gate exam syllabus

7/24/2019 Gate Exam Syllabus

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GATE EXAM SYLLABUS

Syllabus for Mechanical Engineering (ME)

ENGINEER ING MATHEM AT ICS

Linear Algebra: Matrix algebra, Systems of linear equations, Eigen values and eigen vectors.

Calculus: Functions of single variable, Limit, continuity and dierentiability, Mean value theorems,Evaluation of denite and im!ro!er integrals, "artial derivatives, #otal derivative, Maxima and

minima, $radient, %ivergence and &url, 'ector identities, %irectional derivatives, Line, Surface and

'olume integrals, Sto(es, $auss and $reen)s theorems.

Diferential equations: First order equations *linear and nonlinear+, igher order linear

dierential equations -ith constant coecients, &auchy)s and Euler)s equations, /nitial and

boundary value !roblems, La!lace transforms, Solutions of one dimensional heat and -ave

equations and La!lace equation.

Complex variables: 0nalytic functions, &auchy)s integral theorem, #aylor and Laurent series.

Probability and Statistics: %enitions of !robability and sam!ling theorems, &onditional

!robability, Mean, median, mode and standard deviation, 1andom variables, "oisson,2ormal and

3inomial distributions.

Numerical Methods: 2umerical solutions of linear and non4linear algebraic equations /ntegration

by tra!e5oidal and Sim!son)s rule, single and multi4ste! methods for dierential equations.

AP PL IED MECHAN IC S AN D DESIG N

ngineering Mechanics!Free body diagrams and equilibrium6 trusses and frames6 virtual -or(6

(inematics and dynamics of !articles and of rigid bodies in !lane motion, including im!ulse and

momentum *linear and angular+ and energy formulations6 im!act.

Strength o" Materials!Stress and strain, stress4strain relationshi! and elastic constants, Mohr)s

circle for !lane stress and !lane strain, thin cylinders6 shear force and bending moment diagrams6

bending and shear stresses6 de7ection of beams6 torsion of circular shafts6 Euler)s theory of

columns6 strain energy methods6 thermal stresses.

#heory o" Machines!%is!lacement, velocity and acceleration analysis of !lane mechanisms6

dynamic analysis of slider4cran( mechanism6 gear trains6 7y-heels.

$ibrations!Free and forced vibration of single degree of freedom systems6 eect of dam!ing6

vibration isolation6 resonance, critical s!eeds of shafts.

Design! %esign for static and dynamic loading6 failure theories6 fatigue strength and the S42

diagram6principlesof the design of machine elements such as bolted, riveted and -elded 8oints,

shafts, s!ur gears, rolling and sliding contact bearings, bra(es and clutches.

FL UI D MECHANICS AN D THER MAL SC IENCES

%luid Mechanics!Fluid !ro!erties6 7uid statics, manometry, buoyancy6 control4volume analysis of

mass, momentum and energy6 7uid acceleration6 dierential equations of continuity and


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momentum6 3ernoulli)s equation6 viscous 7o- of incom!ressible 7uids6 boundary layer6 elementary

turbulent 7o-6 7o- through !i!es, head losses in !i!es, bends etc.

&eat'#rans"er!Modes of heat transfer6 one dimensional heat conduction, resistance conce!t,

electrical analogy, unsteady heat conduction, ns6 dimensionless !arameters in free and forced

convective heat transfer, various correlations for heat transfer in 7o- over 7at !lates and through

!i!es6 thermal boundary layer6 eect of turbulence6 radiative heat transfer, blac( and grey

surfaces, sha!e factors, net-or( analysis6 heat exchanger !erformance, LM#% and 2#9 methods.

#hermodynamics!eroth, First and Second la-s of thermodynamics6 thermodynamic system and

!rocesses6 &arnot cycle.irreversibility and availability6 behaviour of ideal and real gases, !ro!erties

of !ure substances, calculation of -or( and heat in ideal !rocesses6 analysis of thermodynamic

cycles related to energy conversion.

Applications!Power Engineering: Steam #ables, 1an(ine, 3rayton cycles -ith regeneration and

reheat.I.C. Engines: air4standard ;tto, %iesel cycles. Refrigeration and air-conditioning: 'a!our

refrigeration cycle, heat !um!s, gas refrigeration, 1everse 3rayton cycle6 moist air: !sychrometric

chart, basic !sychrometric !rocesses. Turbomachinery:"elton4-heel, Francis and


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)perations +esearch!Linear !rogramming, sim!lex and du!lex method, trans!ortation,

assignment, net-or( 7o- models, sim!le queuing models, "E1# and &"M.

$0#E E?0M

Sy lla bus for Gene ral Ap ti tud e (G A)

$erbal Ability!English grammar, sentence com!letion, verbal analogies, -ord grou!s,

instructions, critical reasoning and verbal deduction.

Numerical Ability!2umerical com!utation, numerical estimation, numerical reasoning and data

inter!retation.

/ES ME&02/&0L S@LL039SE2$L/S 02% $E2E10L S#9%/ES

General English

The English paper will be designed to test general understanding of English and everyday use of words. .

General Knowledge

General Knowledge including knowledge of current events and matters of every day observation and experience. The knowledge of

scientific aspects of everyday life is expected at the level of an educated person. The paper will also include questions on History of

ndia and Geography of a nature which the candidate should be able to answer without special study.

!E"H#$"#%Paper I

1. TE!M"#$%&MI'S&"ycles and " Engines' (asic concepts' )pen and "losed systems. Heat and work. *eroth' +irst and ,econd

%aw' #pplication to non&+low and +low processes. Entropy' #vailability' rreversibility and Tds relations. "laperyron and real gas

equations' -roperties of ideal gases and vapours. ,tandard vapour' Gas power and efrigeration cycles. Two stage compressor. "&

and ,.. Engines. -re&ignition' /etonation and /iesel&knock' +uel in0ection and "arburation' ,upercharging. Turbo&prop and ocket

engines' Engine "ooling' Emission 1 "ontrol' +lue gas analysis' !easurement of "alorific values. "onventional and $uclear fuels'

Elements of $uclear power production.

. !E!IGE!&TI"% &%# &I! '"%#ITI"I%I%G&!odes of heat transfer. )ne dimensional steady and unsteady conduction. "omposite

slab and Equivalent esistance. Heat dissipation from extended surfaces' Heat exchangers' )verall heat transfer coefficient' Empiricalcorrelations for heat transfer in laminar and turbulent flows and for free and forced "onvection' Thermal boundary layer over a flat plate

+undamentals of diffusive and connective mass transfer' (lack body and basic concepts in adiation' Enclosure theory' ,hape factor'

$et work analysis. Heat pump and efrigeration cycles and systems' efrigerants. "ondensers' Evaporates and Expansion devices'

-sychrometry' "harts and application to air conditioning' ,ensible heating and cooling' Effective temperature' comfort indices' %oad

calculations' ,olar refrigeration' controls' /uct design.

*. +,I# ME'&%I'S&-roperties and classification of fluids' !anometry' forces on immersed surfaces' "enter of pressure' (uoyancy

Elements of stability of floating bodies. Kinematics and /ynamics.

rrotational and incompressible. nviscid flow. 2elocity potential' -ressure field and +orces on immersed bodies. (ernoulli3s equation'

+ully developed flow through pipes' -ressure drop calculations' !easurement of flow rate and -ressure drop. Elements of boundary


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layer theory' ntegral approach' %aminar and tubulent flows' ,eparations. +low over weirs and notches. )pen channel flow' Hydraulic

0ump. /imensionless numbers' /imensional analysis' ,imilitude and modelling. )ne&dimensional isentropic flow' $ormal shock wave'

+low through convergent & divergent ducts' )blique shock&wave' ayleigh and +anno lines.

-. +,I# M&'I%E!$ &%# STE&M GE%E!&T"!S&-erformance' )peration and control of hydraulic -ump and impulse and reaction

Turbines' ,pecific speed' "lassification. Energy transfer' "oupling' -ower transmission' ,team generators +ire&tube and water&tube

boilers. +low of steam through $o44les and /iffusers' 5etness and condensation. 2arious types of steam and gas Turbines' 2elocity

diagrams. -artial admission. eciprocating' "entrifugal and axial flow "ompressors' !ultistage compression' role of !ach $umber'

eheat' egeneration' Efficiency' Governance.

-aper

1. TE"!$ " M&'I%ESKinematic and dynamic analysis of planer mechanisms. "ams. Gears and gear trains. +lywheels.

Governors. (alancing of rigid rotors and field balancing. (alancing of single and multicylinder engines' %inear vibration analysis of

mechanical systems. "ritical speeds and whirling of shafts #utomatic controls.

. M&'I%E #ESIG%&/esign of 6oints 7 cotters' keys' splines' welded 0oints' threaded fasteners' 0oints formed by interference fits.

/esign of friction drives 7 couplings and clutches' belt and chain drives' power screws.

/esign of -ower transmission systems 7 gears and gear drives shaft and axle' wire ropes.

/esign of bearings 7 hydrodynamics bearings and rolling element bearings.

*. ST!E%GT " M&TE!I&+S&,tress and strain in two dimensions' -rincipal stresses and strains' !ohr3s construction' linear elastic

materials' isotropy and anisotropy' stress&strain relations' uniaxial loading' thermal stresses. (eams 7 (ending moment and shear force

diagram' bending stresses and deflection of beams. ,hear stress distribution. Torsion of shafts' helical springs. "ombined stresses'

thick&and thin&walled pressure vessels. ,truts and columns. ,train energy concepts and theories of failure.

-. E%GI%EE!I%G M&TE!I&+S&(asic concepts on structure of solids. "rystalline maferials. /etects in crystalline materials. #lloys and

binary phase diagrams. ,tructure and properties of common engineering materials. Heat treatment of steels. -lastics' "eramics andcomposite materials. "ommon applications of various materials.

/. P!"#,'TI"% E%GI%EE!I%G&!etal +orming 7 (asic -rinciples of forging' drawing and extrusion8 High energy rate forming8

-owder metallurgy.

!etal "asting 7 /ie casting' investment casting' ,hall !oulding' "entrifugal "asting' Gating 1 iser design8 melting furnaces.

+abrication -rocesses 7 -rinciples of Gas' #rc' ,hielded arc 5elding8 #dvanced 5elding -rocesses' 5eldability7 !etallurgy of 5elding

!etal "utting 7 Turning' !ethods of ,crew -roduction' /rilling' (oring' !illing' Gear !anufacturing' -roduction of flat surfaces' Grinding

1 +inishing -rocesses. "omputer "ontrolled !anufacturing ,ystems&"$"' /$"' +!,' #utomation and obotics.

"utting Tools !aterials' Tool Geometry' !echanism of Tool 5ear' Tool %ife 1 !achinability8 !easurement of cutting forces. Economics

of !achining. 9nconventional !achining -rocesses. 6igs and +ixtures. +its and tolerances' !easurement of surface texture'

"omparators #lignment tests and reconditioning of !achine Tools.

0. I%#,ST!I&+ E%GI%EE!I%G-roduction -lanning and "ontrol 7 +orecasting & !oving average' exponential smoothing' )perations'

scheduling8 assembly line balancing' -roduct development' (reak&even analysis' "apacity planning' -ET and "-!.

"ontrol )perations 7 nventory control #(" analysis' E): model' !aterials requirement planning. 6ob design' 6ob standards' 5ork

measurement' :uality !anagement & :uality analysis and control. )perations esearch 7 %inear -rogramming & Graphical and ,implex

methods' Transportation and assignment models. ,ingle server queueing model.
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2alue Engineering 7 2alue analysis for cost;value.

. E+EME%TS " '"MP,T&TI"%&"omputer )rganisation' +low charting' +eatures of "ommon computer %anguages & +)T#$' d

(ase ' %otus ' " and elementary -rogramming.

IAS MATHEMATICS SYLLABUS

PaperI

(1) +inear &lgebra2

2ector spaces over and "' linear dependence and independence' subspaces' bases' dimension8%inear transformations' rank and nullity' matrix of a linear transformation.

#lgebra of !atrices8 ow and column reduction' Echelon form' congruence3s and similarity8 ankof a matrix8 nverse of a matrix8 ,olution of system of linear equations8 Eigenvalues andeigenvectors' characteristic polynomial' "ayley&Hamilton theorem' ,ymmetric' skew&symmetric'Hermitian' skew&Hermitian' orthogonal and unitary matrices and their eigenvalues.

() 'alculus2

eal numbers' functions of a real variable' limits' continuity' differentiability' mean&value theorem'Taylor?s theorem with remainders' indeterminate forms' maxima and minima' asymptotes8 "urvetracing8 +unctions of two or three variables7 limits' continuity' partial derivatives' maxima and

minima' %agrange?s method of multipliers' 6acobian.

iemann?s definition of definite integrals8 ndefinite integrals8 nfinite and improper integrals8 /oubleand triple integrals @evaluation techniques onlyA8 #reas' surface and volumes.

(*) &naly3ic Geo4e3ry2

"artesian and polar coordinates in three dimensions' second degree equations in three variables'reduction to canonical forms' straight lines' shortest distance between two skew lines8 -lane'sphere' cone' cylinder' paraboloid' ellipsoid' hyperboloid of one and two sheets and theirproperties.

(-) "rdinary #ifferen3ial E5ua3ions2

+ormulation of differential equations8 Equations of first order and first degree' integrating factor8)rthogonal tra0ectory8 Equations of first order but not of first degree' "lairaut?s equation' singularsolution.

,econd and higher order linear equations with constant coefficients' complementary function'particular integral and general solution.

,econd order linear equations with variable coefficients' Euler&"auchy equation8 /etermination ofcomplete solution when one solution is known using method of variation of parameters.


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%aplace and nverse %aplace transforms and their properties8 %aplace transforms of elementaryfunctions. #pplication to initial value problems for =nd order linear equations with constantcoefficients.

(/) #yna4ics 6 S3a3ics2

ectilinear motion' simple harmonic motion' motion in a plane' pro0ectiles8 constrained motion85ork and energy' conservation of energy8 Kepler?s laws' orbits under central forces.

Equilibrium of a system of particles8 5ork and potential energy' friction8 common catenary8 -rincipleof virtual work8 ,tability of equilibrium' equilibrium of forces in three dimensions.

(0) 7ec3or &nalysis2

,calar and vector fields' differentiation of vector field of a scalar variable8 Gradient' divergence andcurl in cartesian and cylindrical coordinates8 Higher order derivatives8 2ector identities and vectorequations.

#pplication to geometry7 "urves in space' "urvature and torsion8 ,erret&+renet3s formulae.

Gauss and ,tokes3 theorems' Green3s identities.

PaperII

(1) &lgebra2

Groups' subgroups' cyclic groups' cosets' %agrange3s Theorem' normal subgroups' quotientgroups' homomorphism of groups' basic isomorphism theorems' permutation groups' "ayley3stheorem.

ings' subrings and ideals' homomorphisms of rings8 ntegral domains' principal ideal domains'Euclidean domains and unique factori4ation domains8 +ields' quotient fields.

() !eal &nalysis2

eal number system as an ordered field with least upper bound property8 ,equences' limit of asequence' "auchy sequence' completeness of real line8 ,eries and its convergence' absolute and

conditional convergence of series of real and complex terms' rearrangement of series."ontinuity and uniform continuity of functions' properties of continuous functions on compact sets.

iemann integral' improper integrals8 +undamental theorems of integral calculus.

9niform convergence' continuity' differentiability and integrability for sequences and series offunctions8 -artial derivatives of functions of several @two or threeA variables' maxima and minima.

(*) 'o4ple8 &nalysis2

#nalytic functions' "auchy&iemann equations' "auchy?s theorem' "auchy?s integral formula'power series representation of an analytic function' Taylor3s series8 ,ingularities8 %aurent?s series8"auchy?s residue theorem8 "ontour integration.

(-) +inear Progra44ing2

%inear programming problems' basic solution' basic feasible solution and optimal solution8Graphical method and simplex method of solutions8 /uality.

Transportation and assignment problems.

(/) Par3ial differen3ial e5ua3ions2

+amily of surfaces in three dimensions and formulation of partial differential equations8 ,olution ofquasilinear partial differential equations of the first order' "auchy?s method of characteristics8 %inearpartial differential equations of the second order with constant coefficients' canonical form8Equation of a vibrating string' heat equation' %aplace equation and their solutions.


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(0) %u4erical &nalysis and 'o4pu3er progra44ing2

$umerical methods7 ,olution of algebraic and transcendental equations of one variable bybisection' egula&+alsi and $ewton&aphson methods8 solution of system of linear equations byGaussian elimination and Gauss&6ordan @directA' Gauss&,eidel@iterativeA methods. $ewton?s@forward and backwardA interpolation' %agrange?s interpolation.

$umerical integration7 Trape4oidal rule' ,impson?s rules' Gaussian quadrature formula.

$umerical solution of ordinary differential equations7 Euler and unga Kutta&methods.

"omputer -rogramming7 (inary system8 #rithmetic and logical operations on numbers8 )ctal andHexadecimal systems8 "onversion to and from decimal systems8 #lgebra of binary numbers.

Elements of computer systems and concept of memory8 (asic logic gates and truth tables' (ooleanalgebra' normal forms.

epresentation of unsigned integers' signed integers and reals' double precision reals and longintegers.

#lgorithms and flow charts for solving numerical analysis problems.

() Mechanics and luid #yna4ics2

Generali4ed coordinates8 /? #lembert?s principle and %agrange?s equations8 Hamilton equations8!oment of inertia8 !otion of rigid bodies in two dimensions.

Equation of continuity8 Euler?s equation of motion for inviscid flow8 ,tream&lines' path of a particle8-otential flow8 Two&dimensional and axisymmetric motion8 ,ources and sinks' vortex motion8$avier&,tokes equation for a viscous fluid.

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