GATE Mechanical Engineering Question Papers

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 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 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
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, 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.