GATE Syllabus 2027: Revised Syllabus Released, Subject Wise Topics and Deleted Topics

Tenses; articles; adjectives; prepositions; conjunctions; verb-noun agreement; other parts of speech; sentence completion; verbal analogies; word groups; instructions; critical reasoning; verbal deduction.

Data graphs (bar graphs, pie charts); 2- and 3-dimensional plots; maps and tables; numerical computation and estimation; ratios; percentages; powers, exponents, and logarithms; permutations and combinations; equations and inequalities; time and work; distance and speed; mensuration; elementary statistics and probability.

Translation, rotation, scaling, mirroring, assembling, and grouping of shapes; paper folding, cutting, and patterns in 2 and 3 dimensions.

Matrix algebra; systems of linear equations; eigenvalues and eigenvectors; LU decomposition.

Functions of single variable; limit, continuity, and differentiability; mean value theorems; indeterminate forms; definite and improper integrals; double and triple integrals; partial derivatives; total derivative; gradient, divergence, and curl; vector identities; line, surface, and volume integrals; Gauss, Green, and Stokes theorems.

First-order equations (linear and nonlinear); higher-order linear ODEs with constant coefficients; Euler-Cauchy equation; Laplace transform for solving linear ODEs; initial and boundary value problems; PDEs: heat equation, wave equation, Laplace equation.

Analytic functions; Cauchy-Riemann equations; Cauchy’s integral theorem and formula; Taylor and Laurent series; residue theorem.

Definitions of probability and sampling theorems; conditional probability; mean, median, mode, standard deviation; random variables; normal, Poisson, and binomial distributions; correlation and regression analysis; tests of significance. Statistical independence added in CE Engineering Mathematics for GATE 2027.

Numerical solutions of linear and non-linear algebraic equations; integration by trapezoidal and Simpson’s rules; single- and multi-step methods for differential equations.

Boolean algebra; combinational circuits; Karnaugh map minimisation; multiplexers, demultiplexers, encoders, decoders; sequential circuits: flip-flops, latches, counters, shift registers; Mealy and Moore finite state machines; propagation delay.

Machine instructions and addressing modes; ALU, data-path, and control unit; instruction pipelining and pipeline hazards; memory hierarchy: cache, main memory; I/O interface: interrupt and DMA modes. Secondary storage / magnetic disk is no longer explicitly listed in GATE 2027 CS — verify in official PDF.

Programming in C; recursion; arrays, stacks, queues, linked lists, trees; binary search trees; binary heaps; graphs.

Searching, sorting, hashing; asymptotic worst-case time and space complexity; algorithm design: greedy, dynamic programming, divide-and-conquer; graph traversals; minimum spanning trees (Kruskal, Prim); shortest paths (Dijkstra, Bellman-Ford).

Regular expressions and finite automata; context-free grammars and push-down automata; regular and context-free languages; Pumping Lemma; Turing machines and undecidability.

Lexical analysis; parsing: LL and LR, CLR, LALR; syntax-directed translation; runtime environments; intermediate code generation; local optimisation; data flow analyses: constant propagation, liveness analysis, common subexpression elimination.

System calls; processes and threads; inter-process communication; concurrency and synchronisation; deadlock; CPU and I/O scheduling; memory management and virtual memory; file systems.

ER-model; relational model: relational algebra, tuple calculus; SQL; integrity constraints; normal forms; file organisation; indexing (B and B+ trees); transactions and concurrency control.

ISO/OSI and TCP/IP models; LAN technologies (Ethernet); flow and error control; switching; IPv4/IPv6; routing algorithms (distance vector, link state); TCP/UDP and sockets; application layer protocols (DNS, HTTP); network security basics. ARP, ICMP, DHCP, SMTP, FTP, and UDP are no longer explicitly listed in GATE 2027 CS — check the official PDF for current scope.

Network elements, topologies, KCL, KVL; superposition, Thevenin, Norton, maximum power transfer theorems; time and frequency domain analysis; DTFT, DFT, FFT; Z-transform; Laplace transform; LTI systems; frequency response.

Energy bands in semiconductors; intrinsic and extrinsic semiconductors; carrier transport: diffusion and drift; p-n junction diode; BJT; MOSFET; short-channel effects; device fabrication basics.

Small signal equivalent circuits of diodes, BJTs, and MOSFETs; single-stage and multi-stage amplifiers; differential amplifiers; feedback amplifiers; power amplifiers; oscillators; operational amplifiers; active filters.

Number representations; Boolean algebra; combinational circuits: adders, MUX, encoders; sequential circuits: latches, flip-flops, counters; logic families; ADC and DAC.

Transfer function models; block diagrams and signal flow graphs; Routh-Hurwitz criterion; Bode plots; Nyquist stability criterion; root locus; PID controllers; state space representation; transient and steady-state analysis.

Analog modulation: AM, FM, PM; sampling theorem; pulse code modulation; digital modulation: ASK, FSK, PSK, QAM; matched filter; bit error rate; spread spectrum; Shannon’s theorem; information theory basics.

Maxwell’s equations; boundary conditions; EM wave propagation; transmission lines: impedance matching, Smith chart; waveguides; antennas: radiation patterns, gain, directivity; far-field analysis.

Network elements; KCL and KVL; mesh and nodal analysis; superposition, Thevenin, Norton theorems; transient response of DC and AC networks; resonance; two-port networks; three-phase circuits.

Coulomb’s law; electric flux density; Gauss’s law; divergence theorem; energy in electrostatic fields; conductor and dielectric properties; capacitance; Biot-Savart and Ampere’s laws; Faraday’s law; Maxwell’s equations.

Continuous and discrete-time signals; LTI systems; convolution; Fourier series and Fourier transform; Laplace transform; Z-transform; sampling theorem.

Single- and three-phase transformers: equivalent circuit, phasor diagram, regulation; three-phase induction motors: equivalent circuit, torque-speed characteristics; synchronous generators and motors: excitation, phasor diagrams, parallel operation; DC machines: characteristics, starting and speed control.

Per-unit representation; bus impedance and admittance matrices; load flow; voltage control; power factor correction; symmetrical components; analysis of balanced and unbalanced faults; circuit breaker basics; protection of lines, feeders, and generators.

Mathematical modelling of physical systems; feedback principles; Bode plot; Routh-Hurwitz criterion; Nyquist criterion; root locus; lead, lag, and PID controllers; state space analysis; observability and controllability.

Bridges and potentiometers; PMMC, moving iron, dynamometer, and induction-type instruments; measurement of voltage, current, power, energy, and power factor; instrument transformers; digital voltmeters; oscilloscopes; error analysis.

Diodes, BJTs, and op-amp characteristics and applications; combinational and sequential logic circuits; multiplexers; Schmitt trigger; A/D and D/A converters; 8085 microprocessor architecture, programming, and interfacing.

Thyristor, MOSFET, IGBT characteristics and triggering; DC-DC converters (Buck, Boost, Buck-Boost); single- and three-phase AC-DC rectifiers; voltage and current source inverters; PWM techniques; drive applications.

Free body diagrams; equilibrium; trusses; beams; virtual work; kinematics and dynamics of particles and rigid bodies; impulse and momentum; vibrations: free, forced, and damped; stress, strain, elastic constants; Euler’s theory of columns; theories of failure; fatigue; design of joints, bearings, and gears.

Fluid properties; fluid statics; continuity equation; Bernoulli equation; flow through pipes; boundary layers; turbomachinery; thermodynamic laws and cycles; air cycles; vapour power cycles; refrigeration; psychrometrics; conduction; convection; radiation. New in GATE 2027: high-speed compressible flow, nozzle analysis, boiling & condensation heat transfer, combustion basics, pump characteristics.

Engineering materials: crystal structure, phase diagrams, heat treatment; metal casting, forming, welding; machining operations; metrology and inspection; operations research: queuing, inventory, PERT/CPM; work study; scheduling.

Strength of materials; structural analysis: trusses, beams, arches, cables, influence lines, plastic analysis; new in 2027: principles of virtual work; matrix methods; design of concrete structures; design of steel structures; construction materials and management.

Origin and classification of soils; three-phase diagram; permeability and seepage; effective stress; consolidation; shear strength; bearing capacity; slope stability; shallow and deep foundations.

Fluid mechanics; open channel flow; pipe networks; hydraulic machines; hydrology: precipitation, runoff, flood routing; ground water; irrigation and drainage.

Water quality parameters; water treatment; sewage characterisation; primary, secondary, and tertiary wastewater treatment (new in GATE 2027); sludge disposal; solid waste management; air and noise pollution.

Highway planning; geometric design; traffic engineering: flow, speed, density; intersections; pavement design: flexible and rigid; railway and airport engineering basics.

Principles and classification of surveys; chain, compass, levelling, theodolite surveys; tacheometry; triangulation; errors in surveying; photogrammetry; remote sensing; GNSS and GIS basics.

Counting (permutation, combination); probability axioms; sample space; independent and mutually exclusive events; marginal and conditional probability; Bayes’ theorem; random variables (discrete and continuous); uniform, Bernoulli, binomial, geometric, exponential, Poisson, and Gaussian distributions; correlation and covariance; central limit theorem; confidence intervals; Z-test, T-test, chi-square test; ANOVA; probability inequalities (Markov, Chebyshev, Chernoff).

Vector spaces; subspaces; linear dependence and independence; projection matrix; orthogonal matrix; idempotent matrix; partition matrix; quadratic forms; systems of linear equations; Gaussian elimination; eigenvalues and eigenvectors; determinant; rank; nullity; LU decomposition; singular value decomposition (SVD).

Single-variable calculus: limits, continuity, differentiability, mean value theorem, L’Hôpital’s rule, maxima and minima, Taylor’s theorem, definite and indefinite integrals; partial derivatives; total derivative; gradient; Jacobian; constrained optimization (Lagrange multipliers); gradient descent (1st and 2nd order); convexity and concavity.

Programming in Python; basic data structures: stacks, queues, linked lists, trees, graphs, hash tables; linear and binary search; sorting algorithms (selection, bubble, insertion, merge, quick); asymptotic analysis (Big-O notation, time and space complexity); basic graph algorithms (BFS, DFS, shortest path).

Supervised Learning: linear regression, logistic regression, SVM (kernel methods), naive Bayes, K-nearest neighbour (KNN), decision trees, ensemble methods (bagging, boosting, random forest, gradient boosting).
Neural Networks: perceptron, MLP, backpropagation, activation functions (ReLU, sigmoid, tanh, softmax), CNN (convolution, pooling, batch normalisation), RNN, LSTM, GRU.
Unsupervised Learning: K-means, Gaussian mixture model (GMM), K-medoids, hierarchical clustering, PCA, t-SNE.
Model Evaluation: cross-validation, bias-variance tradeoff, overfitting, regularisation (L1/L2, dropout), accuracy, precision, recall, F1-score, AUC-ROC.
Reinforcement Learning: Markov decision processes (MDPs), reward functions, Q-learning basics.

Search algorithms: BFS, DFS, best-first search, A* algorithm; heuristic functions; admissible heuristics; propositional logic; predicate logic; inference (modus ponens, resolution); Bayesian networks (structure, exact inference, variable elimination); hidden Markov models (HMM); NLP basics: tokenisation, bag-of-words, TF-IDF; computer vision basics.