AP PGECET Syllabus 2027: Subject Wise Topics, Topic Wise Weightage and PDF Download

Set theory, relations and functions, mathematical logic, graph theory, combinatorics, Boolean algebra, probability and statistics, linear algebra, calculus, differential equations, Laplace transforms, Z-transforms, Fourier series

C data types, operators, control structures, functions, arrays, pointers, structures, file handling; C++ OOP (encapsulation, inheritance, polymorphism, templates, STL basics); Java fundamentals (classes, objects, interfaces, exception handling, collections, generics)

Arrays, linked lists (singly, doubly, circular), stacks, queues, deque, priority queues, binary trees, BST, AVL trees, B-trees, heaps, graphs (adjacency matrix/list, BFS, DFS, shortest path — Dijkstra, Bellman-Ford, Floyd-Warshall; spanning trees — Kruskal, Prim), hashing (chaining and open addressing), sorting algorithms (bubble, selection, insertion, merge, quick, heap), searching algorithms

Asymptotic notation (Big-O, Omega, Theta), divide and conquer (merge sort, binary search), greedy algorithms (activity selection, fractional knapsack, Kruskal, Prim), dynamic programming (LCS, 0/1 knapsack, matrix chain), backtracking, NP-completeness; finite automata (DFA, NFA), regular expressions, context-free grammars, pushdown automata, Turing machine, decidability and undecidability

Number systems and codes, Boolean algebra, combinational circuits (adders, multiplexers, decoders, encoders), sequential circuits (flip-flops, registers, counters), instruction set architecture, addressing modes, ALU design, pipelining (hazards — data, control, structural; forwarding), memory hierarchy (cache — direct mapping, set-associative, fully associative; replacement — LRU, FIFO; virtual memory — paging, segmentation, TLB), I/O interfaces, DMA

Process states, CPU scheduling (FCFS, SJF, SRTF, Round Robin, Priority, Multi-level Queue), inter-process communication, process synchronisation (semaphores, monitors, classical problems — dining philosophers, producer-consumer, readers-writers), deadlock (detection, prevention, avoidance — Banker’s algorithm), memory management (paging, segmentation, virtual memory, page replacement — FIFO, LRU, Optimal), file systems, disk scheduling (FCFS, SSTF, SCAN, C-SCAN, LOOK)

ER model, relational model, relational algebra (select, project, join, union, difference), SQL (DDL, DML with joins / subqueries / GROUP BY / HAVING, DCL, views, triggers, stored procedures), normalisation (1NF, 2NF, 3NF, BCNF, 4NF), transaction management, ACID properties, serializability, concurrency control (2PL, timestamp-based ordering), indexing (B-tree, B+ tree, hash indexing), query optimisation basics

OSI and TCP/IP reference models, physical layer (Nyquist and Shannon capacity theorems), data link layer (error detection — CRC, Hamming; flow control — stop-and-wait, sliding window; HDLC; MAC protocols — CSMA/CD, CSMA/CA), network layer (IP addressing, subnetting, CIDR, NAT, routing — Dijkstra, Bellman-Ford; RIP, OSPF, BGP; IPv4 vs IPv6), transport layer (TCP — three-way handshake, congestion control; UDP), application layer (HTTP/HTTPS, DNS, SMTP, FTP, SNMP)

SDLC models (Waterfall, Incremental, Spiral, Agile — Scrum, XP), software requirements (SRS), design (modular design, cohesion and coupling, UML basics), testing (black-box — equivalence partitioning, boundary value analysis; white-box — statement, branch, path coverage; unit, integration, system, regression testing), software metrics (cyclomatic complexity, function points), project management (PERT, CPM, COCOMO estimation)

Linear algebra (matrices, eigenvalues, eigenvectors), calculus, vector calculus (gradient, divergence, curl, Stokes’ and Gauss’ theorems), differential equations, complex analysis, probability and statistics, Fourier series and Fourier transform, Laplace transform, Z-transform

P-N junction diode (forward and reverse bias, V-I characteristics), Zener diode (voltage regulation), BJT (CE, CB, CC — h-parameters, small-signal models), JFET and MOSFET characteristics (transfer curve, transconductance), biasing circuits (fixed, self-bias, voltage divider), feedback amplifiers (types, gain), oscillators (Barkhausen criterion, Colpitts, Hartley, Wien bridge, crystal), op-amp circuits (inverting, non-inverting, summing, differentiator, integrator, comparator, Schmitt trigger), rectifiers, filters, power amplifiers (Class A, B, AB, C)

Continuous and discrete-time signals (energy, power, periodic, aperiodic, causal), LTI systems (linearity, time invariance, causality, stability — BIBO), convolution (continuous and discrete), Fourier transform and properties, DTFT, DFT and FFT algorithm, Z-transform (ROC, inverse), Laplace transform and pole-zero analysis, sampling theorem (Nyquist rate), aliasing, signal reconstruction using ideal LPF

Open-loop and closed-loop systems, transfer function, block diagram algebra (reduction rules), signal flow graphs (Mason’s gain formula), time-domain analysis (first and second order — rise time, settling time, overshoot, steady-state error, error constants), Routh-Hurwitz stability criterion, Bode plot (gain and phase margins), root locus (construction rules), Nyquist stability criterion, PID controllers, state-space representation (state equations, controllability, observability)

AM (DSB-FC, DSB-SC, SSB — modulation index, bandwidth, power), FM (deviation ratio, Carson’s rule), PM, superheterodyne receiver, noise figure; digital: PCM (sampling, quantisation, encoding), DM, ADM, digital modulation (ASK, FSK, PSK, QPSK, QAM — bandwidth and BER), multiplexing (TDM, FDM, WDM), error detection and correction codes, information theory (entropy, Shannon-Hartley capacity), spread spectrum (FHSS, DSSS)

Number systems and conversions, Boolean algebra, K-map simplification (SOP, POS — up to 5 variables), logic gates, combinational circuits (adder, subtractor, multiplexer, demultiplexer, encoder, decoder, priority encoder, comparator), sequential circuits (SR, D, JK, T flip-flops; registers — SISO, SIPO, PISO, PIPO; counters — synchronous, asynchronous, modulo-N), memory devices (SRAM, DRAM, ROM, EPROM, Flash), PLDs (PLA, PAL)

Electrostatics (Coulomb’s law, Gauss’s law, electric potential, capacitance), magnetostatics (Biot-Savart law, Ampere’s law, inductance), Faraday’s law, Maxwell’s equations (integral and differential forms), plane wave propagation (wave equation, skin depth, polarisation), transmission line theory (characteristic impedance, reflection coefficient, VSWR, standing waves, Smith chart), rectangular waveguides (TE/TM modes, cutoff frequency), microwave devices (klystron, magnetron, TWT), antennas (radiation pattern, beam width, gain, directivity, effective aperture, dipole, Yagi-Uda, parabolic reflector, antenna arrays)

CMOS technology, logic families (TTL, CMOS — fan-in, fan-out, noise margins, propagation delay), VLSI design flow (RTL to GDSII), CMOS fabrication steps; 8085/8086 microprocessor — architecture (registers, ALU, BIU, EU), instruction set, addressing modes, assembly language, memory and I/O interfacing, interrupts, DMA; 8051 microcontroller basics; DSP processors — FIR and IIR filter design basics

KVL and KCL, mesh and node analysis, Thevenin’s and Norton’s theorems, superposition, reciprocity, maximum power transfer, resonance (series and parallel RLC), coupled circuits (mutual inductance, dot convention), three-phase circuits (balanced — star and delta; unbalanced), phasors, complex power (real, reactive, apparent, power factor correction), transient analysis of RL, RC, RLC circuits (step and impulse response)

DC generators (EMF equation, armature reaction, commutation, types — shunt, series, compound); DC motors (torque equation, speed characteristics, speed control — flux control, armature voltage control; starters); single-phase and three-phase transformers (EMF equation, equivalent circuit, phasor diagram, efficiency and regulation, OC and SC tests, parallel operation, auto-transformer); three-phase induction motors (slip, torque-speed characteristics, starting — DOL, star-delta, auto-transformer; speed control — pole changing, VFD); single-phase induction motors; synchronous generators and motors (phasor diagram, excitation characteristics, power-angle curve, parallel operation)

Transmission line parameters (resistance, inductance — GMR, transposition; capacitance — GMD), short / medium / long line models (ABCD parameters, Ferranti effect), per-unit system, load flow analysis (Gauss-Seidel and Newton-Raphson methods), fault analysis (symmetrical three-phase faults; unsymmetrical faults using symmetrical components — SLG, LL, DLG), circuit breakers (types, rating, restriking voltage), relay protection (overcurrent, distance, differential relays), power system stability (steady-state and transient stability, swing equation, equal-area criterion)

Transfer functions, block diagram reduction, signal flow graphs, time-domain response (first and second order systems), steady-state error and error constants, Routh-Hurwitz stability criterion, Bode plot (gain and phase margins), root locus method, Nyquist stability criterion, PID controller tuning, state-space methods (controllability, observability, state feedback), digital control basics (z-domain analysis)

Power semiconductor devices (SCR — triggering, commutation; TRIAC, DIAC, MOSFET, IGBT), single-phase and three-phase controlled rectifiers (fully and semi-controlled — waveform analysis, average output voltage, power factor), DC-DC converters (Buck, Boost, Buck-Boost, Cuk — duty cycle and voltage relationships), single-phase and three-phase inverters (120° and 180° mode, SPWM, space vector PWM), AC voltage controllers, cycloconverters, UPS systems, electric drive applications

Error analysis (accuracy, precision, sensitivity, resolution, loading effect), PMMC instruments, moving iron instruments, electrodynamometer instruments (wattmeter, power factor meter), energy meters (single-phase and three-phase), AC and DC bridges (Wheatstone, Kelvin, Maxwell, Hay, Schering), oscilloscopes (CRT and DSO), transducers (LVDT, strain gauges — gauge factor; thermocouples and RTDs; pressure transducers — piezoelectric, capacitive), signal conditioning (amplification, filtering, A/D conversion), data acquisition systems

Linear algebra (matrices, eigenvalues), calculus (differentiation, integration, partial derivatives), vector calculus, differential equations (ODEs — first and second order; PDEs — basics), numerical methods (Newton-Raphson, Runge-Kutta 4th order, Gauss elimination, trapezoidal and Simpson’s rule), probability and statistics, Laplace transforms, Fourier series

Statics: forces, moments, equilibrium, centroid and centre of gravity, moment of inertia; Dynamics: kinematics and kinetics of particles and rigid bodies, work-energy and impulse-momentum; Strength of Materials: stress and strain (Hooke’s law, Poisson’s ratio, elastic constants), Mohr’s circle, bending moment and shear force diagrams, bending stress (flexure formula), shear stress in beams, deflection of beams (double integration, Macaulay’s), torsion of circular shafts, columns and struts (Euler’s formula, Rankine-Gordon), thick and thin cylinders, springs, fatigue (S-N curve, endurance limit)

First and second laws of thermodynamics, entropy, availability and exergy; thermodynamic cycles (Carnot, Otto, Diesel, Dual, Brayton, Rankine — efficiency formulae); steam properties and steam tables; IC engines (two-stroke, four-stroke, carburation, fuel injection); refrigeration (vapour compression — COP, T-s and p-h diagrams; absorption basics); psychrometrics; Heat Transfer: conduction (Fourier’s law, fins), convection (Newton’s cooling law, forced and natural convection — Nusselt, Prandtl, Reynolds numbers), radiation (Stefan-Boltzmann law, view factors, grey body, radiation shields), heat exchangers (LMTD and NTU-effectiveness methods)

Fluid properties (viscosity, surface tension, capillarity), hydrostatics (pressure distribution, buoyancy, metacentre), continuity equation, Bernoulli’s equation and applications (Venturimeter, orifice plate, Pitot tube), momentum equation, viscous flow (laminar — Hagen-Poiseuille; turbulent — Darcy-Weisbach; Reynolds number; Moody chart), pipe flow (minor losses, pipe networks), boundary layer theory, turbines (Pelton, Francis, Kaplan — velocity triangles, specific speed; hydraulic efficiency), centrifugal pumps (specific speed, characteristic curves, cavitation, similarity laws), compressible flow (Mach number, isentropic flow, normal shocks)

Kinematic pairs and chains, Grashof’s law, velocity and acceleration analysis of mechanisms (graphical and analytical), gear terminology (module, pressure angle, pitch, backlash), gear trains (simple, compound, epicyclic — torque and speed calculations), belt and chain drives, governors (Watt, Porter, Hartnell — sensitivity, range, isochronous), flywheel (fluctuation of energy and speed), gyroscope (couple and precessional motion), vibrations (free undamped and damped SHM, forced vibrations, resonance, transmissibility), critical speed (whirling) of shafts, balancing of rotating masses (in a plane and multiple planes), balancing of reciprocating masses

Casting (sand, die, investment, shell casting — defects and remedies); metal forming (forging — open and closed die; rolling; extrusion; drawing; sheet metal — blanking, piercing, bending, deep drawing); machining (turning, milling, drilling, grinding — tool geometry, rake and clearance angles, chip formation, cutting forces, Taylor’s tool life equation, cutting fluids, surface finish); NC/CNC machining (G and M codes, point-to-point, contouring); welding (arc, MIG/MAG, TIG, resistance — spot and seam; submerged arc; electron beam and laser beam; HAZ, weld defects); non-conventional machining (EDM, ECM, USM, LBM, WJM); metrology (limits, fits and tolerances, surface finish — Ra and Rz; gauges — go/no-go; SPC — control charts, acceptance sampling, process capability)

Work study (method study — flow process chart, man-machine chart; motion economy — therbligs; time study — performance rating, allowances, standard time; work sampling); plant layout (product, process, fixed-position, cellular); material handling; inventory control (EOQ, EBQ, reorder point, safety stock, ABC analysis, JIT, MRP); production planning and control (routing, scheduling, loading, dispatching); project management (PERT — expected time, critical path; CPM — crashing, time-cost trade-off); forecasting (moving average, exponential smoothing, regression); linear programming (graphical, simplex basics); queuing theory (M/M/1 model); reliability and maintenance (MTTF, MTBF, preventive and predictive maintenance)

Statically determinate structures (beams, trusses — method of joints and sections; frames), deflection of beams (double integration, Macaulay’s, conjugate beam, moment area methods), energy methods (Castigliano’s theorem, virtual work, unit load method), statically indeterminate structures — slope-deflection method (beams and frames), moment distribution method (with and without sway), stiffness and flexibility methods (matrix formulation), influence line diagrams (beams, girders), three-hinged arches (analysis, pressure line), cable and suspension bridge analysis

Working stress method; limit state design per IS 456:2000 (partial safety factors, design of singly and doubly reinforced beams — balanced and under-reinforced; flanged beams — effective width; one-way and two-way slabs — IS code coefficients; short and long columns — axial load and uniaxial bending; isolated and combined footings; retaining walls — cantilever and counterfort); pre-stressed concrete (pre-tensioning and post-tensioning; losses of prestress — elastic shortening, friction, creep, shrinkage, relaxation; flexural analysis of pre-stressed sections)

Structural steel sections and properties, limit state design per IS 800:2007; design of tension members (gross area, net area, block shear), compression members (effective length, slenderness ratio), beams (lateral torsional buckling), beam-columns; bolted connections (lap and butt joints — bearing failure, shear failure, block shear), welded connections (fillet and butt welds — IS code provisions); plate girders (web buckling, flange design, stiffeners); gantry girders; plastic analysis and design (plastic moment, load factor, collapse mechanisms)

Soil composition (three-phase system — void ratio, porosity, degree of saturation, unit weights, specific gravity), grain size analysis (sieve analysis, hydrometer), Atterberg limits, soil classification (IS and Unified systems), compaction (Proctor test — OMC and MDD; field methods), permeability (Darcy’s law, constant head and falling head tests; seepage velocity), seepage analysis (flow nets — construction and use; seepage through dams, piping), consolidation (Terzaghi’s 1-D theory, coefficient of consolidation, time factor, degree of consolidation, settlement calculations — immediate, primary, secondary), shear strength (Mohr-Coulomb criterion, direct shear, triaxial CU/CD/UU, vane shear, SPT, CPT), bearing capacity (Terzaghi’s general formula, IS 6403, net and gross bearing capacity, settlement-based design), pile foundations (static formulae — Meyerhof, Vesic; group efficiency), slope stability (friction circle method, Swedish circle / Bishop’s modified method), lateral earth pressure (Rankine and Coulomb — active, passive, at rest)

Open channel flow (Manning’s and Chezy’s equations, specific energy, critical flow — Froude number, hydraulic jump — types and length; gradually varied flow — profile classification), pipe flow (energy equation, Darcy-Weisbach, minor losses, pipes in series and parallel, Hardy-Cross method for pipe networks), pumps and turbines; hydrology: precipitation (types, IDF curves), runoff (rational formula, SCS-CN method), infiltration (Horton’s equation, phi index), evapotranspiration, stream flow measurement; unit hydrograph (theory, S-curve, Snyder’s synthetic), flood routing (Muskingum, reservoir routing); irrigation engineering (types — surface, drip, sprinkler; duty, delta, base period; canal design; waterlogging; irrigation structures — weirs, barrages, head works); dams (types, design principles, spillways)

Highway engineering: geometric design per IRC standards (horizontal alignment — curves, superelevation, widening; vertical alignment — grades, summit and valley curves; cross-section elements; sight distances — SSD, ISD, OSD); pavement design (flexible — CBR method per IRC:37; rigid — Westergaard’s plate theory, IRC:58); pavement materials (bitumen grades, concrete mix design); traffic engineering (traffic volume surveys, PCU, speed studies, O-D surveys, intersection design, traffic signals — IRC:93, road markings); railway engineering (track components — rails, sleepers, ballast, fastenings; gauges; gradients; curves and superelevation; points and crossings; maintenance); airport planning (runway orientation — wind rose; runway length corrections; pavement design; taxiways; apron)

Water supply: sources (surface and ground water), quality parameters (physical, chemical, biological — BIS standards), treatment (aeration, coagulation — jar test; sedimentation — settling velocity; filtration — slow sand, rapid sand, pressure; disinfection — chlorination, UV; softening — lime-soda, zeolite); distribution systems (pipes, service reservoirs); wastewater: collection systems (separate, combined), self-cleansing velocity, sewer materials; treatment — primary (screening, grit removal, sedimentation), secondary (activated sludge — BOD, sludge return; trickling filter; oxidation pond; UASB), tertiary; sludge treatment (thickening, digestion, dewatering); solid waste management (collection, transport, composting, sanitary landfill, incinerator); air pollution (sources, pollutants, NAAQS standards, Gaussian dispersion model, control devices — ESP, scrubber, cyclone); noise pollution (dB(A) measurement, standards, control measures)