Gate 2021 syllabus mechanical engineering

GATE SYLLABUS 2021 

MECHANICAL

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 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.

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 center ;

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 S-N 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 Sciences

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 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, 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; 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 (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.