GATE 2025 Syllabus

The Syllabus of GATE 2025 is based on the disciplines studied in the qualifying examination. IIT Bombay has specified the GATE 2025 syllabus according to the 29 papers that will be conducted for admissions to the M.Tech programmes. Below is the complete information about the GATE syllabus which includes the topics of each paper & chapter. The GATE 2025 exam pattern will consist of the number of questions, type of question, marking scheme, papers, etc. In the GATE exam, a total of 65 questions will be asked. The duration of the exam will be three hours. The question paper will be of 100 marks. Candidates can read from the given GATE syllabi & secure high marks in the examination.

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Engineering Mathematics

• Discrete Mathematics
• Propositional and first-order logic.
• Sets, relations, functions, partial orders and lattices.
• Graphs: connectivity, matching, colouring.
• Combinatorics: counting, recurrence relations, generating functions
• Linear Algebra, Matrices, determinants, a system of linear equations, eigenvalues and eigenvectors, LU decomposition
• Calculus, Limits, continuity, and differentiability.
• Maxima and minima.
• Mean value theorem.
• Integration
• Probability Random Variables.
• Uniform, normal, exponential, Poisson and binomial distributions.
• Mean, median, mode and standard deviation.
• Conditional probability and Bayes theorem

Digital Logic

• Boolean algebra. Combinational and sequential circuits. Minimization. Number representations and computer arithmetic (fixed and floating-point).
• Computer Organization and Architecture
• Machine instructions and addressing modes. ALU, data path and control unit. Instruction pipelining. Memory hierarchy: cache, main memory, and secondary storage; I/O, interface (Interrupt and DMA mode).

Programming and Data Structures

• Programming in C. Recursion. Arrays, stacks, queues, linked lists, trees, binary search trees, binary heaps, graphs.
• Algorithms
• Searching, sorting, hashing. Asymptotic worst-case time and space complexity. Algorithm design techniques: greedy, dynamic programming and divide-and-conquer. Graph search, minimum spanning trees, and shortest paths.

Theory of Computation

• Regular expressions and finite automata. Context-free grammars and pushdown automata. Regular and context-free languages, pumping lemma. Turing machines and undecidability.
• Compiler Design
• Lexical analysis, parsing, syntax-directed translation. Runtime environments. Intermediate code generation.
• Operating System
• Processes, threads, inter-process communication, concurrency, and synchronization. Deadlock. CPU scheduling. Memory management and virtual memory. File systems.

Databases

• ER-model. Relational model: relational algebra, tuple calculus, SQL. Integrity constraints, normal forms. File organization, indexing (e.g., B and B+ trees). Transactions and concurrency control.
• Computer Networks
• The concept of layering. LAN technologies (Ethernet). Flow and error control techniques, switching. IPv4/IPv6, routers and routing algorithms (distance vector, link state). TCP/UDP and sockets, congestion control. Application layer protocols (DNS, SMTP, POP, FTP, HTTP). Basics of Wi-Fi. Network security: authentication, basics of a public key and private key cryptography, digital signatures and certificates, firewalls.

GATE 2025 Civil Syllabus:

Section 1: Engineering Mathematics

• Linear Algebra: Matrix algebra; Systems of linear equations; Eigenvalues and Eigenvectors.
• Calculus: Functions of a single variable, Limit, continuity and differentiability, Mean value theorems, Evaluation of definite and improper integrals, Partial derivatives, Total derivative, Maxima and minima, Gradient, Divergence and Curl, Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green’s theorems.
• Differential equations: First-order equations (linear and nonlinear), Higher order linear differential equations with constant coefficients, Cauchy’s and Euler’s equations, Initial and boundary value problems, Laplace transforms, Solutions of one-dimensional heat and wave equations and Laplace equation.
• Complex variables: Analytic functions, Cauchy’s integral theorem, Taylor, and Laurent series.
• Probability and Statistics: Definitions of probability and sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Poisson, Normal and Binomial distributions.
• Numerical Methods: Numerical solutions of linear and non-linear algebraic equations Integration by trapezoidal and Simpson’s rule, single and multi-step methods for differential equations.

Section 2: Structural Engineering

• Mechanics: Bending moment and shear force in statically determinate beams.
• Simple stress and strain relationship: Stress and strain in two dimensions, principal stresses, stress transformation, Mohr’s circle. Simple bending theory, flexural and shear stresses, unsymmetrical bending, shear centre. Thin-walled pressure vessels, uniform torsion, buckling of column, combined and direct bending stresses.
• Structural Analysis: Analysis of statically determinate trusses, arches, beams, cables and frames, displacements in statically determinate structures and analysis of statically indeterminate structures by force/ energy methods, analysis by displacement methods (slope deflection and moment distribution methods), influence lines for determinate and indeterminate structures. Basic concepts of matrix methods of structural analysis.
• Concrete Structures: Concrete Technology- properties of concrete, basics of mix design.
• Steel Structures: Analysis and design of tension and compression members, beams, and columns, column bases. Connections- simple and eccentric, beam-column connections, plate girders, and trusses. Plastic analysis of beams and frames.

Section 3: Geotechnical Engineering

• Soil Mechanics: Origin of soils, soil classification, three-phase system, fundamental definitions, relationship and interrelationships, permeability &seepage, effective stress principle, consolidation, compaction, shear strength.
• Foundation Engineering: Sub-surface investigations- scope, drilling boreholes, sampling, penetration tests, plate load test. Earth pressure theories, the effect of the water table, layered soils. Stability of slopes-infinite slopes, finite slopes. Foundation types-foundation design requirements. Shallow foundations-bearing capacity, the effect of shape, water table, and other factors, stress distribution, settlement analysis in sands & clays. Deep foundations–pile types, dynamic & static formulae, load capacity of piles in sands & clays, negative skin friction

Section 4: Water Resources Engineering

• Fluid Mechanics and Hydraulics: Properties of fluids, the principle of conservation of mass, momentum, energy and corresponding equations, potential flow, applications of momentum and Bernoulli’s equation, laminar and turbulent flow, flow in pipes, pipe networks. The concept of the boundary layer and its growth. Uniform flow, critical flow, and gradually varied flow in channels, specific energy concept, hydraulic jump. Forces on immersed bodies, flow measurements in channels, tanks, and pipes. Dimensional analysis and hydraulic modelling. Kinematics of flow, velocity triangles and specific speed of pumps and turbines.
• Hydrology: Hydrologic cycle, rainfall, evaporation, infiltration, stage-discharge relationships, unit hydrographs, flood estimation, reservoir capacity, reservoir and channel routing. Well, hydraulics.
• Irrigation: Duty, delta, estimation of evapotranspiration and crop water requirements.
• The design of lined and unlined canals, waterways, headworks, gravity dams, and spillways. The design of weirs on permeable foundation. Types of an irrigation system, irrigation methods. Waterlogging and drainage, sodic soils.

Section 5: Environmental Engineering

• Water requirements: Quality standards, basic unit processes, and operations for water
• Drinking water standards, water requirements, basic unit operations and unit processes for surface water treatment, and distribution of water. Sewage and sewerage treatment, quantity and characteristics of wastewater. Primary, secondary and tertiary treatment of wastewater, sludge disposal, and effluent discharge standards. Domestic wastewater treatment, the number of characteristics of domestic wastewater, primary and secondary treatment Unit operations and unit processes of domestic wastewater, and sludge disposal.
• Air Pollution: Types of pollutants, their sources and impacts, air pollution meteorology, air pollution control, air quality standards and limits.
• Municipal Solid Wastes: Characteristics, generation, collection and transportation of solid wastes, engineered systems for solid waste management (reuse/ recycle, energy recovery, treatment, and disposal).
• Noise Pollution: Impacts of noise, permissible limits of noise pollution, measurement of noise and control of noise pollution.

Section 6: Transportation Engineering

• Highway Planning: Geometric design of highways, testing, and specifications of paving materials, and the design of flexible and rigid pavements.
• Traffic Engineering: Traffic characteristics, the theory of traffic flow, intersection design, traffic signs and signal design, and 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; Horizontal and vertical curves. Photogrammetry - scale, flying height; remote sensing - basics, platform and sensors, visual image interpretation; Basics of Geographical information system (GIS) and Geographical Positioning system (GPS)
• The Importance of surveying, principles and classifications, mapping concepts, coordinate system, map projections, measurements of distance and directions, levelling, theodolite traversing, plane table surveying, errors and adjustments, and curves.

GATE 2025 Engineering Mathematics Syllabus

• The section comprising of arithmetical questions, Engineering Mathematics’ main aim is to test the applicant’s ability to understand complex concepts of mathematics involved in Engineering with ease and their application to problems.
• Linear Algebra, Matrix algebra, systems of linear equations, eigenvalues and eigenvectors.
• Calculus, Functions of single variable, limit, continuity and differentiability, Mean value theorems, indeterminate forms; evaluation of definite and improper integrals; double and triple integrals; partial derivatives, total derivative, Taylor series (in one and two variables), maxima and minima, Fourier series; gradient, divergence and curl, vector identities, directional derivatives, line, surface and volume integrals, applications of Gauss, Stokes and Green’s theorems.
• Differential equations, First order equations (linear and nonlinear); higher-order linear differential equations with constant coefficients; Euler-Cauchy equation; initial and boundary value problems; Laplace transforms; solutions of heat, wave, and Laplace's equations.
• Complex variables Analytic functions; Cauchy-Riemann equations; Cauchy’s integral theorem and integral formula; Taylor and Laurent series. Probability and Statistics: Definitions of probability, sampling theorems, Conditional probability; mean, median, mode and standard deviation; random variables, binomial, Poisson and normal distributions.
• Numerical Methods Numerical solutions of linear and non-linear algebraic equations; integration by trapezoidal and Simpson’s rules; single and multi-step methods for differential equations.

 GATE 2025 syllabus for Applied Mechanics & Design

• Engineering Mechanics Free-body diagrams and equilibrium; trusses and frames; virtual work; kinematics and dynamics of particles and of rigid bodies in plane motion; impulse and momentum (linear and angular) and energy formulations, collisions.
• Mechanics of Materials Stress and strain, elastic constants, Poisson's ratio; Mohr’s circle for plane stress and plane strain; thin cylinders; shear force and bending moment diagrams; bending and shear stresses; deflection of beams; torsion of circular shafts; Euler’s theory of columns; energy methods; thermal stresses; strain gauges and rosettes; testing of materials with universal testing machine; testing of hardness and impact strength.
• Theory of Machines Displacement, velocity and acceleration analysis of plane mechanisms; dynamic analysis of linkages; cams; gears and gear trains; flywheels and governors; balancing of reciprocating and rotating masses; gyroscope.
• Vibrations Free and forced vibration of single degree of freedom systems, the effect of damping; vibration isolation; resonance; critical speeds of shafts.
• Machine Design Design for static and dynamic loading; failure theories; fatigue strength and the S-N diagram; principles of the design of machine elements such as bolted, riveted and welded joints; shafts, gears, rolling and sliding contact bearings, brakes, and clutches, springs.

 GATE 2025 syllabus for Fluid Mechanics and Thermal Sciences

• Fluid Mechanics-Fluid properties; fluid statics, manometer, buoyancy, forces on submerged bodies, stability of floating bodies; control-volume analysis of mass, momentum and energy; fluid acceleration; differential equations of continuity and momentum; Bernoulli’s equation; dimensional analysis; viscous flow of incompressible fluids, boundary layer, elementary turbulent flow, flow through pipes, head losses in pipes, bends and fittings.
• Heat Transfer-Modes of heat transfer; one-dimensional heat conduction, resistance concept and electrical analogy, heat transfer through fins; 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 and through pipes, the effect of turbulence; heat exchanger performance, LMTD and NTU methods; radiative heat transfer, Stefan-Boltzmann law, Wien's displacement law, black and grey surfaces, view factors, radiation network analysis.
• Thermodynamics-Thermodynamic systems and processes; properties of pure substances, the behaviour of ideal and real gases; zeroth and first laws of thermodynamics, calculation of work and heat in various processes; second law of thermodynamics; thermodynamic property charts and tables, availability and irreversibility; thermodynamic relations.
• Applications- Power Engineering: Air and gas compressors; vapour and gas power cycles, concepts of regeneration and reheat. I.C. Engines: Air-standard Otto, Diesel, and Dual cycles. Refrigeration and air-conditioning: Vapour and gas refrigeration and heat pump cycles; properties of moist air, psychrometric chart, basic psychrometric processes
• Turbomachinery- Impulse and reaction principles, velocity diagrams, Pelton-wheel, Francis and Kaplan turbines.
• Materials, Manufacturing and Industrial Engineering
• Engineering Materials- Structure and properties of engineering materials, phase diagrams, heat treatment, and stress-strain diagrams for engineering materials.
• Casting, Forming and Joining Processes Different types of castings, the design of patterns, moulds and cores; solidification and cooling; riser and gating design. Plastic deformation and yield criteria; fundamentals of hot and cold working processes; load estimation for bulk (forging, rolling, extrusion, drawing) and sheet (shearing, deep drawing, bending) metal forming processes; principles of powder metallurgy. Principles of welding, brazing, soldering and adhesive bonding. Machining and Machine Tool Operations: Mechanics of machining; basic machine tools; single and multi-point cutting tools, tool geometry and materials, tool life and wear; economics of machining; principles of non-traditional machining processes; principles of work holding, the design of jigs and fixtures.
• Metrology and Inspection Limits fits and tolerances; linear and angular measurements; comparators; gauge design; interferometry; form and finish measurement; alignment and testing methods; tolerance analysis in manufacturing and assembly.

 GATE 2025 syllabus for Computer Integrated Manufacturing

• Basic concepts of CAD/CAM and their integration tools. Production Planning and Control: Forecasting models, aggregate production planning, scheduling, and materials requirement planning. Inventory Control: Deterministic models; safety stock inventory control systems. Operations Research: Linear programming, simplex method, transportation, assignment, network flow models, simple queuing models, PERT and CPM.
• Linear Algebra- Vector space, basis, linear dependence and independence, matrix algebra, eigenvalues and eigenvectors, rank, solution of linear equations – existence and uniqueness
• Calculus-Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, partial derivatives, maxima and minima, multiple integrals, line, surface and volume integrals, Taylor series
• Differential Equations-First order equations (linear and nonlinear), Higher order linear differential equations, Cauchy's and Euler's equations, methods of solution using a variation of parameters, complementary function and particular integral, partial differential equations, variable separable method, initial and boundary value problems
• Vector Analysis- Vectors in plane and space, vector operations, gradient, divergence and curl, Gauss's, Green's and Stoke's theorems
• Complex Analysis Analytic functions, Cauchy's integral theorem, Cauchy's integral formula; Taylor's and Laurent's series, residue theorem
• Numerical Methods Solution of nonlinear equations, single and multi-step methods for differential equations, convergence criteria
• Probability and Statistics Mean, median, mode and standard deviation; combinatorial probability, probability distribution functions - binomial, Poisson, exponential and normal; Joint and conditional probability; Correlation and regression analysis

Networks, Signals & Systems:

• Network solution methods- Nodal and mesh analysis; Network theorems: superposition, Thevenin and Norton’s, maximum power transfer; Wye-Delta transformation; Steady state sinusoidal analysis using phasors; Time-domain analysis of simple linear circuits; Solution of network equations using Laplace transform; Frequency domain analysis of RLC circuits; Linear 2-port network parameters: driving point and transfer functions; State equations for networks
• Continuous-time signals Fourier series and Fourier transform representations, sampling theorem, and applications; Discrete-time signals: discrete-time Fourier transform (DTFT), DFT, FFT, Z-transform, interpolation of discrete-time signals; LTI systems: definition and properties, causality, stability, impulse response, convolution, poles and zeros, parallel and cascade structure, frequency response, group delay, phase delay, digital filter design techniques
• Electronic Devices Energy bands in intrinsic and extrinsic silicon
• Carrier transport- Diffusion current, drift current, mobility and resistivity; Generation and recombination of carriers; Poisson and continuity equations; P-N junction, Zener diode, BJT, MOS capacitor, MOSFET, LED, photodiode and solar cell
• Integrated circuit fabrication process- Oxidation, diffusion, ion implantation, photolithography and twin-tub CMOS process

Analog Circuits:

• Circuits, Small signal equivalent circuits of diodes, BJTs, and MOSFETs
• Simple diode circuits- Clipping, clamping, and rectifiers
• BJT and MOSFET amplifiers- Single-stage BJT and MOSFET amplifiers biasing, bias stability, mid-frequency small-signal analysis, and frequency response; multi-stage, differential, feedback, power and operational; Simple op-amp circuits; Active filters
• Sinusoidal oscillators
• The criterion for oscillation, single-transistor, and op-amp configurations; Function generators, wave-shaping circuits, and 555 timers; Voltage reference circuits; Power supplies: ripple removal and regulation
• Digital Circuits
• Combinatorial circuits- Boolean algebra, minimization of functions using Boolean identities and Karnaugh map, logic gates and their static CMOS implementations, arithmetic circuits, code converters, multiplexers, decoders and PLAs
• Sequential circuits latches and flip-flops, counters, shift registers and finite state machines; Data converters: sample and hold circuits, ADCs and DACs
• Semiconductor memories- ROM, SRAM, DRAM
• An 8-bit microprocessor (8085)- Architecture, programming, memory and I/O interfacing

Control Systems:

• Control Systems- Basic control system components; Feedback principle; Transfer function; Block diagram representation; Signal flow graph; Transient and steady-state analysis of LTI systems; Frequency response; Routh-Hurwitz and Nyquist stability criteria; Bode and root-locus plots; Lag, lead and lag-lead compensation; State variable model and solution of state equation of LTI systems

Communications:

• Random processes- autocorrelation and power spectral density, properties of white noise, filtering of random signals through LTI systems
• Analog communications- amplitude modulation and demodulation, angle modulation and demodulation, spectra of AM and FM, superheterodyne receivers, circuits for analogue communications
• Information theory entropy, mutual information, and channel capacity theorem
• Digital communications PCM, DPCM, digital modulation schemes, amplitude, phase and frequency shift keying (ASK, PSK, FSK), QAM, MAP and ML decoding, matched filter receiver, calculation of band, SNR and BER for digital modulation; Fundamentals of error correction, Hamming codes; Timing and frequency synchronization, inter-symbol interference and its mitigation; Basics of TDMA, FDMA and CDMA

Electromagnets:

• Electrostatics
• Maxwell’s equations Differential and integral forms and their interpretation, boundary conditions, wave equation, Poynting vector
• Plane waves and properties
• Reflection and refraction, polarization, phase and group velocity, propagation through various media, skin depth
• Transmission lines Equations, characteristic impedance, impedance matching, impedance transformation, S-parameters, Smith chart
• Waveguide modes, boundary conditions, cut-off frequencies, dispersion relations
• Antenna: Antenna types, radiation pattern, gain, directivity, return loss, antenna arrays; Basics of radar; Light propagation in the optical fibre.