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

Matrix theory, rank of a matrix, system of linear equations (consistency — Gauss elimination), eigenvalues and eigenvectors, Cayley-Hamilton theorem, diagonalisation, quadratic forms (positive definite, semi-definite).

Functions of single and multiple variables, limits and continuity, partial derivatives, Jacobians, maxima and minima (Lagrange multipliers), definite and indefinite integrals, double and triple integrals, Taylor’s and Maclaurin’s series, gradient, divergence, curl, Green’s theorem, Stokes’ theorem, Gauss divergence theorem.

First-order ODEs (linear, Bernoulli, exact equations), second-order ODEs with constant coefficients (CF + PI method), Cauchy-Euler equations, Laplace transforms (properties, inverse Laplace), solving ODEs using Laplace transforms, PDE basics (wave, heat, and Laplace equations).

Complex numbers, analytic functions, Cauchy-Riemann equations, Cauchy’s integral theorem and formula, Taylor and Laurent series, singularities and poles, residue theorem, contour integration.

Sample space and events, conditional probability, Bayes’ theorem, random variables (discrete and continuous), probability distributions (Binomial, Poisson, Normal, Exponential, Uniform), mean, variance and standard deviation, joint distributions, correlation and regression, sampling theory basics (Central Limit Theorem, confidence intervals).

Solution of algebraic and transcendental equations (Bisection, Regula-Falsi, Newton-Raphson), numerical integration (Trapezoidal rule, Simpson’s 1/3 and 3/8 rules), interpolation (Newton’s forward/backward difference, Lagrange), numerical solution of ODEs (Euler’s method, Modified Euler, Runge-Kutta 4th order).

Fourier series (periodic functions, Dirichlet conditions, half-range expansions), Fourier transforms (properties, convolution theorem, Parseval’s theorem), Z-transforms (properties, inverse Z-transform, applications in difference equations).

Boolean algebra and minimisation (K-maps, Quine-McCluskey), logic families, combinational circuits (adders, subtractors, multiplexers, decoders, encoders), sequential circuits (flip-flops, registers, counters), CPU organisation, instruction formats, addressing modes, pipelining (hazards, stalls), cache memory (mapping techniques, replacement policies), virtual memory, memory hierarchy, I/O systems and DMA.

C programming (pointers, arrays, strings, recursion, structures, dynamic memory allocation), stacks and queues (array and linked-list implementations), linked lists (singly, doubly, circular), trees (binary trees, BST, AVL trees, heaps — min-heap and max-heap), graphs (representations, BFS, DFS), hash tables (hash functions, collision resolution — chaining and open addressing).

Asymptotic complexity (Big-O, Omega, Theta), recurrence relations (Master theorem), sorting algorithms (insertion, merge, quick, heap sort), searching (binary search), graph algorithms (BFS, DFS, Dijkstra’s, Bellman-Ford, Floyd-Warshall), minimum spanning tree (Kruskal’s, Prim’s), dynamic programming (0/1 knapsack, LCS, matrix chain), greedy algorithms (activity selection, Huffman coding), NP-completeness basics.

Finite automata (DFA, NFA, epsilon-NFA — conversion algorithms), regular expressions and regular grammars, pumping lemma for regular languages, context-free grammars (derivation, parse trees, ambiguity), pushdown automata (acceptance by empty stack and final state), pumping lemma for CFLs, Turing machines (design, decidability), the halting problem and undecidability.

Phases of a compiler, lexical analysis (tokens, regular expressions, DFA-based scanners), parsing techniques (top-down: recursive descent, LL(1); bottom-up: shift-reduce, LR, LALR parsers), FIRST and FOLLOW sets, syntax-directed definitions, intermediate code generation (three-address code, quadruples), code optimisation (peephole, loop transformations), symbol tables, type checking.

Process management (states, PCB, fork), CPU scheduling (FCFS, SJF, SRTF, Round-Robin, priority — preemptive and non-preemptive), threads and concurrency, synchronisation (mutex, semaphores, monitors), classical problems (producer-consumer, readers-writers, dining philosophers), deadlock (conditions, detection, Banker’s algorithm, prevention), memory management (paging, segmentation, virtual memory, page replacement — FIFO, LRU, OPT), file systems, I/O management.

ER model and ER diagrams, relational model (relational algebra — select, project, join, union, difference), SQL (DDL, DML, joins, subqueries, aggregate functions, group by, having), normalisation (1NF, 2NF, 3NF, BCNF — decomposition and dependency preservation), transaction management (ACID properties, serializability), concurrency control (two-phase locking, timestamp ordering), indexing (B-trees, B+ trees, hashing).

OSI and TCP/IP reference models, physical layer (encoding, modulation, multiplexing), data link layer (framing, error detection — CRC, MAC protocols — CSMA/CD, CSMA/CA, sliding window protocols — Go-Back-N, Selective Repeat), network layer (IP addressing, subnetting, CIDR, routing algorithms — link state and distance vector, OSPF, BGP basics), transport layer (TCP, UDP, flow and congestion control), application layer (HTTP, DNS, DHCP, FTP, SMTP), network security basics.

SDLC models (Waterfall, Agile, Spiral, RAD), requirements engineering, software design principles (coupling, cohesion, modularisation), testing (unit, integration, system, black-box, white-box — path coverage, basis path), software metrics (cyclomatic complexity, function points), project management (PERT and CPM, COCOMO model), UML basics.

Internet architecture, HTML and XML basics, web services (REST, SOAP concepts), mobile computing (wireless protocols, mobile IP), cloud computing fundamentals (IaaS, PaaS, SaaS), cybersecurity basics (symmetric and asymmetric encryption, digital signatures, firewalls), digital image processing fundamentals, data mining basics (classification, clustering).

KCL and KVL, mesh and node analysis, superposition theorem, Thevenin’s and Norton’s equivalent circuits, maximum power transfer, transient analysis (RL, RC, and RLC circuits — step and impulse response), AC circuits and phasors, resonance (series and parallel), two-port network parameters (Z, Y, H, ABCD), reciprocity and symmetry.

Semiconductor physics (energy bands, carrier concentrations, drift and diffusion), P-N junction diode (I-V characteristics, Zener diode, breakdown), BJT (CE/CB/CC — small-signal model, biasing), FET and MOSFET characteristics (enhancement and depletion), operational amplifiers (ideal characteristics, virtual ground, open-loop and closed-loop).

Single-stage BJT and FET amplifiers (CE, CS, CC, CD — gain and frequency response), feedback amplifiers (four topologies, gain desensitivity, bandwidth), multistage amplifiers, RC phase-shift, Wien bridge, Colpitts, and Hartley oscillators, wave-shaping circuits, power amplifiers (Class A, B, AB — efficiency), voltage regulators (Zener, series, shunt).

Boolean algebra and minimisation (K-maps), logic families (TTL, CMOS — noise margin, fan-out, propagation delay), combinational circuits (adders, subtractors, multiplexers, demultiplexers, encoders, decoders, comparators), sequential circuits (SR, D, JK, T flip-flops — setup and hold times, registers, synchronous and asynchronous counters), ADC (flash, successive approximation, dual slope) and DAC (R-2R ladder, weighted resistor).

Continuous-time and discrete-time signals and systems (linearity, time-invariance, causality, stability), impulse response and convolution (CT and DT), Fourier series, CTFT (properties, frequency response of LTI systems), Laplace transform (ROC, poles and zeros, transfer function), DTFT, Z-transform (ROC, properties, inverse ZT, difference equations), sampling theorem, aliasing, signal reconstruction.

Open-loop and closed-loop systems, block diagram algebra, signal flow graphs (Mason’s gain formula), first and second-order system response (rise time, settling time, overshoot, steady-state error, error constants), Routh-Hurwitz stability criterion, root locus technique, Bode plots (gain and phase margin), Nyquist stability criterion, PID controllers, lead, lag, and lead-lag compensators.

Analog modulation (AM — DSB-FC, DSB-SC, SSB, VSB; FM and PM; demodulation), digital modulation (ASK, FSK, PSK, BPSK, QPSK, QAM — bandwidth and BER), noise in communication systems (SNR, noise figure), information theory (entropy, source coding, channel capacity — Shannon-Hartley theorem), error-control coding basics (Hamming codes, parity checks).

Coulomb’s law and electric field, Gauss’s law, electric potential, dielectrics, Biot-Savart’s law, Ampere’s law, Faraday’s law, Maxwell’s equations (integral and differential forms), plane wave propagation in free space and dielectrics (phase velocity, skin depth), transmission lines (standing waves, reflection coefficient, VSWR, Smith chart basics), rectangular waveguides (TE and TM modes, cutoff frequency), antenna fundamentals (radiation pattern, gain, directivity, half-wave dipole, patch antenna).

Determinate structures (truss analysis — method of joints and sections, beams — SFD and BMD), indeterminate structures (slope-deflection method, moment distribution method, stiffness method basics), influence lines for beams and trusses, plastic analysis of beams and frames (collapse mechanisms), arches (two-hinged, three-hinged, fixed).

Limit state design (IS 456:2000) of singly and doubly reinforced beams, T-beams, one-way and two-way slabs, short and long columns (with and without eccentricity), isolated and combined footings, retaining walls; bond, anchorage, and development length; working stress method basics; Steel structures: plastic analysis, tension and compression members, beams, beam-columns, weld and bolt connections.

Soil classification (BIS and USCS), index properties and Atterberg limits, permeability (Darcy’s law, tests), seepage and flow nets, consolidation theory (Terzaghi’s 1D consolidation — settlement, time rate), shear strength (Mohr-Coulomb criterion, direct shear, triaxial test, vane shear), bearing capacity of shallow foundations (Terzaghi’s and general bearing capacity equations, IS 6403), pile foundations (static capacity, negative skin friction), earth pressure theories (Rankine’s and Coulomb’s), slope stability basics.

Fluid properties and hydrostatics, continuity equation, Bernoulli’s equation and applications (venturimeter, orifice meter, pitot tube), momentum equation, pipe flow (Darcy-Weisbach, minor losses, series and parallel pipes, water hammer), open channel flow (Manning’s equation, specific energy, critical flow, hydraulic jump, gradually varied flow), measurement devices (notches and weirs), pumps and turbines basics.

Highway planning and geometric design (alignment, gradient, sight distances — SSD, ISD, OSD, curve design), pavement design (flexible — IRC 37 CBR method; rigid — Westergaard’s method), traffic engineering (volume studies, speed-density relationships, signal design — Webster’s method, PCU factors, level of service), railway engineering basics, airport planning basics.

Water demand forecasting (per capita demand), water quality standards (IS 10500), treatment processes (coagulation, sedimentation, filtration, chlorination and disinfection), distribution systems; sewage quantity estimation, BOD, COD, sewage treatment (screens, grit chambers, primary sedimentation, activated sludge, trickling filters, tertiary treatment, sludge disposal); air pollution sources and control, solid waste management.

Chain and compass surveying (local attraction, magnetic declination), leveling (differential, fly, reciprocal leveling, errors), theodolite surveying (horizontal and vertical angle measurement), tacheometric surveying, plane table surveying, total station operations, GPS and remote sensing basics, GIS concepts.

Free body diagrams, equilibrium of rigid bodies, friction (dry friction, belt and rope friction), centroids and moments of inertia; stress and strain (normal, shear, volumetric), Hooke’s law, elastic constants (E, G, K, Poisson’s ratio), thermal stresses; SFD and BMD for beams, bending stress (neutral axis, section modulus), shear stress distribution, torsion of circular shafts, deflection of beams (Macaulay’s method, Castigliano’s theorem), thin and thick cylinders (Lame’s equations), Euler’s column theory, Mohr’s circle for stress.

Kinematics of mechanisms (four-bar linkage, slider-crank, degrees of freedom — Grubler’s equation), velocity and acceleration analysis (instantaneous centre method, relative velocity method), gears (spur, helical, bevel, worm — gear trains: simple, compound, epicyclic), cams and followers (uniform velocity, SHM, uniform acceleration follower motions), flywheels and governors (Watt, Porter, Hartnell), balancing of rotating masses (static and dynamic), balancing of single and multi-cylinder engines.

Fluid statics (manometers, hydrostatic forces, buoyancy), continuity and momentum equations, Bernoulli’s equation and applications, viscous flow (Couette flow, Hagen-Poiseuille, Darcy-Weisbach equation), boundary layer theory (Blasius solution, boundary layer thickness, separation), dimensional analysis (Buckingham Pi theorem, similarity laws), turbomachinery (centrifugal pumps — velocity triangles, characteristic curves, cavitation; Pelton, Francis, Kaplan turbines).

First law (closed and open systems, enthalpy, SFEE), second law (Clausius and Kelvin-Planck statements, entropy, irreversibility, availability/exergy), Carnot cycle and efficiency, air-standard cycles (Otto, Diesel, Dual, Brayton — thermal efficiency), vapour power cycles (Rankine — basic, reheat, regenerative), refrigeration cycles (vapour-compression, COP, absorption refrigeration basics), gas mixtures, psychrometrics (DBT, WBT, relative humidity, specific humidity, psychrometric chart).

Conduction (Fourier’s law, steady-state 1D — slabs, cylinders, spheres; thermal resistance networks; extended surfaces/fins — fin efficiency and effectiveness; transient conduction — lumped capacitance, Biot number, Fourier number), convection (Newton’s law of cooling, forced convection correlations — Nu, Re, Pr — internal and external flow; natural convection), radiation (Stefan-Boltzmann law, emissivity, blackbody, grey body, view factors, enclosure analysis), heat exchangers (LMTD method, NTU-effectiveness method).

Casting (sand casting, die casting, investment casting — design, defects and remedies), welding (arc, MIG, TIG, resistance, friction welding — processes, HAZ, defects), metal forming (rolling, forging, extrusion, deep drawing, wire drawing — stresses and forces), machining (turning — mechanics, tool geometry, tool life — Taylor’s equation; milling, drilling, grinding), metrology (limits, fits and tolerances, gauges, surface roughness — Ra, Rz, measuring instruments), non-traditional machining (EDM, ECM, LBM, USM).

Work study (method study — process charts; work measurement — time study, standard time, allowances), production planning and control, plant layout types, materials handling, inventory management (EOQ model, safety stock, ABC analysis), quality control (SPC — control charts, acceptance sampling — OC curve, AQL), network analysis (CPM and PERT — critical path, float, crashing), queuing theory basics (M/M/1 queue), linear programming basics.

KCL and KVL, mesh and node analysis, network theorems (Thevenin’s, Norton’s, superposition, maximum power transfer), AC circuits (phasor analysis, impedance, admittance, power triangle, power factor, reactive power), resonance (series and parallel RLC), transient analysis (RL, RC, RLC using Laplace), two-port networks (Z, Y, H, ABCD parameters), star-delta conversion, reciprocity theorem.

Coulomb’s law and electric field intensity, Gauss’s law, electric potential and capacitance, energy in electric fields; Biot-Savart’s law and magnetic field, Ampere’s law, magnetic flux density, Faraday’s law of electromagnetic induction, self and mutual inductance, energy stored in magnetic fields; Maxwell’s equations (integral and differential forms), electromagnetic wave propagation basics, Poynting vector.

Transformers (ideal and practical equivalent circuit, voltage regulation, efficiency, OC and SC tests, auto-transformer, parallel operation, three-phase transformers), DC machines (shunt, series, compound — EMF equation, torque, speed-torque characteristics, losses, starters, speed control), induction motors (rotating magnetic field, slip, equivalent circuit, torque-slip characteristics, starting methods, speed control — V/f control, pole changing), synchronous machines (alternator — OCC, SCC, armature reaction, voltage regulation; synchronous motor — Vee curves, hunting; parallel operation).

Transmission line parameters (R, L, C per unit length), short, medium (nominal-T, nominal-pi) and long line models, ABCD parameters, performance (voltage regulation, efficiency); load flow analysis (bus admittance matrix, Gauss-Seidel and Newton-Raphson methods); fault analysis (three-phase fault — fault MVA; sequence networks and unsymmetrical faults — SLG, LL, LLG); power system stability (steady-state stability limit, transient stability — equal-area criterion, swing equation); protection (overcurrent relays, differential protection, distance protection, circuit breakers).

Transfer functions, block diagram algebra, signal flow graphs (Mason’s gain formula), first and second-order system response (time-domain specifications, steady-state error, error constants), Routh-Hurwitz criterion, root locus technique (construction rules, effect of poles/zeros), Bode plots (gain and phase margin), Nyquist stability criterion, PID controllers, lead and lag compensators, state-space analysis (state equations, transition matrix, controllability, observability).

Types and sources of errors, Wheatstone, Kelvin, Maxwell, Hay, Schering, and Anderson bridges, PMMC, moving-iron, dynamometer, and induction-type instruments, energy meters (single-phase and three-phase), CTs and PTs, oscilloscopes (CRO — triggering, Lissajous figures), transducers (thermocouples, RTDs, thermistors, strain gauges, LVDT, piezoelectric), signal conditioning circuits.

Power semiconductor devices (SCR, TRIAC, GTO, MOSFET, IGBT — V-I characteristics, triggering), single-phase and three-phase uncontrolled and controlled rectifiers (firing angle, output voltage, ripple factor, power factor), DC-DC converters (buck, boost, buck-boost — voltage conversion ratio), single-phase and three-phase VSI (half-bridge, full-bridge, PWM techniques), AC voltage controllers (phase angle control), cycloconverters basics, electric drives basics.