# Gate Mechanical Engineering Syllabus & Practices Test

[WpProQuiz 4] |

**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; trusses and frames;

virtual work; kinematics and dynamics of particles and of rigid bodies in plane

motion; impulse and momentum (linear and angular) and energy formulations,

collisions.

**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; 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, manometry, buoyancy, 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

in compressible fluids, boundary layer, elementary turbulent flow, flow through pipes,

head losses in pipes, bends and fittings.

**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 analysis.

**Thermodynamics:** Thermodynamic systems and processes; properties of pure

substances, behaviour 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.

**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, design of jigs and fixtures.

Metrology and Inspection: Limits, fits and tolerances; linear and angular

measurements; comparators; gauge design; interferometry; form and finish

measurement; alignment and testing methods; tolerance analysis in manufacturing

and assembly.

**Computer Integrated Manufacturing:** Basic concepts of CAD/CAM and their

integration tools.

**Production Planning and Control:** Forecasting models, aggregate production

planning, scheduling, materials requirement planning.

**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.