GATE PI syllabus 2026

Matrix algebra, Systems of linear equations, Eigen values and Eigen vectors.

• Functions of single variable, Limit, continuity and differentiability, Mean value theorems, Evaluation of definite and improper integrals, Partial derivatives, Total derivative, Maxima and minima, Grad, Divergence and Curl, Vector identities, Directional derivatives
• Line, Surface and Volume integrals
• Stokes, Gauss and Green’s theorems.

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.

Analytic functions, Cauchy’s integral theorem, Taylor series.

Definitions of probability and sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Linear regression, Random variables, Poisson, normal, binomial and exponential distributions.

Numerical solutions of linear and nonlinear algebraic equations, Integration by trapezoidal and Simpson’s rules, Single and multi-step methods for differential equations.

• Structure, physical and mechanical properties, and applications of common engineering materials (metals and alloys, semiconductors, ceramics, polymers, and composites – metal, polymer and ceramic based)
• Iron-carbon equilibrium phase diagram
• Heat treatment of metals and alloys and its influence on mechanical properties
• Stress-strain behavior of metals and alloys.

• Engineering mechanics – equivalent force systems, free body concepts, equations of equilibrium
• Trusses
• Strength of materials – stress, strain and their relationship
• Failure theories
• Mohr’s circle (stress)
• Deflection of beams, bending and shear stresses
• Euler’s theory of columns
• Thick and thin cylinders
• Torsion.

• Analysis of planar mechanisms, cams and followers
• Governors and fly wheels
• Design of bolted, riveted and welded joints
• Interference/shrink fit joints
• Friction and lubrication
• Design of shafts, keys, couplings, spur gears, belt drives, brakes and clutches
• Pressure vessels.

• Fluid mechanics – fluid statics, Bernoulli’s equation, flow through pipes, laminar and turbulent flows, equations of continuity and momentum, capillary action
• Dimensional analysis
• Thermodynamics – zeroth, first and second laws of thermodynamics, thermodynamic systems and processes, calculation of work and heat for systems and control volumes
• Air standard cycles
• Heat transfer – basic applications of conduction, convection and radiation.

• Types of casting processes and applications
• Sand casting: patterns – types, materials and allowances
• molds and cores–materials, making, and testing
• design of gating system and riser
• casting techniques of cast iron, steels, and nonferrous metals and alloys
• analysis of solidification and microstructure development
• Other cast techniques: Pressure die casting, Centrifugal casting, Investment casting, Shell mold casting
• Casting defects and their inspection by non-destructive testing.

• Stress-strain relations in elastic and plastic deformation
• von Mises and Tresca yield criteria, Concept of flow stress
• Hot, warm and cold working
• Bulk forming processes – forging, rolling, extrusion and wire drawing
• Sheet metal working processes – blanking, punching, bending, stretch forming, spinning and deep drawing
• Ideal work and slab analysis
• Defects in metal working and their causes.

• Classification of joining processes
• Principles of fusion welding processes using different heat sources (flame, arc, resistance, laser, electron beam), Heat transfer and associated losses
• Arc welding processes - SMAW, GMAW, GTAW, plasma arc, submerged arc welding processes
• Principles of solid state welding processes – friction welding, friction stir welding, ultrasonic welding
• Welding defects - causes and inspection
• Principles of adhesive joining, brazing and soldering processes.

Production of metal/ceramic powders, compaction and sintering of metals and ceramic powders, Cold and hot isostatic pressing.

• Polymer processing – injection, compression and blow molding, extrusion, calendaring and thermoforming
• Molding of composites.

• Orthogonal and oblique machining, Single point cutting tool and tool signature, Chip formation, cutting forces, Merchant’s analysis, Specific cutting energy and power
• Machining parameters and material removal rate
• tool materials, Tool wear and tool life
• Thermal aspects of machining, cutting fluids, machinability
• Economics of machining
• Machining processes - turning, taper turning, thread cutting, drilling, boring, milling, gear cutting, thread production
• Finishing processes – grinding, honing, lapping and super-finishing.

• Lathe, milling, drilling and shaping machines–construction and kinematics
• Jigs and fixtures – principles, applications, and design.

• Principles and applications of USM, AJM, WJM, AWJM, EDM and Wire EDM, LBM, EBM, PAM, CHM, ECM
• Effect of process parameters on material removal rate, surface roughness and power consumption
• Additive manufacturing techniques.

• Basic concepts of CAD and CAM, Geometric modeling, CNC
• Automation in Manufacturing
• Industrial Robots – configurations, drives and controls
• Cellular manufacturing and FMS - Group Technology, CAPP.

• Accuracy and precision
• Types of errors
• Limits, fits and tolerances
• Gauge design, Interchangeability, Selective assembly
• Linear, angular, and form measurements (straightness, flatness, roundness, runout and cylindricity) by mechanical and optical methods
• Inspection of screw threads and gears
• Surface roughness measurement by contact and non-contact methods.

• Quality – concept and costs
• Statistical quality control – process capability analysis, control charts for variables and attributes and acceptance sampling
• Six sigma
• Total quality management
• Quality assurance and certification - ISO 9000, ISO 14000.

• Reliability, availability and maintainability
• Distribution of failure and repair times
• Determination of MTBF and MTTR, Reliability models
• Determination of system reliability
• Preventive and predictive maintenance and replacement, Total productive maintenance.

• Principles of product design, tolerance design
• Quality and cost considerations
• Product life cycle
• Standardization, simplification, diversification
• Value engineering and analysis
• Concurrent engineering
• Design for “X”.

• Taylor’s scientific management, Gilbreth’s contributions
• Productivity – concepts and measurements
• Method study, Micro-motion study, Principles of motion economy
• Work measurement – time study, Work sampling, Standard data, PMTS
• Ergonomics
• Job evaluation and merit rating.

• Facility location factors and evaluation of alternate locations
• Types of plant layout and their evaluation
• Computer aided layout design techniques
• Assembly line balancing
• Materials handling systems.

• Linear programming – problem formulation, simplex method, duality and sensitivity analysis
• Transportation and assignment models
• Integer programming
• Constrained and unconstrained nonlinear optimization
• Markovian queuing models
• Simulation – manufacturing applications.

• Element cost accounting and methods of depreciation
• Break-even analysis
• Techniques for evaluation of capital investments
• Financial statements
• Activity based costing.

• Forecasting techniques – causal and time series models, moving average, exponential smoothing, trend and seasonality
• Aggregate production planning
• Master production scheduling
• MRP, MRPII and ERP
• Routing, scheduling and priority dispatching
• Push and pull production systems, concepts of Lean and JIT manufacturing systems
• Logistics, distribution, and supply chain management
• Inventory – functions, costs, classifications, deterministic inventory models, quantity discount
• Perpetual and periodic inventory control systems.

Scheduling techniques – Gantt chart, CPM, PERT and GERT.

• Basic English grammar: tenses, articles, adjectives, prepositions, conjunctions, verb-noun agreement, and other parts of speech
• Basic vocabulary: words, idioms, and phrases in context
• Reading and comprehension, Narrative sequencing.

• Data interpretation: data graphs (bar graphs, pie charts, and other graphs representing data), 2- and 3-dimensional plots, maps, and tables
• Numerical computation and estimation: ratios, percentages, powers, exponents and logarithms, permutations and combinations, and series
• Mensuration and geometry
• Elementary statistics and probability.

Logic: deduction and induction, Analogy, Numerical relations and reasoning.

• Transformation of shapes: translation, rotation, scaling, mirroring, assembling, and grouping
• paper folding, cutting, and patterns in 2 and 3 dimensions.