GATE

Mathematics (MA)

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Linear Algebra: Finite dimensional vector spaces; Linear transformations and their matrix representations, rank; systems of linear equations, eigen values and eigen vectors, minimal polynomial, Cayley-Hamilton Theroem, diagonalisation, Hermitian, Skew-Hermitian and unitary matrices; Finite dimensional inner product spaces, Gram-Schmidt orthonormalization process, self-adjoint operators.

Complex Analysis: Analytic functions, conformal mappings, bilinear transformations; complex integration: Cauchy’s integral theorem and formula; Liouville’s theorem, maximum modulus principle; Taylor and Laurent’s series; residue theorem and applications for evaluating real integrals.

Real Analysis: Sequences and series of functions, uniform convergence, power series, Fourier series, functions of several variables, maxima, minima; Riemann integration, multiple integrals, line, surface and volume integrals, theorems of Green, Stokes and Gauss; metric spaces, completeness, Weierstrass approximation theorem, compactness; Lebesgue measure, measurable functions; Lebesgue integral, Fatou’s lemma, dominated convergence theorem.

Ordinary Differential Equations: First order ordinary differential equations, existence and uniqueness theorems, systems of linear first order ordinary differential equations, linear ordinary differential equations of higher order with constant coefficients; linear second order ordinary differential equations with variable coefficients; method of Laplace transforms for solving ordinary differential equations, series solutions; Legendre and Bessel functions and their orthogonality.

Algebra: Normal subgroups and homomorphism theorems, automorphisms; Group actions, Sylow’s theorems and their applications; Euclidean domains, Principle ideal domains and unique factorization domains. Prime ideals and maximal ideals in commutative rings; Fields, finite fields.

Functional Analysis: Banach spaces, Hahn-Banach extension theorem, open mapping and closed graph theorems, principle of uniform boundedness; Hilbert spaces, orthonormal bases, Riesz representation theorem, bounded linear operators.

Numerical Analysis: Numerical solution of algebraic and transcendental equations: bisection, secant method, Newton-Raphson method, fixed point iteration; interpolation: error of polynomial interpolation, Lagrange, Newton interpolations; numerical differentiation; numerical integration: Trapezoidal and Simpson rules, Gauss Legendrequadrature, method of undetermined parameters; least square polynomial approximation; numerical solution of systems of linear equations: direct methods (Gauss elimination, LU decomposition); iterative methods (Jacobi and Gauss-Seidel); matrix eigenvalue problems: power method, numerical solution of ordinary differential equations: initial value problems: Taylor series methods, Euler’s method, Runge-Kutta methods.

Partial Differential Equations: Linear and quasilinear first order partial differential equations, method of characteristics; second order linear equations in two variables and their classification; Cauchy, Dirichlet and Neumann problems; solutions of Laplace, wave and diffusion equations in two variables; Fourier series and Fourier transform and Laplace transform methods of solutions for the above equations.

Mechanics: Virtual work, Lagrange’s equations for holonomic systems, Hamiltonian equations.

Topology: Basic concepts of topology, product topology, connectedness, compactness, countability and separation axioms, Urysohn’s Lemma.

Probability and Statistics: Probability space, conditional probability, Bayes theorem, independence, Random variables, joint and conditional distributions, standard probability distributions and their properties, expectation, conditional expectation, moments; Weak and strong law of large numbers, central limit theorem; Sampling distributions, UMVU estimators, maximum likelihood estimators, Testing of hypotheses, standard parametric tests based on normal, X2 , t, F – distributions; Linear regression; Interval estimation.

Linear programming:Linear programming problem and its formulation, convex sets and their properties, graphical method, basic feasible solution, simplex method, big-M and two phase methods; infeasible and unbounded LPP’s, alternate optima; Dual problem and duality theorems, dual simplex method and its application in post optimality analysis; Balanced and unbalanced transportation problems, u -u method for solving transportation problems; Hungarian method for solving assignment problems.

Calculus of Variation and Integral Equations: Variation problems with fixed boundaries; sufficient conditions for extremum, linear integral equations of Fredholm and Volterra type, their iterative solutions.

Instrumentation Engineering (IN)

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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

Basics of Circuits and Measurement Systems: Kirchoff’s laws, mesh and nodal Analysis. Circuit theorems. One-port and two-port Network Functions. Static and dynamic characteristics of Measurement Systems.Error and uncertainty analysis.Statistical analysis of data and curve fitting.

Transducers, Mechanical Measurement and Industrial Instrumentation: Resistive, Capacitive, Inductive and piezoelectric transducers and their signal conditioning. Measurement of displacement, velocity and acceleration (translational and rotational), force, torque, vibration and shock.Measurement of pressure, flow, temperature and liquid level.Measurement of pH, conductivity, viscosity and humidity.

Analog Electronics: Characteristics of diode, BJT, JFET and MOSFET. Diode circuits.Transistors at low and high frequencies, Amplifiers, single and multi-stage. Feedbackamplifiers.Operational amplifiers, characteristics and circuit  configurations. Instrumentationamplifier. Precisionrectifier.V-to-I and I-to-V converter. Op- Amp based active filters. Oscillators and signal generators.

Digital Electronics: Combinational logic circuits, minimization of Boolean functions. IC families, TTL, MOS and CMOS. Arithmetic circuits. Comparators, Schmitt trigger, timers and mono-stable multi-vibrator. Sequential circuits, flip-flops, counters, shift registers. Multiplexer, S/H circuit. Analog-to-Digital and Digital-to-Analog converters. Basics of number system. Microprocessor applications, memory and input-output interfacing.Microcontrollers.

Signals, Systems and Communications: Periodic and aperiodic signals. Impulse response, transfer function and frequency response of first- and second order systems.Convolution, correlation and characteristics of linear time invariant systems.Discrete time system, impulse and frequency response. Pulse transfer function. IIR and FIR filters. Amplitude and frequency modulation and demodulation.Sampling theorem, pulse code modulation.Frequency and time division multiplexing. Amplitude shift keying, frequency shift keying and pulse shift keying for digital modulation.

Electrical and Electronic Measurements: Bridges and potentiometers, measurement of R, L and C. Measurements of voltage, current, power, power factor and energy. A.C & D.C current probes. Extension of instrument ranges. Q-meter and waveform analyzer.Digital voltmeter and multi-meter.Time, phase and frequency measurements.Cathode ray oscilloscope. Serial and parallel communication.Shielding and grounding.

Control Systems and Process Control: Feedback principles. Signal flow graphs. Transient Response, steady-state-errors.Routh and Nyquist criteria. Bode plot, root loci. Time delay systems.Phase and gain margin.State space representation of systems.Mechanical, hydraulic and pneumatic system components.Synchro pair, servo and step motors. On-off, cascade, P, P-I, P-I-D, feed forward and derivative controller, Fuzzy controllers.

Analytical, Optical and Biomedical Instrumentation: Mass spectrometry. UV, visible and IR spectrometry.X-ray and nuclear radiation measurements. Optical sources and detectors, LED, laser, Photo-diode, photo-resistor and their characteristics.Interferometers, applications in metrology. Basics of fiber optics. Biomedical instruments, EEG, ECG and EMG. Clinical measurements. Ultrasonic transducers and Ultrasonography. Principles of Computer Assisted Tomography.

Geology and Geophysics (GG)

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Part A: Common to Geology and Geophysics

Earth and Planetary system, size, shape, internal structure and composition of the earth; atmosphere and greenhouse effect; isostasy; elements of seismology; physical properties of the interior of the earth; continents and continental processes; physical oceanography; geomagnetism and paleomagnetism, continental drift, plate tectonics. Weathering; soil formation; action of river, wind, glacier and ocean; earthquakes, volcanism and orogeny. Basic structural geology, mineralogy and petrology.Geological time scale and geochronology; stratigraphic principles; major stratigraphic divisions of India. Engineering properties of rocks and soils. Ground water geology.Geological and geographical distribution of ore, coal and petroleum resources of India.

Introduction to remote sensing.Physical basis and applications of gravity, magnetic, electrical, electromagnetic, seismic and radiometric prospecting for oil, mineral and ground water; introductory well logging.

Part B – Section 1: Geology

Crystalsymmetry, forms, twinning; crystal chemistry; optical mineralogy, classification of minerals, diagnostic physical and optical properties of rock forming minerals.

Igneous rocks – classification, forms and textures, magmatic differentiation; phase diagrams and trace elements as monitors of magma evolutionary processes; mantle melting models and derivation and primary magmas. Metamorphism; controlling factors, metamorphic facies, grade and basic types; metamorphism of pelitic, mafic and impure carbonate rocks; role of fluids in metamorphism; metamorphic P-T-t paths and their tectonic significance; Igneous and metamorphic provinces of India; structure and petrology of sedimentary rocks; sedimentary processes and environments, sedimentary facies, basin analysis; association of igneous, sedimentary and metamorphic rocks with tectonic setting.

Stress, strain and material response; brittle and ductile deformation; 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; basement cover relationship.

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.

Oremineralogy and optical properties of ore minerals; ore forming processes vis-à-vis ore- rock association (magmatic, hydrothermal, sedimentary and metamorphogenic ores); oresand metamorphism; fluid inclusions as an ore genetic tool; prospecting and exploration of economic minerals; sampling, ore reserve estimation, geostatistics, mining methods. Coal and petroleum geology; origin and distribution of mineral and fuel deposits inIndia; marine geology and ocean resources; ore dressing and mineral economics.

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

Engineering properties of rocks and soils; rocks as construction materials; role of geology in the construction of engineering structures including dams, tunnels and excavation sites; natural hazards. Ground water geology – exploration, well hydraulics and water quality.

Basic principles of remote sensing – energy sources and radiation principles, atmospheric absorption, interaction of energy with earth’s surface, air-photo interpretation, multispectral remote sensing in visible, infrared, thermal IR and microwave regions, digital processing of satellite images. GIS – basic concepts, raster and vector mode operation.

Part B – Section 2: Geophysics

The earth as a planet; different motions of the earth; gravity field of the earth, Clairaut’s theorem, size and shape of earth; geochronology; seismology and interior of the earth; variation of density, velocity, pressure, temperature, electrical and magnetic properties of the earth; earthquakes-causes and measurements, magnitude and intensity, focal mechanisms, earthquake quantification, source characteristics, seismotectonics and seismic hazards; digital seismographs, geomagnetic field, paleomagnetism; oceanic and continental lithosphere; plate tectonics; heat flow; upper and lower atmospheric phenomena.

Scalar and vector potential fields; Laplace, Maxwell and Helmholtz equations for solution of different types of boundary value problems in Cartesian, cylindrical and spherical polar coordinates; Green’s theorem; Image theory; integral equations in potential theory; Eikonal equation and Ray theory. Basic concepts of forward and inverse problems of geophysics, Ill- posedness of inverse problems.

‘G’ and ‘g’ units of measurement, absolute and relative gravity measurements; Land, airborne, shipborne and bore-hole gravity surveys; various corrections in gravity data reduction – free air, Bouguer and isostatic anomalies; density estimates of rocks; regional and residual gravity separation; principle of equivalent stratum; upward and downward continuation; wavelength filtering; preparation and analysis of gravity maps; gravity anomalies and their interpretation – anomalies due to geometrical and irregular shaped bodies, depth rules, calculation of mass.

Earth’s magnetic field – elements, origin and units of measurement, magnetic susceptibility of rocks and measurements, magnetometers, Land, airborne and marine magnetic surveys, corrections, preparation of magnetic maps, upward and downward continuation, magnetic anomalies-geometrical shaped bodies, depth estimates, Image processing concepts in processing of magnetic anomaly maps; Interpretation of processed magnetic anomaly data.

Conduction of electricity through rocks, electrical conductivities of metals, non-metals, rock forming minerals and different rocks, concepts of D.C. resistivity measurement, various electrode configurations for resistivity sounding and profiling, application of filter theory, Type-curves over multi-layered structures, Dar-Zarrouck parameters, reduction of layers, coefficient of anisotropy, interpretation of resistivity field data, equivalence and suppression, self-potential and its origin, field measurement, Induced polarization, time and frequency domain IP measurements; interpretation and applications of IP, ground- water exploration, environmental and engineering applications.

Basic concept of EM induction, Origin of electromagnetic field, elliptic polarization, methods of measurement for different source-receiver configuration, components in EM measurements. Skin-depth, interpretation and applications; earth’s natural electromagnetic field, tellurics, magneto-tellurics; geomagnetic depth sounding principles, electromagnetic profiling, methods of measurement, processing of data and interpretation. Geological applications including groundwater, mining and hydrocarbon exploration.

Seismic methods of prospecting; Elastic properties of earth materials; Reflection, refraction and CDP surveys; land and marine seismic  sources , generation and propagation of elastic waves, velocity – depth models, 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, processing and interpretation; CDP stacking charts, binning, filtering, dip- moveout, static and dynamic corrections, Digital seismic data processing, seismic deconvolution and migration methods, attribute analysis, bright and dim spots, seismic stratigraphy, high resolution seismics, VSP, AVO. Reservoir geophysics.

Geophysical signal processing, sampling theorem, aliasing, Nyquist frequency, Fourier series, periodic waveform, Fourier and Hilbert transform, Z-transform and wavelet transform; power spectrum, delta function, auto correlation, cross correlation, convolution, deconvolution, principles of digital filters, windows, poles and zeros.

Principles and techniques of geophysical well-logging. SP, resistivity, induction, gamma ray, neutron, density, sonic, temperature, dip meter, caliper, nuclear magnetic, cement bond logging, micro-logs. 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.

Radioactive methods of prospecting and assaying of minerals (radioactive and non radioactive) deposits, half-life, decay constant, radioactive equilibrium, G M counter, scintillation detector, semiconductor devices, application of radiometric for exploration and radioactive waste disposal.

Geophysical inverse problems; non-uniqueness and stability of solutions; quasi-linear and non-linear methods including Tikhonov’s regularization method, Backus-Gilbert method, simulated annealing, genetic algorithms and artificial neural network.

Ecology and Evolution (EY)

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Ecology

Population ecology; metapopulation dynamics; growth rates; density independent growth; density dependent growth; niche concept; Species interactions: Plant-animal interactions; mutualism, commensalism, competition and predation; trophic interactions; functional ecology; ecophysiology; behavioural ecology; Community ecology: Community assembly, organization and evolution; biodiversity: species richness, evenness and diversity indices; endemism; species-area relationships; Ecosystem structure, function and services; nutrient cycles; biomes; habitat ecology; primary and secondary productivity; invasive species; global and climate change; applied ecology.

Evolution

Origin, evolution and diversification of life; natural selection; levels of selection. Types of selection (stabilizing, directional etc.); sexual selection; genetic drift; gene flow; adaptation; convergence; species concepts; Life history strategies; adaptive radiation; biogeography and evolutionary ecology; Origin of genetic variation; Mendelian genetics; polygenic traits, linkage and recombination; epistasis, gene-environment interaction; heritability; population genetics; Molecular evolution; molecular clocks; systems of classification: cladistics and phenetics; molecular systematics; gene expression and evolution.

Mathematics and Quantitative Ecology

Mathematics and statistics in ecology; Simple functions (linear, quadratic, exponential, logarithmic, etc); concept of derivatives and slope of a function; permutations and combinations; basic probability (probability of random events; sequences of events, etc); frequency distributions and their descriptive statistics (mean, variance, coefficient of variation, correlation, etc).

Statistical hypothesis testing: Concept of p-value; Type I and Type II error, test statistics like t-test and Chi-square test; basics of linear regression and ANOVA.

Behavioural Ecology

Classical ethology; neuroethology; evolutionary ethology; chemical, acoustic and visual signaling Mating systems; sexual dimorphism; mate choice; parenting behaviour Competition; aggression; foraging behaviour; predator–prey interactions; Sociobiology: kin selection, altruism, costs and benefits of group-living.

Electrical Engineering (EE)

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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

Electric Circuits and Fields: Network graph, KCL, KVL, node and mesh analysis, transient response of dc and ac networks; sinusoidal steady-state analysis, resonance, basic filter concepts; ideal current and voltage sources, Thevenin’s, Norton’s and Superposition and Maximum Power Transfer theorems, two-port networks, three phase circuits; Gauss Theorem, electric field and potential due to point, line, plane and spherical charge distributions; Ampere’s and Biot-Savart’s laws; inductance; dielectrics; capacitance.

Signals and Systems: Representation of continuous and discrete-time signals; shifting and scaling operations; linear, time-invariant and causal systems; Fourier series representation of continuous periodic signals; sampling theorem; Fourier, Laplace and Z transforms.

Electrical Machines: Single phase transformer – equivalent circuit, phasor diagram, tests, regulation and efficiency; three phase transformers – connections, parallel operation; auto- transformer; energy conversion principles; DC machines – types, windings, generator characteristics, armature reaction and commutation, starting and speed control of motors; three phase induction motors – principles, types, performance characteristics, starting and speed control; single phase induction motors; synchronous machines – performance, regulation and parallel operation of generators, motor starting, characteristics and applications; servo and stepper motors.

Power Systems: Basic power generation concepts; transmission line models and performance; cable performance, insulation; corona and radio interference; distribution systems; per-unit quantities; bus impedance and admittance matrices; load flow; voltage control; power factor correction; economic operation; symmetrical components; fault analysis; principles of over-current, differential and distance protection; solid state relays and digital protection; circuit breakers; system stability concepts, swing curves and equal area criterion; HVDC transmission and FACTS concepts.

Control Systems: Principles of feedback; transfer function; block diagrams; steady-state errors; Routh and Niquist techniques; Bode plots; root loci; lag, lead and lead-lag compensation; state space model; state transition matrix, controllability and observability.

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-meters; oscilloscopes; potentiometric recorders; error analysis.

Analog and Digital Electronics: Characteristics of diodes, BJT, FET; 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; multi-vibrators; sample and hold circuits; A/D and D/A converters; 8-bit microprocessor basics, architecture, programming and interfacing.

Power Electronics and Drives: Semiconductor power 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; basis concepts of adjustable speed dc and ac drives.

Electronics and Communication Engineering (EC)

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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 and 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, and 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, Basics of LASERs.

Device technology: integrated circuits fabrication process, oxidation, diffusion, ion implantation, photolithography, n-tub, p-tub and twin-tub CMOS process.

Analog Circuits: Small Signal Equivalent circuits of diodes, BJTs, MOSFETs and analog CMOS. Simple diode circuits, clipping, clamping, rectifier.Biasing and bias stability of transistor and FET amplifiers. Amplifiers: single-and multi-stage, differential and operational, feedback, and power. 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, 555 Timers. Power supplies.

Digital circuits: Boolean algebra, minimization of Boolean functions; logic gates; digital IC families (DTL, TTL, ECL, MOS, CMOS). Combinatorial circuits: arithmetic circuits, code converters, multiplexers, decoders, PROMs and PLAs. 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 ofLaplace transform, continuous-time and discrete-time Fourier series, continuous-time and discrete-time Fourier Transform, DFT and FFT, z-transform. Sampling theorem. Linear Time-Invariant (LTI) Systems: definitions and properties; causality, stability, impulse response, convolution, poles and zeros, parallel and cascade structure, frequency response, group delay, phase delay. Signal transmission through LTI systems.

Control 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: Random signals and noise: probability, random variables, probability density function, autocorrelation, power spectral density. 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. Fundamentals of information theory and channel capacity theorem.

Digital communication systems: pulse code modulation (PCM), differential pulse code modulation (DPCM), digital modulation schemes: amplitude, phase and frequency shift keying schemes (ASK, PSK, FSK), matched filter receivers, bandwidth consideration and probability of error calculations for these schemes. Basics of TDMA, FDMA and CDMA and GSM.

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; S parameters, pulse excitation.

Waveguides: modes in rectangular waveguides; boundary conditions; cut-off frequencies; dispersion relations. Basics of propagation in dielectric waveguide and optical fibers. Basics of Antennas: Dipole antennas; radiation pattern; antenna gain.

Chemistry (CY)

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Physical Chemistry

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

Equilibrium: Kinetic theory of gases; 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; Debye-Hückel theory; 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, temperature dependence of chemical reactions; elementary, consecutive, and parallel reactions; steady state approximation; theories of reaction rates – collision and transition state theory, relaxation kinetics, kinetics of photochemical reactions and free radical polymerization, homogeneous catalysis, adsorption isotherms and heterogeneous catalysis.

Inorganic Chemistry

Main group elements: General characteristics, allotropes, structure and reactions of simple and industrially important compounds: boranes, carboranes, silicones, silicates, boron nitride, borazines and phosphazenes. Hydrides, oxides and oxoacids of pnictogens (N, P), chalcogens (S, Se &Te) and halogens, xenon compounds, pseudo halogens and interhalogencompounds.Shapes of molecules and hard- soft acid base concept. Structure and Bonding (VBT) of B, Al, Si, N, P, S, Cl compounds.

Allotropes of carbon: graphite, diamond, C60. Synthesis and reactivity of inorganic polymers of Si and P.

Transition Elements: General characteristics of d and f block elements; coordination

chemistry: structure and isomerism, stability, theories of metal- ligand bonding (CFT and LFT), mechanisms of substitution and electron transfer reactions of coordination complexes. Electronic spectra and magnetic properties of transition metal complexes, lanthanides and actinides. 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. Bioinorganic chemistry of Na, K. Mg, Ca, Fe, Co, Zn, Cu andMo.

Solids: Crystal systems and lattices, miller planes, crystal packing, crystal defects; Bragg’s aw, ionic crystals, band theory, metals and semiconductors, Different structures of AX, AX2, ABX3 compounds, spinels. Instrumental methods of analysis: Atomic absorption and emission spectroscopy including ICP-AES, UV- visible spectrophotometry, NMR, mass, Mossbauer spectroscopy (Fe and Sn), ESR spectroscopy, chromatography including GC and HPLC and electro-analytical methods (Coulometry, cyclic voltammetry, polarography – amperometry, and ion selective electrodes).

Organic Chemistry

Stereochemistry: Chirality of organic molecules with or without chiral centres. Specification of configuration in compounds having one or more stereogeniccentres. Enantiotopic and diastereotopic atoms, groups and faces.Stereoselective and stereospecific  synthesis.Conformational analysis of acyclic and cyclic compounds.Geometricalisomerism.Configurational and conformational effects on reactivity and selectivity/specificity.

Reaction mechanism: Methods of determining reaction mechanisms. Nucleophilic and electrophilic substitutions and additions to multiple bonds.Elimination reactions. Reactive intermediates- carbocations, carbanions, carbenes, nitrenes, arynes, free radicals. Molecular rearrangements involving electron deficient atoms.

Organic synthesis: Synthesis, reactions, mechanisms and selectivity involving the following- alkenes, alkynes, arenes, alcohols, phenols, aldehydes, ketones, carboxylic acids and their derivatives, halides, nitro compounds and amines. Use of compounds of Mg, Li, Cu, B and Si in organic synthesis.Concepts in multistep synthesis- retrosynthetic analysis, disconnections, synthons, synthetic equivalents, reactivity umpolung, selectivity, protection and deprotection of functional groups.

Pericyclic reactions: Electrocyclic, cycloaddition and sigmatropic reactions. Orbital correlation, FMO and PMO treatments.

Photochemistry: Basic principles. Photochemistry of alkenes, carbonyl compounds, and arenes.Photooxidation and photoreduction.Di-π- methane rearrangement, Barton reaction.

Heterocyclic compounds: Structure, preparation, properties and reactions of furan, pyrrole, thiophene, pyridine, indole and their derivatives.

Biomolecules: Structure, properties and reactions of mono- and di-saccharides, physicochemical properties of amino acids, chemical synthesis of peptides, structural features of proteins, nucleic acids, steroids, terpenoids, carotenoids, and alkaloids.

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

Computer Science and Information Technology (CS)

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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.

Combinatory: 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.

Computer Science and Information Technology

Digital Logic: Logic functions, Minimization, Design and synthesis of combinational and sequential circuits; Number representation and computer arithmetic (fixed and floating point).

Computer Organization and Architecture: Machine instructions and addressing modes, ALU and data-path, CPU control design, Memory interface, I/O interface (Interrupt and DMA mode), Instruction pipelining, Cache and main memory, Secondary storage.

Programming and Data Structures: Programming in C; Functions, Recursion, Parameter passing, Scope, Binding; Abstract data types, Arrays, Stacks, Queues, Linked Lists, Trees, Binary search trees, Binary heaps.

Algorithms: Analysis, Asymptotic notation, Notions of space and time complexity, Worst and average case analysis; Design: Greedy approach, Dynamic programming, Divide-and- conquer; Tree and graph traversals, Connected components, Spanning trees, Shortest paths; Hashing, Sorting, Searching. Asymptotic analysis (best, worst, average cases) of time and space, upper and lower bounds, Basic concepts of complexity classes – P, NP, NP-hard, NP- complete.

Theory of Computation: Regular languages and finite automata, Context free languages and Push-down automata, Recursively enumerable sets and Turing machines, Undecidability.

Compiler Design: Lexical analysis, Parsing, Syntax directed translation, Runtime environments, Intermediate and target code generation, Basics of code optimization.

Operating System: Processes, Threads, Inter-process communication, Concurrency, Synchronization, Deadlock, CPU scheduling, Memory management and virtual memory, File systems, I/O systems, Protection and security.

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

Information Systems and Software Engineering: information gathering, requirement and feasibility analysis, data flow diagrams, process specifications, input/output design, process life cycle, planning and managing the project, design, coding, testing, implementation, maintenance.

Computer Networks: ISO/OSI stack, LAN technologies (Ethernet, Token ring), Flow and error control techniques, Routing algorithms, Congestion control, TCP/UDP and sockets, IP(v4), Application layer protocols (icmp, dns, smtp, pop, ftp, http); Basic concepts of hubs, switches, gateways, and routers. Network security – basic concepts of public key and private key cryptography, digital signature, firewalls.

Web technologies: HTML, XML, basic concepts of client-server computing.

Chemical Engineering (CH)

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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, Residue theorem.

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.

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, Residue theorem.

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.

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, Residue theorem.

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. First law application to  close and open systems. Second law and Entropy.

Thermodynamic properties of pure  substances: equation of state and departure function, properties of mixtures: partial  molar properties, fugacity, excess properties and activity coefficients;

phase equilibria:  predicting VLE of systems; chemical reaction equilibrium. 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 laws, molecular diffusion in fluids, mass transfer coefficients, film,  penetration and surface renewal theories; momentum, heat and mass transfer analogies;  stage-wise and continuous contacting and stage efficiencies; HTU & NTU concepts
design and operation of equipment for distillation, absorption, leaching, liquid-liquid  extraction, 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 distribution, single parameter model; 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, transfer functions and dynamic responses of simple  systems, process reaction curve, controller modes (P, PI, and PID); control valves;  analysis of closed loop systems including stability, frequency response and controller  tuning, cascade, feed forward control.

Plant Design and Economics: Process 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.

Civil Engineering (CE)

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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 moment and shear force 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 and shear stresses,  unsymmetrical  bending, shear centre. Thin walled pressure vessels, uniform torsion,  buckling of column, combined and direct bending stresses.

Structural Analysis: Analysis of statically determinate trusses, arches, beams, cables  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: Concrete Technology- properties of concrete, basics of mix  design. Concrete design- basic working stress and limit state design concepts, analysis of  ultimate load capacity and design of members subjected to flexure, shear, compression  and torsion by limit state methods. 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 interrelationships, permeability &seepage, effective stress  principle, consolidation, compaction, shear strength.

Foundation Engineering: Sub-surface investigations- scope, drilling bore holes,  sampling, penetration 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 & clays.  Deep foundations–pile types, dynamic &static formulae, load capacity of piles in sands  & clays, negative skin friction.

Water Resources Engineering

Fluid Mechanics and Hydraulics: Properties of fluids, principle of conservation of  mass, momentum, energy and corresponding equations, potential flow, applications of  momentum and Bernoulli’s equation, laminar and turbulent flow, 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 measurements in channels, tanks and pipes. Dimensional  analysis and hydraulic modeling. Kinematics of flow, velocity triangles and specific  speed of pumps and turbines.

Hydrology: Hydrologic cycle, rainfall, evaporation, infiltration, stage discharge  relationships, unit hydrographs, flood estimation, reservoir capacity, 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 spillways.  Design of weirs on permeable foundation. Types of irrigation system, irrigation  methods. Water logging and drainage, sodic soils.

Environmental Engineering

Water requirements: Quality standards, basic unit processes and operations for water  treatment. Drinking water standards, water requirements , basic unit operations and  unit processes for surface water treatment, distribution of water. Sewage and sewerage
treatment, quantity and characteristics of wastewater. Primary, secondary and tertiary  treatment of wastewater, sludge disposal, effluent discharge standards. Domestic  wastewater treatment, quantity of characteristics of domestic wastewater, primary and  secondary treatment Unit operations and unit processes of domestic wastewater, sludge  disposal.

Air Pollution: Types of pollutants, their sources and impacts, air pollution meteorology,  air pollution control, air quality standards and limits.

Municipal Solid Wastes: Characteristics, generation, collection and transportation of  solid wastes, engineered systems for solid waste management (reuse/ recycle, energy  recovery, treatment and disposal).

Noise Pollution: Impacts of noise, permissible limits of noise pollution, measurement of  noise and control of noise pollution.

Transportation Engineering

Highway Planning: Geometric design of highways, testing and specifications of paving  materials, design of flexible and rigid pavements.
Traffic Engineering: Traffic characteristics, theory of traffic flow, intersection design,  traffic signs and signal design, highway capacity.
Surveying  Importance of surveying, principles and classifications, mapping concepts, coordinate  system, map projections, measurements of distance and directions, leveling, theodolite  traversing, plane table surveying, errors and adjustments, curves.

Biotechnology (BT)

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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.

Differential Equations: Linear and nonlinear first order ODEs, higher order ODEs with  constant coefficients, Cauchy’s and Euler’s equations, Laplace transforms, PDE- 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: Solution of linear and nonlinear algebraic equations, Integration  of trapezoidal and Simpson’s rule, Single and multistep methods for differential  equations.

Biotechnology

Microbiology: Prokaryotic and eukaryotic cell structure; Microbial nutrition, growth  and control; Microbial metabolism (aerobic and anaerobic respiration, photosynthesis);  Nitrogen fixation; Chemical basis of mutations and mutagens; Microbial genetics  (plasmids, transformation, transduction, conjugation); Microbial diversity and  characteristic features; Viruses.

Biochemistry: Biomolecules and their conformation; Weak inter-molecular interactions  in bio macromolecules; Chemical and functional nature of enzymes; Kinetics of single  substrate and bi-substrate enzyme catalyzed reactions; Bioenergetics; Metabolism (Glycolysis, TCA and Oxidative phosphorylation); Membrane transport and pumps; Cell  cycle and cell growth control; Cell signaling and signal transduction.

Molecular Biology and Genetics: Molecular structure of genes and chromosomes; DNA  replication and control; Transcription and its control; Translational processes;  Regulatory controls in prokaryotes and eukaryotes; Mendelian inheritance; Gene  interaction; Complementation; Linkage, recombination and chromosome mapping;  Extrachromosomal inheritance; Chromosomal variation; Population genetics;  Transposable elements, Molecular basis of genetic diseases and applications.

Process Biotechnology: Bioprocess technology for the production of cell biomass and  primary/secondary metabolites, such as baker’s yeast, ethanol, citric acid, amino acids,  exo-polysacharides, antibiotics and pigments etc.; Microbial production, purification and bio- process application(s) of industrial enzymes; Production and purification of  recombinant proteins on a large scale; Chromatographic and membrane based  bioseparation methods; Immobilization of enzymes and cells and their application for  bioconversion processes.

Biotechnology

Microbiology: Prokaryotic and eukaryotic cell structure; Microbial nutrition, growth  and control; Microbial metabolism (aerobic and anaerobic respiration, photosynthesis);  Nitrogen fixation; Chemical basis of mutations and mutagens; Microbial genetics  (plasmids, transformation, transduction, conjugation); Microbial diversity and  characteristic features; Viruses.

Biochemistry: Biomolecules and their conformation; Weak inter-molecular interactions  in bio macromolecules; Chemical and functional nature of enzymes; Kinetics of single  substrate and bi-substrate enzyme catalyzed reactions; Bioenergetics; Metabolism  (Glycolysis, TCA and Oxidative phosphorylation); Membrane transport and pumps; Cell  cycle and cell growth control; Cell signaling and signal transduction.

Molecular Biology and Genetics: Molecular structure of genes and chromosomes; DNA  replication and control; Transcription and its control; Translational processes;  Regulatory controls in prokaryotes and eukaryotes; Mendelian inheritance; Gene  interaction; Complementation; Linkage, recombination and chromosome mapping;  Extrachromosomal inheritance; Chromosomal variation; Population genetics;  Transposable elements, Molecular basis of genetic diseases and applications.

Process Biotechnology: Bioprocess technology for the production of cell biomass and  primary/secondary metabolites, such as baker’s yeast, ethanol, citric acid, amino acids,  exo-polysacharides, antibiotics and pigments etc.; Microbial production, purification and
bioprocess application(s) of industrial enzymes; Production and purification of  recombinant proteins on a large scale; Chromatographic and membrane based  bioseparation methods; Immobilization of enzymes and cells and their application for  bioconversion processes.

Biotechnology

Microbiology: Prokaryotic and eukaryotic cell structure; Microbial nutrition, growth  and control; Microbial metabolism (aerobic and anaerobic respiration, photosynthesis);  Nitrogen fixation; Chemical basis of mutations and mutagens; Microbial genetics  (plasmids, transformation, transduction, conjugation); Microbial diversity and characteristic features; Viruses.

Biochemistry: Biomolecules and their conformation; Weak inter-molecular interactions  in bio macromolecules; Chemical and functional nature of enzymes; Kinetics of single  substrate and bi-substrate enzyme catalyzed reactions; Bioenergetics; Metabolism  (Glycolysis, TCA and Oxidative phosphorylation); Membrane transport and pumps; Cell  cycle and cell growth control; Cell signaling and signal transduction.
Molecular Biology and Genetics: Molecular structure of genes and chromosomes; DNA  replication and control; Transcription and its control; Translational processes;  Regulatory controls in prokaryotes and eukaryotes; Mendelian inheritance; Gene  interaction; Complementation ; Linkage, recombination and chromosome mapping;  Extrachromosomal inheritance; Chromosomal variation; Population genetics;  Transposable elements, Molecular basis of genetic diseases and applications.

Process Biotechnology: Bioprocess technology for the production of cell biomass and primary/secondary metabolites, such as baker’s yeast, ethanol, citric acid, amino acids,  exo-polysacharides, antibiotics and pigments etc.; Microbial production, purification and  bio – process application(s) of industrial enzymes; Production and purification of  recombinant proteins on a large scale; Chromatographic and membrane based  bioseparation methods; Immobilization of enzymes and cells and their application for  bioconversion processes.

Aerobic and anaerobic biological processes for stabilization of solid / liquid wastes;  Bioremediation.

Bioprocess Engineering: Kinetics of microbial growth, substrate utilization and product formation; Simple structured models; Sterilization of air and media; Batch fedbatch  and continuous processes; Aeration and agitation; Mass transfer in bioreactors;  Rheology  of fermentation fluids; Scale-up concepts; Design of fermentation media;  Various types of microbial and enzyme reactors; Instrumentation in bioreactors.

Plant and Animal Biotechnology: Special features and organization of plant cells; Tot  potency; Regeneration of plants; Plant products of industrial importance; Biochemistry  of major metabolic pathways and products; Autotrophic and heterotrophic growth;  Plant growth regulators and elicitors;

Cell suspension culture development:  methodology, kinetics of growth and production formation, nutrient optimization;
Production of secondary metabolites by plant suspension cultures; Hairy root cultures  and their cultivation. Techniques in raising transgencies.

Characteristics of animal cells: Metabolism, regulation and nutritional requirements for mass cultivation of animal cell cultures; Kinetics of cell growth and product for mass cultivation of animal cell cultures; Kinetics of cell growth and product  carrier culture; Hybridoma technology; Live stock improvement; Cloning in animals;  Genetic engineering in animal cell culture; Animal cell preservation.

Immunology: The origin of immunology; Inherent immunity; Humoral and cell  mediated immunity; Primary and secondary lymphoid organ; Antigen; B and T cells and  Macrophages; Major histocompatibility complex (MHC); Antigen processing and  presentation; Synthesis of antibody and secretion; Molecular basis of antibody diversity;  Polyclonal and monoclonal antibody; Complement; Antigen-antibody reaction;  Regulation of immune response; Immune tolerance; Hyper sensitivity; Autoimmunity;  Graft versus host reaction.

Recombinant DNA Technology: Restriction and modification enzymes; Vectors:  plasmid, bacteriophage and other viral vectors, cosmids, Ti plasmid, yeast artificial  chromosome; cDNA and genomic DNA library; Gene isolation; Gene cloning; Expression of cloned gene; Transposons and gene targeting; DNA labeling; DNA sequencing;  Polymerase chain reactions; DNA fingerprinting; Southern and northern blotting; In-situ  hybridization; RAPD; RFLP; Site-directed mutagenesis; Gene transfer technologies; Gene  therapy.

Bioinformatics: Major bioinformatics resources (NCBI, EBI, ExPASy); Sequence and  structure databases; Sequence analysis  (biomolecular sequence file formats, scoring  matrices, sequence alignment, phylogeny); Genomics and Proteomics (Large scale genome  sequencing strategies; Comparative genomics; Understanding DNA microarrays  and protein arrays); Molecular modeling and simulations (basic concepts including  concept of force fields).

Architecture and Planning (AR)

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City planning: Evolution of cities; principles of city planning; types of cities & new  towns; planning regulations and building byelaws; eco-city concept; sustainable  development.

Housing: Concept of housing; neighborhood concept; site planning principles; housing  typology; housing standards; housing infrastructure; housing policies, finance and  management; housing programs in India; self-help housing.

Landscape Design: Principles of landscape design and site planning; history of  landscape styles; landscape elements and materials; plant characteristics & planting  design; environmental considerations in landscape planning.

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, 3D-Studio, 3D  Max.

Environmental Studies in Building Science: Components of Ecosystem; ecological  principles concerning environment; climate responsive design; energy efficient building  design; thermal comfort; solar architecture; principles of lighting and styles for  illumination; basic principles of architectural acoustics; environment pollution, their  control & abatement.

Visual and Urban Design: Principles of visual composition; proportion, scale, rhythm,  symmetry, harmony, datum, balance, form, colour, texture; sense of place and space,  division of space; barrier free design; focal point, vista, image ability, visual survey,  figure-background relationship.

History of Architecture: Indian – Indus valley, Vedic, Buddhist, Indo-Aryan, Dravidian  and Mughal periods; European – Egyptian, Greek, Roman, medieval and renaissance  periods- construction and architectural styles; vernacular and traditional architecture.

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; art novuea, eclecticism, international styles, post  modernism, deconstruction in architecture.

Building Services: Water supply, sewerage and drainage systems; sanitary fittings and  fixtures; plumbing systems, principles of internal & external drainage systems,  principles of electrification of buildings, intelligent buildings; elevators & escalators,  their standards and uses; air-conditioning systems; fire fighting systems, building safety  and security 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 techniques e.g., PERT, CPM etc;

Materials and Structural Systems: Behavioral characteristics of all types of building  materials e.g. mud, timber, bamboo, brick, concrete, steel, glass, FRP, different polymers,  composites; 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; tall buildings; principles of disaster resistant structures.

Planning Theory: Regional planning; settlement system planning; history of human  settlements; growth of cities & metropolises; principles of Ekistics; rural-urban  migration; urban conservation; urban renewal; Five-year plan; structural and sectoral  plan.

Techniques of Planning: Planning survey techniques; preparation of urban and regional  structure plans, development plans, action plans; site planning principles and design;  statistical methods of data analysis; application of G.I.S and remote sensing techniques  in urban and regional planning; decision making models.

Traffic and Transportation Planning: Principles of traffic engineering and  transportation planning; traffic survey methods; design of roads, intersections, grade  separators and parking areas; hierarchy of roads and levels of services; traffic and  transport management in urban areas, intelligent transportation system; mass  transportation planning; para-transits and other modes of transportation, pedestrian &  slow moving traffic planning.

Infrastructure, Services and Amenities: Principles of water supply and sanitation  systems; water treatment; solid waste disposal systems; waste treatment, recycle &  reuse; urban rainwater harvesting; power supply and communication systems —  network, design & guidelines; demography related standards at various levels of the  settlements for health, education, recreation, religious & public-semi public facilities.

Development Administration and Management: Planning laws; development control  and zoning regulations; laws relating to land acquisition; development enforcements,  urban land ceiling; land management techniques; planning and municipal  administration; disaster mitigation management; 73rd & 74th Constitutional  amendments; valuation & taxation; revenue resources and fiscal management; public
participation and role of NGO & CBO; Institutional networking & capacity building.

Agricultural Engineering (AG)

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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.
Differential 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; bio-fuels; 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; mechanics of animal traction; 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  stress, active and passive earth pressures; stability of slopes.

Hydrological cycle; meteorological parameters and their 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.

Measurement of distance and area; chain surveying, methods of traversing;  measurement of angles and bearings, plane table surveying; types of leveling; contouring; instruments for surveying and leveling; computation of earth work.

Mechanics of soil erosion, soil erosion types; wind and water 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; earthen dams; water harvesting structures, farm ponds, watershed management.

Soil-water-plant relationship, water requirement of crops; consumptive use and evapo-transpiration irrigation scheduling;  irrigation efficiencies; design of irrigation channels;  measurement of soil moisture, irrigation water and infiltration; surface, sprinkler and  drip methods of irrigation; design and evaluation of irrigation methods.

Drainage coefficient; planning, design and layout of surface and sub-surface drainage  systems; leaching requirement and salinity control; irrigation and drainage water  quality.

Groundwater occurrence confined and unconfined aquifers, evaluation of aquifer  properties; well hydraulics; groundwater recharge.

Classification of pumps; pump characteristics; pump selection and installation.

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 – pasteurization and sterilization of liquid foods; preservation of food by cooling and freezing; refrigeration and cold storage basics and applications;  psychrometry – properties of air-vapors mixture; concentration and drying 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; fluidization of granular solids-pneumatic, bucket, screw and belt conveying; cleaning and grading; Effectiveness of grain cleaners.

Hydrothermal treatment, drying and milling of cereals, pulses and oilseeds; Processing  of seeds, spices, fruits and vegetables; By-product utilization from processing industries.

Controlled and modified atmosphere storage; Perishable food storage, godowns, bins  and grain silos.

Aerospace Engineering (AE)

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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 Equations: 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; takeoff  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  turbulent boundary layer.

Compressible Flows: Dynamics and 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 visualization 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.

Turbo machinery: 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.

Syllabus for GATE

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About GATE

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  • Graduate Aptitude Test in Engineering (GATE) is an all India examination that primarily tests the comprehensive understanding of the candidate in various tests undergraduate subjects in Engineering/Technology/Architecture and postgraduate level subjects in sciences.
  • The GATE score of a candidate reflects a relative performance level in a particular subject in the exam.
  • The score is used for admissions to post-graduate programs  (eg. M.E., M.Tech, direct Ph.D.) in Indian institutes of higher education with financial assistance provided by MHRD and other Government agencies.
  • The score may also be used by Public and Private Sector Undertakings for employment screening purposes.
  • The Indian Institute of Science (IISc) and seven Indian Institutes of Technology (IITs  at Bombay, Delhi, Guwahati, Kanpur, Kharagpur, Madras and Roorkee) jointly administer the conduct of GATE. The operations related to GATE in each of the 8  zones are managed by a Zonal GATE Office at IISc. or IITs. The Organizing Institute  (OI) is responsible for the end-to-end process and coordination amongst the  administering Institutes. The Organizing Institute for GATE 2014 is IIT Kharagpur.

Financial Assistance

  • A valid GATE score is essential for obtaining financial assistance during Master’s  programs and direct Doctoral programs in Engineering/ Technology/ Architecture,  and Doctoral programs in relevant branches of Science in Institutes supported by  the MHRD or other Government agencies. As per the directives of the MHRD, the  following procedure is to be adopted for admission to the post-graduate programs  (Master’s and Doctoral) with MHRD scholarship/ assistantship. Depending upon the  norms adopted by a specific institute or department of the Institute, candidate may  be admitted directly into a course based on his/her performance in GATE only or  based on his/her performance in GATE and an admission test/interview conducted  by the department to which he/she has applied and/or the candidate’s academic  record. If the candidate is to be selected through interview for post-graduate  programs, the minimum of 70% weightage will be given to the performance in GATE  and the remaining 30% weightage will be given to the candidate’s performance in  interview and/or academic record, as per MHRD guidelines.
  • The admitting institutes  could however prescribe a minimum passing percentage of marks in the  test/interview. Some colleges /institutes specify GATE qualification as the mandatory  requirement even for admission without MHRD scholarship/ assistantship.
  • To avail of the financial assistance (scholarship), the candidate must first secure  admission to a program in these Institutes, by a procedure that could vary from  institute to institute. Qualification in GATE is also a minimum requirement to apply  for various fellowships awarded by many Government organizations. Candidates are  advised to seek complete details of admission procedures and availability of MHRD  scholarship/assistantship from the concerned admitting institution. The criteria for  postgraduate admission with scholarship/ assistantship could be different for  different institutions. The management of the post-graduate scholarship/  assistantship is the responsibility of the admitting institution. Similarly, reservation  of seats under different categories is as per the policies and norms prevailing at the  admitting institution and Government of India rules. GATE offices will not entertain  any enquiry about admission, reservation of seats and/or award of  scholarship/assistantship.

 Employment

  • Several public sector undertakings (PSUs) have, in the past, used GATE scores for  screening for providing a salaried employment. A select few such organizations  are: Bhabha Atomic Research Centre, Bharat Heavy Electricals Limited, Indian Oil  Corporation Limited, National Thermal Power Corporation, Power Grid India, etc. It  is expected that such PSUs would use GATE Scores this year as well.

Note: GATE administration is not responsible for employment opportunities. The  qualified candidates must check newspapers and other reliable sources for any such  information.

 Administration

  • GATE is administered and conducted jointly by the Indian Institute of Science (IISc)  and seven Indian Institutes of Technology (IITs) on behalf of the National  Coordination Board (NCB)-GATE, Department of Higher Education, Ministry of  Human Resource Development (MHRD), Government of India. The GATE committee,  which comprises of representatives from these administering institutes, is the sole  authority for regulating the examination and declaring the results.
  • GATE is conducted through the collaboration of eight zones. The zones and the  corresponding administrative institutes are:

Zone-1: Indian Institute of Science Bangalore
Zone-2: Indian Institute of Technology Bombay
Zone-3: Indian Institute of Technology Delhi
Zone-4: Indian Institute of Technology Guwahati
Zone-5: Indian Institute of Technology Kanpur
Zone-6: Indian Institute of Technology Kharagpur
Zone-7: Indian Institute of Technology Madras
Zone-8: Indian Institute of Technology Roorkee

  • The overall co-ordination and responsibility of conducting GATE 2014 lies  with Indian Institute of Technology Kharagpur, which is designated as  the Organizing Institute (OI) for GATE 2014.
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