GATE Syllabus 2021: CSE, CE, EE, ME, ECE, AR, AE, IN, PI, CY…
AE
AG
AR
BT
CE
CH
CS
CY
EY
GG
EC
EE
ME
IN
XE,XE
PI
MT
MN
TF
Others
GATE Syllabus 2021
GATE Syllabus 2021: GATE exam syllabus for 2021 will be released by IIT Delhi for 24 papers (subjects). The GATE exam has three sections namely General Aptitude, Engineering Math, and Specific subject selected by the candidates. GATE Syllabus 2021 for the subject code of AE, AG, BT, CE, EE, IN, ME, CH, CS, EC, MN, MT, PE, PI, TF and XE divided into 3 sections like Engineering Mathematics – 15 Marks; Subject of the paper – 70 Marks; General Aptitude – 15 Marks. And GATE Syllabus 2021 for the subject code of Subject of AR, CY, EY, GG, MA, PH and XL divided into 2 sections like – 85 Marks; General Aptitude – 15 Marks. The GATE Syllabus 2021 will be similar to the last year’s syllabus.
GATE Syllabus: General Aptitude (GA)
 Verbal Ability: English grammar, sentence completion, verbal analogies, word groups, instructions, critical reasoning and verbal deduction.
 Numerical Ability: Numerical computation, numerical estimation, numerical reasoning and data interpretation.
GATE 2021 Exam Details
Information Brochure PDF
GATE 2021 Official Link
GATE Syllabus: Aerospace Engineering (AE)
Engineering Mathematics
 Linear Algebra: Matrix algebra, Vector algebra. systems of linear equations, Rank of a matrix, Eigenvalues & Eigen Vector.
 Calculus: Functions of single variable, limits, mean value theorem. continuity and differentiability, chain rule, partial derivatives. maxima and minima, gradient, divergence and curl, directional derivatives. Integration – Line, surface and volume integrals, Theorems of Stokes, Gauss & Green also.
 Differential Equations: First order linear & nonlinear differential equations. higher order linear ODEs with constant coefficients. Partial differential equations & separation of variables methods.
 Special Topics: Laplace Transforms, Fourier Series. Numerical methods for linear and nonlinear algebraic equations, Numerical integration & differentiation.
Flight Mechanics
 Basics: Atmosphere: Properties, standard atmosphere, Classification of aircraft. Airplane (fixed wing aircraft) configuration & various parts.
 Performance of Airplane: Pressure altitude; equivalent, calibrated, indicated airspeeds. Primary flight instruments: Altimeter, ASI, VSI, Turnbank indicator, Drag polar. takeoff & landing; steady climb & descent, absolute & service ceiling. cruise, cruise climb, endurance or loiter, load factor, turning flight, Vn diagram; Winds: head, tail & crosswinds also.
 Static stability: Angle of attack, sideslip; longitudinal stick fixed & free stability, horizontal tail position and size, Roll, pitch & yaw controls; directional stability, vertical tail position and size; dihedral stability, hinge moments, stick forces; Wing dihedral, sweep & position.
 Dynamic stability: Equations of motion; Euler angles; aerodynamic forces and moments, stability & control derivatives; decoupling of longitudinal and lateraldirectional dynamics, lateraldirectional modes, longitudinal modes.
Space Dynamics
 Central force motion; determination of trajectory & orbital period in simple cases; Orbit transfer, inplane & outofplane.
Aerodynamics
 Fluid Mechanics: Conservation laws: Mass, momentum (Integral & differential form). Potential flow Theory: sources, sinks, doublets, Viscosity, line vortex and their superposition; Reynolds number.
 Airfoils & wings: Airfoil nomenclature; Aerodynamic coefficients: lift, drag, moment; KuttaJoukoswki theorem; Kutta condition, Thin airfoil theory, starting vortex, Critical and drag divergence Mach number; Finite wing theory: Induced drag, Prandtl lifting line theory.
 Compressible Flows:– Basic concepts of compressibility, Conservation equations; Onedimensional compressible flows, Rayleigh flow, Fanno flow, Isentropic flows, PrandtlMeyer flow, normal & oblique shocks; Flow through nozzles & diffusers also.
 Special Topics: Elementary ideas of viscous flows including boundary layers; Wind Tunnel Testing: Measurement & visualization technique.
Structures
 The strength of Materials: States of stress and strain, Stress & strain transformation, Principal stresses, Mohr’s Circle, Plane stress and strain, Threedimensional Hooke’s law. Failure theories: Maximum stress, Tresca and von Mises; Castigliano’s principles, Strain energy, Analysis of statically determinate & indeterminate trusses and beams, Elastic flexural buckling of columns also.
 Flight vehicle structures: Characteristics of aircraft structures & materials, Loads on aircraft, Torsion, bending & flexural shear of thinwalled sections.
 Structural Dynamics: Free & forced vibrations of undamped and damped SDOF systems, Free vibrations of undamped 2DOF systems.
 Special Topics: Vibration of beams, Theory of elasticity – Equilibrium and compatibility equations, Airy’s stress function.
Propulsion
 Basics Concept: Thermodynamics, boundary layers & heat transfer and combustion thermochemistry.
 Thermodynamics of aircraft engines: Thrust, efficiency & engine performance of turbojet, turboshaft, turboprop, turbofan and ramjet engines, thrust augmentation of turbojets & turbofan engines. Aerothermodynamics of nonrotating propulsion components such as intakes, combustor & nozzle also.
 Axial compressors: Angular momentum, work & compression, Efficiency of the compressor & degree of reaction, the characteristic performance of a single axial compressor stage.
 Axial turbines: Axial turbine stage efficiency.
 Centrifugal compressor: Centrifugal compressor stage dynamics, impeller & diffuser, inducer.

Rocket propulsion: Thrust equation & specific impulse, gravity losses, vehicle acceleration, multistaging of rockets, drag. Classification: chemical rockets, the Performance of solid & liquid propellant rockets.
GATE Syllabus: Agricultural Engineering (AG)
Engineering Mathematics
 Linear Algebra: Determinants & Matrices, Systems of linear equations, Eigen Values & Eigen Vectors.
 Calculus: Limit, continuity & differentiability; maxima and minima; partial derivatives; sequences and series; tests for convergence; Taylor series, Fourier series.
 Vector Calculus: Gradient; divergence and curl; line integrals, surface integrals & volume integrals. Stokes theorems, Gauss theorems and Green’s theorems.
 Differential Equations: Linear & nonlinear first order Ordinary Differential Equations (ODE). Higher order linear ODEs with constant coefficients; Laplace transforms. Cauchy’s and Euler’s equations; Partial Differential Equations – Laplace, heat and wave equations also.
 Probability and Statistics: Random variables; Mean, median, mode and standard deviation; correlation and regression analysis; Poisson, normal and binomial distributions; tests of significance, analysis of variance (ANOVA).
 Numerical Methods: Solutions of linear & nonlinear algebraic equations; numerical solutions of ODE; The Numerical integration – trapezoidal and Simpson’s rule.
Farm Machinery
 Machine Design: Design and selection of machine elements – pulleys, gears, chains & sprockets and belts; overload safety devices used in farm machinery; measurement of force, speed, displacement, torque and acceleration on machine elements.
 Farm Machinery: forces acting on a tillage tool; Soil tillage; hitch systems and hitching of tillage implements. functional requirements, principles of working, construction & operation of manual, animal and power operated equipment for tillage, planting, sowing, fertilizer application, intercultivation, spraying, chaff cutting, mowing, harvesting, threshing and transport; testing of agricultural machinery & equipment; cost analysis of implements and tractors; calculation of performance parameters – field capacity, efficiency, application rate and losses also.
Farm Power
 Sources of Power: Sources of power on the farm – human, animal, electrical, wind, mechanical, solar and biomass; biofuels.
 Farm Power: Thermodynamic principles of I.C. engines; I.C. engine cycles; fuels and combustion; engine components; lubricants and their properties. I.C. engine systems – fuel, cooling, ignition, lubrication, electrical, intake and exhaust; selection, operation, maintenance & repair of I.C. engines; power efficiencies and measurement; fuel consumption, calculation of power, torque, heat load and power losses.
 Tractors and Power tillers: Type, selection, maintenance and repair of tractors and power tillers; power transmission systems – gear trains, differential, final drives and power takeoff; tractor clutches and brakes; mechanics of tractor chassis; traction theory; threepoint hitches free link and restrained link operations; tractor tests and performance; mechanical steering and hydraulic control systems used in tractors. Human engineering & safety in the design of tractor, agricultural implements also.
Soil and Water Conservation Engineering
 Fluid Mechanics: Ideal & real fluids, properties of fluids; hydrostatic pressure and its measurement; hydrostatic forces on plane and curved surface; Bernoulli’s theorem; continuity equation; laminar and turbulent flow in pipes, Darcy Weisbach and HazenWilliams equations, Moody’s diagram; flow in open channels, flow through orifices and notches.
 Soil Mechanics: Engineering properties of soils; fundamental definitions and relationships; permeability and seepage analysis; index properties of soils; shear strength, Mohr’s circle of stress, the stability of slopes, active and passive earth pressures.
 Hydrology: Hydrological cycle and components; meteorological parameters, their measurement and analysis of precipitation data; hydrograph analysis, unit hydrograph theory and application; runoff estimation; flood routing, hydrological reservoir and channel routing; streamflow measurement.
 Surveying and Leveling: Measurement of distance and area; instruments for surveying and levelling; chain surveying, methods of traversing; measurement of angles and bearings, plane table surveying; theodolite traversing; types of levelling; contouring; computation of areas and volume.
 Soil and Water Erosion: Mechanics of soil erosion, soil erosion types, wind and water erosion, factors affecting erosion; biological and engineering measures to control erosion; soil loss estimation; terraces and bunds; The vegetative waterways; gully control structures, drop, drop inlet and chute spillways; earthen dams.
 Watershed Management: Watershed characterization; land use capability classification; check dams and farm ponds, rainwater harvesting structures also.
Irrigation and Drainage Engineering
 SoilWaterPlant Relationship: Water requirement of crops; consumptive use & evapotranspiration; soil moisture and irrigation water infiltration, measurement of infiltration.
 Irrigation Water Conveyance and Application Methods: Design of irrigation channels and underground pipelines; The irrigation scheduling; irrigation efficiencies; surface, sprinkler, microirrigation methods, design & evaluation of irrigation methods.
 Agricultural Drainage: Drainage coefficient; planning, design and layout of surface and subsurface drainage systems; irrigation and drainage water quality and reuse; leaching requirement and salinity control.
 Groundwater Hydrology: Groundwater occurrence; Darcy’s Law, steady flow in confined, unconfined aquifers, evaluation of aquifer properties; groundwater recharge.
 Wells and Pumps: Types of wells, steady flow through wells; pump characteristics; classification of pumps; pump selection and installation.
Agricultural Processing Engineering
 Drying: Psychrometry – properties of the airvapours mixture; concentration and drying of liquid foods – evaporators, hydrothermal treatment; tray, drum, spray dryers; pulses and oilseeds, drying and milling of cereals.
 Size Reduction and Conveying: Mechanics & energy requirement in size reduction of granular solids; size separation by screening; particle size analysis for comminuted solids; fluidization of granular solidspneumatic, bucket, screw and belt conveying; effectiveness of grain cleaners; cleaning and grading; centrifugal separation of solids, liquids & gases also.
 Processing and Byproduct Utilization: Processing of fruits, seeds, spices and vegetables; Byproduct utilization from processing industries.
 Storage Systems: Controlled & modified atmosphere storage; godowns, perishable food storage, bins & grain silos.
Dairy and Food Engineering
 Heat and Mass Transfer: Steady state heat transfer in conduction, convection and radiation; working principles of heat exchangers; transient heat transfer in simple geometry; diffusive and convective mass transfer; material and energy balances in food processing systems; simultaneous heat and mass transfer in agricultural processing operations; water activity, sorption and desorption isotherms also.
 Preservation of Food: Kinetics of microbial death – pasteurization and sterilization of milk and other liquids foods; refrigeration and cold storage basics and applications, preservation of food by cooling and freezing.
GATE Syllabus 2021: Architecture and Planning (AR)
Architecture and Design
 Visual composition in 2D and 3D; Principles of Architecture & Art; Organization of space; Architectural Graphics; Computer Graphics– concepts of BIM, CAD, 3D modelling and Architectural rendition; Programming languages and automation. Planning and design considerations for different building types; Anthropometrics; Site planning; Circulation horizontal and vertical; Space Standards; Barrierfree design; Building Codes; National Building Code also.
 Elements, construction, architectural styles and also examples of different periods of Indian & Western History of Architecture; Oriental, Traditional & Vernacular architecture; Influence of modern art on architecture; Architectural developments since Industrial Revolution; Art nouveau, Eclecticism, Post Modernism, International styles, Deconstruction in architecture; Works of renowned national and international architects; Recent trends in Contemporary Architecture.
Building Materials, Construction and Management
 Behavioural char. and applications of different building materials viz. mud, bamboo, brick, timber, concrete, steel, glass, AAC, FRP, different polymers, composites.
 Building construction techniques, methods & details; Principles of Modular Coordination; Building systems & prefabrication of building elements; Estimation, valuation, specification, professional practice; Construction planning & and equipment; Project management techniques e.g. CPM, PERT, etc.
Building and Structures
 Principles of the strength of materials; Design of structural elements in steel, wood and RCC; Structural systems in RCC and Steel; Elastic and Limit State design; Form and Structure; Principles of Prestressing; Principles and design of disaster resistant structures; High Rise and Long Span structures, gravity and lateral load resisting systems also.
Environmental Planning and Design
 Ecosystem natural and manmade ecosystem; Environmental considerations in design & planning; Ecological principles; Concepts of Environmental Impact Analysis; Thermal comfort, ventilation and air movement; Climate responsive design. The Solar architecture; Principles of lighting & illumination; Principles of architectural acoustics; ECBC; Green Building Concepts & Rating; Environmental pollution types, causes, controls & abatement strategies; Building Performance Simulation & Evaluation also.
Urban Design
 Concepts and theories of urban design; Townscape; Public Perception; Public Realm; Urban design interventions for sustainable development & transportation; Historical & modern examples of urban design; Public spaces, character, spatial qualities, Sense of Place; Elements of urban built environment – urban form, structure, spaces, pattern, texture, fabric, grain etc; Principles, tools & techniques of urban design; Site planning; Landscape design; Urban renewal & conservation; Development controls – FAR, densities, building byelaws.
Urban Planning and Housing
 Planning process; Types of plans – City Development Plan, Master Plan, Structure Plan, Zonal Plan, Town Planning Scheme, Action Area Plan, Regional Plan; Salient concepts, theories and also principles of urban planning; Sustainable urban development; Emerging concepts of cities – Smart City, EcoCity, Transit Oriented Development (TOD), SRZ, SEZ, etc.
 Housing; Concepts, principles & examples of the neighbourhood; Housing typologies; Affordable Housing; Slums; Housing for special areas & needs; Residential densities; National Housing Policies, Programs and Schemes, Standards for housing and community facilities also.
Planning Techniques and Management
 Tools and techniques of Surveys – Topographical, Physical, Landuse and Socioeconomic Surveys; Graphic presentation of spatial data; Methods of nonspatial and spatial data analysis; Application of G.I.S and also Remote Sensing techniques in urban & regional planning; Decision support system & Land Information System.
 Urban Economics; Social, Economical and environmental costbenefit analysis; Law of demand and supply of land & its use in planning; Techniques of financial appraisal; Management of Infrastructure Projects; Development guidelines such as URDPFI; Local selfgovernance; Planning Legislation & implementation – Land Acquisition Act, PPP etc.
Services, Infrastructure and Transportation
 Building Services: Water supply; Sanitary fittings and fixtures; Plumbing systems; Sewerage and drainage systems; Principles of the internal and external drainage system; Intelligent Buildings; Principles of electrification of buildings; Elevators and Escalators – standards and uses; AirConditioning systems; Building Safety and Security systems, also Firefighting Systems.
 Urban Infrastructure – Transportation, Sewerage, Drainage, Water Supply, Solid Waste Management, Electricity & Communications.
 Process and Principles of Transportation Planning and Traffic Engineering; Road capacity; Traffic flow characteristics, Traffic survey methods, and Traffic analyses and design considerations; Landuse – transportation – urban form interrelationships; Travel demand forecasting; Design of roads, intersections, grade separators & parking areas; Hierarchy of roads and level of service; Traffic and transport management and control in urban areas; Paratransit and other modes of transportation, Pedestrian and slowmoving traffic planning; Mass transportation planning; Intelligent Transportation Systems also.
 Principles of water supply and sanitation systems; Water supply and distribution system, water treatment, and Water harvesting systems; Principles, Planning and Design of stormwater drainage system; Methods of solid waste management – collection, transportation and disposal; Sewage disposal methods; Recycling and Reuse of solid waste; Power Supply & Communication Systems, design, network & guidelines also.
GATE Syllabus 2021: Biotechnology
Engineering Mathematics
 Linear Algebra: Determinants & Matrices, Systems of linear equations, Eigenvalues and Eigenvectors.
 Calculus: Limit, continuity, differentiability, Maxima and minima, Partial derivatives, Sequences & series, Test for convergence, Fourier Series.
 Differential Equations: Linear and nonlinear first order ODEs, higher order ODEs with constant coefficients, Cauchy’s & Euler’s equations, Laplace transforms and PDELaplace, heat and wave equations.
 Numerical Methods: Solution of linear & nonlinear algebraic equations, Integration of trapezoidal and Simpson’s rule, Single & multistep methods for differential equations also.
 Probability and Statistics: Mean, median, Random variables, mode & standard deviation, Poisson, normal and binomial distributions, Correlation & regression analysis.
General Biotechnology
 Biochemistry: Biomoleculesstructure & functions; Biological membranes, action potential, structure and transport processes; Enzymes classification, kinetics and mechanism of action; Basic concepts & designs of metabolism (carbohydrates, amino acids, lipids & nucleic acids also) photosynthesis, respiration & electron transport chain; Bioenergetics.
 Microbiology: Viruses structure and classification; Microbial classification and diversity (bacterial, algal and fungal); Microbial growth and nutrition; Methods in microbiology; Aerobic and anaerobic respiration; Microbial diseases and hostpathogen interaction; Nitrogen fixation.
 Cell Biology: Prokaryotic & eukaryotic cell structure; Cell cycle & cell growth control, Cell signalling and CellCell communication and signal transduction.
 Molecular Biology and Genetics: Molecular structure of genes & chromosomes; Transcription, Nucleic acid replication, translation and their regulatory mechanisms in prokaryotes & eukaryotes; Mutations and mutagenesis; Complementation; Mendelian inheritance; Gene interaction; Linkage, recombination and chromosome mapping; Extrachromosomal inheritance; Horizontal gene transfer and Transposable elements; Microbial genetics (transformation, plasmids, transduction, and conjugation); RNA interference; DNA damage and repair; Molecular basis of genetic diseases; Chromosomal variation also.
 Analytical Techniques: Principles of microscopylight, electron, fluorescent & confocal; Centrifugation high speed & ultra; Principles of spectroscopyUV, CD, IR, FTIR, visible, Raman, MS, NMR; Principles of chromatography ion exchange, hydrophobic interaction, gel filtration, affinity, HPLC, FPLC, GC; Electrophoresis; Microarray.
 Immunology: History of Immunology; Antigen; Antibody structure and function; Innate, humoral and cellmediated immunity; Molecular basis of antibody diversity; Antigenantibody reaction; Synthesis of antibody and secretion; Complement; Primary and secondary lymphoid organ; Major histocompatibility complex (MHC); B and T cells and macrophages; Antigen processing and presentation; also Polyclonal and monoclonal antibody; Regulation of immune response; Immune tolerance; Autoimmunity; Hypersensitivity; Graft versus host reaction also.
 Bioinformatics: Major bioinformatic resources and search tools; Sequence analysis (biomolecular sequence file formats, scoring matrices, sequence alignment, phylogeny); Sequence and structure databases; Data mining and analytical tools for genomic and proteomic studies; Molecular dynamics and simulations (basic concepts including force fields, proteinnucleic acid, proteinprotein, and proteinligand interaction also).
Recombinant DNA Technology
 Restriction & modification enzymes; Vectors; plasmid, bacteriophage & other viral vectors, Ti plasmid, cosmids, and yeast artificial chromosome; cDNA and genomic DNA library; Gene isolation, cloning & expression; mammalian & plant expression vectors; Transposons & gene targeting; DNA labeling; DNA sequencing; Polymerase chain reactions; Insitu hybridization; DNA fingerprinting; Southern & northern blotting; RAPD, RFLP; Sitedirected mutagenesis; Gene transfer technologies; Gene therapy also.
Plant and Animal Biotechnology
 Totipotency; Plant growth regulators & elicitors; Regeneration of plants; Tissue culture & Cell suspension culture system: methodology, kinetics of growth and, nutrient optimization; Production of secondary metabolites by plant suspension cultures; Plant products of industrial importance; Hairy root culture; transgenic plants.
 Animal cell culture; Animal cell and tissue preservation; Media composition and growth conditions; Anchorage and nonanchorage dependent cell culture; Micro & macrocarrier culture; Kinetics of cell growth; Hybridoma technology; Stem cell technology; Transgenic animals; Animal cloning.
Bioprocess Engineering and Process Biotechnology
 Chemical engineering principles applied to biological system, Principle of reactor design, mass & heat transfer, ideal and nonideal multiphase bioreactors; Media formulation & optimization; Rheology of fermentation fluids, Aeration and agitation; Kinetics of microbial growth, substrate utilization & product formation; Batch, fedbatch & continuous processes; Sterilization of air and media; Also Various types of microbial and enzyme reactors; Unit operations in solidliquid separation & liquidliquid extraction; Instrumentation control & optimization; Process scaleup, economics & feasibility analysis also.
 Engineering principle of bioprocessing Upstream production & downstream; Microbial, animal & plant cell culture platforms; Production of biomass, primary and secondary metabolites; Bioprocess design and development from lab to industrial scale; Biofuels, Bioplastics, industrial enzymes, antibiotics; Industrial application of chromatographic and membranebased bioseparation methods; Large scale production and purification of recombinant proteins; also Immobilization of biocatalysts (enzymes & cells) for bioconversion processes; BioremediationAerobic, anaerobic processes for stabilization of solid/liquid wastes.
GATE Syllabus: Civil Engineering (CE)
Engineering Mathematics
 Linear Algebra: Matrix algebra, Eigenvalues & Eigenvectors, and Systems of linear equations.
 Calculus: Functions of single variable; Mean value theorems, local maxima and minima, Taylor and Maclaurin series; Limit, continuity & differentiability; Evaluation of definite & indefinite integrals, application of definite integral to obtain area and volume; Total derivative; Partial derivatives; Gradient, Divergence and Curl, Directional derivatives, Vector identities, Line, Surface and Volume integrals, Stokes theorems, Gauss theorems and Green’s theorems.
 Ordinary Differential Equation (ODE): First order (linearnonlinear) equations; EulerCauchy equations; higher order linear equations with constant coefficients; Laplace transform and its application in solving linear ODEs; initial and boundary value problems.
 Partial Differential Equation (PDE): Fourier series; solutions of onedimensional diffusion equation; separation of variables; first and second order onedimensional wave equation and also twodimensional Laplace equation.
 Probability and Statistics: Definitions of probability & sampling theorems; Conditional probability; Continuous random variables: normal and exponential distributions; Discrete Random variables: also Poisson & Binomial distributions; Descriptive statistics – Mean, median, mode & standard deviation; Hypothesis testing.
 Numerical Methods: Accuracy and precision; error analysis. The solution of linear & nonlinear algebraic equations; Least square approximation, numerical differentiation, Newton’s & Lagrange polynomials, Integration by trapezoidal & Simpson’s rule, single and multistep methods for 1storder differential equations.
Structural Engineering
 Engineering Mechanics: System of forces, freebody diagrams, equilibrium equations; Friction and its applications; Internal forces in structures; Centre of mass; Kinematics of a point mass and rigid body; Euler’s equations of motion; Energy methods; Impulsemomentum; Principles of virtual work.
 Solid Mechanics: Bending moment & shear force in statically determinate beams; Theories of failures; Simple stress and strain relationships; Simple bending theory, shear centre, flexural and shear stresses; Uniform torsion, buckling of column, direct & combined bending stresses also.
 Structural Analysis: Statically determinate & indeterminate structures by force/energy methods; Analysis of trusses, cables, arches, beams, and frames; Method of superposition; Displacement methods: Influence lines; Slope deflection & moment distribution methods; Stiffness & flexibility methods of structural analysis.
 Construction Materials & Management: Construction Materials: Structural steel – composition, material behaviour & properties; Bricks and mortar; Concrete – constituents, mix design, shortterm and longterm properties; Timber; Bitumen. Construction Management: Tendering and construction contracts; Types of construction projects; Rate analysis and standard specifications; also Project planning and network analysis – PERT & CPM; Cost Estimation.
 Concrete Structures: Working stress, Limit state & Ultimate load design concepts; Bond & development length; Design of beams, slabs, columns; Analysis of beam sections at transfer & service loads; Prestressed concrete.
 Steel Structures: Working Stress & Limit state design concepts; Design of tension & compression members, beams & beamcolumns, column bases; Plastic analysis of beams & frames; Connections – simple & eccentric, beamcolumn connections, plate girders & trusses.
Geotechnical Engineering
 Soil Mechanics: Origin of soils, soil structure & fabric; Unified and Indian standard soil classification system; Threephase system & phase relationships, index properties; Permeability – one dimensional flow, Darcy’s law; Seepage through soils – twodimensional flow, uplift pressure, flow nets, piping; Compaction in laboratory & field conditions; Principle of effective stress, capillarity, seepage force & quicksand condition; Onedimensional consolidation, time rate of consolidation; Mohr’s circle, effective, stress paths, & total shear strength parameters, also characteristics of clays & sand also.
 Foundation Engineering: Subsurface investigations – scope, drilling boreholes, plate load test, sampling, standard penetration & cone penetration tests; Stability of slopes – finite & infinite slopes, method of slices and Bishop’s method; Earth pressure theories – Rankine & Coulomb; Stress distribution in soils – Boussinesq’s & Westergaard’s theories, and pressure bulbs; Combined footing and raft foundation; Shallow foundations – Terzaghi’s & Meyerhoff’s bearing capacity theories, effect of water table; Contact pressure; also Deep foundations – types of piles, dynamic & static formulae, load capacity of piles in sands & clays, negative skin friction, pile load test; Settlement analysis in sands and clays.
Water Resources Engineering
 Fluid Mechanics: Properties of fluids, fluid statics; Continuity, momentum, energy and corresponding equations; Laminar and turbulent flow; Potential flow, applications of momentum and energy equations; Concept of the boundary layer and its growth; Flow in pipes, pipe networks.
 Hydraulics: Forces on immersed bodies; Dimensional analysis & hydraulic similitude; Flow measurement in channels and pipes; Kinematics of flow, velocity triangles; Basics of hydraulic machines, specific speed of pumps & turbines; Channel Hydraulics – Energydepth relationships, specific energy, critical flow, uniform flow, slope profile, hydraulic jump, and gradually varied flow also.
 Hydrology: Hydrologic cycle, evaporation, evapotranspiration, precipitation, watershed, infiltration, unit hydrographs, hydrograph analysis, flood estimation & routing, reservoir and channel routing, reservoir capacity, surface runoff models, groundwater hydrology – steady state well hydraulics & aquifers; Application of Darcy’s law.
 Irrigation: Duty, delta, estimation of evapotranspiration; Design of lined & unlined canals, head works, gravity dams & spillways; Crop water requirements; Design of weirs on the permeable foundation; Types of irrigation systems, irrigation methods; Canal regulatory works, crossdrainage structures, outlets & escapes; and also Water logging and drainage.
Environmental Engineering
 Water and Waste Water: Quality standards, operations for water treatment, basic unit processes. Drinking water standards, basic unit operations and unit processes for surface water treatment, water requirements and distribution of water. Sewage & sewerage treatment, quantity & char of wastewater. Primary, secondary & tertiary treatment of wastewater, and effluent discharge standards. Domestic wastewater treatment, primary and secondary treatment, Quantity of characteristics of domestic wastewater; also Unit operations & unit processes of domestic wastewater, sludge disposal.
 Air Pollution: Types of pollutants, their sources and impacts, air pollution control, air pollution meteorology, air quality standards and limits.
 Municipal Solid Wastes: Characteristics, generation, collection & transportation of solid wastes, engineered systems for solid waste management (reuse/recycle, treatment and disposal, and energy recovery).
 Noise Pollution: Impacts of noise, permissible limits of noise pollution, control of noise pollution, and measurement of noise.
Transportation Engineering
 Transportation Infrastructure: Highway alignment & engineering surveys; Geometric design of railway track; Geometric design of highways – crosssectional elements, sight distances, vertical & horizontal alignments; Airport runway length, taxiway & exit taxiway design.
 Highway Pavements: Highway materials – desirable properties & quality control tests; Bituminous paving mixes Design; Flexible pavement Design using IRC: 372012; Design factors for flexible & rigid pavements; Design of rigid pavements using IRC: 582011; Distresses in concrete pavements.
 Traffic Engineering: Traffic studies on flow, travel time, speed – delay and OD study, PCU, parking study, peak hour factor, accident study & analysis, statistical analysis of traffic data; Types of intersections & channelization; Microscopic & macroscopic parameters of traffic flow, fundamental relationships; Control devices, signal design by Webster’s method; also Highway capacity & level of service of rural highways and urban roads.
Geomatics Engineering
 Principles of surveying; Errors and their adjustment; Maps – scale, coordinate system; Traversing & triangulation survey; Distance & angle measurement – Levelling and trigonometric levelling; Horizontal & vertical curves; Total station.
 Photogrammetry – scale, flying height; Basics of Geographical information system (GIS) & Geographical Positioning system (GPS); Remote sensing – basics, platform & sensors, visual image interpretation.
GATE Syllabus 2021: Chemical Engineering (CH)
Engineering Mathematics
 Linear Algebra: Matrix algebra, Systems of linear equations, Eigenvalues & Eigenvectors.
 Differential Equation (ODE): First order (linearnonlinear) equations; EulerCauchy equations; higher order linear equations with constant coefficients; Laplace transform and its application in solving linear ODEs; initial and boundary value problems.
 Calculus: Functions of single variable; Mean value theorems, local maxima and minima, Taylor and Maclaurin series; Limit, continuity & differentiability; Evaluation of definite & indefinite integrals, application of definite integral to obtain area and volume; Total derivative; also Partial derivatives; Gradient, Divergence and Curl, Directional derivatives, Vector identities, Line, Surface and Volume integrals, Stokes theorems, Gauss theorems and Green’s theorems.
 Complex variables: Complex number, polar form of the complex number, and triangle inequality.
 Probability and Statistics: Definitions of probability & sampling theorems; Conditional probability; Continuous random variables: normal and exponential distributions; Discrete Random variables: Poisson & Binomial distributions; Descriptive statistics – Mean, median, mode & standard deviation; Hypothesis testing.
 Numerical Methods: Accuracy and precision; error analysis. The solution of linear & nonlinear algebraic equations; Least square approximation, numerical differentiation, Newton’s & Lagrange polynomials, Integration by trapezoidal & Simpson’s rule, single and multistep methods for 1storder differential equations also.
Fluid Mechanics & Mechanical Operations
 Fluid statics, Newtonian & nonNewtonian fluids, shellbalances including differential form of Bernoulli equation & energy balance, dimensional analysis & similitude, Macroscopic friction factors, flow through pipeline systems, pumps & compressors, flow meters, elementary boundary layer theory, flow past immersed bodies including packed & fluidized beds, Turbulent flow: fluctuating velocity, universal velocity profile & pressure drop also.
 Particle size & shape, particle size distribution, size reduction & classification of solid particles; centrifuge & cyclones; free & hindered settling; thickening & classification, filtration, agitation & mixing; conveying of solids.
Process Calculations & Thermodynamics
 Steady and unsteady state mass & energy balances including multiphase, reacting & nonreacting systems, multicomponent. Use of tie components; Gibb’s phase rule & degree of freedom analysis; recycle, bypass & purge calculations.
 First & Second laws of thermodynamics; Second law & Entropy; Applications of first law to close & open systems; properties of mixtures: partial molar properties, fugacity, excess properties & activity coefficients, Thermodynamic properties of pure substances: Equation of State & residual properties; phase equilibria: predicting VLE of systems; chemical reaction equilibrium also.
Mass Transfer
 Fick’s laws, mass transfer coefficients, molecular diffusion in fluids, film, penetration & surface renewal theories; stagewise & continuous contacting & stage efficiencies; momentum, heat & mass transfer analogies; HTU & NTU concepts; design & operation of equipment for distillation, absorption, liquidliquid extraction, leaching, drying, humidification, adsorption, & dehumidification.
Heat Transfer
 Steady & unsteady heat conduction, convection & radiation, thermal boundary layer & heat transfer coefficients, boiling, condensation & evaporation; types of heat exchangers, evaporators, and their process calculations. Design of double pipe, shell & tube heat exchangers, and also single & multiple effect evaporators.
Chemical Reaction Engineering
 Theories of reaction rates; kinetics of homogeneous reactions, single & multiple reactions in ideal reactors, interpretation of kinetic data, nonideal reactors; residence time distribution, and single parameter model; kinetics of heterogeneous catalytic reactions; nonisothermal reactors; diffusion effects in catalysis also.
Plant Design & Economics
 Principles of process economics & cost estimation including depreciation, and total annualized cost, cost indices, payback period, the rate of return, discounted cash flow, optimization in process design, and sizing of chemical engineering equipment such as compressors, multistage contactors, and heat exchangers.
Instrumentation & Process Control
 Measurement of process variables; sensors, transducers & their dynamics, transfer functions and dynamic responses of various systems, process modeling & linearization, systems with inverse response, controller modes (P, PI, PID), and process reaction curve; control valves; also analysis of closed loop systems including stability, controller tuning, frequency response, cascade & feedforward control.
Chemical Technology
 Inorganic chemical industries (chloralkali industry, sulfuric acid, and phosphoric acid), fertilizers (Urea, Ammonia, SSP, TSP); natural products industries (Sugar, Oil, Pulp and Paper, and Fats); polymerization industries (polyethene, polypropylene, PVC & polyester synthetic fibres); petroleum refining and petrochemicals also.
GATE Syllabus: Computer Science and Information Technology (CS)
Engineering Mathematics
 Linear Algebra: Determinants and Matrices, the system of linear equations, eigenvalues and eigenvectors, LU decomposition.
 Discrete Mathematics: Propositional and firstorder logic. Sets, functions, relations, partial orders and lattices. Groups. Graphs: connectivity, matching, colouring. Combinatorics: counting, recurrence relations, and generating functions.
 Probability: Random variables. Binomial distributions, Uniform, normal, exponential, and Poisson. Mean, median, mode, and standard deviation; Bayes theorem, Conditional probability also.
 Calculus: Limits, continuity and differentiability; Integration; Maxima and minima. Mean value theorem.
Computer Organization & Architecture
 Machine instructions & addressing modes; Instruction pipelining; ALU, data‐path and control unit; Memory hierarchy: cache, main memory & secondary storage; I/O interface (Interrupt & DMA mode).
Digital Logic
 Boolean algebra; Sequential and Combinational circuits; Minimization; Number representations & computer arithmetic (fixed & floating point).
Programming and Data Structures
 The C Programming; Recursion; Arrays, queues, stacks, linked lists, trees, binary search trees, binary heaps, graphs.
Theory of Computation
 Regular expressions & finite automata; Contextfree grammars & pushdown automata; Turing machines and undecidability; Regular & contextfree languages, pumping lemma also.
Algorithms
 Searching, hashing, and sorting; Asymptotic worstcase time & space complexity. Graph search, minimum spanning trees, shortest paths; Algorithm design techniques: greedy, dynamic programming and divide‐and‐conquer.
Compiler Design
 Lexical analysis, parsing, syntaxdirected translation; Intermediate code generation; Runtime environments.
Operating System
 Processes, inter‐process communication, threads, concurrency and synchronization; Deadlock; CPU scheduling; Memory management and virtual memory; File Systems.
GATE Syllabus 2021: Chemistry (CY)
Physical Chemistry
 Structure: Postulates of quantum mechanics. Timedependent and timeindependent Schrödinger equations. Particle in a box; Harmonic oscillator; Born interpretation. Rigid rotor; Hydrogen atom: atomic orbitals. Multielectron atoms: Variation & firstorder perturbation techniques. orbital approximation; Chemical bonding: Valence bond theory and LCAOMO theory. Hybrid orbitals. Applications of LCAOMOT to H2+, heteronuclear diatomic molecules like HF, H2 and other homonuclear diatomic molecules, CO, NO, and to simple delocalized π– electron systems; Hückel approximation and its application to annular π – electron systems. Point groups and character tables. Symmetry elements and operations. Origin of selection rules for rotational, electronic, vibrational, and Raman spectroscopy of diatomic and polyatomic molecules. The Einstein coefficients; Relationship of transition moment integral with molar extinction coefficient, oscillator strength. The Principles of nuclear magnetic resonance: nuclear g factor, chemical shift, nuclear coupling also.
 Equilibrium: Laws of thermodynamics. Standard states, Thermochemistry; Thermodynamic functions and their relationships: GibbsHelmholtz and Maxwell relations, The Van’t Hoff equation. Criteria of spontaneity and equilibrium; Partial molar quantities; Absolute entropy; Thermodynamics of mixing; Chemical potential. Chemical equilibria; Fugacity, activity and activity coefficients; Dependence of equilibrium constant on temperature and pressure. Nonideal solutions; Ionic mobility and conductivity; DebyeHückelOnsager equation. DebyeHückel limiting law; Standard electrode potentials and electrochemical cells. Potentiometric and conductometric titrations. Phase rule; ClausiusClapeyron equation. Phase diagram of one component systems: H2O, CO2, S; twocomponent systems: liquidvapour, liquidliquid and solidliquid systems. Azeotropes and eutectics; Fractional distillation. Statistical thermodynamics: Boltzmann distribution, microcanonical and canonical ensembles, partition functions, and thermodynamic properties also.
 Surfaces & Interfaces: Physisorption & chemisorption; Langmuir, Freundlich and BET isotherms. Surface tension, viscosity; Selfassembly. Surface catalysis: LangmuirHinshelwood mechanism. Physical chemistry of colloids, micelles, and macromolecules.
 Surfaces & Interfaces: Physisorption and chemisorption; Langmuir, Freundlich, BET isotherms. Surface catalysis: LangmuirHinshelwood mechanism. Surface tension, viscosity; Physical chemistry of colloids, micelles and macromolecules; Selfassembly.
 Kinetics: Transition state theory: Eyring equation, thermodynamic aspects. Potential energy surfaces & classical trajectories. Steadystate approximation; Mechanisms of complex reactions. Elementary, parallel, opposing consecutive reactions. Unimolecular reactions; also Kinetics of polymerization & enzyme catalysis. Fast reaction kinetics: relaxation and flow methods; Kinetics of photochemical, photophysical processes.
Inorganic Chemistry
 Main Group Elements: Hydrides, oxides, oxoacids, halides, nitrides, sulfides – shapes & reactivity. Structure and bonding of boranes, boron nitride, carboranes, silicones, silicates, borazines and phosphazenes. Allotropes of carbon. Pseudohalogens, Chemistry of noble gases, and interhalogen compounds; also Acidbase concepts.
 Lanthanides and Actinides: Recovery. Periodic properties, spectra and magnetic properties.
 Transition Elements: Coordination chemistry – isomerism, and structure theories of bonding (VBT, CFT, MOT). Energy level diagrams in various crystal fields, applications of CFT, CFSE, JahnTeller distortion. Electronic spectra of transition metal complexes: spectroscopic term symbols, Orgel diagrams, selection rules, chargetransfer spectra. Reaction mechanisms: kinetic and thermodynamic stability, substitution and redox reactions; Magnetic properties of transition metal complexes. also
 Organometallics: 18Electron rule; metalcarbonyl, metalalkyl, metalolefin & metalcarbene complexes and metallocenes. Types of organometallic reactions; Fluxionality in organometallic complexes. Homogeneous catalysis – Hydrogenation, acetic acid synthesis, hydroformylation, metathesis and olefin oxidation; Heterogeneous catalysis – FischerTropsch reaction, ZieglerNatta polymerization.
 Bioinorganic Chemistry: Ion (Na+ & K+) transport, electron transfer reactions, oxygen binding, transport & utilization, nitrogen fixation, metalloenzymes containing magnesium, iron, cobalt, molybdenum, copper and zinc.
 Instrumental Methods of Analysis: UVvisible spectrophotometry, mass spectrometry, NMR and ESR spectroscopy. Chromatography including GC and HPLC. Electroanalytical methods polarography, ionselective electrodes, cyclic voltammetry; Thermoanalytical methods.
 Solids: Crystal systems and lattices, crystal packing, Miller planes, crystal defects, ionic crystals, Bragg’s law, structures of AX, AX2, ABX3 type compounds, band theory, spinels, metals & semiconductors also.
Organic Chemistry
 Stereochemistry: Chirality of organic molecules with/without chiral centres & determination of their absolute configurations. The Relative stereochemistry in compounds having more than one stereogenic centre. Homotopic, groups and faces, enantiotopic and diastereotopic atoms. Stereoselective and stereospecific synthesis; Geometrical isomerism; Conformational analysis of acyclic and cyclic compounds; Configurational and conformational effects, and also neighbouring group participation on reactivity and selectivity or specificity.
 Organic Synthesis: Synthesis, mechanisms, reactions and selectivity involving the following classes of compounds – alkenes, alkynes, arenes, phenols, alcohols, aldehydes, carboxylic acids, ketones, esters, nitriles, halides, nitro compounds, amines and amides. Uses of Mg, B, Li, Cu, Zn, and Sibased reagents in organic synthesis. Concepts of multistep synthesis – retrosynthetic analysis, synthons strategic disconnections, and synthetic equivalents. Carboncarbon bond formation through coupling reactions – Heck, Stille, Suzuki, and Sonogoshira. Umpolung reactivity – formyl and acyl anion equivalents. Selectivity in organic synthesis – chemo, regio, stereoselectivity. Protection & deprotection of functional groups. Stereoselective addition to C=O groups (Cram and FelkinAnh models); also Concepts of asymmetric synthesis – resolution (including enzymatic), desymmetrization, use of chiral auxiliaries.
 Reaction Mechanisms: Basic mechanistic concepts – kinetic Vs thermodynamic control, Hammond’s postulate, and CurtinHammett principle. Nucleophilic and electrophilic substitution reactions (both aromatic, aliphatic). Methods of determining reaction mechanisms through the identification of products, intermediates, isotopic labelling. Addition reactions to carboncarbon & carbonheteroatom (N, O) multiple bonds. Elimination Reactions; Reactive intermediates – carbocations, carbenes, nitrenes, carbanions, arynes and free radicals; also Molecular rearrangements involving electron deficient atoms also.
 Pericyclic Reactions & Photochemistry: Electrocyclic, cycloaddition, sigmatropic reactions; Orbital correlations – FMO and PMO treatments. Photochemistry of alkenes, arenas and carbonyl compounds. Photooxidation and photoreduction; Diπmethane rearrangement, Barton reaction.
 Biomolecules: Structure, properties and reactions of mono and disaccharides, chemical synthesis of peptides, physicochemical properties of amino acids, structural features of proteins, terpenoids, carotenoids, nucleic acids, steroids, and alkaloids also.
 Heterocyclic Compounds: Structure, preparation, pyrrole, thiophene, properties and reactions of furan, pyridine, indole, quinoline, and isoquinoline.
 Spectroscopy: Applications of UVvisible, NMR IR, and Mass spectrometry in the structural determination of organic molecules.
GATE Syllabus 2021: Electronics and Communications Engineering (EC)
Engineering Mathematics
 Calculus: Partial derivatives, Maxima & minima, Mean value theorems, theorems of integral calculus, evaluation of definite and improper integrals, multiple integrals, line, Taylor series, surface and volume integrals.
 Linear Algebra: matrix algebra, eigen values and eigen vectors, rank, solution of linear equations – existence and uniqueness; Vector space, basis, linear dependence and independence.
 Differential Equations: First order equations (linear and nonlinear), higher order linear differential equations, methods of solution using the variation of parameters, Cauchy’s and Euler’s equations, complementary function and particular integral, partial differential equations, initial and boundary value problems, the variable separable method also.
 Vector Analysis: Vector operations, gradient, Vectors in plane and space, divergence and curl, Gauss’s theorems, Green’s theorems and Stoke’s theorems.
 Complex Variable: Analytic functions, Cauchy’s integral formula, Cauchy’s integral theorem; Taylor’s series and Laurent’s series, residue theorem.
 Numerical Methods: Single & multistep methods for differential equations, Solution of nonlinear equations, convergence criteria.
 Probability and Statistics: Mean, median, mode and standard deviation; combinatorial probability, probability distribution functions – binomial distribution, Poisson distribution, exponential distribution and normal distribution; Correlation and regression analysis; Joint and conditional probability.
Networks, Signals and Systems
 Network theorems: superposition, Thevenin and Norton’s, maximum power transfer; Network solution methods: nodal and mesh analysis; Wye‐Delta transformation; Steady state sinusoidal analysis using phasors; Solution of network equations using Laplace transform; Time domain analysis of simple linear circuits; Frequency domain analysis of RLC circuits; State equations for networks; Linear 2‐port network parameters: driving point and transfer functions also.
 Continuoustime signals: Fourier series & Fourier transform representations, sampling theorem; Discretetime signals: discretetime Fourier transform (DTFT), DFT, FFT, interpolation of discretetime signals, Ztransform; LTI systems: definition and properties, stability, impulse response, causality, convolution, poles and zeros, parallel and cascade structure, frequency response, phase delay, digital filter design techniques, group delay also.
Electronic Devices
 Energy bands in intrinsic and extrinsic silicon; Generation and recombination of carriers; Carrier transport: diffusion current, drift current, mobility, resistivity; Poisson and continuity equations; PN junction, Zener diode, MOS capacitor, BJT, MOSFET, LED, photodiode, solar cell; Integrated circuit fabrication process: oxidation, ion implantation, diffusion, photolithography and twintub CMOS process also.
Analog Circuits
 Small signal equivalent circuits of diode, BJT, MOSFET; Simple diode circuits: clipping, clamping, rectifiers; Singlestage BJT and MOSFET amplifiers: biasing, bias stability, midfrequency small signal analysis, and frequency response; BJT and MOSFET amplifiers: multistage, feedback, differential, power, and operational; Active filters; Simple opamp circuits; Sinusoidal oscillators: criterion for oscillation, singletransistor, & opamp configurations; also Function generators, waveshaping circuits and 555 timers; Power supplies: ripple removal and regulation; Voltage reference circuits.
Digital Circuits
 Number systems; Combinatorial circuits: Boolean algebra, minimization of functions using Boolean identities, Karnaugh map, logic gates & their static CMOS implementations, code converters, arithmetic circuits, multiplexers, decoders and PLAs; Sequential circuits: latches and flip‐flops, counters, shift‐registers and finite state machines; Semiconductor memories: ROM, DRAM, SRAM; Data converters: sample and hold circuits, ADCs and DACs; 8bit microprocessor (8085): architecture, programming, memory & Input/Output interfacing also.
Control Systems
 Basic control system components; Transfer function; Feedback principle; Block diagram representation; Transient and steadystate analysis of LTI systems; Signal flow graph; Frequency response; RouthHurwitz and Nyquist stability criteria; Bode and rootlocus plots; State variable model and solution of state equation of LTI systems; Lag, lead and laglead compensation.
Communications
 Random processes: autocorrelation & power spectral density, filtering of random signals through LTI systems, properties of white noise; Information theory: entropy, mutual information and channel capacity theorem; Analog communications: amplitude modulation and demodulation, spectra of AM and FM, angle modulation and demodulation, superheterodyne receivers, circuits for analog communications; Digital communications: PCM, DPCM, digital modulation schemes, phase amplitude, and also frequency shift keying (ASK, PSK, FSK), QAM, MAP and ML decoding, calculation of bandwidth, matched filter receiver, SNR and BER for digital modulation; Fundamentals of error correction, Hamming codes; also Timing & frequency synchronization, intersymbol interference & its mitigation; Basics of TDMA, FDMA and CDMA.
Electromagnetics
 Electrostatics; Maxwell’s equations: differential or integral forms and their interpretation, wave equation, boundary conditions, Poynting vector; Plane waves and properties: reflection and refraction, polarization, phase and group velocity, skin depth, propagation through various media; Transmission lines: characteristic impedance, equations, impedance matching, impedance transformation, Smith chart, Sparameters; Waveguides: modes, boundary conditions, dispersion relations, cutoff frequencies; Antennas: radiation pattern, antenna types, gain and directivity, return loss, antenna arrays; also Light propagation in optical fibres; Basics of radar.
GATE Syllabus: Electrical Engineering (EE)
Engineering Mathematics
 Calculus: Partial derivatives, Maxima & minima, Mean value theorems, theorems of integral calculus, evaluation of definite and improper integrals, multiple integrals, line, Taylor series, surface and volume integrals.
 Linear Algebra: matrix algebra, eigen values and eigen vectors, rank, solution of linear equations – existence and uniqueness; Vector space, basis, linear dependence and independence.
 Differential Equations: First order equations (linear and nonlinear), higher order linear differential equations, methods of solution using the variation of parameters, Cauchy’s and Euler’s equations, complementary function and particular integral, partial differential equations, initial and boundary value problems, the variable separable method also.
 Vector Analysis: Vector operations, gradient, Vectors in plane and space, divergence and curl, Gauss’s theorems, Green’s theorems and Stoke’s theorems.
 Complex Variable: Analytic functions, Cauchy’s integral formula, Cauchy’s integral theorem; Taylor’s series and Laurent’s series, residue theorem.
 Numerical Methods: Single & multistep methods for differential equations, Solution of nonlinear equations, convergence criteria.
 Probability and Statistics: Mean, median, mode and standard deviation; combinatorial probability, probability distribution functions – binomial distribution, Poisson distribution, exponential distribution and normal distribution; Correlation and regression analysis; Joint and conditional probability also.
 Transform Theory: Laplace Transform, Fourier Transform, z‐Transform.
Electric Circuits
 Network graph, Node and Mesh analysis, KCL, KVL, Transient response of dc and ac networks, Resonance, Passive filters, Sinusoidal steady‐state analysis, Ideal current and voltage sources, Thevenin’s, Superposition and Norton’s, Maximum power transfer theorem, Two‐port networks, Power and power factor in ac circuits, Three phase circuits also.
Electromagnetic Fields
 Coulomb’s Law, Electric Flux Density, Electric Field Intensity, Gauss’s Law, Divergence, Electric field and potential due to point, line, plane and spherical charge distributions, Capacitance of simple configurations, Effect of dielectric medium, Biot‐Savart’s law, Curl, Faraday’s law, Ampere’s law, Lorentz force, Inductance, Magnetomotive force, Magnetic circuits, Reluctance, also Self and Mutual inductance of simple configurations.
Signals and Systems
 Representation of continuous and discrete‐time signals, Linear TimeInvariant and Causal systems, Shifting and scaling operations, Fourier series representation of continuous periodic signals, Sampling theorem, Applications of Fourier Transform, zTransform, Laplace Transform.
Electrical Machines
 Single phase transformer: equivalent circuit, phasor diagram, regulation and efficiency, open circuit and short circuit tests; Three phase transformers: connections, parallel operation; Auto‐transformer, Electromechanical energy conversion principles, DC machines: separately excited, series/shunt, motoring and generating mode of operation and their char, starting and speed control of dc motors; Three phase induction motors: principle of operation, performance, types, torquespeed characteristics, equivalent circuit, noload and blocked rotor tests, starting and speed control; Operating principle of single phase induction motors; also.
 Synchronous machines: cylindrical and salient pole machines, regulation, performance, and parallel operation of generators, starting of the synchronous motor, and characteristics; Types of losses and efficiency calculations of electric machines.
Power Systems
 Power generation concepts, ac and dc transmission concepts, Series and shunt compensation, Models and performance of transmission lines and cables, Electric field distribution and insulators, Per‐unit quantities, Distribution systems, Bus admittance matrix, GaussSeidel and NewtonRaphson load flow methods, Voltage and Frequency control, Symmetrical components, Power factor correction, Symmetrical and unsymmetrical fault analysis, Principles of over‐current, differential and distance protection; also Circuit breakers, Equal area criterion, System stability concepts.
Control Systems
 Mathematical modeling and representation of systems, Feedback principle, transfer function, Transient and Steady‐state analysis of linear timeinvariant systems, Block diagrams and Signal flow graphs, RouthHurwitz and Nyquist criteria, Bode plots, Root loci, Stability analysis, Lead, Lag, and Lead‐Lag compensators also; P, PI and PID controllers; State transition matrix, State space model.
Electrical & Electronic Measurements
 Bridges and Potentiometers, Measurement of voltage, current, energy, power, and power factor; Instrument transformers, Digital voltmeters and multimeters, Phase, Time and Frequency measurement; Oscilloscopes, and Error analysis.
Analog and Digital Electronics
 Characteristics of diodes, BJT, MOSFET; Amplifiers: Biasing, Equivalent circuit and Frequency response; Simple diode circuits: clipping, clamping, rectifiers; Oscillators and Feedback amplifiers; Operational amplifiers: Characteristics & applications; Simple active filters, VCOs and Timers, Combinational & Sequential logic circuits, Multiplexer, Schmitt trigger, Demultiplexer, Sample and hold circuits, A/D & D/A converters, 8085Microprocessor: Programming, Architecture, and Interfacing.
Power Electronics
 Characteristics of semiconductor power devices: Diode, Triac, GTO, Thyristor, MOSFET, IGBT; DC to DC conversion: Buck, Boost, and BuckBoost converters; Single and three phase configuration of uncontrolled rectifiers, Bidirectional ac to dc voltage source converters, Line commutated thyristorbased converters, Issues of line current harmonics, Distortion factor of ac to dc converters, Power factor, Single phase & three phase inverters, Sinusoidal pulse width modulation also.
GATE Syllabus: Mechanical Engineering (ME)
Engineering Mathematics
 Calculus: Functions of single variable, limit, continuity and differentiability, mean value theorems, indeterminate forms; double and triple integrals; evaluation of definite and improper integrals; partial derivatives, total derivative, Taylor series (in one and two variables), Fourier series, maxima and minima; gradient, divergence and curl, directional derivatives, vector identities, line, surface, volume integrals, applications of Gauss, Stokes, Green’s theorems also.
 Linear Algebra: matrix algebra, eigen values and eigen vectors, rank, solution of linear equations – existence and uniqueness; Vector space, basis, linear dependence and independence.
 Differential Equations: First order equations (linear and nonlinear), higher order linear differential equations, methods of solution using the variation of parameters, Cauchy’s and Euler’s equations, complementary function and particular integral, partial differential equations, also initial and boundary value problems, variable separable method.
 Complex Variable: Analytic functions, Cauchy’s integral formula, Cauchy’s integral theorem; Taylor’s series and Laurent’s series, residue theorem.
 Numerical Methods: Single & multistep methods for differential equations, Solution of nonlinear equations, convergence criteria.
 Probability and Statistics: Mean, median, mode and standard deviation; combinatorial probability, probability distribution functions – binomial distribution, Poisson distribution, exponential distribution & normal distribution; Correlation and regression analysis; Joint and conditional probability.
Applied Mechanics & Design
 Engineering Mechanics: Freebody diagrams and equilibrium; virtual work; trusses and frames; dynamics & kinematics of particles and of rigid bodies in plane motion; impulse & momentum (linear & angular) and energy formulations, collisions.
 Mechanics of Materials: Stress and strain, elastic constants, Poisson’s ratio; thin cylinders; Mohr’s circle for plane stress & plane strain; shear force & bending moment diagrams; deflection of beams; bending & shear stresses; torsion of circular shafts; energy methods; Euler’s theory of columns; thermal stresses; strain gauges and rosettes; testing of hardness & impact strength; testing of materials with universal testing machine also.
 Theory of Machines: Displacement, velocity and acceleration analysis of plane mechanisms; cams; gears and gear trains; dynamic analysis of linkages; flywheels and governors; gyroscope; balancing of reciprocating and rotating masses.
 Vibrations: Free & forced vibration of single degree of freedom systems, the effect of damping; resonance; vibration isolation; critical speeds of shafts.
 Machine Design: Design for static and dynamic loading; fatigue strength and the SN diagram; failure theories; principles of the design of machine elements such as bolted, riveted and welded joints; also gears, shafts, rolling & sliding contact bearings, brakes & clutches, springs.
Fluid Mechanics & Thermal Sciences
 Fluid Mechanics: Fluid properties; also fluid statics, buoyancy, manometry, forces on submerged bodies, stability of floating bodies; and fluid acceleration; controlvolume analysis of mass, momentum and energy; Bernoulli’s equation; differential equations of continuity and momentum; dimensional analysis; viscous flow of incompressible fluids, elementary turbulent flow, boundary layer, flow through pipes, head losses in pipes, bends and fittings also.
 HeatTransfer: Modes of heat transfer; one dimensional heat conduction, heat transfer through fins, resistance concept & electrical analogy; unsteady heat conduction, lumped parameter system, Heisler’s charts; thermal boundary layer, dimensionless parameters in free, and forced convective heat transfer, heat transfer correlations for flow over flat plates & through pipes, effect of turbulence; heat exchanger performance, LMTD, NTU methods; also radiative heat transfer, Wien’s displacement law, StefanBoltzmann law, black and grey surfaces, view factors, radiation network analysis also.
 Thermodynamics: Thermodynamic systems & processes; properties of pure substances, the behaviour of ideal & real gases; zeroth & first laws of thermodynamics, the second law of thermodynamics, calculation of work and heat in various processes; thermodynamic relations; thermodynamic property charts & tables, availability and irreversibility.
 Applications: Power Engineering: Air & gas compressors, vapour & gas power cycles, concepts of regeneration and reheat. I.C. Engines: Diesel and dual cycles, Airstandard Otto. Refrigeration and airconditioning: Vapour and gas refrigeration and heat pump cycles; psychrometric chart, properties of moist air, basic psychrometric processes. Turbomachinery: Impulse and reaction principles, Peltonwheel, velocity diagrams, Francis & Kaplan turbines also.
Materials, Manufacturing & Industrial Engineering
 Engineering Materials: Structure & properties of engineering materials, heat treatment, phase diagrams, stressstrain diagrams for engineering materials.
 Casting, Forming & Joining Processes: Different types of castings, the design of patterns, moulds and cores; riser and gating design, solidification and cooling. fundamentals of hot and cold working processes; Plastic deformation and yield criteria; load estimation for bulk (forging, drawing, rolling, extrusion) and sheet (shearing, bending, deep drawing) metal forming processes; also principles of powder metallurgy. Principles of welding, brazing, soldering, adhesive bonding.
 Machining and Machine Tool Operations: basic machine tools; Mechanics of machining; single and multipoint cutting tools, tool geometry and materials, tool life and wear; economics of machining; principles of work holding, the design of jigs and fixtures; principles of nontraditional machining processes.
 Metrology and Inspection: Limits, fits and tolerances; comparators; gauge design; interferometry; linear and angular measurements; form and finish measurement; tolerance analysis in manufacturing and assembly; alignment and testing methods.
 Computer Integrated Manufacturing: Basic concepts of CADCAM, and their integration tools.
 Production Planning & Control: Forecasting models, scheduling, aggregate production planning, materials requirement planning.
 Inventory Control: Deterministic models, and safety stock inventory control systems.
 Operations Research: Linear programming, simplex method, transportation, assignment, network flow models, simple queuing models, PERT and CPM.
GATE Syllabus 2021
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AG  GATE Syllabus for Agricultural Engineering  Click here 
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CS  GATE Syllabus for Computer Science and Information Technology  Click here 
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EC  GATE Syllabus for Electronics and Communication Engineering 
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EE  GATE Syllabus for Electrical Engineering  Click here 
EY  GATE Syllabus for Ecology and Evolution  Click here 
GG  GATE Syllabus for Geology and Geophysics  Click here 
IN  GATE Syllabus for Instrumentation Engineering  Click here 
MA  GATE Syllabus for Mathematics  Click here 
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MT  GATE Syllabus for Metallurgical Engineering  Click here 
PE  GATE Syllabus for Petroleum Engineering  Click here 
PH  GATE Syllabus for Physics  Click here 
PI  GATE Syllabus for Production and Industrial Engineering  Click here 
ST  GATE Syllabus for Statistics  Click here 
TF  GATE Syllabus for Textile Engineering and Fibre Science  Click here 
XE  Engineering Sciences Syllabus  
XEA  GATE Syllabus for Engineering Mathematics – Compulsory section  Click here 
XEB  GATE Syllabus for Fluid Mechanics  Click here 
XEC  GATE Syllabus for Materials Science  Click here 
XED  GATE Syllabus for Solid Mechanics  Click here 
XEE  GATE Syllabus for Thermodynamics  Click here 
XEF  GATE Syllabus for Polymer Science and Engineering  Click here 
XEG  GATE Syllabus for Food Technology  Click here 
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XL  Life Sciences Syllabus  
XLP  GATE Syllabus for Chemistry – Compulsory section  Click here 
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