GATE Syllabus

# GATE 2025 syllabus – PI: Production and Industrial Engineering

GATE 2025 syllabus for Production and Industrial Engineering (PI) details the latest GATE syllabus for the subject released by the official gate organizing institute IIT Roorkee 2025. We also created an easy-to-use ad-free mobile app for the GATE syllabus, previous year papers with keys, gate calculator, virtual calculator, and more. Download iStudy App for all GATE preparation needs.

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## GATE 2025 Syllabus – Production and Industrial Engineering (PI)

#### Section 1: Engineering Mathematics

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

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

Differential Equations
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.

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

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

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#### Section 2: General Engineering

Engineering Materials
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.

Applied Mechanics
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.

Theory of Machines and Design
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.

Thermal and Fluids Engineering
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.

#### Section 3: Manufacturing Processes I

Casting
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 casting techniques: Pressure die casting, Centrifugal casting, Investment casting, Shell mold casting; Casting defects and their inspection by non-destructive testing.

Metal Forming
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.

Joining of Materials
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.

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

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

#### Section 4: Manufacturing Processes II

Machining
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.

Machine Tools
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.

Computer Integrated Manufacturing
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.

If you are preparing for GATE, download iStudy Mobile App for all GATE Syllabus, Previous Question Papers and Keys, preparation guide, Exam updates, Gate Virtual calculator, Gate Score calculator, and IITs & NITs cutoffs. It is a lightweight, easy to use, no images, and no ads platform to make students’ lives easier.
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#### Section 5: Quality and Reliability

Metrology and Inspection
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 Management
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, ISO14000.

Reliability and Maintenance
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.

#### Section 6: Industrial Engineering

Product Design and Development
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’.

Work System Design
Taylor’s scientific management, Gilbreths’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 Design
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.

#### Section 7: Operations research and Operations management

Operation Research
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.

Engineering Economy and Costing
Elementary cost accounting and methods of depreciation; Break-even analysis; Techniques for evaluation of capital investments; Financial statements; Activity based costing.

Production control
Forecasting techniques – causal and time series models, moving average, exponential smoothing, trend and seasonality; Aggregate production planning; Master production scheduling; MRP, MRP-II 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.

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

If you are preparing for GATE, download iStudy Mobile App for all GATE Syllabus, Previous Question Papers and Keys, preparation guide, Exam updates, Gate Virtual calculator, Gate Score calculator, and IITs & NITs cutoffs. It is a lightweight, easy to use, no images, and no ads platform to make students’ lives easier.
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#### ST: Statistics

Calculus:
Finite, countable and uncountable sets; Real number system as a complete ordered field, Archimedean property; Sequences of real numbers, convergence of sequences, bounded sequences, monotonic sequences, Cauchy criterion for convergence; Series of real numbers, convergence, tests of convergence, alternating series, absolute and conditional convergence; Power series and radius of convergence; Functions of a real variable: Limit, continuity, monotone functions, uniform continuity, differentiability, Rolle’s theorem, mean value theorems, Taylor’s theorem, L’Hospital rules, maxima and minima, Riemann integration and its properties, improper integrals; Functions of several real variables: Limit, continuity, partial derivatives, directional derivatives, gradient, Taylor’s theorem, total derivative, maxima and minima, saddle point, method of Lagrange multipliers, double and triple integrals and their applications.

Matrix Theory:
Subspaces of and , span, linear independence, basis and dimension, row space and column space of a matrix, rank and nullity, row reduced echelon form, trace and determinant, inverse of a matrix, systems of linear equations; Inner products in and , Gram-Schmidt orthonormalization; Eigenvalues and eigenvectors, characteristic polynomial, Cayley-Hamilton theorem, symmetric, skew-symmetric, Hermitian, skew-Hermitian, orthogonal, unitary matrices and their eigenvalues, change of basis matrix, equivalence and similarity, diagonalizability, positive definite and positive semi-definite matrices and their properties, quadratic forms, singular value decomposition.

Probability:
Axiomatic definition of probability, properties of probability function, conditional probability, Bayes’ theorem, independence of events; Random variables and their distributions, distribution function, probability mass function, probability density function and their properties, expectation, moments and moment generating function, quantiles, distribution of functions of a random variable, Chebyshev, Markov and Jensen inequalities.

Standard discrete and continuous univariate distributions:
Bernoulli, binomial, geometric, negative binomial, hypergeometric, discrete uniform, Poisson, continuous uniform, exponential, gamma, beta, Weibull, normal.

Jointly distributed random variables and their distribution functions, probability mass function, probability density function and their properties, marginal and conditional distributions, conditional expectation and moments, product moments, simple correlation coefficient, joint moment generating function, independence of random variables, functions of random vector and their distributions, distributions of order statistics, joint and marginal distributions of order statistics; multinomial distribution, bivariate normal distribution, sampling distributions: central, chi-square, central t, and central F distributions.

Convergence in distribution, convergence in probability, convergence almost surely, convergence in r-th mean and their inter-relations, Slutsky’s lemma, Borel-Cantelli lemma; weak and strong laws of large numbers; central limit theorem for i.i.d. random variables, delta method.

Stochastic Processes:
Markov chains with finite and countable state space, classification of states, limiting behaviour of n-step transition probabilities, stationary distribution, Poisson process, birthand-death process, pure-birth process, pure-death process, Brownian motion and its basic properties.

#### GENERAL APTITUDE (Common for all branches)

Verbal Aptitude

Basic English Grammar
Tenses, articles, adjectives, prepositions, conjunctions, verb-noun agreement, and other parts of speech

Basic Vocabulary
Words, idioms, and phrases in context

Narrative Sequencing

Quantitative Aptitude

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

Analytical Aptitude

Logic
Deduction and Induction

Analogy

Numerical Relations and Reasoning

Spatial Aptitude

Transformation of Shapes
Translation, rotation, scaling, mirroring, assembling, and grouping

Paper folding, cutting, and patterns in 2 and 3 dimensions

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We wish you great luck with GATE preparations.

1. Shilpi Bhargava

for getting seat in iit’s , one has to be amongst top 50 ranks.
as far is preparation for giving GATE through just have a look at previous years question papers and prepare accordingly.

2. tarun

I am kalmesh engineering student completed the engineering in the descipline of industrial and production. I want to know about how much seats are in iit and nit college belongs to production and industrial engineering. I hope u will reply me soon. Thanking you.

3. jagdish choudhary

respected sir,
I am jagdish engineering student completed the engineering in the descipline of industrial and production. I want to know about how much seats are in iit and nit college belongs to production and industrial engineering. I hope u will reply me soon. Thanking you

4. niraj jain

respected sir,
i am the student of production dept. i am going to start the gate preparation ,so give me the basic ideas about the start for gate preparation.

5. Rakesh kumar vishnu

we r in the 2nd year of production engineering.we are willing to prepare gate examination .just give your ideas.

6. avinash kumar

respected sir,
i am a student of mechanical engg.(manufacturing).so i want to know about syllabus.

7. kalmesh

respected sir,
I am kalmesh engineering student completed the engineering in the descipline of industrial and production. I want to know about how much seats are in iit and nit college belongs to production and industrial engineering. I hope u will reply me soon. Thanking you.