GATE 2027 Syllabus: Revised Syllabus Released, Subject Wise Topics and PDF Download

English grammar, sentence completion, verbal analogies, word groups, instructions, critical reasoning, verbal deduction, reading comprehension passages.

Numerical computation, numerical estimation, numerical reasoning and data interpretation, charts and graphs, ratios and proportions, percentages, speed-distance-time, work-and-time, simple and compound interest.

Matrix algebra, systems of linear equations, eigenvalues and eigenvectors, LU decomposition, vector spaces, rank.

Functions of single and multiple variables, limits, continuity, differentiability, mean value theorems, Taylor series, definite and indefinite integrals, partial derivatives, maxima and minima, gradient, divergence, curl, vector identities, line-surface-volume integrals.

First-order ODEs (linear and nonlinear), higher-order linear ODEs with constant coefficients, Euler-Cauchy equation, partial differential equations, Laplace transforms, Fourier series.

Propositional and first-order logic, sets, relations, functions, partial orders, lattices, graphs, combinatorics — counting, recurrences, generating functions.

Random variables, conditional probability, Bayes’ theorem, mean, median, mode, standard deviation, probability distributions — Uniform, Normal, Exponential, Poisson, Binomial.

Numerical solutions of linear and non-linear equations, integration by trapezoidal and Simpson’s rule, single-step and multi-step methods for ODEs.

Complex numbers, analytic functions, Cauchy’s integral theorem, Laurent series, residue theorem.

Boolean algebra, combinational circuits (multiplexers, decoders, adders), sequential circuits (flip-flops, counters, shift registers), minimisation (K-map), number representations, computer arithmetic.

Machine instructions, addressing modes, ALU design, data-path and control unit, instruction pipelining and hazards, memory hierarchy (cache, main memory, virtual memory), I/O interface, interrupts and DMA.

C programming constructs, recursion, arrays, stacks, queues, linked lists, trees, binary search trees, binary heaps, graphs.

Searching and sorting, hashing, time and space complexity, asymptotic analysis, algorithm design (divide-and-conquer, greedy, dynamic programming), graph algorithms (BFS, DFS, Dijkstra, Bellman-Ford, Floyd-Warshall, MST).

Regular languages and finite automata (DFA, NFA), context-free languages and pushdown automata, pumping lemma, Turing machines, decidability and undecidability, complexity classes P, NP, NP-completeness.

Lexical analysis, parsing (LL, LR), syntax-directed translation, runtime environments, intermediate code generation, code generation and optimisation.

Processes and threads, inter-process communication, concurrency — synchronisation, deadlock (detection, avoidance, prevention), CPU scheduling, memory management (paging, segmentation, virtual memory), file systems, I/O scheduling.

ER model, relational model, relational algebra, SQL (DDL, DML, queries, joins), integrity constraints, normal forms (1NF–BCNF), indexing (B-tree, B+-tree, hashing), transactions, concurrency control, recovery.

OSI and TCP/IP models, LAN technologies (Ethernet, IEEE 802.11), switching, IPv4/IPv6 addressing, routing protocols (RIP, OSPF, BGP), TCP/UDP, flow and congestion control, application-layer protocols (HTTP, DNS, SMTP, FTP), network security basics.

Engineering Mechanics: statics (free body diagrams, equilibrium), dynamics (kinematics, work-energy, impulse-momentum). Mechanics of Materials: stress, strain, bending, shear, Mohr’s circle, deflection of beams, torsion, columns. Theory of Machines: velocity and acceleration analysis, cams, gears, gear trains, governors, flywheels, balancing. Vibrations: free, forced, damped oscillations, resonance, critical speeds. Machine Design: fatigue, S-N diagram, failure theories, shafts, gears, bearings, bolts, springs.

Fluid Mechanics: fluid properties, continuity, Bernoulli equation, viscous flow, boundary layer, pipe flow, turbomachinery. Heat Transfer: conduction, convection, radiation, fins, heat exchangers (LMTD and NTU). Thermodynamics: first and second laws, Carnot, Rankine, Brayton, and refrigeration cycles. Power Engineering: compressors, gas turbines, steam turbines. I.C. Engines: Otto, Diesel, and dual cycles. Refrigeration: vapour and gas cycles, psychrometrics.

Engineering Materials: phase diagrams, heat treatment, composites, polymers. Casting: solidification, gating, riser design. Forming: rolling, forging, extrusion, drawing, powder metallurgy. Welding: welding, brazing, soldering. Machining: chip formation, tool geometry, tool life, NC/CNC, abrasive machining. Metrology: tolerances, fits, gauges, interferometry. Industrial Engineering: PERT/CPM, inventory models (EOQ), queuing theory, linear programming, simplex method.

Engineering Mechanics: force systems, equilibrium, kinematics. Solid Mechanics: stress, strain, bending moment and shear force diagrams, Mohr’s circle, torsion, buckling. Structural Analysis: determinate and indeterminate structures, trusses, arches, influence lines, slope deflection, moment distribution, stiffness and flexibility methods. RCC Design (IS 456): beams, slabs, columns, prestressed concrete. Steel Design (IS 800): tension/compression members, connections, plate girders. Construction Materials: concrete mix design, structural steel.

Soil classification (IS system), compaction, permeability and seepage (Darcy’s law, flow nets), one-dimensional consolidation (Terzaghi’s theory), shear strength (Mohr-Coulomb, triaxial test), bearing capacity (Terzaghi, Meyerhoff), settlement analysis, earth pressure theories (Rankine, Coulomb), slope stability (Bishop’s method), pile foundations.

Fluid Mechanics: pipe flow, open channel flow (specific energy, critical flow, hydraulic jump, gradually varied flow). Hydrology: precipitation, infiltration, runoff, unit hydrographs, flood routing, groundwater. Irrigation Engineering: canal design, duty and delta, water requirements, weirs, gravity dams, spillways.

Water treatment: coagulation, sedimentation, filtration, disinfection, distribution systems. Sewage treatment: primary, secondary (activated sludge, trickling filters), sludge treatment. Air pollution: pollutant types, control methods, standards. Solid waste: collection, transport, sanitary landfill, composting.

Highway planning: geometric design (cross-section, sight distances, horizontal and vertical alignments), IRC standards. Pavement design: flexible (IRC 37-2012), rigid (IRC 58-2011). Traffic Engineering: flow-speed-density relationships, signal design (Webster’s method), LOS, PCU. Railway engineering: track components, gauge. Airport: runway length calculations.

Surveying principles, chain and tape surveying, levelling, theodolite survey, tacheometry, horizontal and vertical curves, total station, remote sensing basics, GIS, GPS.

Network analysis (KVL, KCL, mesh and node analysis), network theorems (Thevenin, Norton, Superposition, Maximum power transfer), transient and steady-state RLC response, resonance, two-port networks, three-phase circuits.

Coulomb’s law, electric field intensity, Gauss’s law, magnetic field intensity, Biot-Savart’s law, Ampere’s law, Faraday’s law, Maxwell’s equations, boundary conditions, Poynting theorem, wave propagation in media.

Continuous and discrete-time signals, LTI systems, Fourier series and Fourier transform, Laplace transform, Z-transform, sampling theorem, state variable representation.

Transformers: equivalent circuit, losses, efficiency, regulation, three-phase connections. DC machines: generators, motors, speed control, starting methods. Induction motors: torque-slip characteristic, starting, speed control, equivalent circuit. Synchronous machines: cylindrical and salient rotor generators, power angle, synchronous motor starting.

Power system components, per-unit system, load flow analysis (Gauss-Seidel, Newton-Raphson), short circuit analysis, symmetrical components, protective relaying, circuit breakers, power system stability (equal area criterion), HVDC basics.

Transfer functions, block diagrams, signal flow graphs, time-domain analysis (transient, steady-state), frequency-domain analysis (Bode plots, Nyquist, gain and phase margins), root locus, PID controllers, state-space representation, controllability and observability.

Diodes, BJTs, MOSFETs (biasing and amplifier circuits), operational amplifier applications (inverting, non-inverting, integrator, differentiator, active filters), ADC and DAC, Boolean algebra, combinational and sequential logic.

Power semiconductor devices (SCR, MOSFET, IGBT), phase-controlled rectifiers, DC-DC converters (Buck, Boost, Buck-Boost), DC-AC inverters (single and three-phase), AC drives basics.

Network analysis and theorems, transient and steady-state response, signals — continuous and discrete-time LTI systems, Fourier series and transform, Laplace transform, Z-transform, sampling theorem, two-port networks.

Semiconductor physics, p-n junction diode, Zener diode, BJT (characteristics, biasing), MOSFET (structure, characteristics, SPICE models), LED, photodetectors, solar cells, IC fabrication basics.

Small-signal models (BJT, MOSFET), single-stage and multi-stage amplifiers, frequency response, feedback amplifiers, operational amplifier applications (oscillators, active filters, comparators, waveform generators), ADC and DAC.

Boolean algebra, combinational circuits (multiplexers, decoders, adders), sequential circuits (flip-flops, counters, shift registers), semiconductor memories, PLDs, 8085 microprocessor basics.

Analog communication (AM, FM, PM, SNR analysis, superheterodyne receivers), digital communication (PCM, ASK, FSK, PSK, QAM, BER, matched filters), fundamentals of information theory, channel capacity (Shannon’s theorem).

Maxwell’s equations, plane wave propagation, reflection and transmission at interfaces, transmission lines (impedance matching, Smith chart, S-parameters), waveguides (modes, cut-off frequencies), antennas (radiation pattern, directivity, gain, half-wave dipole, arrays), optical fiber basics.

Mine Development: methods of access (shaft, adit, decline), importance and choice of method, systems of underground mine development. Mine Surveying: levels and levelling, theodolite traverses, triangulation, underground surveying, surface and underground correlation, errors and adjustments, curves, photogrammetry, field astronomy, GPS, total station and remote sensing in mining.

Engineering Mechanics: equivalent force systems, two-dimensional frames and trusses, particle kinematics and dynamics. Geo-technical properties of rocks: strength, deformability, permeability; rock mass classification (RMR, Q-system); instrumentations and in-situ stress measurement techniques (updated, GATE 2027); Kirsch’s equations; stress analysis around openings; failure criteria; rock support design; slope and dump stability analysis (updated, GATE 2027). Ground control: strata control methods, support systems, rock reinforcement, prediction of subsidence due to mining, pressure arch and caving, design of mine openings.

Surface Mining: planning, stripping methods, bench configuration, blasting, haul road design, economic stripping ratio, reclamation. Highwall Mining: principles and applications. Underground Coal Mining: bord and pillar, longwall mining, coal mine development. Underground Metalliferous Mining: open stope methods (room and pillar, sublevel stoping, shrinkage stoping); supported methods (cut and fill, square set); caving methods (sublevel caving, block caving). Mining Machinery: loading, drilling, hoisting, ventilation, and surface equipment.

Surface Environment: air, water, and soil pollution; pollution control; subsidence; noise; vibration; land reclamation; EIA. Mine Ventilation: air quantity standards, properties of mine air, methane and control, ventilation planning, ventilation hardware, surveys and measurements, network analysis, natural and mechanical ventilation, fans, auxiliary ventilation, reversal of ventilation. Underground Hazards: mine gases and sampling, gas outbursts, fires, explosions, inundation, spontaneous combustion, rockbursts, methane drainage, safety provisions and emergency management, rescue apparatus and first aid.

Mine Economics: mineral resource classification; cost analysis; capital and operating costs; mine investment analysis; project appraisal; discounted cash flow analysis. Mine Legislation: Mines Act 1952, Mines Rules 1955, Mine Regulations — provisions relating to safety and hazards. Mine Management: mine planning, production planning, project management.

Spatial descriptions and transformations, Denavit-Hartenberg (DH) representation, forward and inverse kinematics, Jacobian and singularity analysis, robot dynamics (Newton-Euler, Lagrangian formulation), trajectory planning, workspace analysis.

PID control for robot joints, joint-space and Cartesian-space control, computed torque control, force and torque control, impedance control, adaptive control basics.

DC motors, stepper motors, servo motors, hydraulic and pneumatic actuators; encoders (incremental, absolute), proximity sensors, force and torque sensors, vision sensors, IMUs.

Image acquisition and representation, feature extraction, edge detection, object detection and recognition, camera calibration, stereo vision, depth sensing.

NC/CNC machining, PLC programming, industrial robot applications, Flexible Manufacturing Systems (FMS), Computer-Integrated Manufacturing (CIM), Industrial IoT basics.