Syllabus of GATE
- Electronics and Telecommunication Engineering
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.
Networks 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 equation using Laplace transform; frequency domain analysis of RLC circuits. 2-ports network parameters; driving point and transfer functions. State equations for networks.
Energy bands in silicon, intrinsic and extrinsic silicon. Carrier transport in silicon; diffusion current , drift current , mobility , and receptivity , Generation and recombination of carries p-n junction diode, Zener diode, tunnel diode, BJT, JFET, MOS capacitor , MOSFET. LED, p-l-n and avalanche photo diode, Basics of LASERs. Device technology; integrated circuits fabrication process, oxidation, diffusion, ion implantation, photolithography, n-tub and twin tub CMOS process.
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 generator and wave-shaping circuits , 555 timers. Power supplies.
Boolean algebra, minimizations 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 of Laplace 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, Signal transmission through LTI 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-Intergral-Derivative (PID) control. State variable representation and solution of state equation of LTI control systems.
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. Superheterod 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 error calculations for these schemes. Basics of TDMA, FDMA, and CDMA and GSM.
Elements of vector calculus: divergence and curl; Gauss’s 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 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; radiations pattern; antenna gain.
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 integral, Strokes , 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 equations.
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’s 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.
Applied Mechanics and Design
Engineering Mechanics: Free body diagrams and equilibrium; trusses and frames; virtual work; kinematics and dynamics of particles and of rigid bodies in plane motion, including impulse and momentum (linear and angular) and energy formulations; impact.
Strength of Materials : Stress and strain; stress-strain relationship and elastic constants, Mohr’s circle for plane stress and plane strain, thin cylinders, shear force and bending moment diagrams; bending and shear stresses; deflection of beams; torsion of circular shafts; Euler’s theory of column; strain energy methods; thermal stresses. Theory of Machines: Displacement velocity, and acceleration analysis of plane mechanisms; dynamic analysis of slider-crank mechanism; gear trains; flywheels.
Vibrations: Free and forced vibration of single degree of freedom system; effect of damping; vibration isolation resonance, critical speeds of shafts. Design: Design for static and dynamic loading; failure theories; fatigue strength and the S-N diagram, principles, of the design of machine elements such as bolted, riveted and welded joints, shafts, spur gears, rolling sliding contact bearings, brakes and cluctes.
Fluid Mechanics and Thermal Sciences
Fluid Mechanics : Fluid properties ; fluid static, Manometry, buoyancy; control-volume analysis of mass, momentum and energy; fluid acceleration; differential equations of continuity and momentum ; Bernoulli’s equation; viscous flow of incompressible fluids; boundary layer; elementary turbulent flow; flow through pipes, head losses in pipes, bends etc.
Heat-Transfer: Modes of heat transfer; one dimensional heat conduction, resistance concept electrical analogy, unsteady heat conduction, fins; dimensionless parameters in free and forced convective heat transfer, various correlations for heat transfer in flow over flat plates and through pipes; thermal boundary layer; effect of turbulence; radiative heat transfer; black and grey surfaces shape, factors, network analysis; heat exchanger performance LMTD and NTU methods.
Thermodynamics: Zeroth, First and Second laws of thermodynamics, thermodynamics system and processes; Carnot cycle, irreversibility and availability; behaviour of ideal and real gases; properties of pure substances, calculation of work and heat in ideal processes. Analysis of thermodynamics cycles related to energy conversion.
Application: Power Engineering Steam Tables, Rankine, Brayton cycles with regenerating and reheat I.C. Engines; air-standard Otto, Diesel cycles, Refrigeration and air-conditioning, Vapour refrigeration cycle. Heat pumps, gas refrigeration, Reverse Brayton cycle; moist air; psychometrics chart, basic psychometrics processes. Turbo machinery:, Pelton-wheel Francis and Kaplan turbines – impulse and reaction principles, velocity diagrams.
Manufacturing and Industrial Engineering
Engineering Materials: Structure and properties of engineering materials, heat treatment, stress-strain diagrams for engineering materials.
Metal Casting: Design of patterns, moulds and cores; solidification and cooling; riser and gating design, design considerations.
Forming: Plastic deformation and yield criteria; fundamentals of hot and cold working processes; load estimation for bulk (forging, rolling, extrusion, drawing) and sheet (shearing, deep drawling, bending) metal forming processes; principles of powder metallurgy.
Joining: Physics of welding; brazing and soldering; adhesive bonding; design considerations in welding Machining and Machine Tool Operations: Mechanics of matching single and multi-point cutting tools, tool geometry and materials. Tool life and wear; economics of machining; principles of non-traditional matching processes; principles of work holding; principles of design of jigs and fixtures.
Metrology and Inspection: Limits, fits and tolerances; linear and angular measurements ; comparators gauge design ; interferometry; form and finish measurement ; alignment and testing method; tolerance analysis in manufacturing and assembly.
Computer Integrated Manufacturing: Basic-concepts of CAD/CAM and their integration tools. Production Planning and Control: Forecasting models, aggregate production planning. Scheduling, materials requirement planning.
Inventory Control: Deterministic and probabilistic models; safety stock inventory control systems.
Operations Research : Linear programming, simplex, and duplex method, transportation, assignment , network flow models , simple queuing models , PERT and CPM.
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’s 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 , Correlations 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.
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. Theremin’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.
Signal 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 operational; 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 – principles, types, performance characteristics, starting and speed control; single phase induction motors; synchronous machines – performance , regulation and parallel operation of generations, motor starting, characteristics and application; 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 Nyquist 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 instrument measurment of voltage, current, power, energy and power factor; transformers; digital voltmeters and multimeters; phase; time and frequency measurement Q-meters; oscilloscopes , potentionmetric recorders; error analysis.Analog and Digital Electronics : Characteristics of diodes , BJT, FET; amplifiers – biasing, equivalent circuit and frequency response; oscillators and feedback amplifier; operational amplifier – characteristics and applications ; simple active filters – VCOs and timers; combinational and sequential logic circuits; multiplexers; 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 trias, 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.
Linear Algebra: Matrix algebra, System of linear equations, Eigen values and Eigen vectors.
Calculus : Functions of single variable, Limit, continuity an 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, lnitial and boundary value problems, Laplace transforms, Solutions of one dimensions heart 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.
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 max design. Concrete design-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.
Soil Mechanics: Origin of soils, soil classification, three-phase system, fundamental definitions, relationship and interrelationships, permeability and 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 and clays, negative skin friction.
Water Resources Engineering
Fluid Mechanics and Hydraulic: Properties of fluids principle of fluids principle of conservation of mass, momentum energy and corresponding equations, potential flow, application of momentum and Bernoulli’s equation , laminar and turbulent flow, flow in pipes, networks. Concepts 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. Kinematics of flow, velocity triangles and specific speed of pumps and turbines.
Hydrology : Hydrology cycle, rainfall, evaporation, infiltration, stage discharge relationship 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 coils.
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.
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.
Computer Science Engineering
Theory of Computation : Regular languages and finite automata, Context free languages and push-down automata. Recursively enumerable sets and Turing machines, Undesirability; NP-completeness.
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 pipeling, 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 tress, 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 travels, Connected components, Spanning trees, Shortest paths, Hashing, Sorting Searching. 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.
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.
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 relationship, asymptotics.
Graph Theory : Connectivity, spanning tress, Cut vertices & edges; covering, matching, independent sets; Coloring; Planarity; isomorphism.
Linear Algebra : Algebra of matrices, determinates, 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 Theorem , Theorems, of integral calculus, evaluation of definite & improper integrals, Partial derivatives, Total derivatives, maxima & minima.
Formal Languages and Automata
Regular Languages: finite automata, regular expressions, regular grammar. Context free languages: push down automata, context free grammars.
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 communications interface, instruction pipelining, cache, main and secondary storage.
Data structures and Algorithms : The notion of abstract data types, stack, queue , list, set, string, free, binary, search tree, heap, graph, tree and graph traversals, connected components , spanning trees, shortest paths, hashing, sorting, searching, design techniques (greedy, dynamic, divide and conquer, Algorithm design by induction) 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.
Programming Methodology : Scope, binding, parameter, passing, recursion, C programming – data types and declarations, assignment and control flow statements , 1-d and 2-d arrays, functions, pointers, concepts of object-oriented programming – classes, objects, inheritance, polymorphism, operator overloading.
Operating Systems (in the context of Unix) : Classical concepts (concurrency, synchronization, deadlock), processes, threads and interprocess communication , CPU, scheduling, memory management , file systems, I/O systems, protection and security , shell programming.
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.
Databases: E – R diagrams, relational model, database design, integrity constraints normal forms, query languages (SQL), file structures (Sequential indexed), b-trees, transaction and concurrency control.
Data Communication and Networks : ISO/OSI stack, transmission , media, data encoding, multiplexing, flow and error control, LAN technologies (Ethernet, token ring). Network devices – switches, gateways, routers, ICMP , applications layer protocols, – SMTP, POP3 , HTTP, DNS, FTP, Telnet, network security – basic concepts of public key and private key cryptography, digital signature, firewalls.