The Graduate Aptitude Test in Engineering (GATE) is a national level entrance examination in India, which is generally recognized by many prestigious public sector undertakings as well as private sector enterprises. It is conducted jointly by seven Indian Institutes of Technology, namely Delhi, Kanpur, Kharagpur, Madras, Mumbai, Roorkee and Guwahati and IISc Bangalore. The test is an aptitude exam primarily aimed towards professionals in the graduate level.
GATE Syllabus for Mechanical Engineering
The GATE syllabus for Mechanical Engineering is divided into four sections:
- Section 1: Engineering Mathematics
- Section 2: Applied Mechanics and Design
- Section 3: Fluid Mechanics and Thermal Sciences
- Section 4: Materials, Manufacturing, and Industrial Engineering
Section-1: Engineering Mathematics
Linear Algebra: Matrix algebra, systems of linear equations, eigenvalues and eigenvectors.
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, 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 and standard deviation; random variables, binomial, Poisson and normal
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.
Section-2: Applied Mechanics and Design
Engineering Mechanics: Free-body diagrams and equilibrium; friction and its applications including
rolling friction, belt-pulley, brakes, clutches, screw jack, wedge, vehicles, etc.; trusses and frames;
virtual work; kinematics and dynamics of rigid bodies in plane motion; impulse and momentum (linear
and angular) and 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; concept of 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 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 of
reciprocating 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 the SN diagram; principles of the design of machine elements such as bolted, riveted and welded joints;
shafts, gears, rolling and sliding contact bearings, brakes and clutches, springs.
Section-3: Fluid Mechanics and Thermal Science
Fluid Mechanics: Fluid properties; fluid statics, forces on submerged bodies, stability of floating
bodies; control-volume analysis of 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 free and forced convective
heat transfer, heat transfer correlations for flow over flat plates and through pipes, effect of
turbulence; heat exchanger performance, LMTD and NTU methods; radiative heat transfer, StefanBoltzmann law, Wien’s displacement law, black and grey surfaces, view factors, radiation network
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; 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; 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.
Section-4: Materials, Manufacturing and Industrial Engineering
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
Computer Integrated Manufacturing: Basic concepts of CAD/CAM and their integration tools; additive
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.
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