GATE 2008 SYLLABUS

AE - AEROSPACE ENGINEERING

ENGINEERING MATHEMATICS

Linear Algebra: Matrix algebra, systems of linear equations, eigen values and eigen vectors. Calculus: Functions of single variable, limit, continuity and differentiability, mean value theorems, evaluation of definite and improper integrals, partial derivatives, total derivative, maxima and minima, gradient, divergence and curl, vector identities, directional derivatives, line, surface and volume integrals. Theorems of Stokes, Gauss and Green.

Differential Calculus: First order linear and nonlinear equations, higher order linear ODEs with constant coefficients, Cauchy and Euler equations, initial and boundary value problems, Laplace transforms. Partial differential equations and separation of variables methods.

Numerical methods: Numerical solution of linear and nonlinear algebraic equations, integration by trapezoidal and Simpson rule, single and multi-step methods for differential equations.

FLIGHT MECHANICS

Atmosphere: Properties, standard atmosphere. Classification of aircraft. Airplane (fixed wing aircraft) configuration and various parts.

Airplane performance: Pressure altitude; equivalent, calibrated, indicated air speeds; Primary flight instruments: Altimeter, ASI, VSI, Turn-bank indicator. Drag polar; take off and landing; steady climb & descent,-absolute and service ceiling; cruise, cruise climb, endurance or loiter; load factor, turning flight, V-n diagram; Winds: head, tail & cross winds.

Static stability: Angle of attack, sideslip; roll, pitch & yaw controls; longitudinal stick fixed & free stability, horizontal tail position and size; directional stability, vertical tail position and size; dihedral stability. Wing dihedral, sweep & position; hinge moments, stick forces.

Dynamic stability: Euler angles; Equations of motion; aerodynamic forces and moments, stability & control derivatives; decoupling of longitudinal and lat-directional dynamics; longitudinal modes; lateral-directional modes.

SPACE DYNAMICS

Central force motion, determination of trajectory and orbital period in simple cases. Orbit transfer,in-plane and out-of-plane. Elements of rocket motor performance.

AERODYNAMICS

Basic Fluid Mechanics: Incompressible irrotational flow, Helmholtz and Kelvin theorem, singularities and superposition, viscous flows, boundary layer on a flat plate. Airfoils and wings: Classification of airfoils, aerodynamic characteristics, high lift devices, Kutta Joukowski theorem; lift generation; thin airfoil theory; wing theory; induced drag; qualitative treatment of low aspect ratio wings.

Viscous Flows: Flow separation, introduction to turbulence, transition, structure of a turbulentboundary layer.

Compressible Flows: Dynamics & Thermodynamics of I-D flow, isentropic flow, normal shock, oblique shock, Prandtl-Meyer flow, flow in nozzles and diffusers, inviscid flow in a c-d nozzle, flow in diffusers. subsonic and supersonic airfoils, compressibility effects on lift and drag, critical and drag divergence Mach number, wave drag.

Wind Tunnel Testing: Measurement and visualisation techniques.

STRUCTURES

Stress and Strain: Equations of equilibrium, constitutive law, strain-displacement relationship, compatibility equations, plane stress and strain, Airy's stress function.

Flight Vehicle Structures: Characteristics of aircraft structures and materials, torsion, bending and flexural shear. Flexural shear flow in thin-walled sections. Buckling. Failure theories. Loads on aircraft.

Structural Dynamics: Free and forced vibration of discrete systems. Damping and resonance.

Dynamics of continuous systems.

PROPULSION

Thermodynamics of Aircraft Gas Turbine engines, thrust and thrust augmentation.

Turbomachinery: Axial compressors and turbines, centrifugal pumps and compressors. Aerothermodynamics of non rotating propulsion components: Intakes, combustor and nozzle. Thermodynamics of ramjets and scramjets. Elements of rocket propulsion.

AG - AGRICULTURAL ENGINEERING

ENGINEERING MATHEMATICS:

Linear Algebra: Matrices and Determinants, Systems of linear equations, Eigen values and eigen vectors.

Calculus: Limit, continuity and differentiability; Partial Derivatives; Maxima and minima; Sequences and series; Test for convergence; Fourier series.

Vector Calculus: Gradient; Divergence and Curl; Line; surface and volume integrals; Stokes, Gauss and Green's theorems.

Diferential Equations: Linear and non-linear first order ODEs; Higher order linear ODEs with constant coefficients; Cauchy's and Euler's equations; Laplace transforms; PDEs - Laplace, heat and wave equations.

Probability and Statistics: Mean, median, mode and standard deviation; Random variables; Poisson, normal and binomial distributions; Correlation and regression analysis.

Numerical Methods: Solutions of linear and non-linear algebraic equations; integration of trapezoidal and Simpson's rule; single and multi-step methods for differential equations.

FARM MACHINERY AND POWER:

Sources of power on the farm-human, animal, mechanical, electrical, wind, solar and biomass; design and selection of machine elements - gears, pulleys, chains and sprockets and belts; overload safety devices used in farm machinery; measurement of force, torque, speed, displacement and acceleration on machine elements.

Soil tillage; forces acting on a tillage tool; hitch systems and hitching of tillage implements; functional requirements, principles of working, construction and operation of manual, animal and power operated equipment for tillage. sowing, planting, fertilizer application, inter-cultivation, spraying, mowing, chaff cutting, harvesting, threshing and transport; testing of agricultural machinery and equipment; calculation of performance parameters -field capacity, efficiency, application rate and losses; cost analysis of implements and tractors.

Thermodynamic principles of I.C. engines; I.C. engine cycles; engine components; fuels and combustion; lubricants and their properties; I.C. engine systems - fuel, cooling, lubrication, ignition, electrical, intake and exhaust; selection, operation, maintenance and repair of I.C. engines; power efficiencies and measurement; calculation of power, torque, fuel consumption, heat load and power losses.

Tractors and power tillers - type, selection, maintenance and repair; tractor clutches and brakes; power transmission systems - gear trains, differential, final drives and power take-off; mechanics of tractor chassis; traction theory; three point hitches- free link and restrained link operations; mechanical steering and hydraulic control systems used in tractors; human engineering and safety in tractor design; tractor tests and performance.

SOIL AND WATER CONSERVATION ENGINEERING:

Ideal and real fluids, properties of fluids; hydrostatic pressure and its measurement; hydrostatic forces on plane and curved surface; continuity equation; Bernoulli's theorem; laminar and turbulent flow in pipes, Darcy-Weisbach and Hazen-Williams equations, Moody's diagram; flow through orifices and notches; flow in open channels.

Engineering properties of soils, fundamental definitions and relationships; index properties of soils; permeability and seepage analysis; shear strength, Mohr's circle of stresses; active and passive earth pressures; stability of slopes.

Hydrological cycle; precipitation measurement, analysis of precipitation data; abstraction from precipitation; runoff; hydrograph analysis, unit hydrograph theory and application; stream flow measurement; flood routing, hydrological reservoir and channel routing.

Mechanics of soil erosion, factors affecting erosion; soil loss estimation; biological and engineering measures to control erosion, terraces and bunds; vegetative waterways; gully control structures, drop, drop inlet and chute spillways; farm ponds; earthen dams; principles of watershed management.

Water requirement of crops; consumptive use and evapo-transpiration; irrigation scheduling; irrigation efficiencies; design of prismatic and silt loaded channels; methods of irrigation water application; design and evaluation of irrigation methods; drainage coefficient; surface and subsurface drainage systems; leaching requirement and salinity control; irrigation and drainage water quality; classification of pumps; pump characteristics; pump selection; types of aquifer; evaluation of aquifer properties; well hydraulics; ground water recharge.

AGRICULTURAL PROCESSING AND FOOD ENGINEERING:

Steady state heat transfer in conduction, convection and radiation; transient heat transfer in simple geometry; condensation and boiling heat transfer; working principles of heat exchangers; diffusive and convective mass transfer; simultaneous heat and mass transfer in agricultural processing operations.

Material and energy balances in food processing systems; water activity, sorption and desorption isotherms; centrifugal separation of solids, liquids and gases; kinetics of microbial death - pasteurisation and sterilization of liquid foods; preservation of food by cooling and freezing; psychrometry - properties of air-vapour mixture; concentration and dehydration of liquid foods - evaporators, tray, drum and spray dryers.

Mechanics and energy requirement in size reduction of granular solids; particle size analysis for comminuted solids; size separation by screening; fluidisation of granular solids; cleaning and grading efficiency and effectiveness of grain cleaners; conditioning and hydrothermal treatments for grains; dehydration of food grains; processes and machines for processing of cereals, pulses and oilseeds; design considerations for grain silos.

AR - ARCHITECTURE AND PLANNING

City planning: Historical development of cities; principles of city planning; new towns; survey methods, site planning, planning regulations and building bye-laws.

Housing: Concept of shelter; housing policies and design; community planning; role of government agencies; finance and management.

Landscape Design: Principles of landscape design and site planning; history and landscape styles; landscape elements and materials; planting design.

Computer Aided Design: Application of computers in architecture and planning; understanding elements of hardware and software; computer graphics; programming languages - C and Visual Basic and usage of packages such as AutoCAD.

Environmental and Building Science: Elements of environmental science; ecological principles concerning environment; role of micro-climate in design; climatic control through design elements; thermal comfort; elements of solar architecture; principles of lighting and illumination; basic principles of architectural acoustics; air pollution, noise pollution and their control.

Visual and Urban Design: Principles of visual composition; proportion, scale, rhythm, symmetry, harmony, balance, form and colour; sense of place and space, division of space; focal point, vista, imageability, visual survey.

History of Architecture: Indian - Indus valley, Vedic, Buddhist, Indo-Aryan, Dravidian and Mughal periods; European - Egyptian, Greek, Roman, medieval and renaissance periods.

Development of Contemporary Architecture: Architectural developments and impacts on society since industrial revolution; influence of modern art on architecture; works of national and international architects; post modernism in architecture.

Building Services: Water supply, Sewerage and Drainage systems; Sanitary fittings and fixtures; principles of electrification of buildings; elevators, their standards and uses; air-conditioning systems; fire fighting systems.

Building Construction and Management: Building construction techniques, methods and details; building systems and prefabrication of building elements; principles of modular coordination; estimation, specification, valuation, professional practice; project management, PERT, CPM.

Materials and Structural Systems: Behavioural characteristics of all types of building materials e.g. mud, timber, bamboo, brick, concrete, steel, glass, FRP; principles of strength of materials; design of structural elements in wood, steel and RCC; elastic and limit state design; complex structural systems; principles of pre-stressing.

Planning Theory: Planning process; multilevel planning; comprehensive planning; central place theory; settlement pattern; land use and land utilization.

Techniques of Planning: Planning surveys; Preparation of urban and regional structure plans, development plans, action plans; site planning principles and design; statistical methods; application of remote sensing techniques in urban and regional planning.

Traffic and Transportation Planning: Principles of traffic engineering and transportation planning; methods of conducting surveys; design of roads, intersections and parking areas; hierarchy of roads and levels of services; traffic and transport management in urban areas; traffic safety and traffic laws; public transportation planning; modes of transportation.

Services and Amenities: Principles and design of water supply systems, sewerage systems, solid waste disposal systems, power supply and communication systems; Health, education, recreation and demography related standards at various levels of the settlements.

Development Administration and Management: Planning laws; development control and zoning regulations; laws relating to land acquisition; development enforcements, land ceiling; regional and urban plan preparations; planning and municipal administration; taxation, revenue resources and fiscal management; public participation and role of NGO.

CE - CIVIL ENGINEERING

ENGINEERING MATHEMATICS

Linear Algebra: Matrix algebra, Systems of linear equations, Eigen values and eigenvectors.

Calculus: Functions of single variable, Limit, continuity and differentiability, Mean value theorems, Evaluation of definite and improper integrals, Partial derivatives, Total derivative, Maxima and minima, Gradient, Divergence and Curl, Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green's theorems.

Differential equations: First order equations (linear and nonlinear), Higher order linear differential equations with constant coefficients, Cauchy's and Euler's equations, Initial and boundary value problems, Laplace transforms, Solutions of one dimensional heat and wave equations and Laplace equation.

Complex variables: Analytic functions, Cauchy's integral theorem, Taylor and Laurent series.

Probability and Statistics: Definitions of probability and sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Poisson, Normal and Binomial distributions.

Numerical Methods: Numerical solutions of linear and non-linear algebraic equations Integration by trapezoidal and Simpson's rule, single and multi-step methods for differential equations.

STRUCTURAL ENGINEERING

Mechanics: Bending moments and shear forces in statically determinate beams; simple stress and strain: relationship; stress and strain in two dimensions, principal stresses, stress transformation, Mohr's circle; simple bending theory; flexural shear stress; thin-walled pressure vessels; uniform torsion.

Structural Analysis: Analysis of statically determinate trusses, arches and frames; displacements in statically determinate structures and analysis of statically indeterminate structures by force/energy methods; analysis by displacement methods (slope-deflection and moment-distribution methods); influence lines for determinate and indeterminate structures; basic concepts of matrix methods of structural analysis.

Concrete Structures: Basic working stress and limit states design concepts; analysis of ultimate load capacity and design of members subject to flexure, shear, compression and torsion (beams, columns and isolated footings); basic elements of prestressed concrete: analysis of beam sections at transfer and service loads.

Steel Structures: Analysis and design of tension and compression members, beams and beam-columns, column bases; connections - simple and eccentric, beam-column connections, plate girders and trusses; plastic analysis of beams and frames.

GEOTECHNICAL ENGINEERING

Soil Mechanics: Origin of soils; soil classification; three-phase system, fundamental definitions, relationship and inter-relationships; permeability and seepage; effective stress principle: consolidation, compaction; shear strength.

Foundation Engineering: Sub-surface investigation - scope, drilling bore holes, sampling, penetrometer tests, plate load test; earth pressure theories, effect of water table, layered soils; stability of slopes - infinite slopes, finite slopes; foundation types - foundation design requirements; shallow foundations; bearing capacity, effect of shape, water table and other factors, stress distribution, settlement analysis in sands and clays; deep foundations - pile types, dynamic and static formulae, load capacity of piles in sands and clays.

WATER RESOURCES ENGINEERING

Fluid Mechanics and Hydraulics: Hydrostatics, applications of Bernoulli equation, laminar and turbulent flow in pipes, pipe networks; concept of boundary layer and its growth; uniform flow, critical flow and gradually varied flow in channels, specific energy concept, hydraulic jump; forces on immersed bodies; flow measurement in channels; tanks and pipes; dimensional analysis and hydraulic modeling. Applications of momentum equation, potential flow, kinematics of flow; velocity triangles and specific speed of pumps and turbines.

Hydrology: Hydrologic cycle; rainfall; evaporation infiltration, unit hydrographs, flood estimation, reservoir design, reservoir and channel routing, well hydraulics.

Irrigation: Duty, delta, estimation of evapo-transpiration; crop water requirements; design of lined and unlined canals; waterways; head works, gravity dams and Ogee spillways. Designs of weirs on permeable foundation, irrigation methods.

ENVIRONMENTAL ENGINEERING

Water requirements; quality and standards, basic unit processes and operations for water treatment, distribution of water. Sewage and sewerage treatment: quantity and characteristic of waste water sewerage; primary and secondary treatment of waste water; sludge disposal; effluent discharge standards.

TRANSPORTATION ENGINEERING

Highway planning; geometric design of highways; testing and specifications of paving materials; design of flexible and rigid pavements.

CH - CHEMICAL ENGINEERING

ENGINEERING MATHEMATICS

Linear Algebra: Matrix algebra, Systems of linear equations, Eigen values and eigenvectors.

Calculus: Functions of single variable, Limit, continuity and differentiability, Mean value theorems, Evaluation of definite and improper integrals, Partial derivatives, Total derivative, Maxima and minima, Gradient, Divergence and Curl, Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green's theorems.

Differential equations: First order equations (linear and nonlinear), Higher order linear differential equations with constant coefficients, Cauchy's and Euler's equations, Initial and boundary value problems, Laplace transforms, Solutions of one dimensional heat and wave equations and Laplace equation.

Complex variables: Analytic functions, Cauchy's integral theorem, Taylor and Laurent series.

Probability and Statistics: Definitions of probability and sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Poisson, Normal and Binomial distributions.

Numerical Methods: Numerical solutions of linear and non-linear algebraic equations Integration by trapezoidal and Simpson's rule, single and multi-step methods for differential equations.

CHEMICAL ENGINEERING

Process Calculations and Thermodynamics: Laws of conservation of mass and energy; use of tie components; recycle, bypass and purge calculations; degree of freedom analysis.

First and Second laws of thermodynamics and their applications; equations of state and thermodynamic properties of real systems; phase equilibria; fugacity, excess properties and correlations of activity coefficients; chemical reaction equilibria.

Fluid Mechanics and Mechanical Operations: Fluid statics, Newtonian and non-Newtonian fluids, Bernoulli equation, Macroscopic friction factors, energy balance, dimensional analysis, shell balances, flow through pipeline systems, flow meters, pumps and compressors, packed and fluidized beds, elementary boundary layer theory, size reduction and size separation; free and hindered settling; centrifuge and cyclones; thickening and classification, filtration, mixing and agitation; conveying of solids.

Heat Transfer: Conduction, convection and radiation, heat transfer coefficients, steady and unsteady heat conduction, boiling, condensation and evaporation; types of heat exchangers and evaporators and their design.

Mass Transfer: Fick's law, molecular diffusion in fluids, mass transfer coefficients, film, penetration and surface renewal theories; momentum, heat and mass transfer analogies; stagewise and continuous contacting and stage efficiencies; HTU & NTU concepts design and operation of equipment for distillation, absorption, leaching, liquid-liquid extraction, crystallization, drying, humidification, dehumidification and adsorption.

Chemical Reaction Engineering: Theories of reaction rates; kinetics of homogeneous reactions, interpretation of kinetic data, single and multiple reactions in ideal reactors, non-ideal reactors; residence time; non-isothermal reactors; kinetics of heterogeneous catalytic reactions; diffusion effects in catalysis.

Instrumentation and Process Control: Measurement of process variables; sensors, transducers and their dynamics, dynamics of simple systems, dynamics such as CSTRs, transfer functions and responses of simple systems, process reaction curve, controller modes (P, PI, and PID); control valves; analysis of closed loop systems including stability, frequency response (including Bode plots) and controller tuning, cascade, feed forward control.

Plant Design and Economics: Design and sizing of chemical engineering equipment such as compressors, heat exchangers, multistage contactors; principles of process economics and cost estimation including total annualized cost, cost indexes, rate of return, payback period, discounted cash flow, optimization in Design.

Chemical Technology: Inorganic chemical industries; sulfuric acid, NaOH, fertilizers (Ammonia, Urea, SSP and TSP); natural products industries (Pulp and Paper, Sugar, Oil, and Fats); petroleum refining and petrochemicals; polymerization industries; polyethylene, polypropylene, PVC and polyester synthetic fibers.

CS - COMPUTER SCIENCE AND ENGINEERING

ENGINEERING MATHEMATICS

Mathematical Logic: Propositional Logic; First Order Logic.

Probability: Conditional Probability; Mean, Median, Mode and Standard Deviation; Random Variables; Distributions; uniform, normal, exponential, Poisson, Binomial.

Set Theory & Algebra: Sets; Relations; Functions; Groups; Partial Orders; Lattice; Boolean Algebra.

Combinatorics: Permutations; Combinations; Counting; Summation; generating functions; recurrence relations; asymptotics.

Graph Theory: Connectivity; spanning trees; Cut vertices & edges; covering; matching; independent sets; Colouring; Planarity; Isomorphism.

Linear Algebra: Algebra of matrices, determinants, systems of linear equations, Eigen values and Eigen vectors.

Numerical Methods: LU decomposition for systems of linear equations; numerical solutions of non linear algebraic equations by Secant, Bisection and Newton-Raphson Methods; Numerical integration by trapezoidal and Simpson's rules.

Calculus: Limit, Continuity & differentiability, Mean value Theorems, Theorems of integral calculus, evaluation of definite & improper integrals, Partial derivatives, Total derivatives, maxima & minima.

THEORY OF COMPUTATION

Formal Languages and Automata Theory: Regular languages and finite automata, Context free languages and Push-down automata, Recursively enumerable sets and Turing machines, Un-decidability;

Analysis of Algorithms and Computational Complexity: Asymptotic analysis (best, worst, average case) of time and space, Upper and lower bounds on the complexity of specific problems, NP-completeness.

COMPUTER HARDWARE

Digital Logic: Logic functions, Minimization, Design and synthesis of Combinational and Sequential circuits; Number representation and Computer Arithmetic (fixed and floating point);

Computer Organization: Machine instructions and addressing modes, ALU and Data-path, hardwired and micro-programmed control, Memory interface, I/O interface (Interrupt and DMA mode), Serial communication interface, Instruction pipelining, Cache, main and secondary storage.

SOFTWARE SYSTEMS

Data structures: Notion of abstract data types, Stack, Queue, List, Set, String, Tree, Binary search tree, Heap, Graph;

Programming Methodology: C programming, Program control (iteration, recursion, Functions), Scope, Binding, Parameter passing, Elementary concepts of Object oriented, Functional and Logic Programming;

Algorithms for problem solving: Tree and graph traversals, Connected components, Spanning trees, Shortest paths; Hashing, Sorting, Searching; Design techniques (Greedy, Dynamic Programming, Divide-and-conquer);

Compiler Design: Lexical analysis, Parsing, Syntax directed translation, Runtime environment, Code generation, Linking (static and dynamic); Operating Systems: Classical concepts (concurrency, synchronization, deadlock), Processes, threads and Inter-process communication, CPU scheduling, Memory management, File systems, I/O systems, Protection and security.

Databases: Relational model (ER-model, relational algebra, tuple calculus), Database design (integrity constraints, normal forms), Query languages (SQL), File structures (sequential files, indexing, B+ trees), Transactions and concurrency control;

Computer Networks: ISO/OSI stack, sliding window protocol, LAN Technologies (Ethernet, Token ring), TCP/UDP, IP, Basic concepts of switches, gateways, and routers.

CH - CHEMISTRY

PHYSICAL CHEMISTRY

Structure: Quantum theory - principles and techniques; applications to particle in a box, harmonic oscillator, rigid rotor and hydrogen atom; valence bond and molecular orbital theories and Huckel approximation, approximate techniques: variation and perturbation; symmetry, point groups; rotational, vibrational, electronic, NMR and ESR spectroscopy.

Equilibrium: First law of thermodynamics, heat, energy and work; second law of thermodynamics and entropy; third law and absolute entropy; free energy; partial molar quantities; ideal and non-ideal solutions; phase transformation: phase rule and phase diagrams- one, two, and three component systems; activity, activity coefficient, fugacity and fugacity coefficient ; chemical equilibrium, response of chemical equilibrium to temperature and pressure; colligative properties; kinetic theory of gases; thermodynamics of electrochemical cells; standard electrode potentials: applications - corrosion and energy conversion; molecular partition function (translational, rotational, vibrational and electronic).

Kinetics: Rates of chemical reactions, theories of reaction rates, collision and transition state theory; temperature dependence of chemical reactions; elementary reactions, consecutive elementary reactions; steady state approximation, kinetics of photochemical reactions and free radical polymerization, homogenous and heterogeneous catalysis.

INORGANIC CHEMISTRY

Non-Transition Elements: General characteristics, structure and reactions of simple and industrially important compounds, boranes, carboranes, silicates, silicones, diamond and graphite; hydrides, oxides and oxoacids of N, P, S and halogens; boron nitride, borazines and phosphazenes; xenon compounds. Shapes of molecules, hard-soft acid base concept.

Transition Elements: General characteristics of d and f block elements; coordination chemistry: structure and isomerism, stability, theories of metal-ligand bonding (CFT and LFT), electronic spectra and magnetic properties of transition metal complexes and lanthanides; metal carbonyls, metal-metal bonds and metal atom clusters, metallocenes; transition metal complexes with bonds to hydrogen, alkyls, alkenes, and arenes; metal carbenes; use of organometallic compounds as catalysts in organic synthesis; mechanisms of substitution and electron transfer reactions of coordination complexes. Role of metals with special reference to Na, K, Mg, Ca, Fe, Co, Zn, and Mo in biological systems.

Solids: Crystal systems and lattices, Miller planes, crystal packing, crystal defects; Bragg's Law; ionic crystals, band theory, metals and semiconductors. Spinels.

Instrumental methods of analysis: atomic absorption, UV-visible spectrometry, chromatographic and electro-analytical methods.

ORGANIC CHEMISTRY

Synthesis, reactions and mechanisms involving the following: Alkenes, alkynes, arenes, alcohols, phenols, aldehydes, ketones, carboxylic acids and their derivatives; halides, nitro compounds and amines; stereochemical and conformational effects on reactivity and specificity; reactions with diborane and peracids. Michael reaction, Robinson annulation, reactivity umpolung, acyl anion equivalents; molecular rearrangements involving electron deficient atoms.

Photochemistry: Basic principles, photochemistry of olefins, carbonyl compounds, arenes, photo oxidation and reduction.

Pericyclic reactions: Cycloadditions, electrocyclic reactions, sigmatropic reactions; Woodward-Hoffmann rules.

Heterocycles: Structural properties and reactions of furan, pyrrole, thiophene, pyridine, indole.

Biomolecules: Structure, properties and reactions of mono- and di-saccharides, physico-chemical properties of amino acids, structural features of proteins and nucleic acids.

Spectroscopy: Principles and applications of IR, UV-visible, NMR and mass spectrometry in the determination of structures of organic compounds.

EC - ELECTRONICS AND COMMUNICATION ENGINEERING

ENGINEERING MATHEMATICS

Linear Algebra: Matrix Algebra, Systems of linear equations, Eigen values and eigen vectors.

Calculus: Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier series. Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green's theorems.

Differential equations: First order equation (linear and nonlinear), Higher order linear differential equations with constant coefficients, Method of variation of parameters, Cauchy's and Euler's equations, Initial and boundary value problems, Partial Differential Equations and variable separable method.

Complex variables: Analytic functions, Cauchy's integral theorem and integral formula, Taylor's and Laurent' series, Residue theorem, solution integrals.

Probability and Statistics: Sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Discrete and continuous distributions, Poisson, Normal and Binomial distribution, Correlation and regression analysis.

Numerical Methods: Solutions of non-linear algebraic equations, single and multi-step methods for differential equations.

Transform Theory: Fourier transform, Laplace transform, Z-transform.

ELECTRONICS & COMMUNICATION ENGINEERING

Networks: Network graphs: matrices associated with graphs; incidence, fundamental cut set and fundamental circuit matrices. Solution methods: nodal and mesh analysis. Network theorems: superposition, Thevenin and Norton's maximum power transfer, Wye-Delta transformation. Steady state sinusoidal analysis using phasors. Linear constant coefficient differential equations; time domain analysis of simple RLC circuits, Solution of network equations using Laplace transform: frequency domain analysis of RLC circuits. 2-port network parameters: driving point and transfer functions. State equations for networks.

Electronic Devices: Energy bands in silicon, intrinsic and extrinsic silicon. Carrier transport in silicon: diffusion current, drift current, mobility, resistivity. Generation and recombination of carriers. p-n junction diode, Zener diode, tunnel diode, BJT, JFET, MOS capacitor, MOSFET, LED, p-I-n and avalanche photo diode, LASERs. Device technology: integrated circuits fabrication process, oxidation, diffusion, ion implantation, photolithography, n-tub, p-tub and twin-tub CMOS process.

Analog Circuits: Equivalent circuits (large and small-signal) of diodes, BJTs, JFETs, and MOSFETs. Simple diode circuits, clipping, clamping, rectifier. Biasing and bias stability of transistor and FET amplifiers. Amplifiers: single-and multi-stage, differential, operational, feedback and power. Analysis of amplifiers; frequency response of amplifiers. Simple op-amp circuits. Filters. Sinusoidal oscillators; criterion for oscillation; single-transistor and op-amp configurations. Function generators and wave-shaping circuits. Power supplies.

Digital circuits: Boolean algebra, minimization of Boolean functions; logic gates digital IC families (DTL, TTL, ECL, MOS, CMOS). Combinational circuits: arithmetic circuits, code converters, multiplexers and decoders. Sequential circuits: latches and flip-flops, counters and shift-registers. Sample and hold circuits, ADCs, DACs. Semiconductor memories. Microprocessor(8085): architecture, programming, memory and I/O interfacing.

Signals and Systems: Definitions and properties of Laplace transform, continuous-time and discrete-time Fourier series, continuous-time and discrete-time Fourier Transform, z-transform. Sampling theorems. Linear Time-Invariant (LTI) Systems: definitions and properties; casuality, stability, impulse response, convolution, poles and zeros frequency response, group delay, phase delay. Signal transmission through LTI systems. Random signals and noise: probability, random variables, probability density function, autocorrelation, power spectral density.

Controls Systems: Basic control system components; block diagrammatic description, reduction of block diagrams. Open loop and closed loop (feedback) systems and stability analysis of these systems. Signal flow graphs and their use in determining transfer functions of systems; transient and steady state analysis of LTI control systems and frequency response. Tools and techniques for LTI control system analysis: root loci, Routh-Hurwitz criterion, Bode and Nyquist plots. Control system compensators: elements of lead and lag compensation, elements of Proportional-Integral-Derivative(PID) control. State variable representation and solution of state equation of LTI control systems.

Communications: Analog communication systems: amplitude and angle modulation and demodulation systems, spectral analysis of these operations, superheterodyne receivers; elements of hardware, realizations of analog communication systems; signal-to-noise ratio (SNR) calculations for amplitude modulation (AM) and frequency modulation (FM) for low noise conditions. Digital communication systems: pulse code modulation (PCM), differential pulse code modulation (DPCM), delta modulation (DM); digital modulation schemes-amplitude, phase and frequency shift keying schemes (ASK, PSK, FSK), matched filter receivers, bandwith consideration and probability of error calculations for these schemes.

Electromagnetics: Elements of vector calculus: divergence and curl; Gauss' and Stokes' theorems, Maxwell's equations: differential and integral forms. Wave equation, Poynting vector. Plane waves: propagation through various media; reflection and refraction; phase and group velocity; skin depth. Transmission lines: characteristic impedance; impedance transformation; Smith chart; impedance matching; pulse excitation. Waveguides: modes in rectangular waveguides; boundary conditions; cut-off frequencies; dispersion relations. Antennas: Dipole antennas; antenna arrays; radiation pattern; reciprocity theorem, antenna gain.

EE - ELECTRICAL ENGINEERING

ENGINEERING MATHEMATICS

Linear Algebra: Matrix Algebra, Systems of linear equations, Eigen values and eigen vectors.

Calculus: Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier series. Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green's theorems.

Differential equations: First order equation (linear and nonlinear), Higher order linear differential equations with constant coefficients, Method of variation of parameters, Cauchy's and Euler's equations, Initial and boundary value problems, Partial Differential Equations and variable separable method.

Complex variables: Analytic functions, Cauchy's integral theorem and integral formula, Taylor's and Laurent' series, Residue theorem, solution integrals.

Probability and Statistics: Sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Discrete and continuous distributions, Poisson, Normal and Binomial distribution, Correlation and regression analysis.

Numerical Methods: Solutions of non-linear algebraic equations, single and multi-step methods for differential equations.

Transform Theory: Fourier transform, Laplace transform, Z-transform.

ELECTRICAL ENGINEERING

Electrical Circuits and Fields: Network graph, KCL, KVL, node/ cut set, mesh/ tie set analysis, transient response of d.c. and a.c. networks; sinusoidal steady-state analysis; resonance in electrical circuits; concepts of ideal voltage and current sources, network theorems, driving point, immittance and transfer functions of two port networks, elementary concepts of filters; three phase circuits; Fourier series and its application; Gauss theorem, electric field intensity and potential due to point, line, plane and spherical charge distribution, dielectrics, capacitance calculations for simple configurations; Ampere's and Biot-Savart's law, inductance calculations for simple configurations.

Electrical Machines: Single phase transformer - equivalent circuit, phasor diagram, tests, regulation and efficiency; three phase transformers - connections, parallel operation; auto transformer and three-winding transformer; principles of energy conversion, windings of rotating machines: D. C. generators and motors - characteristics, starting and speed control, armature reaction and commutation; three phase induction motors-performance characteristics, starting and speed control; single-phase induction motors; synchronous generators-performance, regulation, parallel operation; synchronous motors - starting, characteristics, applications, synchronous condensers; fractional horse power motors; permanent magnet and stepper motors.

Power Systems: Electric power generation - thermal, hydro, nuclear; transmission line parameters; steady-state performance of overhead transmission lines and cables and surge propagation; distribution systems, insulators, bundle conductors, corona and radio interference effects; per-unit quantities; bus admittance and impedance matrices; load flow; voltage control and power factor correction; economic operation; symmetrical components, analysis of symmetrical and unsymmetrical faults; principles of over current, differential and distance protections; concept of solid state relays and digital protection; circuit breakers; concept of system stability-swing curves and equal area criterion; basic concepts of HVDC transmission.

Control Systems: Principles of feedback; transfer function; block diagrams: steady-state errors; stability-Routh and Nyquist criteria; Bode plots; compensation; root loci; elementary state variable formulation; state transition matrix and response for Linear Time Invariant systems.

Electrical and Electronic Measurements: Bridges and potentiometers, PMMC, moving iron, dynamometer and induction type instruments; measurement of voltage, current, power, energy and power factor; instrument transformers; digital voltmeters and multimeters; phase, time and frequency measurement; Q-meter, oscilloscopes, potentiometric recorders, error analysis.

Analog and Digital Electronics: Characteristics of diodes, BJT, FET, SCR; amplifiers-biasing, equivalent circuit and frequency response; oscillators and feedback amplifiers, operational amplifiers- characteristics and applications; simple active filters; VCOs and timers; combinational and sequential logic circuits, multiplexer, Schmitt trigger, multivibrators, sample and hold circuits, A/D and D/A converters; microprocessors and their applications.

Power Electronics and Electric Drives: Semiconductor power devices-diodes, transistors, thyristors, triacs, GTOs, MOSFETs and IGBTs - static characteristics and principles of operation; triggering circuits; phase control rectifiers; bridge converters-fully controlled and half controlled; principles of choppers and inverters, basic concepts of adjustable speed dc and ac drives.

GG - GEOLOGY AND GEOPHYSICS

PART - I

Earth and planetary system; size, shape, internal structure and composition of the earth; atmosphere and greenhouse effect; isostasy; elements of seismology; continents and continental processes; physical oceanography; palaeomagnetism, continental drift plate tectonics, geothermal energy.

Weathering; soil formation; action of river, wind and glacier; oceans and oceanic features; earthquakes, volcanoes, orogeny and mountain building; elements of structural geology; crystallography; classification, composition and properties of minerals and rocks; engineering properties of rocks and soils, role of geology in the construction of engineering structures.

Processes of ore formation, occurrence and distribution of ores on land and on ocean floor; coal and petroleum resources in India; ground water geology including well hydraulics, geological time scale and geochronology; stratigraphic principles and stratigraphy of India; basics concepts of gravity, magnetic and electrical prospecting for ores and ground water.

PART - IIA: GEOLOGY

Crystal symmetry, forms, twinning; crystal chemistry; optical mineralogy, classification of minerals, diagnostic properties of rock minerals.

Mineralogy, structure, texture and classification of igneous, sedimentary and metamorphic rock, their origin and evolution; application of thermodynamics; structure and petrology of sedimentary rocks; sedimentary processes and environments, sedimentary facies, basin studies; basement cover relationship;

Primary and secondary structures; geometry and genesis of folds, faults, joints, unconformities, cleavage, schistosity and lineation; methods of projection. Tectonites and their significance; shear zone; superposed folding.

Morphology, classification and geological significance of important invertebrates, vertebrates, microfossils and palaeoflora; stratigraphic principles and Indian stratigraphy; geomorphic processes and agents; development and evolution of landforms; slope and drainage; processes on deep oceanic and near-shore regions; quantitative and applied geomorphology; air photo interpretation and remote sensing; chemical and optical properties of ore minerals; formation and localization of ore deposits; prospecting and exploration of economic minerals; coal and petroleum geology; origin and distribution of mineral and fuel deposits in India; ore dressing and mineral economics.

Cosmic abundance; meteorites; geochemical evolution of the earth; geochemical cycles; distribution of major, minor and trace elements; isotope geochemistry; geochemistry of waters including solution equilibria and water rock interaction.

Engineering properties of rocks and soils; rocks as construction material; geology of dams, tunnels and excavation sites; natural hazards; the fly ash problem; ground water geology and exploration; water quality; impact of human activity; Remote sensing techniques for the interpretation of landforms and resource management.

PART - II B: GEOPHYSICS

The earth as a planet; different motions of the earth; gravity filed of the earth and its shape; geochronology; isostasy, seismology and interior of the earth; variation of density, velocity, pressure, temperature, electrical and magnetic properties inside the earth; earthquakes-causes and measurements; zonation and seismic hazards; geomagnetic field, palaeomagnetism; oceanic and continental lithosphere; plate tectonics; heat flow; upper and lower atmospheric phenomena.

Theories of scalar and vector potential fields; Laplace, Maxwell and Helmholtz equations for solution of different types of boundary value problems for Cartesian, cylindrical and spherical polar coordinates; Green's theorem; Image theory; integral equations and conformal transformations in potential theory; Eikonal equation and ray theory.

'G' and 'g' units of measurement, density of rocks, gravimeters, preparation, analysis and interpretation of gravity maps; derivative maps, analytical continuation; gravity anomaly type curves; calculation of mass.

Earth's magnetic field, units of measurement, magnetic susceptibility of rocks, magnetometers, corrections, preparation of magnetic maps, magnetic anomaly type curve, analytical continuation, interpretation and application; magnetic well logging.

Conduction of electricity through rocks, electrical conductivities of metals, metallic, non-metallic and rock forming minerals, D.C. resistivity units and methods of measurement, electrode configuration for sounding and profiling, application of filter theory, interpretation of resistivity field data, application; self potential origin, classification, field measurement, interpretation of induced polarization time frequency, phase domain; IP units and methods of measurement, interpretation and application; ground-water exploration.

Origin of electromagnetic field elliptic polarization, methods of measurement for different source-receiver configuration components in EM measurements, interpretation and applications; earth's natural electromagnetic field, tellurics, magneto-tellurics; geomagnetic depth sounding principles, methods of measurement, processing of data and interpretation.

Seismic methods of prospecting: Reflection, refraction and CDP surveys; land and marine seismic sources, generation and propagation of elastic waves, velocity increasing with depth, geophones, hydrophones, recording instruments (DFS), digital formats, field layouts, seismic noises and noise profile analysis, optimum geophone grouping, noise cancellation by shot and geophone arrays, 2D and 3D seismic data acquisition and processing, CDP stacking charts, binning, filtering, dip-moveout, static and dynamic corrections, deconvolution, migration, signal processing, Fourier and Hilbert transforms, attribute analysis, bright and dim spots, seismic stratigraphy, high resolution seismics, VSP.

Principles and techniques of geophysical well-logging, SP, resistivity, induction, micro gamma ray, neutron, density, sonic, temperature, dip meter, caliper, nuclear magnetic, cement bond logging. Quantitative evaluation of formations from well logs; well hydraulics and application of geophysical methods for groundwater study; application of bore hole geophysics in ground water, mineral and oil exploration. Remote sensing techniques and application of remote sensing methods in geophysics.

IN - INSTRUMENTATION ENGINEERING

ENGINEERING MATHEMATICS

Linear Algebra: Matrix Algebra, Systems of linear equations, Eigen values and eigen vectors.

Calculus: Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier series. Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green's theorems.

Differential equations: First order equation (linear and nonlinear), Higher order linear differential equations with constant coefficients, Method of variation of parameters, Cauchy's and Euler's equations, Initial and boundary value problems, Partial Differential Equations and variable separable method.

Complex variables: Analytic functions, Cauchy's integral theorem and integral formula, Taylor's and Laurent' series, Residue theorem, solution integrals.

Probability and Statistics: Sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Discrete and continuous distributions, Poisson, Normal and Binomial distribution, Correlation and regression analysis.

Numerical Methods: Solutions of non-linear algebraic equations, single and multi-step methods for differential equations.

Transform Theory: Fourier transform, Laplace transform, Z-transform.

INSTRUMENTATION ENGINEERING

Measurement Basics and Metrology: Static and dynamic characteristics of measurement systems. Standards and calibration. Error and uncertainty analysis, statistical analysis of data, and curve fitting. Linear and angular measurements; Measurement of straightness, flatness, roundness and roughness.

Transducers, Mechanical Measurements and Industrial Instrumentation: Transducers - elastic, resistive, inductive, capacitive, thermo-electric, piezoelectric, photoelectric, electro-mechanical, electro-chemical, and ultrasonic. Measurement of displacement, velocity (linear and rotational), acceleration, shock, vibration, force, torque, power, strain, stress, pressure, flow, temperature, humidity, viscosity, and density. energy storing elements, suspension systems and dampers.

Analog Electronics: Characteristics of diodes, BJTs, JFETs and MOSFETs; Diode circuits; Amplifiers: single and multi-stage, feedback; Frequency response; Operational amplifiers - design, characteristic, linear and non-linear applications: difference amplifiers; instrumentation amplifiers; precision rectifiers, I-to-V converters, active filters, oscillators, comparators, signal generators, wave shaping circuits.

Digital Electronics: Combinational logic circuits, minimization of Boolean functions; IC families (TTL, MOS, CMOS), arithmetic circuits, multiplexer and decoders. Sequential circuits: flip-flops, counters, shift registers. Schmitt trigger, timers, and multivibrators. Analog switches, multiplexers, S/H circuits. Analog-to-digital and digital-to-analog converters. Basics of computer organization and architecture. 8-bit microprocessor (8085), applications, memory, I/O interfacing, and microcontrollers.

Signals and Systems: Vectors and matrices; Fourier series; Fourier transforms; Ordinary differential equations. Impulse and frequency responses of first and second order systems. Laplace transform and transfer function, convolution and correlation. Amplitude and frequency modulations and demodulations. Discrete time systems, difference equations, impulse and frequency responses; Z-transforms and transfer functions; IIR and FIR filters.

Electrical and Electronic Measurements: Measurement of R, L and C; bridges and potentiometers. Measurement of voltage, current, power, power factor, and energy; Instrument transformers; Q meter, waveform analyzers. Digital volt-meters and multi-meters. Time, phase and frequency measurements; Oscilloscope. Noise and interference in instrumentation.

Control Systems & Process Control: Principles of feedback; transfer function, signal flow graphs. Stability criteria, Bode plots, root-loci, Routh and Nyquist criteria. Compensation techniques; State space analysis. System components: mechanical, hydraulic, pneumatic, electrical and electronic; Servos and synchros; Stepper motors. On-off, cascade, P, PI, PID and feed-forward controls. Controller tuning and general frequency response.

Analytical, Optical and Biomedical Instrumentation: Principles of spectrometry, UV, visible, IR mass spectrometry, X-ray methods; nuclear radiation measurements, gas, solid and semi conductor lasers and their characteristics, interferometers, basics of fibre optics, transducers in biomedical applications, cardiovascular system measurements, instrumentation for clinical laboratory.