SYLLABUS OF GATE 2021
Section 1:
Engineering Mathematics :
✓Linear Algebra: Matrix algebra; Systems of linear equations; Eigen values and Eigen vectors.
✓Calculus: Functions of single variable; Limit, continuity and differentiability; Mean value theorems, local maxima and minima; Taylor series; Evaluation of definite and indefinite integrals, application of definite integral to obtain area and volume; Partial derivatives; Total derivative; Gradient, Divergence and Curl, Vector identities; Directional derivatives; Line, Surface and Volume integrals.
✓Ordinary Differential Equation (ODE): First order (linear and non-linear) equations; higher
order linear equations with constant coefficients; Euler-Cauchy equations; initial and boundary value problems.
✓Partial Differential Equation (PDE): Fourier series; separation of variables; solutions of one-dimensional diffusion equation; first and second order one-dimensional wave equation and
two-dimensional Laplace equation.
✓Probability and Statistics: Sampling theorems; Conditional probability; Descriptive statistics – Mean, median, mode and standard deviation; Random Variables – Discrete and
Continuous, Poisson and Normal Distribution; Linear regression.
Numerical Methods: Error analysis. Numerical solutions of linear and non-linear algebraic equations; Newton’s and Lagrange polynomials; numerical differentiation; Integration by trapezoidal and Simpson’s rule; Single and multi-step methods for first order differential equation.
Section 2:
Structural Engineering :
✓Engineering Mechanics: System of forces, free-body diagrams, equilibrium equations; Internal
forces in structures; Frictions and its applications; Centre of mass; Free Vibrations of undamped SDOF system.
✓Solid Mechanics: Bending moment and shear force in statically determinate beams; Simple stress and strain relationships; Simple bending theory, flexural and shear stresses, shear
centre; Uniform torsion, Transformation of stress; buckling of column, combinedand direct bending stresses.
✓Structural Analysis: Statically determinate and indeterminate structures by force/ energy
methods; Method of superposition; Analysis of trusses, arches, beams,cables and frames;
Displacement methods: Slope deflection and moment distribution methods; Influence lines; Stiffness and flexibility methods of structural analysis.
✓Construction Materials and Management: Construction Materials: Structural Steel –Composition, material properties and behaviour; Concrete - Constituents, mix design, short-
term and long-term properties.
✓Construction Management: Types of construction projects; Project planning and network analysis - PERT and CPM; Cost estimation.
✓Concrete Structures: Working stress and Limit state design concepts; Designof beams, slabs, columns; Bond and development length; Pre stressed concrete beams. Steel Structures:
Working stress and Limit state design concepts; Design of tension and compression members, beams and beam- columns, column bases; Connections - simple and eccentric,
beam-column connections, plate girders and trusses; Concept of plastic analysis -beams and frame
Section 3
Geotechnical Engineering :
✓Soil Mechanics: Three-phase system and phase relationships, index properties; Unified and Indian standard soil classification system; Permeability - one dimensional flow, Seepage
through soils – two - dimensional flow, flow nets, uplift pressure, piping, capillarity, seepage force; Principle of effective stress and quicksand condition; Compaction of soils; One-
dimensional consolidation, time rate of consolidation; Shear Strength, Mohr’s circle, effective and total shear strength parameters, Stress-Strain characteristics of clays and sand; Stress paths.
✓Foundation Engineering: Sub-surface investigations - Drilling bore holes, sampling, plate load test, standard penetration and cone penetration tests; Earth pressure theories - Rankine and
Coulomb; Stability of slopes – Finite and infinite slopes, Bishop’s method; Stress distribution in soils – Boussinesq’s theory; Pressure bulbs, Shallow foundations – Terzaghi’s and
Meyerhoff’s bearing capacity theories, effect of water table; Combined footing and raft foundation; Contact pressure; Settlement analysis in sands and clays; Deep foundations –dynamic and static formulae, Axial load capacity of piles in sands and clays, pile load test, pile
under lateral loading, pile group efficiency, negative skin friction.
Section 4
Water Resource Engineering :
✓Fluid Mechanics: Properties of fluids, fluid statics; Continuity, momentum and energy
equations and their applications; Potential flow, Laminar and turbulent flow; Flow in pipes, pipe networks; Concept of boundary layer and its growth; Concept of lift and drag.
✓Hydraulics: Forces on immersed bodies; Flow measurement in channels and pipes; Dimensional analysis and hydraulic similitude; Channel Hydraulics - Energy-depth relationships, specific energy, critical flow, hydraulic jump, uniform flow, gradually varied
flow and water surface profiles.
✓Hydrology: Hydrologic cycle, precipitation, evaporation, evapo-transpiration, watershed, infiltration, unit hydrographs, hydrograph analysis, reservoir capacity, flood estimation and
routing, surface run-off models, ground water hydrology - steady state well hydraulics and aquifers; Application of Darcy’s Law.
✓Irrigation: Types of irrigation systems and methods; Crop water requirements - Duty, delta, evapo-transpiration; Gravity Dams and Spillways; Lined and unlined canals, Design of weirs on permeable foundation; cross drainage structures.
Section 5
Environmental Engineering :
Water and Waste Water Quality and Treatment: Basics of water quality standards –Physical, chemical and biological parameters; Water quality index; Unit processes and
operations; Water requirement; Water distribution system; Drinking water treatment.
Sewerage system design, quantity of domestic wastewater, primary and secondary treatment. Effluent discharge standards; Sludge disposal; Reuse of treated sewage for different applications.
Air Pollution: Types of pollutants, their sources and impacts, air pollution control, air quality standards, Air quality Index and limits.
Municipal Solid Wastes: Characteristics, generation, collection and transportation of solid wastes, engineered systems for solid waste management (reuse/ recycle, energy recovery,
treatment and disposal).
Section 6
Transportation Engineering :
Transportation Infrastructure: Geometric design of highways - cross-sectional elements, sight distances, horizontal and vertical alignments.Geometric design of railway Track – Speed and Cant.
Concept of airport runway length, calculations and corrections; taxiway and exit taxiway design.
Highway Pavements: Highway materials - desirable properties and tests; Desirable properties of bituminous paving mixes; Design factors for flexible and rigid pavements; Design of flexible
and rigid pavement using IRC codes
Traffic Engineering: Traffic studies on flow and speed, peak hour factor, accident study, statistical analysis of traffic data; Microscopic and macroscopic parameters of traffic flow,
fundamental relationships; Traffic signs; Signal design by Webster’s method; Types of intersections; Highway capacity.
Section 7
Geomatics Engineering :
Principles of surveying; Errors and their adjustment; Maps - scale, coordinate system; Distance and angle measurement - Levelling and trigonometric levelling; Traversing and
triangulation survey; Total station
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