GATE 2025 syllabus for mechanical engineering has 4 sections; detailed topics

Topic

Subtopics

Linear Algebra

Matrix algebra, systems of linear equations, eigenvalues and eigenvectors

Calculus

Functions of single variable, limits, continuity, differentiability, mean value theorems, indeterminate forms, evaluation of definite and improper integrals, double and triple integrals, partial derivatives, total derivative, Taylor series (one and two variables), maxima and minima, Fourier series, gradient, divergence and curl, vector identities, directional derivatives, line, surface and volume integrals, applications of Gauss, Stokes, and Green’s theorems

Differential Equations

First order equations (linear and nonlinear), higher order linear differential equations with constant coefficients, Euler-Cauchy equation, initial and boundary value problems, Laplace transforms, solutions of heat, wave, and Laplace's equations

Complex Variables

Analytic functions, Cauchy-Riemann equations, Cauchy’s integral theorem and integral formula, Taylor and Laurent series

Probability and Statistics

Definitions of probability, sampling theorems, conditional probability, mean, median, mode, standard deviation, random variables, binomial, Poisson, and normal distributions

Numerical Methods

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

Topic

Subtopics

Engineering Mechanics

Free-body diagrams and equilibrium, friction (rolling friction, belt-pulley systems, brakes, clutches, screw jack, wedges, vehicles), trusses and frames, virtual work, kinematics and dynamics of rigid bodies in plane motion, impulse and momentum (linear and angular), energy formulations, Lagrange’s equation

Mechanics of Materials

Stress and strain, elastic constants, Poisson's ratio, Mohr’s circle for plane stress and plane strain, thin cylinders, shear force and bending moment diagrams, bending and shear stresses, shear centre, deflection of beams, torsion of circular shafts, Euler’s theory of columns, energy methods, thermal stresses, strain gauges and rosettes, testing of materials (universal testing machine, hardness, impact strength)

Theory of Machines

Displacement, velocity, and acceleration analysis of plane mechanisms, dynamic analysis of linkages, cams, gears and gear trains, flywheels and governors, balancing of reciprocating and rotating masses, gyroscope

Vibrations

Free and forced vibrations of single degree of freedom systems, effect of damping, vibration isolation, resonance, critical speeds of shafts

Machine Design

Design for static and dynamic loading, failure theories, fatigue strength and the S-N diagram, principles of the design of machine elements (bolted, riveted, and welded joints; shafts; gears; rolling and sliding contact bearings; brakes and clutches; springs)

Topic

Subtopics

Engineering Mechanics

Free-body diagrams and equilibrium, friction (rolling friction, belt-pulley systems, brakes, clutches, screw jack, wedges, vehicles), trusses and frames, virtual work, kinematics and dynamics of rigid bodies in plane motion, impulse and momentum (linear and angular), energy formulations, Lagrange’s equation

Mechanics of Materials

Stress and strain, elastic constants, Poisson's ratio, Mohr’s circle for plane stress and plane strain, thin cylinders, shear force and bending moment diagrams, bending and shear stresses, shear centre, deflection of beams, torsion of circular shafts, Euler’s theory of columns, energy methods, thermal stresses, strain gauges and rosettes, testing of materials (universal testing machine, hardness, impact strength)

Theory of Machines

Displacement, velocity, and acceleration analysis of plane mechanisms, dynamic analysis of linkages, cams, gears and gear trains, flywheels and governors, balancing of reciprocating and rotating masses, gyroscope

Vibrations

Free and forced vibrations of single degree of freedom systems, effect of damping, vibration isolation, resonance, critical speeds of shafts

Machine Design

Design for static and dynamic loading, failure theories, fatigue strength and the S-N diagram, principles of the design of machine elements (bolted, riveted, and welded joints; shafts; gears; rolling and sliding contact bearings; brakes and clutches; springs)

Fluid Mechanics

Fluid properties, fluid statics, forces on submerged bodies, stability of floating bodies, control-volume analysis (mass, momentum, and energy), fluid acceleration, differential equations of continuity and momentum, Bernoulli’s equation, dimensional analysis, viscous flow of incompressible fluids, boundary layer, elementary turbulent flow, flow through pipes, head losses in pipes, bends, and fittings, basics of compressible fluid flow

Heat Transfer

Modes of heat transfer, one-dimensional heat conduction (resistance concept and electrical analogy), heat transfer through fins, unsteady heat conduction, lumped parameter system, Heisler's charts, thermal boundary layer, dimensionless parameters in convective heat transfer, heat transfer correlations (flow over flat plates and through pipes, effect of turbulence), heat exchanger performance (LMTD and NTU methods), radiative heat transfer (Stefan-Boltzmann law, Wien's displacement law, black and grey surfaces, view factors, radiation network analysis)

Thermodynamics

Thermodynamic systems and processes, properties of pure substances, behavior of ideal and real gases, zeroth and first laws of thermodynamics, calculation of work and heat in various processes, second law of thermodynamics, thermodynamic property charts and tables, availability and irreversibility, thermodynamic relations

Applications

Power Engineering: Air and gas compressors, vapor and gas power cycles, concepts of regeneration and reheat. I.C. Engines: Air-standard Otto, Diesel, and dual cycles. Refrigeration and Air-Conditioning: Vapor and gas refrigeration and heat pump cycles, properties of moist air, psychrometric chart, basic psychrometric processes. Turbomachinery: Impulse and reaction principles, velocity diagrams, Pelton-wheel, Francis and Kaplan turbines, steam and gas turbines

Topic

Subtopics

Engineering Mechanics

Free-body diagrams and equilibrium, friction (rolling friction, belt-pulley systems, brakes, clutches, screw jack, wedges, vehicles), trusses and frames, virtual work, kinematics and dynamics of rigid bodies in plane motion, impulse and momentum (linear and angular), energy formulations, Lagrange’s equation

Mechanics of Materials

Stress and strain, elastic constants, Poisson's ratio, Mohr’s circle for plane stress and plane strain, thin cylinders, shear force and bending moment diagrams, bending and shear stresses, shear centre, deflection of beams, torsion of circular shafts, Euler’s theory of columns, energy methods, thermal stresses, strain gauges and rosettes, testing of materials (universal testing machine, hardness, impact strength)

Theory of Machines

Displacement, velocity, and acceleration analysis of plane mechanisms, dynamic analysis of linkages, cams, gears and gear trains, flywheels and governors, balancing of reciprocating and rotating masses, gyroscope

Vibrations

Free and forced vibrations of single degree of freedom systems, effect of damping, vibration isolation, resonance, critical speeds of shafts

Machine Design

Design for static and dynamic loading, failure theories, fatigue strength and the S-N diagram, principles of the design of machine elements (bolted, riveted, and welded joints; shafts; gears; rolling and sliding contact bearings; brakes and clutches; springs)

Fluid Mechanics

Fluid properties, fluid statics, forces on submerged bodies, stability of floating bodies, control-volume analysis (mass, momentum, and energy), fluid acceleration, differential equations of continuity and momentum, Bernoulli’s equation, dimensional analysis, viscous flow of incompressible fluids, boundary layer, elementary turbulent flow, flow through pipes, head losses in pipes, bends, and fittings, basics of compressible fluid flow

Heat Transfer

Modes of heat transfer, one-dimensional heat conduction (resistance concept and electrical analogy), heat transfer through fins, unsteady heat conduction, lumped parameter system, Heisler's charts, thermal boundary layer, dimensionless parameters in convective heat transfer, heat transfer correlations (flow over flat plates and through pipes, effect of turbulence), heat exchanger performance (LMTD and NTU methods), radiative heat transfer (Stefan-Boltzmann law, Wien's displacement law, black and grey surfaces, view factors, radiation network analysis)

Thermodynamics

Thermodynamic systems and processes, properties of pure substances, behavior of ideal and real gases, zeroth and first laws of thermodynamics, calculation of work and heat in various processes, second law of thermodynamics, thermodynamic property charts and tables, availability and irreversibility, thermodynamic relations

Applications

Power Engineering: Air and gas compressors, vapor and gas power cycles, concepts of regeneration and reheat. I.C. Engines: Air-standard Otto, Diesel, and dual cycles. Refrigeration and Air-Conditioning: Vapor and gas refrigeration and heat pump cycles, properties of moist air, psychrometric chart, basic psychrometric processes. Turbomachinery: Impulse and reaction principles, velocity diagrams, Pelton-wheel, Francis and Kaplan turbines, steam and gas turbines

Engineering Materials

Structure and properties of engineering materials, phase diagrams, heat treatment, stress-strain diagrams for engineering materials

Casting, Forming and Joining Processes

Different types of castings, design of patterns, moulds and cores, solidification and cooling, riser and gating design, plastic deformation and yield criteria, fundamentals of hot and cold working processes, load estimation for bulk (forging, rolling, extrusion, drawing) and sheet (shearing, deep drawing, bending) metal forming processes, principles of powder metallurgy, principles of welding, brazing, soldering, and adhesive bonding

Machining and Machine Tool Operations

Mechanics of machining, basic machine tools, single and multi-point cutting tools, tool geometry and materials, tool life and wear, economics of machining, principles of non-traditional machining processes, principles of work holding, jigs and fixtures, abrasive machining processes, NC/CNC machines and CNC programming

Metrology and Inspection

Limits, fits and tolerances, linear and angular measurements, comparators, interferometry, form and finish measurement, alignment and testing methods, tolerance analysis in manufacturing and assembly, concepts of coordinate-measuring machine (CMM)

Computer Integrated Manufacturing

Basic concepts of CAD/CAM and their integration tools, additive manufacturing

Production Planning and Control

Forecasting models, aggregate production planning, scheduling, materials requirement planning, lean manufacturing

Inventory Control

Deterministic models, safety stock inventory control systems

Operations Research

Linear programming, simplex method, transportation, assignment, network flow models, simple queuing models, PERT and CPM