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MECHANICAL ENGINEERING GATE : 2006

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Read t he fol l ow ing i nst r uct i ons car efu l l y.

1. This quest ion paper contains al l object ive quest i ons. Q. 1 to Q. 20 car r y on e mar k each andQ. 21 to Q. 85 car ry t w o marks each.

2. Answer al l the quest ions.

3. Quest ions must be answered on Object ive Response Sheet (ORS) by darkening the appropr iate bubble(marked A, B, C, D) using HB pencil against the quest ion number on the left hand side of the ORS. Eachquest i on has on l y one cor r ect answ er . I n case you wish to change an answer, erase the old answercompletely.

4. Wrong answers wil l car ry NEGATIVE marks. In Q.1 to Q.20, 0.25 mark wil l be deducted for each wronganswer. In Q.21 to Q.76, Q.78, Q.80, Q.82 and in Q.84 0.5 mark wil l be deducted for each wrong answer.However, there is no negat ive marking in Q.77, Q.79, Q.81, Q.83. More than one answer bubbled anainsta quest ion wil l be taken as an incor rect response.

5. Write your registration number, your name and name of the examinat ion centre at the specified locationson the r ight half of the ORS.

6. Using HB pencil , darken the appropr iate bubble under each digit of your registrat ion number and thelet ters cor responding to your paper code.

7. Calculator is al lowed in the examinat ion hall .

8. Char ts, graph sheets or tables are NOT al lowed in the examinat ion hall .

9. Rough work can be done on the quest ion paper i tself. Addit ionally, blank pages are given at the end of thequest ion paper for rough work.

10. This quest ion paper contains 20 pr inted pages including pages for rough work. Please check al l pages andrepor t , i f there is any discrepancy.

GATE 2006 MECHANICAL ENGINEERING

Time Al l ow ed : 3 Hou r s M ax imum M ar k s : 150

GATE : 2006 MECHANICAL ENGINEERING

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Q. 1 – Q. 20 car r y one mar k each

1. Match the i teoms in columns I and I I .

Column I Column I I

P. Gauss– Seidel 1. Interpolat ion

method

Q. Forward Newton 2. Non– linear– Gauss method different ial equations

R. Runge– Kutta 3. Numerical integration

method

S. Trapezoidal Rule 4. L inear algebraicequations

(a) P-1, Q-4, R-3, S-2 (b) P-1, Q-4, R-2, S-3

(c) P-1, Q-3, R-2, S-4 (d) P-4, Q-1, R-2, S-3

2. The solut ion of the different ial equat ion

dydx

+ 2xy = e –x2

with y(0) = 1 is

(a) (1 + x) e+x2

(b) (1 + x) e x– 2

(c) (1 – x) e+x2

(d) (1 – x) ex2

3. L et x denot e a r eal number. F ind out t heINCORRECT statement.

(a) S = {x : x > 3} represents the set of al l realnumbers greater than 3

(b) S = {x : x2 < 0} represents the empty set

(c) S = {x : x A and x B} represents the unionof set A and set B

(d) S = {x : a < x < b} represents the set of al l realnumbers between a and b, where a and b arereal numbers

4. A box contains 20 defect ive i tems and 80 non-defect ive i t ems. I f two i tems ar e selected atrandom without replacement, what wil l be theprobabil i ty that both i tems are defect ive?

(a)15

(b)125

(c) 2099

(d)19495

5. For a circular shaft of diameter d subjected totorque T, the maximum value of the shear st ressis

(a) 64T

3d(b)

32T3d

(c) 16T

3d(d)

8T3d

6. For a four -bar linkage in toggle position, the valueof mechanical advantage is

(a) 0.0 (b) 0.5

(c) 1.0 (d)

7. The differential equat ion governing the vibrat ingsystem is

(a) mx cx + k(x – y) = 0

(b) m x y c x y( – ) ( – ) + kx = 0

(c) mx c x y ( – ) kx = 0

(d) m x y c x y( – ) ( – ) + k(x – y) = 0

8. A pin-ended column of length L , modulus ofelast icit y E and second moment of the cr oss-sect i onal ar ea I i s l oaded cent r i cal l y by acompressive load P. The cr it ical buckling load (Pcr)is given by

(a) PEI2

L2cr

(b) PEI

3L2cr 2

(c) PEI

L2cr

(d) PEI

L

2

cr

2

9. The number of inver sions for a sl ider crankmechanism is

(a) 6

(b) 5

(c) 4

(d) 3


3

10. For a Newtonian fluid

(a) Shear stress is propor t ional to shear st rain

(b) Rate of shear st ress is propor t ional to shearstrain

(c) Shear stress is propor t ional to rate of shear strain

(d) Rate of shear st ress is propor t ional to rate ofshear st rain

11. In a two-dimensional velocity field with velocities uand v along the x and y directions respectively, theconvective acceleration along the x-direction is givenby

(a) uux

vuy

(b) u

ux

vvy

(c) uvx

vuy

(d) v

ux

uuy

12. Dew point temper ature is the temperature atwhich condensat ion begins when the air is cooledat constant

(a) volume (b) entropy

(c) pressure (d) enthalpy

13. I n a composi te slab, the temper atur e at theinter face (Tinter ) between two mater ials is equalto the average of the temperatures at the twoends. Assuming steady one-dimensional heatconduct ion, which of the fol lowing statements ist rue about the respective thermal conduct ivit ies?

T1 k1 k2

T2

Tinter

2b b

(a) 2k1 = k2 (b) k1 = k2

(c) 2k1 = 3k2 (d) k1 = 2k2

14. I n a Pelton wheel, the bucket per ipheral speed is10 m/s, the water jet veloci t y is 25 m/s andvolumetr ic flow rate of the jet is 0.1 m3/s. I f thejet deflect ion angle is 120 and the flow is ideal,the power developed is

(a) 7.5 kW (b) 15.0 kW

(c) 22.5 kW (d) 37.5 kW

15. An expendable pat tern is used in

(a) slush cast ing (b) squeeze cast ing

(c) centr ifugal cast ing (d) investment casting

16. The main purpose of spheroidising t reatment isto improve

(a) hardenabil i ty of low carbon steels

(b) machinabil i ty of low carbon steels

(c) hardenabil i ty of high carbon steels

(d) machinabil i ty of high carbon steels

17. NC contour ing is an example of

(a) cont inuous path positioning

(b) point-to-point positioning

(c) absolute positioning

(d) incremental posit ioning

18. A r ing gage is used to measure

(a) outside diameter but not roundness

(b) roundness but not outside diameter

(c) both outside diameter and roundness

(d) only external threads

19. The number of customers ar r iving at a rai lwayreservat ion counter is Poisson dist r ibuted withan ar r ival rate of eight customers per hour. Thereservat ion clerk at this counter takes six minutesper customer on an average with an exponential lydist r ibuted service t ime. The average number ofthe customers in the queue will be

(a) 3 (b) 3.2

(c) 4 (d) 4.2

20. I n an MRP system, component demand is

(a) forecasted

(b) established by the master production schedule

(c) cal culat ed by the M RP system fr om themaster product ion schedule

(d) ignored

Q. 21 – Q. 75 car r y t w o mar k s each

21. Eigenvalues of a matr ix S 3 22 3LNM

OQP are 5 and 1.

What are the eigenvalues of the matr ix S2 = SS?

(a) 1 and 25 (b) 6 and 4

(c) 5 and 1 (d) 2 and 10


4

22. Equat ion of the l ine normal to funct ion

f(x) = (x – 8)2/3 + 1 at P (0, 5) is

(a) y = 3x – 5 (b) y = 3x + 5

(c) 3y = x + 15 (d) 3y = x – 15

23. Assuming i = – 1 and t is a real number,, e dtit

0

p/ 3

zis

(a)3

212

i (b)3

212

– i

(c)12

32

i (d)12

13

2

FHG

IKJi –

24. I f f(x) = 2 – 7 3

5 – 12 – 9

2

2x x

x x

, then lim

x 3f (x) wil l be

(a) –13

(b)5

18

(c) 0 (d)25

25. Match the i tems in columns I and I I .

Column I Column I I

P. Singular matr ix 1. Determinant is notdefined

Q. Non-square matr ix 2. Determinant is alwaysone

R. Real symmetr ic 3. Determinant is zero

matr ix

S. Orthogonal matr ix 4. Eigen values arealways real

5. Eigenvalues are notdefined

(a) P-3, Q-1, R-4, S-2 (b) P-2, Q-3, R-4, S-1

(c) P-3, Q-2, R-5, S-4 (d) P-3, Q-4, R-2, S-1

26. For d y

dx

dydx

y e2

22x 4 3 3 , the part icular integral

is

(a)115

2e x (b)15

2e x

(c) 3 2e x (d) C C1 2e ex x– –3

27. Mult ipl icat ion of matr ices E and F is G. Matr icesE and G are

E cos –sin 0sin cos 0

0 0 1

LNMM

OQPP and G

1 0 00 1 00 0 1

LNMM

OQPP . What is

the matr ix F?

(a)cos – sinsin cos

00

0 0 1

LNMM

OQPP (b)

sin cos– cos sin

00

0 0 1

LNMM

OQPP

(c)cos sin

– sin cos

00

0 0 1

LNMM

OQPP (d)

sin – coscos sin

00

0 0 1

LNMM

OQPP

28. Consider a cont inuous random var iable withprobabil i ty density funct ion

f(t) = 1 + t for – 1 t 0

= 1 – t for 0 t 1

The standard deviat ion of the random var iable is

(a)13 (b)

16

(c)13

(d)16

29. Match the i tems in columns I and I I .

Column I Column I I

P. Addendum 1. Cam

Q. Instantaneous 2. Beam

center of velocity

R. Section modulus 3. Linkage

S. Pr ime circle 4. Gear

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

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

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

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

30. A disk clutch is required to t ransmit 5 kW at2000 rpm. The disk has a fr ict ion l ining withcoefficient of fr iction equal to 0.25. Bore radius offr ict ion lining is equal to 25 mm. Assume uniformcontact pressure of 1 MPa. The value of outsideradius of the fr ict ion l ining is

(a) 39.4 mm

(b) 49.5 mm

(c) 97.9 mm

(d) 142.9 mm


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31. Twenty degree full depth involute profiled 19-toothpinion and 37-tooth gear ar e in mesh. I f themodule is 5 mm, the center distance between thegear pair wil l be

(a) 140 mm (b) 150 mm

(c) 280 mm (d) 300 mm

32. A cyl indr ical shaft is subjected to an alternat ingstress of 100 MPa. Fat igue strength to sustain1000 cycles is 490 MPa. I f the cor rected endurancestrength is 70 MPa, est imated shaft l i fe wil l be

(a) 1071 cycles (b) 15000 cycles

(c) 281914 cycles (d) 928643 cycles

33. According to Von-Mises' distort ion energy theory,the distor t ion energy under three dimensionalstress state is represented by

(a)1

221

222

32

1 2 3 2 1 3E – (

(b)1 2

621

222

32

1 2 3 2 1 3–

( )

E

(c)13 1

222

32

1 2 3 2 1 3

E– ( )

(d)1

3 12

22

32

1 2 3 2 1 3E – ( )

34. A steel bar of 40 mm × 40 mm square cross-sectionis subjected to an axial compr essive l oad of200 kN. I f t he length of the bar is 2 m andE = 200 GPa, the elongat ion of the bar wil l be

(a) 1.25 mm (b) 2.70 mm

(c) 4.05 mm (d) 5.40 mm

35. I f Cf is the coef fici ent of speed fluct uat i on of af lywheel t hen t he r at i o of max /min wi l l be

(a)1 2

1 2

– C

Cf

f

(b)2 – C

1 + 2Cf

f

(c)1 + 2C

1 2Cf

f–

(d)2 +C

2 Cf

f–

36. A bar having a cross-sect ional area of 700mm 2 issubjected to axial loads at the posit ions indicated.The value of st ress in the segment QR is

63 kN 21 kN35 kN 49 Nk

P Q SR

(a) 40 MPa (b) 50 MPa

(c) 70 MPa (d) 120 MPa

37. I f a system is in equil ibr ium and the posit ion ofthe system depends upon many independentvariables, the pr inciple of vir tual work states thatthe par tial der ivat ives of its total potential energywith respect to each of the independent var iablemust be

(a) – 1.0 (b) 0

(c) 1.0 (d)

38. I f point A is in equil ibr ium under the act ion ofthe applied forces, the values of tension TAB andTAC are respectively

(a) 520 N and 300 N (b) 300 N and 520 N

(c) 450 N and 150 N (d) 150 N and 450 N

39. Match the i tems in columns I and I I

Column I Column I I

P. Higher kinemat ic pair 1. Grubler 's equat ion

Q. Lower kinemat ic pair 2. L ine contact

R. Quick return 3. Euler 's equat ion

mechanism

S. Mobil i ty of a l inkage 4. laner

5. Shaper

6. Sur face contact

(a) P-2, Q-6, R-4, S-3 (b) P-6, Q-2, R-4, S-1

(c) P-6, Q-2, R-5, S-3 (d) P-2, Q-6, R-5, S-1


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40. A machine of 250 kg mass is suppor ted onspr ings of total st i ffness 100kN /m. M achinehas an unbalanced rotat ing for ce of 350N atspeed of 3600 r pm. Assumi ng a dampingfact or of 0.15, the value of t r ansmissibi l i t yr at io is

(a) 0.0531 (b) 0.9922

(c) 0.0162 (d) 0.0028

41. I n a four -bar l inkage, S denotes the shor testl ink length, L is the longest l ink length, P andQ are the lengths of other two l inks. At leastone of the thr ee moving l inks wi l l r otate by360 i f

(a) S + L P + Q (b) S + L > P + Q

(c) S + P L + Q (d) S + P > L + Q

42. A 60 mm long and 6 mm t h i ck fi l l et weldcar r ies a steady load of 15 kN along the weld.The shear st r ength of t he weld mater ial isequal to 200 MPa. The factor of safety is

(a) 2.4 (b) 3.4

(c) 4.8 (d) 6.8

43. A t wo-dimensi onal f l ow f i el d has veloci t i esa l on g t h e x an d y d i r ect i on s gi v en byu = x2t and v = – 2xyt r espect i vel y, wher et i s t ime. The equat i on of st r eaml i nes i s

(a) x2 y = constant

(b) x y2 = constant

(c) x y = constant

(d) not possible to determine

44. The velocit y pr ofi le in ful ly developed laminarf l ow i n a pi pe of di amet er D i s gi ven byu = u 0(1 – 4r 2/D 2), wher e r i s t he r adi aldistance fr om the center. I f t he viscosi t y oft he f l u i d i s , t he pr essur e dr op acr oss alength L of the pipe is

(a) u0L

D2

(b)4 0u L

D2

(c)8 0u L

D2

(d)16 0u L

D2

45. A siphon dr aws water fr om a r eser voi r anddi schar ges i t out at at mospher i c pr essur e.Assuming ideal fluid and the reservoir is large,the velocity at point P in the siphon tube is

(a) 2 1gh

(b) 2 2gh

(c) 2 2 1g h h( – )

(d) 2 2 1g h h( )

46. A l ar ge hydr au l i c t u r bi ne i s t o gener at e300 kW at 1000 rpm under a head of 40 m.For init ial t est ing, a 1 : 4 scale model of thetur bine operates under a head of 10 m. Thepower gener ated by the model (in kW) wi l l be

(a) 2.34 (b) 4.68

(c) 9.38 (d) 18.75

47. The statements concern psychromet r ic char t .

1. Constant relat ive humidi ty l ines are uphil lst r aight l ines to the r ight

2. Constant wet bulb temperatur e l ines ar edownhi l l st raight l ines to the r ight

3. Const an t speci f i c vol ume l i nes ar edownhi l l st raight l ines to the r ight

4. Constant enthalpy l ines are concident withconstant wet bulb temperature l ines

Which of the statements ar e cor rect?

(a) 2 and 3 (b) 1 and 2

(c) 1 and 3 (d) 2 and 4

48. A 100 W electr ic bulb was swit ched on in a2.5 m × 3 m × 3 m size ther mal ly insulatedr oom having a temper ature of 20C. The r oomtemper atur e at the end of 24 hours wi l l be

(a) 321C (b) 341C

(c) 450C (d) 470C


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49. A thin layer of water in a field is formed after afarmer has watered it . The ambient air condit ionsare: temperature 20C and relat ive humidity 5%.

An extract of steam tables is given below.

Temp (C) Saturat ion

– 15 – 10 – 5 0.01 5 10 15 20

Pressure (kPa)

0.10 0.26 0.40 0.61 0.87 1.23 1.71 2.34

Neglect ing the heat t ransfer between the waterand the ground, the water temperature in thefield after phase equilibr ium is reached equals

(a) 10.3C (b) – 10.3C

(c) – 14.5C (d) 14.5C

50. A hor izontal -shaft centr i fugal pump l i ft s waterat 65C. The suct i on nozzl e i s one met erbelow pump center l i ne. The pr essur e at t hi spoint equal s 200 kPa gauge and veloci t y i s3 m/s. Steam t ables show satur at ion pr essur eat 65C is 25kPa, and specific volume of thesaturated liquid is 0.001020 m3/kg. The pump NetPosit ive Suct ion Head (NPSH) in meters is

(a) 24 (b) 26

(c) 28 (d) 30

51. Given below is an extract from steam tables.

Specific volume (m3/kg) Enthalpy (kJ/kg) Temperature

(C)

PSat

(bar) Saturated

liquid

Saturated

vapour

Saturated

liquid

Saturated

vapour

45 0.09593 0.001010 15.26 188.45 2394.8

342.24 150 0.001658 0.010337 1610.5 2610.5

Specific enthalpy of water in kJ/Kg at 150 barand 45C is

(a) 203.60 (b) 200.53

(c) 196.38 (d) 188.45

52. Determine the cor rectness or otherwise of thefol lowing Asser t ion [a] and the Reason [r ].

Asser t ion [a]: I n a power plant wor king on aRank ine cycle, the r egener at ive feed wat erheat ing improves the efficiency of the steamturbine.

Reason [r ]: The regenerat ive feed water heat ingraises the average temperature of heat addit ionin the Rankine cycle.

(a) Both [a] and [r ] are t rue and [r ] is the cor rectreason for [a]

(b) Both [a] and [r ] are t rue but [r ] is NOT thecor rect reason for [a]

(c) Both [a] and [r ] are false

(d) [a] is false but [r ] is t rue

53. Determine the cor rectness or otherwise of thefol lowing Asser t ion [a] and the Reason [r ].

Asser t i on [a] : Condenser i s an essen t i alequipment in a steam power plant .

Reason [r ]: for the same mass flow rate and thesame pr essur e r i se, a water pump r equi r essubstantial ly less power than a steam compressor.

(a) Both [a] and [r ] are t rue and [r ] is the cor rectreason for [a]

(b) Both [a] and [r ] are t rue but [r ] is NOT thecor rect reason for [a]

(c) [a] is t rue but [r ] is flase

(d) [a] is false but [r ] is t rue

54. Match items from groups I , I I , I I I , IV and V.

Gr oup I Gr oup I I Gr ou p I I I Gr oup I V Gr oup V

When added to the system, is

Different ial Function Phenomenon

E Heat G Posi t ive I Exact K Path M Transient

F Work H Negat ive J I nexact L Point N Boundary

(a) F – G – J – K – M

E – G – I – K – N

(b) E – G – I – K – M

F – H – I – K – N

(c) F – H – J – L – N

E – H – I – L – M

(d) E – G – J – K – N

F – H – J – K – M


8

55. Gr oup I shows di f fer en t heat addi t i onprocesses in power cycles. L ikewise, Gr oup I Ishows di f fer en t heat r emoval pr ocesses.Gr oup I I I l ists power cycles. Match i tems fr omGroups I , I I and I I I .

Gr oup I Gr oup I I Gr oup I I I P. Pressure

constant S. Pressure

constant 1. Rankine cycle

Q. Volume constant

T. Volume constant

2. Otto cycle

R. Temperature constant

U. Temperature constant

3. Carnot Cycle

4. Diesel cycle 5. Brayton cycle (a) P – S – 5

R – U – 3

P – S – 1

Q – T – 2

(b) P – S – 1

R – U – 3

P – S – 4

P – T – 2

(c) R – T– 3

P – S – 1

P – T – 4

Q – S – 5

(d) P – T – 4

R – S – 3

P – S – 1

P – S – 5

56. Wi t h an i ncr ease i n t he t h i ck ness ofinsulat ion ar ound a cir cular pipe, heat loss tosur roundings due to

(a) convect i on i ncr eases, whi le that due t oconduct ion decr eases

(b) convect i on decr eases, whi le t hat due toconduct ion incr eases

(c) convect ion and conduct ion decr eases

(d) convect ion and conduct ion incr eases

57. The ul t imate tensi le st rength of a mater ial is400M Pa and the elongat ion up to maximumload is 35%. I f the mater ial obeys power lawof har dening, then the t r ue st r ess-t rue str ainr el at i on (st r ess i n M Pa) i n t he pl ast i cdefor mat ion r ange is

(a) = 540 0.30 (b) = 775 0.30

(c) = 5400.35 (d) = 775 0.35

58. I n a sand cast ing oper at ion, the total l iquidhead is maint ained constant such that i t isequal to the mould height . The t ime taken tofi l l the mould with a top gate is tA. I f t he samemould is fi l led with a bot tom gate, then thet ime taken is tB. I gnore the t ime r equi r ed tofi l l t he r unner and fr ict ional effects. Assumeatmospher ic pressure at the top molten metalsur faces. The r elat ion between tA and tB is

(a) tB = 2 tA (b) tB = 2 tA

(c) tB = tA

2(d) tB = 2 2 tA

59. A 4 mm thi ck sheet i s r ol led wi th 300 mmdiamet er r ol l s t o r educe t h ick ness wi t houtany char ge i n i t s w i dt h . The f r i ct i oncoeff ici ent at the wor k -r ol l int er face is 0.1.The minimum possible thickness of the sheetthat can be produced in a single pass is

(a) 1.0 mm (b) 1.5 mm

(c) 2.5 mm (d) 3.7 mm

60. In a wire drawing operation, diameter of a steelwi r e is r educed f r om 10 mm to 8 mm. Themean flow str ess of the mater ial is 400 M Pa.The ideal force requi red for drawing (ignor ingfr ict ion and redundant wor k) is

(a) 4.48 kN

(b) 8.97 kN

(c) 20.11 kN

(d) 31.41 kN

61. M atch the i tems in columns I and I I .

Column I Column I I

P. Wrinkling 1. Yield point elongat ion

Q. Orange peel 2. Anisotropy

R. Stretcher st rains 3. Large grain size

S. Earing 4. Insufficient blankholding force

5. Fine grain size

6. Excessive blankholding force

(a) P – 6, Q – 3, R – 1, S – 2

(b) P – 4, Q – 5, R – 6, S – 1

(c) P – 2, Q – 5, R – 3, S – 4

(d) P – 4, Q – 3, R – 1, S – 2


9

62. I n an ar c welding pr ocess, the vol t age andcur rent ar e 25 V and 300 A r espect ively. Thearc heat t ransfer efficiency is 0.85 and weldignspeed i s 8 mm/sec. The net heat i npu t(in J/mm) is

(a) 64 (b) 797

(c) 1103 (d) 79700

63. I f each abrasive grain is viewed as a cut t ingtool , t hen which of the fol lowing r epr esentsthe cut t ing par ameter s in common gr indingoperat ions?

(a) L ar ge negat i ve r ak e angl e, l ow shearangle and high cut t ing speed

(b) Lar ge posit ive rake angle, low shear angleand high cut t ing speed

(c) L ar ge negat i ve r ak e angle, h i gh shearangle and low cut t ing speed

(d) Zer o r ak e angle, h i gh shear angle andhigh cut t ing speed

64. Arrange the processes in the increasing order oftheir maximum mater ial removal rate.

Elect rochemical M achining (ECM)

Ul t r asonic M achining (USM)

Elect r on Beam M achining (EBM )

Laser Beam M achining (LBM ) and

Electr ic Dischar ge M achining (EDM)

(a) USM , LBM , EBM , EDM , ECM

(b) EBM , LBM , USM , ECM , EDM

(c) LBM , EBM , USM , ECM , EDM

(d) LBM , EBM , USM , EDM , ECM

65. M atch the i tems in columns I and I I .

Col um n I Col um n I I

P. Char py test 1. Fluidity

Q. K noop test 2. Microhardness

R. Spi ral test 3. For mabil i ty

S. Cupping test 4. Toughness

5. Permeabil i ty

(a) P – 4, Q – 5, R – 3, S – 2

(b) P – 3, Q – 5, R – 1, S – 4

(c) P – 2, Q – 4, R – 3, S – 5

(d) P – 4, Q – 2, R – 1, S – 3

66. A manufactur ing shop processes sheet metal jobs,wher ei n each j ob must pass t h r ough t womachines (M 1 and M 2, in t hat or der ). Theprocessing t ime (in hours) for these jobs is

Machine Jobs

P Q R S T U

M1 15 32 8 27 11 16

M2 6 19 13 20 14 7

The opt imal make-span (in hours) of the shop is

(a) 120 (b) 115

(c) 109 (d) 79

67. Consider the fol lowing data for an i tem.

Annual demand: 2500 units per year Order ingcost : Rs. 100 per order Inventory holding rate:25% of unit pr ice

Order quant i ty

(units)

Unit pr ice

(Rs.)

< 500 10

> 500 9

The opt imum order quant ity (in units) is

(a) 447 (b) 471

(c) 500 (d) 600

68. A f i r m i s r equi r ed t o pr ocur e t h r ee i t ems(P, Q, and R). The pr ices quoted for these items(in Rs.) by suppliers S1, S2 and S3 are given intable. The management pol icy requires that eachitem has to be supplied by only one supplier andone supplier supply only one item. The minimumtotal cost (in Rs.) of procurement to the firm is

I tem Supplies

S1 S2 S3

P 110 120 130

O 115 140 140

R 125 145 165

(a) 350 (b) 360

(c) 385 (d) 395


10

69. A stockist wishes to opt imize the number ofper i shable i t ems he needs t o st ock i n anymonth in his store. The demand dist r ibut ionfor this per ishable i t em is

Demand (in units) 2 3 4 5

Probabil i ty 0.10 0.35 0.35 0.20

The stockist pays Rs. 70 for each i tem and hesel ls each at Rs. 90. I f t he stock is left unsoldin any month, he can sel l the i tem at Rs. 50each . Ther e i s no penal t y for unfu l f i l l eddemand. To maximize the expected profi t , theopt imal stock level is

(a) 5 uni t s (b) 4 unit s

(c) 3 uni t s (d) 2 unit s

70. The table gives detai ls of an assembly l ine.

Work stat ion I I I I I I IV V VI

Total task t ime at the

workstat ion (in minutes)

7 9 7 10 9 6

What i s t he l ine eff ici ency of t he assemblyl ine?

(a) 70%

(b) 75%

(c) 80%

(d) 85%

Com mon Dat a for Qu est i on s 71, 72, 73:

I n an or thogonal machining oper at ion:

Uncut thickness = 0.5 mm

Cutt ing speed = 20 m/min Rake angle = 15

Width of cut = 5 mmChip thickness = 0.7 mm

Thr ust for ce = 200 NCut t ing for ce = 1200N

Assume M er chant 's theory.

71. The values of shear angle and shear st rain,r espect ively, ar e

(a) 30.3 and 1.98

(b) 30.3 and 4.23

(c) 40.2 and 2.97

(d) 40.2and 1.65

72. The coef f i ci en t of f r i ct i on at t he t ool -ch ip

inter face is

(a) 0.23

(b) 0.46

(c) 0.85

(d) 0.95

73. The per cen t age of t ot al ener gy di ssi pat ed

due t o f r i ct i on at t he t ool -ch ip i n t er face

i s

(a) 30%

(b) 42%

(c) 58%

(d) 70%

Com mon Dat a for Qu est i ons 74, 75:

A planetar y gear t rain has four gears and one

car r ier. Angular veloci t ies of the gears ar e ,

2, 3 and 4, r espect ively. The car r ier r otates

with angular velocit y 5.

74. What i s t he r el at i on bet ween t he angularveloci t ies of Gear 1 and Gear 4 ?

(a)

1 5

4 5

–– = 6

(b)

4 5

1 5

–– = 6

(c)

1 2

4 3

–– = –

23

FHG

IKJ

(d)

2 5

4 5

–– =

89


11

75. For 1 = 60 r pm clockwise (cw) when lookedfrom the left , what is the angular veloci ty ofthe car r ier and i t s di r ect ion so that Gear 4r otates in counter clockwise (ccw) dir ect ion att wi ce t he angular veloci t y of Gear 1 whenlooked from the left?

(a) 130 r pm, cw (b) 223 rpm, ccw

(c) 256 r pm, cw (d) 156 rpm, ccw

L in k ed Answ er Qu est i ons : Q. 76 – Q. 85car r y t w o mar k s each

St at em en t for L i nk ed An sw er Quest i on s76 & 77:

A simply suppor ted beam of span length 6 mand 75 mm diamet er car r i es a un i for ml ydistr ibuted load of 1.5 kN/m

76. What i s t he max i mum val ue of bendi ngmoment?

(a) 9 kNm

(b) 13.5 kNm

(c) 81 kNm

(d) 125 kNm

77. What i s t he max i mum val ue of bendi ngst ress?

(a) 162.98 M Pa

(b) 325.95 M Pa

(c) 625.95 M Pa

(d) 651.90 M Pa


A vibr ator y system consists of a mass 12.5 kg,a spr ing of st i ffness 1000 N/m, and a dashpotwith damping coefficient of 15 Ns/m.

78. The value of cr i t ical damping of the system is

(a) 0.223 Ns/m

(b) 17.88 Ns/m

(c) 71.4 Ns/m

(d) 223.6 Ns/m

79. The value of logar i thmic decr ement is

(a) 1.35

(b) 1.32

(c) 0.68

(d) 0.66


A football was inflated to a gauge pressure of1 bar when t he ambi ent t emper at ur e was15C. When the game star ted next day, the airtemper atur e at the stadium was 5C.

Assume t hat t he vol ume of t he foot bal lr emains constant at 2500 cm3.

80. The amount of heat lost by t he ai r i n t hefootball and the gauge pr essur e of ai r in thefootball at the stadium respect ively equal

(a) 30.6 J, 1.94 bar

(b) 21.8 J, 0.93 bar

(c) 61.1 J, 1.94 bar

(d) 43.7 J, 0.93 bar

81. Gauge pr essur e of ai r to which the bal l musthave been or iginal ly inflated so that i t wouldequal 1 bar gauge at the stadium is

(a) 2.23 bar (b) 1.94 bar

(c) 1.07 bar (d) 1.00 bar


A smooth flat plate wi th a sharp leading edgei s pl aced al ong a gas st r eam f l ow i ng atU = 10 m/s.

The thickness of the boundar ylayer at sect ionr -s is 10 mm, the br eadth of the plate is 1 m(i nto the paper ) and the densi t y of the gas = 1.0 kg/m3. Assume that the boundary layeris thin, two-dimensional, and fol lows a l inearveloci ty dist r ibut ion, u = U(y/), at the sect ionr -s, wher e y is the height fr om plate.

82. The mass flow rate (in kg/s) across the sect ionq-r is

(a) zer o

(b) 0.05

(c) 0.10

(d) 0.15


12

83. The integr ated drag for ce (in N) on the plate,between p-s, is

(a) 0.67 (b) 0.33

(c) 0.17 (d) zer o


Consi der a PERT net wor k for a pr ojectinvolving six tasks (a to f)

Task Pr edecessor Expected

t ask t ime (in days)

Var iance of the

ask t ime

(in days2)

a – 30 25

b a 40 64

c a 60 81

d b 25 9

e b, c 45 36

f d, e 20 9

84. The expected complet ion t ime of the pr oject is

(a) 238 days

(b) 224 days

(c) 171 days

(d) 155 days

85. The standar d deviat ion of the cr i t ical path ofthe pr oject is

(a) 151 days

(b) 155 days

(c) 200 days

(d) 238 days

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Vikasmedia.careerlauncher.com.s3.amazonaws.com/acads_download... · 2013-11-18 · MECHANICAL ENGINEERING GATE : 2006 5 31. Twenty degree full depth involute profiled 19-tooth pinion