# 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. Air-plane (fixed wing aircraft) configuration & various parts.**Performance of****Airplane**: Pressure altitude; equivalent, calibrated, indicated airspeeds. Primary flight instruments: Altimeter, ASI, VSI, Turn-bank indicator, Drag polar. takeoff & landing; steady climb & descent, absolute & service ceiling. cruise, cruise climb, endurance or loiter, load factor, turning flight, V-n 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 lateral-directional dynamics, lateral-directional modes, longitudinal modes.

#### Space Dynamics

- Central force motion; determination of trajectory & orbital period in simple cases; Orbit transfer, in-plane & out-of-plane.

#### 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; Kutta-Joukoswki 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; One-dimensional compressible flows, Rayleigh flow, Fanno flow, Isentropic flows, Prandtl-Meyer 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, Three-dimensional 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 thin-walled sections.**Structural Dynamics**: Free & forced vibrations of undamped and damped SDOF systems, Free vibrations of undamped 2-DOF 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 non-rotating 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, multi-staging 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 & non-linear 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 & non-linear 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, inter-cultivation, 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; bio-fuels.**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 take-off; tractor clutches and brakes; mechanics of tractor chassis; traction theory; three-point 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 Hazen-Williams 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

**Soil-Water-Plant 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, micro-irrigation methods, design & evaluation of irrigation methods.**Agricultural Drainage**: Drainage coefficient; planning, design and layout of surface and sub-surface 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 air-vapours 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 solids-pneumatic, bucket, screw and belt conveying; effectiveness of grain cleaners; cleaning and grading; centrifugal separation of solids, liquids & gases also.**Processing and By-product Utilization**: Processing of fruits, seeds, spices and vegetables; By-product 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; Barrier-free 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 Pre-stressing; 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 man-made 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 bye-laws.

#### 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, Eco-City, 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 non-spatial 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 cost-benefit 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 self-governance; 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; Air-Conditioning 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; Land-use – transportation – urban form inter-relationships; 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 slow-moving 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 PDE-Laplace, 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**: Biomolecules-structure & 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 host-pathogen interaction; Nitrogen fixation.**Cell Biology**: Prokaryotic & eukaryotic cell structure; Cell cycle & cell growth control, Cell signalling and Cell-Cell 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; Extra-chromosomal 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 microscopy-light, electron, fluorescent & confocal; Centrifugation- high speed & ultra; Principles of spectroscopy-UV, 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 cell-mediated immunity; Molecular basis of antibody diversity; Antigen-antibody 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, protein-nucleic acid, protein-protein, and protein-ligand 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; In-situ hybridization; DNA fingerprinting; Southern & northern blotting; RAPD, RFLP; Site-directed 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 non-anchorage dependent cell culture; Micro & macro-carrier 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 non-ideal multiphase bioreactors; Media formulation & optimization; Rheology of fermentation fluids, Aeration and agitation; Kinetics of microbial growth, substrate utilization & product formation; Batch, fed-batch & continuous processes; Sterilization of air and media; Also Various types of microbial and enzyme reactors; Unit operations in solid-liquid separation & liquid-liquid extraction; Instrumentation control & optimization; Process scale-up, 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 membrane-based bioseparation methods; Large scale production and purification of recombinant proteins; also Immobilization of biocatalysts (enzymes & cells) for bioconversion processes; Bioremediation-Aerobic, 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 (linear|non-linear) equations; Euler-Cauchy 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 one-dimensional diffusion equation; separation of variables; first and second order one-dimensional wave equation and also two-dimensional 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 & non-linear algebraic equations; Least square approximation, numerical differentiation, Newton’s & Lagrange polynomials, Integration by trapezoidal & Simpson’s rule, single and multi-step methods for 1st-order differential equations.

#### Structural Engineering

**Engineering Mechanics:**System of forces, free-body 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; Impulse-momentum; 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, short-term and long-term 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 & beam-columns, column bases; Plastic analysis of beams & frames; Connections – simple & eccentric, beam-column connections, plate girders & trusses.

#### Geotechnical Engineering

**Soil Mechanics**: Origin of soils, soil structure & fabric; Unified and Indian standard soil classification system; Three-phase system & phase relationships, index properties; Permeability – one dimensional flow, Darcy’s law; Seepage through soils – two-dimensional 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**: Sub-surface 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 – Energy-depth 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 run-off 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, cross-drainage 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 – cross-sectional 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: 37-2012; Design factors for flexible & rigid pavements; Design of rigid pavements using IRC: 58-2011; Distresses in concrete pavements.**Traffic Engineering**: Traffic studies on flow, travel time, speed – delay and O-D 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 (linear|non-linear) equations; Euler-Cauchy 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 & non-linear algebraic equations; Least square approximation, numerical differentiation, Newton’s & Lagrange polynomials, Integration by trapezoidal & Simpson’s rule, single and multi-step methods for 1st-order differential equations also.

#### Fluid Mechanics & Mechanical Operations

- Fluid statics, Newtonian & non-Newtonian fluids, shell-balances 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 & non-reacting 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, liquid-liquid 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, non-ideal reactors; residence time distribution, and single parameter model; kinetics of heterogeneous catalytic reactions; non-isothermal 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 (chlor-alkali 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 first-order 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; Context-free grammars & push-down automata; Turing machines and undecidability; Regular & context-free languages, pumping lemma also.

#### Algorithms

- Searching, hashing, and sorting; Asymptotic worst-case 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, syntax-directed 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. Time-dependent and time-independent Schrödinger equations. Particle in a box; Harmonic oscillator; Born interpretation. Rigid rotor; Hydrogen atom: atomic orbitals. Multi-electron atoms: Variation & first-order perturbation techniques. orbital approximation; Chemical bonding: Valence bond theory and LCAO-MO theory. Hybrid orbitals. Applications of LCAO-MOT 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: Gibbs-Helmholtz 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. Non-ideal solutions; Ionic mobility and conductivity; Debye-Hückel-Onsager equation. Debye-Hückel 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; two-component systems: liquid-vapour, liquid-liquid and solid-liquid 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; Self-assembly. Surface catalysis: Langmuir-Hinshelwood mechanism. Physical chemistry of colloids, micelles, and macromolecules.**Surfaces & Interfaces**: Physisorption and chemisorption; Langmuir, Freundlich, BET isotherms. Surface catalysis: Langmuir-Hinshelwood mechanism. Surface tension, viscosity; Physical chemistry of colloids, micelles and macromolecules; Self-assembly.**Kinetics**: Transition state theory: Eyring equation, thermodynamic aspects. Potential energy surfaces & classical trajectories. Steady-state 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 Acid-base 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, Jahn-Teller distortion. Electronic spectra of transition metal complexes: spectroscopic term symbols, Orgel diagrams, selection rules, charge-transfer spectra. Reaction mechanisms: kinetic and thermodynamic stability, substitution and redox reactions; Magnetic properties of transition metal complexes. also**Organometallics**: 18-Electron rule; metal-carbonyl, metal-alkyl, metal-olefin & metal-carbene complexes and metallocenes. Types of organometallic reactions; Fluxionality in organometallic complexes. Homogeneous catalysis – Hydrogenation, acetic acid synthesis, hydroformylation, metathesis and olefin oxidation; Heterogeneous catalysis – Fischer-Tropsch reaction, Ziegler-Natta 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:**UV-visible spectrophotometry, mass spectrometry, NMR and ESR spectroscopy. Chromatography including GC and HPLC. Electroanalytical methods- polarography, ion-selective 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 Si-based reagents in organic synthesis. Concepts of multistep synthesis – retrosynthetic analysis, synthons strategic disconnections, and synthetic equivalents. Carbon-carbon 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 Felkin-Anh 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 Curtin-Hammett 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 carbon-carbon & carbon-heteroatom (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; Di-π-methane rearrangement, Barton reaction.**Biomolecules**: Structure, properties and reactions of mono- and di-saccharides, 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 UV-visible, 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 & multi-step 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.
- Continuous-time signals: Fourier series & Fourier transform representations, sampling theorem; Discrete-time signals: discrete-time Fourier transform (DTFT), DFT, FFT, interpolation of discrete-time signals, Z-transform; 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; P-N junction, Zener diode, MOS capacitor, BJT, MOSFET, LED, photodiode, solar cell; Integrated circuit fabrication process: oxidation, ion implantation, diffusion, photolithography and twin-tub CMOS process also.

#### Analog Circuits

- Small signal equivalent circuits of diode, BJT, MOSFET; Simple diode circuits: clipping, clamping, rectifiers; Single-stage BJT and MOSFET amplifiers: biasing, bias stability, mid-frequency small signal analysis, and frequency response; BJT and MOSFET amplifiers: multi-stage, feedback, differential, power, and operational; Active filters; Simple op-amp circuits; Sinusoidal oscillators: criterion for oscillation, single-transistor, & op-amp configurations; also Function generators, wave-shaping 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; 8-bit microprocessor (8085): architecture, programming, memory & Input/Output interfacing also.

#### Control Systems

- Basic control system components; Transfer function; Feedback principle; Block diagram representation; Transient and steady-state analysis of LTI systems; Signal flow graph; Frequency response; Routh-Hurwitz and Nyquist stability criteria; Bode and root-locus plots; State variable model and solution of state equation of LTI systems; Lag, lead and lag-lead 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, inter-symbol 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, S-parameters; Waveguides: modes, boundary conditions, dispersion relations, cut-off 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 & multi-step 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 Time-Invariant and Causal systems, Shifting and scaling operations, Fourier series representation of continuous periodic signals, Sampling theorem, Applications of Fourier Transform, z-Transform, 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, torque-speed characteristics, equivalent circuit, no-load 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 Newton-Raphson 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 time-invariant systems, Block diagrams and Signal flow graphs, Routh-Hurwitz 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 Buck-Boost converters; Single and three phase configuration of uncontrolled rectifiers, Bidirectional ac to dc voltage source converters, Line commutated thyristor-based 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 & multi-step 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**: Free-body 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 S-N 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; control-volume 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.**Heat-Transfer:**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, Stefan-Boltzmann 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, Air-standard Otto. Refrigeration and air-conditioning: Vapour and gas refrigeration and heat pump cycles; psychrometric chart, properties of moist air, basic psychrometric processes. Turbomachinery: Impulse and reaction principles, Pelton-wheel, velocity diagrams, Francis & Kaplan turbines also.

#### Materials, Manufacturing & Industrial Engineering

**Engineering Materials**: Structure & properties of engineering materials, heat treatment, phase diagrams, stress-strain 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 multi-point 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 non-traditional 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 CAD|CAM, 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

### Download Gate Syllabus 2021

Paper Code | Papers | Download Link (PDF) |
---|---|---|

General Aptitude (GA): Common in all papers | Click here | |

AE | GATE Syllabus for Aerospace Engineering | Click here |

AG | GATE Syllabus for Agricultural Engineering | Click here |

AR | GATE Syllabus for Architecture and Planning | Click here |

BT | GATE Syllabus for Biotechnology | Click here |

CE | GATE Syllabus for Civil Engineering | Click here |

CH | GATE Syllabus for Chemical Engineering | Click here |

CS | GATE Syllabus for Computer Science and Information Technology | Click here |

CY | GATE Syllabus for Chemistry | Click here |

EC | GATE Syllabus for Electronics and Communication Engineering | Click here |

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 |

ME | GATE Syllabus for Mechanical Engineering | Click here |

MN | GATE Syllabus for Mining Engineering | Click here |

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 | |

XE-A | GATE Syllabus for Engineering Mathematics – Compulsory section | Click here |

XE-B | GATE Syllabus for Fluid Mechanics | Click here |

XE-C | GATE Syllabus for Materials Science | Click here |

XE-D | GATE Syllabus for Solid Mechanics | Click here |

XE-E | GATE Syllabus for Thermodynamics | Click here |

XE-F | GATE Syllabus for Polymer Science and Engineering | Click here |

XE-G | GATE Syllabus for Food Technology | Click here |

XE-H | GATE Syllabus for Atmospheric and Oceanic Sciences | Click here |

XL | Life Sciences Syllabus | |

XL-P | GATE Syllabus for Chemistry – Compulsory section | Click here |

XL-Q | GATE Syllabus for Biochemistry | Click here |

XL-R | GATE Syllabus for Botany | Click here |

XL-S | GATE Syllabus for Microbiology | Click here |

XL-T | GATE Syllabus for Zoology | Click here |

XL-U | GATE Syllabus for Food Technology | Click here |

### GATE Cutoff for IIT

Institutes | Links |

IIT Delhi | Click here |

IIT Madras | Click here |

IIT Bombay | Click here |

IIT Kanpur | Click here |

IIT Kharagpur | Click here |

IIT Guwahati | Click here |

IIT Roorkee | Click here |

IIT Indore | Click here |

IIT Hyderabad | Click here |

IIT BHU | Click here |

IIT Jodhpur | Click here |

IIT Mandi | Click here |

IIT (ISM) Dhanbad | Click here |

IIT Gandhinagar | Click here |

IISc Bangalore | Click here |

## In Conclusion

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