• Classification of second order PDEs, general solution of higher order PDEs with constant coefficients, method of separation of variables for Laplace, heat and wave equations

Mathematical sciences: Unit 08

• Numerical solutions of algebraic equations, method of iteration and Newton-Raphson method, rate of convergence, solution of systems of linear algebraic equations using Gauss elimination and Gauss-Seidel methods, finite differences
• Lagrange, Hermite and spline interpolation, numerical differentiation and integration, numerical solutions of ODEs using Picard, Euler, modified Euler and Runge-Kutta methods

Mathematical sciences: Unit 09

• Variation of a functional, Euler-Lagrange equation, necessary and sufficient conditions for extrema
• Variational methods for boundary value problems in ordinary and partial differential equations

Mathematical sciences: Unit 10

• Linear integral equation of the first and second kind of Fredholm and Volterra type , solutions with separable kernels
• Characteristic numbers and eigenfunctions, resolvent kernel

Mathematical sciences: Unit 11

• Generalized coordinates, Lagrange’s equations, Hamilton’s canonical equations, Hamilton’s principle and principle of least action, two-dimensional motion of rigid bodies, Euler’s dynamical equations for the motion of a rigid body about an axis
• Theory of small oscillation

Mathematical sciences: Unit 12

• Sample space, discrete probability, independent events, bayes theorem
• Random variables and distribution functions (univariate and multivariate); expectation and moments
• Independent random variables, marginal and conditional distributions
• Characteristic functions
• Probability inequalities (Tchebysheff's, Markov, Jensen)
• Modes of convergence, weak and strong laws of large numbers, Central Limit theorems (i.i.d. case)
• Markov chains with finite and countable state space, classification of states, limiting behaviour of n-step transition probabilities, stationary distribution, Poisson and birth-and-death processes
• Standard discrete and continuous univariate distributions
• Sampling distributions, standard errors and asymptotic distributions, distribution of order statistics and range
• Methods of estimation, properties of estimators, confidence intervals
• Tests of hypotheses: Most powerful and uniformly most powerful tests, likelihood ratio tests. Analysis of discrete data and chi-square test of goodness of fit. Large sample tests
• Simple nonparametric tests for one and two sample problems, rank correlation and test for independence
• Elementary bayesian inference
• Gauss-Markov models, estimability of parameters, best linear unbiased estimators, confidence intervals, tests for linear hypotheses
• Analysis of variance and covariance
• Fixed, random and mixed effects models
• Simple and multiple linear regression
• Elementary regression diagnostics
• Logistic regression
• Multivariate normal distribution, Wishart distribution and their properties
• Distribution of quadratic forms
• Inference for parameters, partial and multiple correlation coefficients and related tests
• Data reduction techniques: Principal component analysis, discriminant analysis, cluster analysis, canonical correlation
• Simple random sampling, stratified sampling and systematic sampling
• Probability proportional to size sampling
• Ratio and regression methods
• Completely randomized designs, randomized block designs and Latin-square designs
• Connectedness and orthogonality of block designs, bibd
• 2k factorial experiments: confounding and construction
• Hazard function and failure rates, censoring and life testing, series and parallel systems
• Linear programming problem, simplex methods, duality
• Elementary queuing and inventory models
• Steady-state solutions of Markovian queuing models: M/M/1, M/M/1 with limited waiting space, M/M/C, M/M/C with limited waiting space, M/G/1

Physical sciences-Part-A (Core): Unit 01

• Dimensional analysis
• Vector algebra and vector calculus
• Linear algebra, matrices, Cayley-Hamilton theorem
• Eigenvalues and eigenvectors
• Linear ordinary differential equations of first and second order, special functions (Hermite, Bessel, Laguerre and Legendre functions)
• Fourier series, Fourier and Laplace transforms
• Elements of complex analysis, analytic functions; Taylor and Laurent series; poles, residues and evaluation of integrals
• Elementary probability theory, random variables, binomial, Poisson and normal distributions
• Central limit theorem
• Green’s function
• Partial differential equations (Laplace, wave and heat equations in two and three dimensions)
• Elements of computational techniques: Root of functions, interpolation, extrapolation, integration by trapezoidal and Simpson’s rule, solution of first order differential equation using Runge- Kutta method
• Finite difference methods
• Tensors
• Introductory group theory: SU(2), O(3)

Physical sciences-Part-A (Core): Unit 02

• Newton’s laws
• Dynamical systems, phase space dynamics, stability analysis
• Central force motions
• Two body collisions-scattering in laboratory and centre of mass frames
• Rigid body dynamics-moment of inertia tensor
• Non-inertial frames and pseudo forces
• Variational principle
• Generalized coordinates
• Lagrangian and hamiltonian formalism and equations of motion
• Conservation laws and cyclic coordinates
• Periodic motion: small oscillations, normal modes
• Special theory of relativity-Lorentz transformations, relativistic kinematics and mass-energy equivalence
• Poisson brackets and canonical transformations
• Symmetry, invariance and noether’s theorem
• Hamilton-jacobi theory

Physical sciences-Part-A (Core): Unit 03

• Electrostatics: Gauss’s law and its applications, Laplace and Poisson equations, boundary value problems
• Magnetostatics: Biot-Savart law, Ampere's theorem
• Electromagnetic induction
• Maxwell's equations in free space and linear isotropic media; boundary conditions on the fields at interfaces
• Scalar and vector potentials, gauge invariance
• Electromagnetic waves in free space
• Dielectrics and conductors
• Reflection and refraction, polarization, Fresnel’s law, interference, coherence, and diffraction
• Dynamics of charged particles in static and uniform electromagnetic fields
• Dispersion relations in plasma

Physical sciences-Part-A (Core): Unit 04

• Wave-particle duality
• Schrödinger equation (time-dependent and time-independent)
• Eigenvalue problems (particle in a box, harmonic oscillator, etc.)
• Tunneling through a barrier
• Wave-function in coordinate and momentum representations
• Commutators and heisenberg uncertainty principle
• Dirac notation for state vectors
• Motion in a central potential: Orbital angular momentum, angular momentum algebra, spin, addition of angular momenta; hydrogen atom
• Stern-gerlach experiment
• Time-independent perturbation theory and applications
• Variational method
• Time dependent perturbation theory and Fermi's golden rule, selection rules
• Identical particles, Pauli exclusion principle, spin-statistics connection

Physical sciences-Part-A (Core): Unit 05

• Laws of thermodynamics and their consequences
• Thermodynamic potentials, Maxwell relations, chemical potential, phase equilibria
• Phase space, micro and macro-states
• Micro-canonical, canonical and grand-canonical ensembles and partition functions
• Free energy and its connection with thermodynamic quantities
• Classical and quantum statistics
• Ideal bose and fermi gases
• Principle of detailed balance
• Blackbody radiation and planck's distribution law

Physical sciences-Part-A (Core): Unit 06

• Semiconductor devices (diodes, junctions, transistors, field effect devices, homo- and hetero-junction devices), device structure, device characteristics, frequency dependence and applications
• Opto-electronic devices (solar cells, photo-detectors, LEDs)
• Operational amplifiers and their applications
• Digital techniques and applications (registers, counters, comparators and similar circuits)
• A/D and D/A converters
• Microprocessor and microcontroller basics
• Data interpretation and analysis
• Precision and accuracy
• Error analysis, propagation of errors
• Least squares fitting

Physical sciences-Part-B (Advanced): Unit 01

• Lorentz invariance of maxwell’s equation
• Transmission lines and wave guides
• Radiation-from moving charges and dipoles and retarded potentials

Physical sciences-Part-B (Advanced): Unit 02

• Spin-orbit coupling, fine structure
• Wkb approximation
• Elementary theory of scattering: phase shifts, partial waves, Born approximation
• Relativistic quantum mechanics: Klein-Gordon and Dirac equations
• Semi-classical theory of radiation

Physical sciences-Part-B (Advanced): Unit 03

• First and second-order phase transitions
• Diamagnetism, paramagnetism, and ferromagnetism
• Ising model
• Bose-einstein condensation
• Diffusion equation
• Random walk and brownian motion
• Introduction to nonequilibrium processes

Physical sciences-Part-B (Advanced): Unit 04

• Linear and nonlinear curve fitting, chi-square test
• Transducers (temperature, pressure/ vacuum, magnetic fields, vibration, optical, and particle detectors)
• Measurement and control
• Signal conditioning and recovery
• Impedance matching, amplification (Op-amp based, instrumentation amp, feedback), filtering and noise reduction, shielding and grounding
• Fourier transforms, lock-in detector, boxcar integrator, modulation techniques
• High frequency devices (including generators and detectors)

Physical sciences-Part-B (Advanced): Unit 05

• Quantum states of an electron in an atom
• Electron spin
• Spectrum of helium and alkali atom
• Relativistic corrections for energy levels of hydrogen atom, hyperfine structure and isotopic shift, width of spectral lines, LS and JJ couplings
• Zeeman, paschen-bach and stark effects
• Electron spin resonance
• Nuclear magnetic resonance, chemical shift
• Franck-Condon principle
• Born-oppenheimer approximation
• Electronic, rotational, vibrational and raman spectra of diatomic molecules, selection rules
• Lasers: Spontaneous and stimulated emission, Einstein A and B coefficients
• Optical pumping, population inversion, rate equation
• Modes of resonators and coherence length

Physical sciences-Part-B (Advanced): Unit 06

• Bravais lattices
• Reciprocal lattice
• Diffraction and the structure factor
• Bonding of solids
• Elastic properties, phonons, lattice specific heat
• Free electron theory and electronic specific heat
• Response and relaxation phenomena
• Drude model of electrical and thermal conductivity
• Hall effect and thermoelectric power
• Electron motion in a periodic potential, band theory of solids: metals, insulators and semiconductors
• Superconductivity: type-I and type-II superconductors
• Josephson junctions
• Superfluidity
• Defects and dislocations
• Ordered phases of matter: translational and orientational order, kinds of liquid crystalline order
• Quasicrystals

Physical sciences-Part-B (Advanced): Unit 07

• Basic nuclear properties: size, shape and charge distribution, spin and parity
• Binding energy, semi-empirical mass formula, liquid drop model
• Nature of the nuclear force, form of nucleon-nucleon potential, charge-independence and charge-symmetry of nuclear forces
• Deuteron problem
• Evidence of shell structure, single-particle shell model, its validity and limitations
• Rotational spectra
• Elementary ideas of alpha, beta, and gamma decays and their selection rules
• Fission and fusion
• Nuclear reactions, reaction mechanism, compound nuclei and direct reactions
• Classification of fundamental forces
• Elementary particles and their quantum numbers (charge, spin, parity, isospin, strangeness, etc.)
• Gell Mann-Nishijima formula
• Quark model, baryons and mesons
• C, p, and t invariance
• Application of symmetry arguments to particle reactions
• Parity non-conservation in weak interaction
• Relativistic kinematics