gate production engineering 2009

8/13/2019 GATE Production Engineering 2009

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2009 PIPI: PROD U CTION ND INDUSTRI L E N GINE ERIN G

urat ionThree Hour s Ma r imum arks :10 0

Read the follow in ginstructions ca re ful ly .

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1 This ques tion paper contains 16 printed pagesin cluding page s fo r rough work. Please checkall pages andreport di screpan cy, i an y.

2. W ri te your registratio nnumbe r. your nam ea nd na me of th e ex am ination centre at th es pecified locationson theright half of th eO ptical Response Sheet O R S).3. Usi ng HB pencil, darken the appropriate bubble under each digitof your regis tration num ber and theletters corresp onding to your paper code.4. All question sin this paper are of objective type.5. Que stions must be answere d on O ptical Response Sheet ORS)by darkening the appropriate bub blemarkedA , B. C, D) using HB pencil against the q uestion num beron the left handside of th eO RS. Eachquest ion has onlyone correctan sw er. n case you w ish to change an ans wer, erase th e old answercom pletely. M ore th an o ne answ er bubble dag ainsta ques tion wil lbe treated as an in correct response.6. There are a total of 60 ques tions carrying 100 marks. Q uestions 1 th ro ugh 20 are 1-m ark questions.qu estions 21 th rough 60 are 2 -markquestions. 7. Questions51 through 56 3 pairs)are comm on data questions an d question pairs 57, 58 ) an d 59, 60) a relinked an sw er ques tions. T he answ er to th e second question of th e above2 pairs depends on th eanswer

to the first question of th e pair. If the first question in the linked pair is wro ngly an sw er ed or isun-attempted, then the answer to th ese condquestion in thepair will not be evaluated.8. Un-attempted questions will carryzero marks.

9. W ro ng ans wers willcarry N EG A TIV E marks. ForQ.1 to Q.20, ~ m r k will be deducte dfor eachw rong answer. For Q. 21 to Q. 56 , m ark will be deducted for each w rong ans w er . T he question pairsQ.57, Q.58), and Q .5 9, Q .60) are questions with lin ked ans wers. There will be negativemarks only forwrong answ er to th e fi rst question of the linked answ er quest ion pairi.e. for Q.5 7 and Q.59, markwillbe de du cted for eachwrong answ er .T here is nonegative m arking for Q .5 8andQ.60.

10. Calculator without d ata connectivity)i s allowed in the e xam ination hall.11. Charts, graphsheets or tables ar e N O T allowed in the exam ination hall.12. Rough workcan be done on the question paper itself. Additionally, b lank pages areg iven at the end ofthe question paper f or rough work.

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2009

Q Q 2 carry on mark ea chQ.l Thehom ogeneous part of th ed ifferenti al equati on

;.... y2 +p - q y= p,q andr re constantsdx dx

has real distin ct ro ot s ifA) p 2 - q>0C)p2 -4q=0

Q .2 The to tal deri vativ eof the fu nctio n x y isA) xdy + yx B) xd x+ yy

B)p2 4q


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2009 PIQ .7 Asper Kendall'snotation inMIG /cqueuing sys tem , the number ofarr iv alsin a fixed tim efo llo w s

(A) Betadistribu tionC) Poissond istr ib uti on

(B) N orm al d istr ibu tion(D)Uniformdis tribu tion

Q.8 W hic hof th e follow ing forecas ting m odels explic itl y accountsfo r seasona lityof demand ?A )Sim plem ovin gav era ge m odelC) Holt'sm odel

B ) Simple ex ponen ti a lsmoothingm odelD) Winter'sm odel

Q .9 Aty pical Fe-Ca llo y co nta in inggrea te rthan0.8 Cis know nasA) Eutecto id steelC) M ild st eel

B ) H ypoeutec to id st eel(D) H y pereu tec to id stee l

QlO Thecapacity of a m ater ia l to absorb energywhen d efo rm e delastically , andto re lea se it back whenunloaded is te rm ed a sA ) toughnessC)ductil i ty

B ) res il ienceD) m all eab ili ty

Q.ll The productofthecomplex num ers(3- 2)and3 4) resu lts inA) (1+i6) B) (9-i8)

1 3 2Q.12 Thevalueofthed eterm inan t 4 1 1 is

2 1 3A) -28 B) -24

(C) (9+i8)

(C) 32

(D) (17+i6)

D) 36

Q.l3 If m odule andnumber oftee th of a sp ur gear w ithaninvo lu te profile are 3 mmand23 respectiv ely ,thenthepitch diameter inm m )ofthespur gear isA ) 7 .6 7 B ) 15 .34 C) 34.50 D) 69.00

Q .l4 H otchamber diec astin gprocessisNOT su ited for

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A ) Leadand its all oysC)Tin and it s allo ys

B ) Zincandits allo ysD) Aluminum and its allo ys

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Q.15 T hetotal angu la r m ovem ent in degrees) of a lead-s cre wwit h ap it ch of5 .0 mm tod riv e th e work taby adista nce of 200 m m in aNC m achin e is

A)14400 B) 28800

Ql6 A nis otro pyin rol led com ponents is caused by

A ) change ind im ensio nsC) clo sure ofdefe cts

C) 57600 D )72000

B)s caleform atio nD)gra in ori enta tio n

Ql7 W hichofth e fo llowin gprocessesis usedto m anufa ctu re products w it hcontr oll edporosity ?

A) C astingC)Form ing

B)W eldin gD) P ow der meta llurg y

Ql8 W hich ofthe foll ow in gpow ders should be fed for effe ctiv eoxy-f uel cutt ing of s tainless steel?

A) Ste el B) A lu m in um C)C opper

Q l9 Anautocolli m ato r s use d to

A )m easure sm al l angula rdispla cem entsonfl at su rf acesB) com pareknownandunknow ndim ensio nsC) m easu retheflatn ess erro rD)m easu reroundnesse rror betw eencente rs

D ) C eram ic

Q .20 D iam ondcutt in gto ols are not recom m ended for m achining offe rro usmeta lsd uet o

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A)high tool hardness B)high ther rn al conductiv ity of w ork materialC)poor tool to ughnessD) ch em ica l affi nity oftool mat erial with iro n

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5/13

2009

Q 2 to Q 60 carry two marks eachQ.21 The value of x obtained by solving the fo llowing system of linear equations is

+2x2 x3 =42x +x2 x3 = 2

+x2 -X:J =2(A) -12 B)-2 C) 0 (D) 12

Q.22 The displacement and acceleration of a cam fo llower mechanism are plotted in the following figures:

Q.23

Q.24

r 0.06cCllE 0.04Cllu 0.02f/1i

0 10 20 30 40 50 60 70 80 90Rotation angle deg) Rotation angle deg)

The nature of the d isplacement curve isA) Cubic

(C) Simple harmonicB) QuadraticD) Linear

The solution of the differentia l equation d2; =0 with boundary conditions: (i) dy =1 at x =0x d x

and (ii) dy =1 at .x = 1 isd x

A) y =1(B ) y =x(C) y =x + C, where Cis an arbitrary constant(D) y = Cx + C2 , where C1 and C2 are arbitrary constants.

The line integral of the vector function F =2xi + along the x-axis from x = 1 to x =2 isA) 0 B) 2.33 (C) 3 D) 5.33

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Q.25 Using direct ex trusion process, a round billet of 100 mm length and 50 mm diameter is extruded.

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Considering an ideal deformation process (no friction and no redundant work), extrusion ratio 4, andaverage flow stress of material 300 MPa, the pressure (in MPa) on the ram will be(A) 416 B) 624 C)700 D) 832

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6/13

2009

Q.26 A friction clutch is designed to transmit 5horsepower at 1500rpm. The torque in N.m) experiencedby the clu tch isA ) 1.19C) 71.24

B) 7.46D) 447.61

Q.27 A manufacture r has set up an assembly line where first, Task I is performed in Workstation 1 fo0.3 m inutes; then Taskll is perform ed in W orksta tion 2 for 0 .4 minutes; and finally Task ill iperform ed inW orks tation 3for 0.3minutes. Theefficie ncy (in) of this assembly line setup is(A)33.33C) 75.33

B) 64.33D) 83.33

Q.28 Abiaxial stresse le men t is subjectedto tensile andshea r stresses as shown inthe fig ure. If x= 40 MPa,

Y =20MPaand txy = 'tyx = 15 MPa.The principalnormal stresses in M Pa) are :

A) and(C)12 and48

B) 10 and 30D ) 20and 40

yCfy tyx

Q .29 Thearea under thecurveshown, be tween x=1and x= 3 is to be evaluatedusing the trapezoidalru

P I

The followingpoin tson thecurve are given .

Poin t Xcoord inate m )

23

23

The evaluated area in m2 will be

A) B) 8.67

Ycoordinate m )149

(C) 9

y9 -----------

4

1 2 3D) 18


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2009 PI

Q .30 The pressure dropfor la minar f low of aliquidin a smooth pipeat normal tem perature and pressureis(A )directlyproportional to density(C) in dependent of densi ty

(B) inversely proportional to density(D) proportional to(densit y )0

Q .3 A titanium sheet of 5.0 m m thickness is cu t by wire-cut EDM pro cess using a wire of 1.0 rnm diameter.A uniformsparkgapof 0.5 mmon both sidesof the w ire is maintained during cutt ing operation . If thefeed rateof the wire intothe sheet is 20mm/min, the m aterial removal rate (inmrn 3/m in) will be(A ) 150 B) 200 (C ) 300 D)400

Q .3 2 Autogenous gas tungsten arc welding of a steel plate is carried out with welding current of 500 A,voltage of 20 V, and weldspeedof 20 mrn/min. Consider theheat t ransfer e fficiencyfromthe arctothe weld poolas 90 .The beat input per unit length(in kJ/mm) is(A ) 0.25 (B) 0.35 C) 0.45 D) 0.55

Q.33 C onsider steady flow of w ater in a si tua tion w here twopipelines (Pipe 1 and Pipe 2) com bine intoasingle pipe l ine (Pipe 3) as shown in the figure. The cross-sectional areasof al l three pipelines areconstant. The fo llowingdata i s given : PipePipe num ber Area m2 Velocity (m /s)

1 1 123

22.5

2?

A ssuming the water properties andthe velocities to be uniform acrossthe c ross section of the inlets andthe outlet. the ex it velocity ( in rn/s)in pipe 3 is

A) B)1 5

Pipe2

(C) 2

. Pipe 3

D) 2.5

Q.34 M atch the following:

P

Gro up I Layout type s)P . ProcesslayoutQ . Product flow layoutR. F ixed posit ion layoutS. Cellu lar layout(A) P-4,Q-l ,R-3 ,S-2(C ) P-2,Q - I ,R-4,S-3

Group Layoutcharacteristics)1 In flexibleto significant changes in product design2 . Dist inct part families and expanded w orkertraining3 . Low equipment utilization and highskill requirem ent4. Large work-in-process and increased m aterial handling

(B) P-4,Q-3,R-2,S-l(D ) P-1 ,Q-4,R-3,S-2

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8/13

2009

Q.35 Consider the joint probability mass function of random variables and Y as shown in table belowFor instance, P{X = 1, Y = 2} = 0.3

X= I X=2Y=l 0.2 0 .3Y= 0.3 0.1Y=3 0.1

The value ofP{X=21 Y=2} is(A) 0.10 B) 0.25 (C) 0.40 D) 0.75

Q.36 A grocery store faces a demand of 50 units of soap per day. The store orders soap periodically. It cosRs.lOO to initiate a purchase order. It costs Rs. 0.04 per soap per day to store the soap. The lead timbetween placing and receiving the order is 4 days. The optimal inventory policy for ordering soap is(A) order 500 units of soap whenever inventory level drops to 200 units(B) order 500 units of soap whenever inventory level drops to 100 units(C) order 1000 units of soap whenever inventory level drops to 200 unitsD) order lOOO units of soap whenever inventory level drops to 100 units

Q.37 A disk of 200 mm diameter is blanked from a strip of an aluminum alloy of thickness 3.2 nun. Tmaterial shear strength to fracture is 150 MPa. The blanking force in kN) isA) 291 B) 301 (C) 311 D) 321

Q.38 Match the following:Group I Product)P. Refrigerator linersQ. Composite pressure vesselsR. Hollow parts of thermoset plastics.Rubber sheets

A) P-2,Q-l,R-4,S-3C) P-l,Q-4,R-2,S-3

Group Manufacturing process)1 Filament winding2. Thermoforming3. Calendering4. Rotational moulding

(B) P-I,Q-2,R-3 ,S-4D) P-2,Q-4,R-l,S-3

Q.39 Match the following:

Pl

Group I Device)P JigQ. FixtureR. ClampS. Locator

A) P-4,Q-3,R-l,S-2(C) P-l,Q-4,R-3,S-2

Group Function)1 helps to place the workpiece in the same position cycle after cycle2 holds the workpiece only3. holds and positions the workpiece4. holds and positions the workpiece and guides the cutting tool during

machining operationB) P-l,Q-2,R-3,S-4D) P-4,Q-3,R-2,S- l

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200 9 PI0Q.40 A spur g ear hav ingap res su re an gle of 20 , modu le of 4 mman d40 te eth is to beinspect ed fo rits pitch

cir cle dia m eter us ingtw o ro llers (test plu g method). If thecentres of th e roller s li e on th e pitch circle,the suitable rollerdia m eter (in mm and th e re sultingdistan ce (i n mm) betw een the ro lle rs place dinopp osi te spac es willres pec tively be(A) 2.9 and 82.9(C) 5.9 an d 82.9

B) 2.9a nd16 5.9D) 5.9and 16 5.9

Q.41 A compan y make saproductusing threeindepen dent co mpon en tsI II andIII with rel iabili tiesof0 .80 ,0.85an d 0.9 0respe ctively. If th e com pany de cid es to add one redundant unit of co m ponen t I toimpro vere liabi lity, then there lia bility ofthe pro duct is(A) 0.612 B) 0.7 34 (C ) 0.837 D) 0 969

Q.42 Given:A ssertion[a] :M anag ers sp en d tim e onjob ana lys is and jobrating.R eason [r]:Scie ntific man ag em en t of wagestructures th ro ug hjob eva lu ation helps incre asepro ductivity.

(A) B oth [a] and [r]are true and [r] is th ecorre ct re as on for[a].(B ) Both [a] and[r]are tru e, but [r] is notthecorr ect reasonf or [a].(C) Both [a] and [r] are false.(D )[a] istrue but[r] is false.

Q.43 Asp areparts retailsh opha s sa lesof Rs. 4.0 0,0 00 and aprofitof Rs. 50,0 00 fo r a pro duct, in its firstquarter. The pro fit volume(PV)ra tiois25 . Themargin of safety=profit PV ratio. T h e br eak evenpoint of sal es (inRs.) is(A ) 20,0 00(C ) 2,00 ,00 0

(B) 40,0 00D) 4,00,000

Q.4 4 T h e fo llowing in formationre lat es to w orker'spay ment ina compan y:

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Stan dar d pro du ction ofa worker= 12 jobs perhour Standard jobra te = Rs.3.00per jobPay forpr oduct io n lessthan standar d = 85 of standar djob ratePay fo r pro duc tion m ore than stan dard= 12 0 of st an dard jobra te

Threework ers pro du ce atthe rate of 11, 13 an d15 job sper hour. The to tal pay for thre e workersperhour bas ed on di fferen tial wag eincen tive sch eme is(A ) Rs. 117.0 0(C)Rs. 1404.0 0

B) Rs. 128 .85D)Rs. 154 6.20

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Q.45 Match the following:Group I Protection type)

P PatentQ Tradem arkR CopyrightS. Industrial design

(A ) P-2 ,Q-4,R-3,S-l(C) P-2,Q-3,R-4,S-l

Q .46 Match thefollowing:

Group I Design aspect)P Form designQ. Concurrent engineeringR Value analysisS. Pro duct l ife cyc le

(A) P-4,Q-l,R-2,S-3(C) P-4 ,Q-3,R-2,S-l

Group Example in the Indiancon text)l . Manual of a product2. A ppearance of an MP3 player3. Logo of acompany4. M ic roprocessor

(B ) P-4 Q-l R-3,S -2(D) P-4 ,Q-3 ,R-1,S-2

Group Description)1 In troduction, gro wth,m aturity a nd decline2 Determines cos t of each func tion of th e desi gn3. Integration of product design and m anufactur ing4. Appearance, shape, co lour and size of pro duct

(B ) P-3,Q-2,R-4,S-1(D) P-4 ,Q -2 ,R-3 ,S-1

Q.47 In an orthogonal machining operation, the tool life obtained is lO min at a cu tt ing speedof 100m/mw hile at 75 m/m in cutt ing speed, th e tool life is 30 min. Thevalue of index (n) in the Taylo r s toolequation is

(A) 0.262(C) 0.423

(B) 0.323D) 0.521

Q .48 A solid cyl inder of diam eter D and height equal to D, and asol id cube of side L are being sand casusing th e same m aterial . Assuming th ere is no superheat in both the cases, the ratio of solidificalime of the cylinder to the so lidification time of the cube is

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A)(LID):C) 2D/L 2

B) 2LID)

D ) D/L)

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11/13

2009PI

Q.49 Follow ingaresomepossib lecharacteristicsofapileofpowderm ixture:P . Low interparticlefrictionQ. H ighinterparticlefrictionR.Low porosityS.H ighporosityIftheangleofreposeforapileofpowderm ixtureislow,itwillexhibitA) PandRC) QandS

Q .50 M atch thefollowing:Group

P.RelationalDBMSQ.Primarykey

roupII1.SQL2.AND,OR

B) PandSD)QandR

R.Retrievingda ta 3. Tables,columnsandrowsS.Booleansearch 4.ColumnsthatuniquelyidentifyarowA)P-3,Q-4,R-2,S-1C)P-3,Q -4 ,R -l,S-2

CommonD ata QuestionsCommonDataforQuestions51and52:ConsidertheL inearProgramm ingProblem LPP)

Maxim izeSubjectto :

2x1 X2 2x3 50X X2 X3 30XJ,X2, X3 Q

B)P-3,Q -1,R-4,S-2D)P-4,Q -l,R -2 ,S -3

constraint1)constraint2)

The associated simplex tableau at optimality is shown below, where s and s 2 represent the slacks foronstraints1and2,respectively .

x, X2z-row 0 0

X 1 0X2 0 1

Q.51 Basicvariablesintheoptimalsoluti onareA) s ands2C) x,,x2andx 3

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X3 s, S22 1 21 1 10 -1

B) x,andx2D) X3 s,ands2

2

RHS1102010

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12/13

2009

Q.52 Suppose that in theL PP giv en, the right hand side of constr aint 1 changes from 50 to 40. Theobject ive value isA)90 (B ) 100 (C ) 11 (D) 120

CommonDatafor Q uestions 53and54:In acceptance sampling, the probabili ty dis tributio n of th e number of defectiv es X in a sample canap proximated as a Pois son distr ibution, Prob{X =k} = [np).te -np ], for k=0.1,2 .. ,w here n is the samplekandpisth e actual proportio n or percentofdefe ctivei temsi na ba tch.A company r eceiv es a shipm ent batch of N= 2000 i tem s. T he sa mpling pl an fo llo wed by th e company isam ple =50 item s fro m th e batch an d accept the batchifthe num ber ofdefe ctive itemsa re2 o r les s. LetAcceptableQ uali ty Level (A QL) be0 .02a nd t heL o tTole ranceP ercent D efectiv e (LTPD) be 0.05 .

Q .53 Theprobabil ityofin corre ctly rej ectinga go od b atcho r theP roducer s riskis(A ) 0.0805(C) 0.5437

(B ) 0 .3678(D) 0.9195

Q.5 4 T he p robabil ity ofin correctly acceptin g ab ad batc ho r theConsum ers ri ski s(A) 0.0805(C ) 0.5437

CommonDatafor Q u estion s 5 5and56:

(B ) 0.3 678(D ) 0 .9195

n orth ogonal turn ing opera tio n is carri ed outa t 2 0 m /rn in cutting speed, using a cutti ng to o l ofrake an15 . The chip thickness is0.4 mrnand th euncu t chip thickness is0 .2 mrn.Q .55 Theshear plane an gle(in degrees) is

A) 26.8(C) 28.8

Q .56 Thechip velocity (in m /m in ) is

PI

A)8C)12

(B) 27.8(D )2 9.8

(B ) 10(D) 14

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2 9 PILinkedAnswerQuestio nsSta tem ent for L inked A nsw erQuestions57and58 :Four jobs need to bepro cessed sequentially on two m ach ines, first on M ach in eMan d then on Machine N.Each m achine canpro cess only one j ob at a tim e.The processin g tim es (in m in ) aregiven in the ta ble bel ow :

MachineM MachineNJob I 3 6Job IT 5 2Job l l 1 2Job IV 7 5

Q .57 The o ptim al sequenceof jo sth at will m in im iz em akespan(total tim e requir edtocom ple te aU jo bs) isA ) I- II - II I - IVC )IV - III - I-

(B ) Il l - II- I- IV(D )l l - I - IV - II

Q .5 8 When the jo sare pro cessed basedo nth eoptim alsequence that m in im izes m akespan, the total id letime (in min )o nM achine N isA) 1 B) 3 C) 4 D) 6

Sta tement fo r L inked A nswerQuestions 59 and60:Resistancespot weld ing of tw o steelsheets is carried out inlapjo int confi gurati on byusing a weld ing currentof 3 kAand a weld ti m e of0.2 s. A molte nw eld nugget ofvolu m e 2 m m3is obtained.Theeff ective contactre sistance is200 (m icro-o hm s).The mate rial pro pert ies ofs te elare given as: i) latent heat of melting:1400k:J/kg (ii) density: 8000 kg/m 3, (iii)m elting temperature: 1520C, (iv) specific hea t: 0.5 kJ/k g0 C. The

0am bient t emperature is2 0 C.Q .5 9 Heat(inJoules)used for producingw eld nugget w ill be (assum in g 100 heat tr ansfer e ffic iency)

(A) 324 B) 334 C) 344 D) 354

Q .60 H eat(inJoules)dis sip ated to the base metal w ill be (n eglecting all other heatlo sses)A ) 10 B) 16 C) 22 D) 32

ENDOF THE Q U ESTIO N PA P E R

PI 13/16

gate production engineering 2009

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