Gate2025 syllabus

 Section 1: Engineering MathematicsLinear Algebra: Matrix algebra, systems of linear equations, eigen values and eigen vectors.Calculus: Functions of single variable, limit, continuity and differentiability, mean value theorems,indeterminate forms; evaluation of definite and improper integrals; double and triple integrals;partial derivatives, total derivative, Taylor series (in one and two variables), maxima and minima,Fourier series; gradient, divergence and curl, vector identities, directional derivatives, line, surfaceand volume integrals, applications of Gauss, Stokes and Green’s theorems.Differential Equations: First order equations (linear and nonlinear); higher order linear differentialequations 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 theoremand integral formula; Taylor and Laurent series.Probability and Statistics: Definitions of probability, sampling theorems, conditional probability;mean, median, mode and standard deviation; random variables, binomial, Poisson and normaldistributions.Numerical Methods: Numerical solutions of linear and non-linear algebraic equations; integrationby trapezoidal and Simpson’s rules; single and multi-step methods for differential equations.Section 2: Applied Mechanics and DesignEngineering Mechanics: Free-body diagrams and equilibrium; friction and its applicationsincluding rolling friction, belt-pulley, brakes, clutches, screw jack, wedge, vehicles, etc.; trussesand frames; virtual work; kinematics and dynamics of rigid bodies in plane motion; impulse andmomentum (linear and angular) and energy formulations; Lagrange’s equation.Mechanics of Materials: Stress and strain, elastic constants, Poisson's ratio; Mohr’s circle for planestress and plane strain; thin cylinders; shear force and bending moment diagrams; bending andshear stresses; concept of shear centre; deflection of beams; torsion of circular shafts; Euler’stheory of columns; energy methods; thermal stresses; strain gauges and rosettes; testing ofmaterials with universal testing machine; testing of hardness and 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 ofreciprocating and rotating masses; gyroscope.Vibrations: Free and forced vibration 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 theS-N diagram; principles of the design of machine elements such as bolted, riveted and weldedjoints; shafts, gears, rolling and sliding contact bearings, brakes and clutches, springs.Section 3: Fluid Mechanics and Thermal SciencesFluid Mechanics: Fluid properties; fluid statics, forces on submerged bodies, stability of floatingbodies; control-volume analysis of mass, momentum and energy; fluid acceleration; differentialequations of continuity and momentum; Bernoulli’s equation; dimensional analysis; viscous flowof incompressible fluids, boundary layer, elementary turbulent flow, flow through pipes, headlosses in pipes, bends and fittings; basics of compressible fluid flow.Heat Transfer: Modes of heat transfer; one dimensional heat conduction, resistance concept andelectrical analogy, heat transfer through fins; unsteady heat conduction, lumped parameter system,Heisler's charts; thermal boundary layer, dimensionless parameters in free and forced convectiveheat transfer, heat transfer correlations for flow over flat plates and through pipes, effect ofturbulence; heat exchanger performance, LMTD and NTU methods; radiative heat transfer, StefanBoltzmann law, Wien's displacement law, black and grey surfaces, view factors, radiation networkanalysisThermodynamics: Thermodynamic systems and processes; properties of pure substances, behaviorof ideal and real gases; zeroth and first laws of thermodynamics, calculation of work and heat invarious processes; second law of thermodynamics; thermodynamic property charts and tables,availability and irreversibility; thermodynamic relations.Applications: Power Engineering: Air and gas compressors; vapour and gas power cycles,concepts of regeneration and reheat. I.C. Engines: Air-standard Otto, Diesel and dual cycles.Refrigeration and air-conditioning: Vapour and gas refrigeration and heat pump cycles; propertiesof moist air, psychrometric chart, basic psychrometric processes. Turbomachinery: Impulse andreaction principles, velocity diagrams, Pelton-wheel, Francis and Kaplan turbines; steam and gasturbines.Section 4: Materials, Manufacturing and Industrial EngineeringEngineering Materials: Structure and properties of engineering materials, phase diagrams, heattreatment, stress-strain diagrams for engineering materials.Casting, Forming and Joining Processes: Different types of castings, design of patterns, mouldsand 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; singleand multi-point cutting tools, tool geometry and materials, tool life and wear; economics ofmachining; principles of non-traditional machining processes; principles of work holding, jigs andfixtures; 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, networkflow models, simple queuing models, PERT and CPM.