GATE 2013 PI Set D Question Paper

7/28/2019 GATE 2013 PI Set D Question Paper

1/16

2113 Quemoo ~ Code-I D IPI: PRODUCTION AND INDUSTRIAL ENGINEERING

Maxuruun Maries- 100Rad !be IaIIowmg illltruc:tioas QreI'uIIy

1 Do not open the seal of the Question Booklet until you are asked to do so by the mVlgilator2 Take out the Optical Response Sheet (OKS) from thIS Question Booklet WIthout breakmg the sealand read the mstrucbons pnnted on the ORS carefully I f you find that eIthera. The QuestIon Booklet Code pnnted at the nght hand top comer of thIS page does not match WIththe Question Booklet Code at the nght hand top comer of the ORS orb The Question Paper Code preccdmg the RegIStration number on the ORS IS not PI.then exc;bange the booklet unmechately WIth a new sealed Question Booklet.3 00 the nght hand side of the OKS, usmg ONLY a black mk baDpomt pen, (I) darlcen the appropnatebubble under each dIgIt of your regtStrabOn number and (u) wnte your regtStrabOn number, your nameand name of the exanunabon centre and put your SIgnature at the specified Iocabon4 ThIS Question Booklet contams 1(; pages mcludmg blank pages for rough work After you arepenmtted to open the seal, check all pages and report dIScrepancIeS, If any, to the mVlgdator5 There are a total of 65 questIons carrymg 100 marks All these questions are of objective type Eachquesboo has only ODe conect answer Questions must be answered on the left hand stele of the ORSby darUmn& the appropnate bubble (marked A, B, C, D) usmg ONLY a black mk baDpomt penagamst the questIon number Fo r eacb quesbon darken the bobble of the correct allSWft' Morethan one answer bubbled agamst a questIon will be treated as an mcorrect response6 Smce bubbles darkened by the black mk ballpomt pen cannot be erased, candIdates should darlcen thebubbles m the ORS very carefully7 Questions Q 1 - Q 25 carry 1 mark each Questions Q 26 - Q 55 carry 2 marks each Tbe 2 marksquestions mclude two pa11'S of common data questions and two pa11'S of Imked answer questions Theanswer to the second question of the Imked answer questions depertds on the answer to the fIrStquestion of the parr I f the fIrSt question m the Imked parr IS wrongly answered or IS not attempted,then the answer to the second question m the parr will not be evaluated8 Questions Q56 - Q65 belong to General Aptitude (GA) sectIon and carry a total of 15 marksQuestions Q.56 - Q 60 carry I mark each, and questions Q 61 - Q 65 carry 2 marks each9 Questions not attempted will result m zero mark and wrong answers WIll result m NEGATIVE

marks For all 1 mark questIOns, ~ mark will be deducted for each wrong answer For all 2 marksquestions, ~ mark WID be deducted for each wrong answer However, m the case of the Imkedanswer quesboo parr, there WIll be negative marks only for wrong answer to the first question and nonegative marks for wrong answer to the second question

10 Calculator IS allowed wbereas charts, graph sheets or tables are NOT allowed m the exanuoatlon hall11 Rough work can be done on the Question Booklet Itself Blank pages are proVIded at the end of theQuestion Booklet for rough work.12 Before the start of the exanunabon, wnte your name and regIstration number m the space provtdedbelow usmg a black mk ballpomt penI=--IPII


2/16

2013 PRODUCTION & INDUSTRIAL ENGG PI

Q1 to Q 2S carry one mark each.au au a'uQ I The partIal dIfferentIal equatIon - +u - =- , S a

at ax ax(A) Imear equatton of order 2(C) ltnear equatton of order I

(B) non-Imear equatIon of order Ir(D) non-ltnear equatIon of order 2


3/16

.,.,lOU PRODUCTION ItINDlJSTlllAL II:NGG PIQ 7 A cube shaped castmg solidifIeS m 5 IfIIII The solxhficattoD tnne m IfIIII for a cube of the same

Q8

matenaI, wIucb IS 8 bmes heaVIer than the ongmal casbDg, WIU be , ,(A) to (B) 20 (C)24 "1140A steel bar 200 111m m dlDM'n IS turned at a feed of 0 2S mm/rev WIth a depth of cut of 4 mm The_on a I speed of the workpIeCe IS I ~ TbCmaterial removal rate m_ Is S(A) 160 (B) 1676 (C) 1600 v{f 1675.5T In the3-2-J pnDCIpleoffixture desIgn, 3 refers to the DUmber of -r(A) clamps requuaI~ locators on the JIIlIIWY datum face 'Yrr(C) depes of freedom of the WorkpIeCe(0) operabODS earned out OIl the pnmary datum face

-../' rQ.;\ In sunple exponenbal smoothmg fOf1"C3ShDg, to gIVe hIgher welghtage to recent demand/ " \ J mformabon, the smoodung constant IDISt be close to(A) - I (B) zero (C) 0.5 (0) 1Q A company manufactures 1000 toys every day On an average, I ~ of the toys are defective and~ ~ of the defective toys can be reworked mto defect-free ones The average Dumber of defect-freetoys manufactured dally IS /(A) 900 (B) 920 (C)940 (0)960

Q12 W1uch one of he foUowmg IS modeled based on adaptabOll capabilItIeS ofblOloglClll systems?(A) Relational database (B) Fuzzy system(C) Sunulated anneaImg a1gonthm (0) Genebc a1gonthm@ The type of control chart used to morutor the amount of dlSperslOll m a sample IS(A) c-dwt (B) p-chart (C) x


4/16

2013 PKODUcnON "INDUSTIIIAL ENGG PI

4 , Ircular blanks of 10 mm diameter are punched from an alummum sheet of 2 mm thiCknesS Theshear strength of alummum IS 80MPa The mlmmum punchmg force requrred 10 /eN ISy( A) 2.57 (B) 3 29 ~ 03 (D) 6 33..,........ 8 A metnc thread of pitch 2 mm and thread angle 60 IS mspected for Its pitch diameter usmg 3-wue(,

method The diameter of the best SIZe wire 10 mm IS(A) 0 866 (B) I 000

@ M a tc h the CORRECf pairs,r(C) 1154 (0)2000

Processes Charactenstlcs I ApplicationsP Fncllon Weldmg "" I Non-consumable electrodeQ Gas Metal Arc Weldmg \ 2 Jommg of thick platesR Tungsten Inert Gas Weldmg .... Consumable electrode wireS Electroslag Weldmg I"" Jommg of cylmdncal diSSimilar matenals- f ' ) 1'-4, Q-3, R-I, S-2 ...-.(II) P-4, Q;2, R-3, S-I(C) P-2, Q-3, R-4, S-I (D) P-2, Q-4, R-I, S-3~ I n a rollmg process, the state of stress of the matenal undergomg deformatIOn IS4 ) ure compressIOn ~ ( B ) pure shear(C) compressIOn and shear :AD) tension and shear

Q 21 Consider one-(i1menslOnal steady state heat conduCllon along x-axIS (0 x L), through a planei wall, With the boundary surfaces (x=O and x=L) mamtamed at temperatures of OC and 100CHeat IS generated umformJy throughout the wall Choose the CORRECf statement(A) The duecllon ofheat transfer Will be from the surface at 100C to the surface at OC(B) The maximum temperature Wide the wall must be greater than 100C(C) The temperature dlstnbullon IS Imear wlthm the wall(D) The temperature dlstnbullon IS symmetnc about the mid-plane of the wall

Q 22 A cylmder contams 5 m' of an Ideal gas at a pressure of I bar This gas IS compressed 10 arevefSlble ISOthermal process 1111 Its pressure mcreases to 5 bar The work m kJ reqUired for thISprocess IS(A) 804 7 (B) 9532 (C) 981 7 (D) \0122

Q.23 planar closed kmemallC cham IS formed With ngld links PQ = 0m, QR =30m, RS = 5m~Q24

and SP = 27m WIth all revolute Jomts The Imk to be fixed to obtam a double rocker (rockerrocker) mecharusm IS(A) PQ (B)QR (C)RS (O)SPLet X be a normal random vanable With mean I and vanance 4 The probability PIX


5/16

13Q.26 to Q.55 carry two marks each. Q.26 The foUowmg surface mtegrallS 10 be evaluated over a sphere for the glYen steady velocIty vectorfield F =.11 + xi + rJ; defined WIth respect 10 a CartesIan coordmale system bavmg .. J and k as URlt

base vectors1-

Q.27

where S IS the sphere, . t 2 +y' + Z 2 = and. IS the outward InUI normal vector 10 the sphere Thevalue of the surface mlegrallS(A) Jr (B) 2J r (C) 3Jr/4 (D)4Jr

d 21The funcIIon f(l) sabsfteS the dtfferenbal equatKm dl 2 +1=0 and the alllultary condltJons.1(0)=0. df (0)=4 The Laplace transfonn of I(t) IS glYenby f)"- -t I :; 0dt

2 4 4 2(A) - (B) -1 (C) -2-1 (D) '-1s+1 s+ s + s +~ A flywheel c:onnected 10 a pmx:hmg machIne has 10 supply energy of 400 Nm wIule runnmg at a~ mean angular speed of 20 radls I f the total fluctultlon of speed IS 1101 10 exceed 2%. the massIIlOIIIeIIl of DCItla of the flywheel m Icg-wf IS CP " '_ v " r(A) 25 ~ S O (C) 100 (D) 125

Q.29 A smgle nveled lap JO w of two sum1ar plates as shown m the figure below has the foUowmg

p

Pl-D

geometncal and maIienaI ddatIs r w plale wtdth w = 200 mmp plale thlClmess I = 5 mmnumber of nvets n = 3nvet dwneter d,= 10 mmnvet hole dlllJDCler d. = I mmallowable IerlStie stress of plale Gp = 200 MPaallowable bearmg stress of nvet Gc = ISO MPaI f he plates are 10 be desIgned 10 avotd IeanDg fBllure, the maxunum pemusslhle load P m kN IS(A) 83 (B) 125 (C) 167 (D) SOl

SIl6


6/16

2013

/,

PIlODUCl'ION &. INDUSTRIAL ENGG - PI

Two cuttmg tools are bemg compared for a machmmg operation The tool lIfe equatiOns areCarbide toolHSS tool

VT' = 3000VTo. =200,...-,,.

where V IS the cuttmg speed m mlmm flId T IS the tool lIfe m mm The carbIde tool WIll provIdehIgher tool lIfe If the cutting speed m mlmm exceeds(A) 15 0 ~ 3 9 4 (C)493 (0) 60 0

~ 31 "In a CAD package, mIrror Image of a 20 pomt P(5,1O) IS to be obtamed about a Ime whIch passes"-- J through the ongm and makes an angle of 45 counterclockwIse WIth the X-axIS The coordmates of

the transformed pomt wIll be(A) (7 5, 5) (B)(10,5) (C) (7 5, -5) (0) (10, -5 ) In water je t machmmg, the water je t IS ISSUed through a 0 3 rom dIameter onfice at a pressure of400 MPa The denSIty of water IS 1000 kglmJ The coeffiCIent of dIscharge IS 1 0 NegIectmg alllosses dunng water je t formatIon through the onfice, the power of the water je t m kW IS(A) 25 3 (B) 50 6

I Q 33 A lInear programmmg problem IS shown below"------- '

It has

MaxImIZe 3x +7ySubject to 3x+7y:O: 104x+6y:O:S

x,y2:0

(A) an unbounded objecllve functIon(C) exactly two optImal solubOns

(C) 75 9

I--

(0) 101 2~

\(B) exacdy one optllnal solubon(0) mfmltely many opbmaI solutIOns

Q 34 ConsIder a two machme flow shop where jobs are first processed m Machme X and then m/ Machme Y, m the same sequence The processmg tImes of four jobs (1, 2, 3 and 4) on theV machmes areJob Processmg tIme rom)MachmeX MachmeY1 6- 5 l ~ \ ~ t : U ~--2- 3 43 7 64 5 --t-

The sequence of jobs on the machmes that mmllntzes make span IS~ ) 2 - 3 - 1 - 4 (B) 1-2-3-4 (C) 2-1-3-4 (0) 3-1-4-2

PI D 6116


7/16

,PRODUCTION" INDUSTRIAL ENGG - PI

A firm produces 120 units of product m every 8 hour shift. Four operabons as given below areneeded to manufacture each umt of product.Operation Precedence Processmg time (m nun)

P none IQ P 2R P 4S Q,R 3The above operations are to be asSigned to woIkstallons, such that one or more operations areperformed m each woIkstatlon Only one umt of product WIU be processed m each woIkstallon at atime The mmlmum number of woIkstallOns that wlil achieve the prodUCtIon target, Withoutvlolatmg the precedence OOiisuaillB, IS(A) I (B ) 2 ~ ) 3 (D ) 4 ~r Match the CORRECf pa11'SGroup I GroupOP Man-machme chart 'I. I Determmes standanl time of JObsQ Leammg curve / ( 2 FIOds the preferred method of domg workR Tunestudy - ~ 3 Measures work ImprovementS Motion study ~ "4 Shows Idle times(A) P-2, Q-3, R-4, S-I (B) P-3, Q-2, R-4, S-I(C) P-4, Q-I, R-3, S-2 (D) P-4, Q-3,!:!" S-2Q A company plans to purchase a machme whose uptime needs to be atIeast 95% They haveQ shorthsted two models of the rnachme With the foUowmg operational charactenstlcs

MachmeModelMModelN

The company should buy(A) only Model M(C) either Model M or N

MTBF(hr) MTTR(hr)60 448 2

(B) only Model N(D ) neither Model M nor N

A manufacturer produces bars designed to be of lQ..!!!!!!. diameter With a tolerance of :to I mmHlstoncal data mdlcates that manufactured bars have an average d18meler of 9 98 mm With astandard deVllltlOD of 0 15 mm The process capablhty mdex IS po(A) 0 08 (B) 012 (C)o 18 v(D)027

Q 39 Let (P) denote the lmear programmmg formulation of a transportation problem With m sources andn destinations Then, the dual hnear program of (P) has

PlD

(A)mxn vanables and mXn constramts(C)m +n vanables and m +n constramts (B)m x n vanables and m + n constramts(D)m+n vanables and mxn constramts


8/16

2013 PRODUcnON'" INDUSTRIAL ENGG PIFollowmg data refers to an automat and a center lathe, which are bemg compared to machme abatch of parts m a manufacturmg shop

AutomatMachme Set-up Time m "un . J 120MachIne Set up Cost In Rs.lmm 800MachInmg Time per piece In min 2MachInmg Cost m Rs Imm ' 500

" T ( ~Automat wIll be economical If the batch Size exceeds(A) 28 (B) 32 (C) 61

>020

Center Lathe3015025100

(D) 75CylIndrIcal pms of 25 +0010 mm diameter are electroplated In a shop Thickness of the platIng IS302mIcron Neglectmg gage tolerances, the Size of the GO gage In mm to mspect the platedcomponents IS

( ' (A ) 25 042 ~ 25 052 (C) 25 074 (D) 25 084' - " 042 ' Durmg the electrochemIcal machmIng (ECM) of Iron (atomIc weight =56, valency =2) at currentof 1000 A WIth 90% current effiCIency, the materIal removal rate was observed to be 0 26 gmls IfTitanIUm (atomic weIght =48, valency =3) IS machmed by the ECM process at the current of2000 A WIth 90% current effiCiency, the expected materIal removal rate m gmls WIll be

(A) 0 II (B) 0 23 ~ ) 030 (D) 0 52QA3V pecIfic enthalpy and velOCity of steam at mlet and eXit of a steam turbme, running under steadyL:, " state, are as gIven below

Specific enthalpy (kJ/kg)Inlet steam condition 3250Exit steam condition 2360

\ ' 'Velocity (m!s)1805

The rate of heat loss from the turbme per kg of steam flow rate IS 5 k W NeglectIng changes mpoteJ!{fal energy of steam, the power , : v e ~ o p e d m_k!J>y the steam turbme per kg of steam flowrate, IS(A) 9012 'JBf911 2 (C) 17072 5 (D) 170825

Q S l m p l Y supported beam of length L IS subjected to a varyIng distrIbuted load sm (31r x/L) Nm-l,here the distance .. IS measured from the left support The magnitude of the vemcal reactIon force, m N at the left support IS

Q45

PI D

(A) zero (B) l/31& (C) l/1& (D) 2l/1&2The probabIlIty that a student knows the correct artswer to a mullIple chOIce question IS - If the3student does not know the answer, then the student guesses the answer The probabilIty of the

1guessed answer bemg correct IS 4 Given that the student has answered the questIOn correctly, thecondItIonal probabilIty that the student knows the correct answer IS

2(A ) -33(B) -4

5(C) -6

\ ',.-1

8(D) -98116


9/16

2113,

d 21l du~ 1Ibe solubOO to the dtfferenbal equabOll -2 -1-=0 where 1 IS a coostanl, subjeCted to theth thboundary conchbons 11(0) =0 and II(L) = U, ISx(A) I l =U L ( l_e

U )(B)I l=U --elLQ47 The value of the definite mtegral f.' .Ix In(x) tb: IS

4 f3 2(A) -" ie- +-9 9 2 f3 4(B) -" ie- --9 9Common Data Questioos

Common Data for QuestioaI48ud 49

2 f3 4(C) -" ie- +-9 9

(D) u=,,(I+eU )vl l+eIL

4 f3 2(D) - " i e - - -9 9

The demand for soap at a reIaJIer IS 40 kg per tIDy The rctaIIer buys soap from a company m bulk I t thecost of Rs SO per kg The reIaJIer IDCUIS a costof Rs 200 to place an Older to the c o ~ y , and hoIdm&cost of Rs 0 1per kg per tIDy to store the soap ~ Iqd bmc hetwccp the p!acm& I11III ml:eIVI!I& of ordenIS 3dan, The retailer's cumot onIermg pobcy IS to onIer 200 kg every S lDysQ48 I f die reIaJIer uses an optunum order pohcy to mmumze die total cost, the savmg m Rs m the tocaJcost as compared to the current polICy will be

(A) 10 (B) 20 (C)4O (D) SO, ~ T o avolli stock out SItuations, the rctaIIer needs to place orders when die mvenlOly level (m kg)

~ d r o p s t o(A)4O '. (B) 60 (C) 80 vfu) 120

()-

(,

-. -WI'


10/16

2013 PRODUCTION & INDUSTRIAL ENGG PI

Common Data for QuestIons 50 and 51A disc of 200 mm outer and 80 mm mner diameter IS f.!lced at a feed of 0 1 mmlrev With a depth of cut of1 mm The facmg operation IS undertaken at a constant cuttmg speed of 90 mlmm m a CNC lathe The rnam(tangenttal) cuttmg force IS 200 N

( . , ( Assummg approach and over-travel of the cuttmg tool to be zero, the machmmg time m mm IS~ 2 9 3 (B)586 (C)666 (0)\333vrs l NeglecUng the contnbutton of the feed force towards cuttmg power, the specific cuttmg energy mJlmm3 1s

(A)02 (B) 2 (C) 200 ...(12000

Lmked Answer QuestionsStatement for Lmked Answer Questions 52 and 53In orthogonal tummg of a bar of 100 mm diameter With a feed of 0 25 mmlrev, depth of cut of 4 mm andcuttmg velOCity of 90 m/mm, It IS observed that the rnam (tangential) cuttmg force IS perpendicular to thefnctton force actmg at the chip-tool mterface The mam (tangential) cuttmg force IS 1500NQ 52 The orthogonal rake angle of the cuttmg tool m degree IS(A) zero (B) 3 58 (C) 5 (0) 7 16Q 53 The nonnal force acttng at the chip-tool mterface m N IS

(A) 1000 (B) 1500 (C) 2000 (0)2500

, l

y(

PID ,\)1 -- Cr C\ l I - t . ~ o(V ~ $ ' r3


11/16

2013 PR(H)UcnON "INDUSTIlIAL I!NGG PI

SU__ for I.nked Answer QuestIons 54 and 55A project consISts of seven actIvlbeS, whose duratlO11S are Independent normal random vanables, as shownm the table below AcbVlbes are identified by thell" begmnmg node I and endmg nodeJ

AcbVlty Mean durabon Standard devlabon(node I - nodeJ) (mdays) (mdays)1 -2 6 I1-3 9 (V2 -3 2 052 -4 8 053 -4 - 7 ( i)3 -5 8 I4 -5 4 ( I)

The cnbCal path of he project, based on the mean actiVity durabon, IS(A) 1-2-3--4-5 (B) 1-2-3-5 (C) 1-3-5 v$) 1-3-4-5 "" 't-i)6 z 7 " : ' - I ~ ' ' - ' l . ' " " ~ \7 11 ' " -Let ( I denote the culDlllabve dlStnbubon function of the standard nonna\ random vanable Theprobability that all acbVlbeS on the cnbcal path, based on the mean actiVIt)' durabon, are completedm 22 days IS '(A) (1-1(0 333) J!!> (1-'(0 816) (C) (1-'(1 664) (D) (1-1(2235)

PI D 11116


12/16

2013 PROOucnON '" INIIUS'I'IUAL ENGG - PIGeneral Aptitude (GA) QuestionsQ.S6 to Q.60 carry one mark each.Q 56 Complete the sentenceUmversabsm IS to parttculansm as dIffuseness IS to_____

(A) specificity (B ) neutrabty (C) generabtyQ.57 Were you a bIrd. you _______ 0 the sky

(A) would fly (B) shall fly (C) should fly

(0 ) adaptatIon

(0 ) shall have flownQ 58 Whlcb one of the followmg OptIons IS the closest 10 meanmg to the word gIVen below?

Nadir(A) HIghest (B) Lowest (C)Medlum

Q 59 Otoose the grammattcally INCORRECT sentence(A) He IS of Astan ongm(B) They belonged to Mnca(C) She IS an European(0 ) They trugrated from Indta to AustralIa.

Q60 What WIll be the maxImum sum of 44.42.40.(A) 502 (B)S04

Q.61 to Q.6S carry two marks each.

?(C) 506

(0 ) IntegratIon

(0)500

Q 61 Out of all the 2-cbgtt mtegers between I and 100. a 2-dlgtt number has to be selected at random.What IS the probablbty that the selected number IS not dIVISIble by 7?(A) 13190 (B) 12190 (C) 78190 (0 ) 77190

Q 62 A tounst covers halfof hIS JOUIl1CY by tram at 60 kmlh. half of the remamder by bus at 30 kmIh andthe rest by cycle at 10 kmIh The average speed of the tounst ID kmlh dunng hIS enltre Journey IS(A) 36 (B) 30 (C) 24 (0) 18

Q 63 Find the sum of the expressIon1 1 1Ji+J2+J2+Jj+J3+J4+

(A) 7 (B) 8 (0 ) 10Q 64 The current erectIon cost of a structure IS Rs 13,200 I f the labour wages per day mcrease by 115 ofthe current wages and the worlcmg hours decrease by 1124 of the current penod. then the new cost

of erectton 10 Rs IS(A) 16.500 (B) 15.180 (C) 11.000 (0) 10.120

PID 12116


13/16

Q 65 After several defeats m wars, Robert BNCC went Ul exile and wanted to COtnmlt SUICIde Just befon:comnuttmg SUICide, he came across a sp_ aaemptmg tu'elcssly to bave li s Dd. TUlle and apm.!he spiller fatIed but !bat dtd not cider It to Jefram from makmg attempIS Such attempIS by !hes p _ made Bnace cunous Thus, Bnace SWted observing !he near-lIIIpOSSib1e goal of !he sp.w tobave !he Dd. Ultunately, !he spM succeelled m bavmg lis net desplle several fulUJeS Such act of!he sp.w eocouragcd Bnace not to COIIIIIIIl sIlICIde And then. BNce _ back agam and wonmany a battle, and !he JeSlIS hIStoryWInch ODe of !he followmg assa1IOIIS IS beat supported by !he above mfonnataoo?(A) Failure I I !he pt1Iar of success(8) Hooesty IS !he beat polICy(C) ufe begins aod ends With811_(D) No adversity jIISbfies gavmg up hope.

END OF THE QUESTION PAPER

IW


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2013 PRODUCl10N '" NDUSTRIAL ENGG PI

Space for Rough Work

PI D 14116


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2013 PRODUCTION " INDlJSTIIIAL ENGG - PI


PlD lY16


16/16

2013 PRODVCTION " INDVSTIIJAL ENGG PI


PlD 16116

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GATE 2013 PI Set D Question Paper