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ME – MECHANICAL ENGINEERING GATE : 2005

1

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. 30 car r y on e mar k each andQ. 31 to Q. 80 car ry t w o marks each. Q. 81 to Q. 85 each contains par t “a” and “b” . I n these quest ions,par ts “a” as well as “b” car ry t w o marks each.

2. Answer al l the quest ions.

3. Quest ions must be answered on special machine gradable Object ive Response Sheet (ORS) by darkeningthe appropr iate bubble (marked A, B, C, D) against the quest ion number on the left hand side of the ORS,using HB pencil . Each quest i on has on ly one cor r ect answ er . I n case you wish to change an answer,erase the old answer completely using a good soft eraser.

4. There wil l be NEGATI VE marking. In Q.1 to Q. 30, 0.25 mark wil l be deducted for each wrong answerand in Q. 31 to Q. 80, 0.5 mark wil l be deducted for each wrong answer. In Q. 81 to Q. 85, for the par t “a” ,0.5 mark wil l be deducted for a wrong answer. Marks for cor rect answers to par t “b” of Q. 81 to Q. 85 wil lbe given only i f the answer to the corresponding par t “a” is cor rect . However, there is no negat ive markingfor par t “b” of Q. 81 to Q. 85. More than one answer bubbled against a quest ion wil l be deemed as anincor rect response.

5. Write your registrat ion number, name and name of the centre at the specified locat ions on the r ight halfof 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.

9. Use the blank pages given at the end of the quest ion paper for rough work.

10. This quest ion paper contains 24 pr inted pages including pages for rough work. Please check al l pages andrepor t , i f there is any discrepancy.

GATE 2005 MECHANICAL ENGINEERING

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

GATE : 2005 ME – MECHANICAL ENGINEERING

2

Q.1– Q. 30 car r y one mar k each

1. Stokes theorem connects

(a) a l ine integral and a sur face integral

(b) a sur face integral and a volume integral

(c) a l ine integral and a volume integral

(d) gradient of a funct ion and its sur face integral

2. A lot has 10% defect ive i tems. Ten items are cho-sen randomly from this lot . The probabil i ty thatexact ly 2 of the chosen items are defect ive is

(a) 0.0036

(b) 0.1937

(c) 0.2234

(d) 0.3874

3. s in sin6 7

–

x x dxa

a

z e j is equal to

(a) 2 6

0

sin xdxaz

(b) 2 7

0

sin xdxaz

(c) 2 6 7

0

sin sinx x dxa

z e j

(d) zero

4. A is a 3 4 real matr ix and Ax = b is an inconsist-ent system of equations. The highest possible rankof A is

(a) 1 (b) 2

(c) 3 (d) 4

5. Changing the order of the integration in the dou-

bl e i n t egr al I = f x y dydxx

( , )/4

2

0

8 zz l eads t o

I , zz f x y dydxp

q

r

s

b g . What is q?

(a) 4y

(b) 16y2

(c) x

(d) 8

6. The t ime var iat ion of the posit ion of a par t icle inrect i l inear mot ion is given by x = 2t3 + t2 + 2t. I fv is the velocity and a the accelerat ion of thepar t icle in consistent units, the mot ion star tedwith

(a) v = 0, a = 0

(b) v = 0, a = 2

(c) v = 2, a = 0

(d) v = 2, a = 2

7. A simple pendulum of length 5 m, with a bob ofmass 1 kg, is in simple harmonic mot ion. as i tpasses through its mean posit ion, the bob has aspeed of 5 m/s. The net force on the bob at themean posit ion is

(a) zero

(b) 2.5 N

(c) 5 N

(d) 25 N

8. A uniform, slender cyl indr ical rod is made of ahomogeneous and isotropic mater ial . The r odrests on a fr ict ionless sur face. The rod is heateduniformly. I f the radial and longitudinal thermalst r esses ar e r epr esen t ed by r and z,respect ively, then

(a) r = 0, z = 0

(b) r 0, z = 0

(c) r = 0, z 0

(d) r 0, z 0

9. Two ident ical cant i lever beams are suppor ted asshown, with their free ends in contact through ar igid rol ler. After the load P is applied, the freeends wil l have

P

(a) equal deflect ions but not equal slopes

(b) equal slopes but not equal deflect ions

(c) equal slopes as well as equal deflect ions

(d) neither equal slopes nor equal deflect ions

10. The number degrees of freedom of a planar linkagewith 8 l inks and 9 simple revolute joints is

(a) 1 (b) 2

(c) 3 (d) 4


3

11. There are four samples P, Q, R and S, with naturalfrequencies 64, 96, 128 and 256 Hz, respect ively.They are mounted on test setups for conduct ingvibr at ion exper iments. I f a loud pure note offrequency 144 Hz is produced by some instrument,wh i ch of t he sampl es w i l l show t he mostpercept ible induced vibrat ion?

(a) P (b) Q

(c) R (d) S

12. Which one of the fol lowing is a cr i ter ion in thedesign of hydrodynamic journal bear ings?

(a) Sommer feld number

(b) Rat ing l ife

(c) Specific dynamic capacity

(d) Rotat ion factor

13. The velocity components in the x and y directionsof a two dimensional potent ial flow are u and v,

respect ively. Then

ux

is equal to

(a) x

(b) –x

(c) y (d) –

y

14. I n a case of one dimensional heat conduct ion in amedium wi t h constant pr oper t i es, T is the

temperature at posit ion x, at t ime t. Then Tt

is

propor t ional to

(a) Tx

(b)Tx

(c)

2Tx t

(d)

2

2T

x

15. The fol lowing four figures have been drawn torepresent a fict i t ious thermodynamic cycle, onthe p-v and T-s planes.

According to the first law of thermodynamics,equal areas are enclosed by

(a) figures 1 and 2

(b) figures 1 and 3

(c) figures 1 and 4

(d) figures 2 and 3

16. A p-v diagram has been obtained from a test on ar eci pr ocat i ng compr essor . Wh i ch of t hefol lowing represents that diagram?

(a)p

v

p i n

pou t

(b)p

vp i n

pou t

vc

(c)p

v

p i n

pou t

vc

(d)p

v

p i n

pou t

vc


4

17. The fol lowing figure was generated from exper i-mental data relating spectral black body emissivepower to wavelength at three temperatures T1,T2 and T3 (T1>T2>T3).

T1

T2

T3

( m)

Eb(W/m . m)

2

The conclusion is that the measurements are

(a) cor rect because the maxima in Eb show thecor rect t rend

(b) cor rect because Planck’s law is sat isfied

(c) wrong because the Stefan Boltzmann law isnot sat isfied

(d) wrong because Wien’s displacement law is notsat isfied

18. For a typical sample of ambient air (at 35 C, 75%r elat ive humidi t y and standar d atmospher icpressure), the amount of moisture in kg per kgof dry air wil l be approximately

(a) 0.002 (b) 0.027

(c) 0.25 (d) 0.75

19. Water at 42 C is sprayed into a stream of air atatmospher ic pressure, dry bulb temperature of40 C and a wet bulb temperature of 20 C. Theair leaving the spray humidifier is not saturated.Which of the fol lowing statements is t rue?

(a) Air gets cooled and humidified

(b) Air gets heated and humidified

(c) Air gets heated and dehumidified

(d) Air gets cooled and dehumidified

20. Match the i tems of L ist I (Equipment) with theitems of L ist I I (Process) and select the cor rectanswer using the given codes.

L i st I (Equi pmen t ) L ist I I (Pr ocess)

P - Hot Chamber Machine 1. Cleaning

Q - Muller 2. Core making

R - Dielectr ic Baker 3. Die casting

S - Sand Blaster 4. Annealing

5. Sand mixing

(a) P-2, Q-1, R-4, S-5

(b) P-4, Q-2, R-3, S-5

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

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

21. When the temperature of a solid metal increases,

(a) st rength of the metal decreaes but duct i l i tyincreases

(b) both st r ength and duct i l i t y of the met aldecrease

(c) both st r ength and duct i l i t y of the met alincrease

(d) st rength of the metal increases but duct i l i tydecreases

22. The strength of a brazed joint

(a) decreases with increase in gap between thetwo joining sur faces

(b) increases with increase in gap between thetwo joining sur faces

(c) decreases up to cer tain gap between the twojoining sur faces beyond which i t increases

(d) increases up to cer tain gap between the twojoining sur faces beyond which i t decreases

23. A zigzag cavity in a block of high strength al loy isto be finish machined. This can be car r ied out byusing

(a) electr ic discharge machining

(b) electro-chemical machining

(c) laser beam machining

(d) abrasive flow machining

24. I n order to have inter ference fi t , i t is essent ialthat the lower l imit of the shaft should be

(a) greater than the upper l imit of the hole

(b) lesser than the upper l imit of the hole

(c) greater than the lower l imit of the hole

(d) lesser than the lower l imit of the hole


5

25. When 3-2-1 pr inciple is used to suppor t and lo-cate a three dimensional work-piece dur ing ma-chining, the number of degress of freedom thatare restr icted is

(a) 7 (b) 8

(c) 9 (d) 10

26. The f i gu r e bel ow shows a gr aph wh i chquali tat ively relates cut t ing speed and cost perpiece produced.

Cut t ing Speed

Cos

t pe

r pi

ece

3

2

1

TotalCost

The three curves 1, 2 and 3 respect ively represent

(a) machining cost , non-pr oduct ive cost , toolchanging cost

(b) non-pr oduct ive cost , machining cost , toolchanging cost

(c) tool changing cost , machin ing cost , non-product ive cost

(d) t ool changing cost , non-pr oduct i ve cost ,machining cost

27. Which among the NC operat ions given below arecontinuous path operat ions?

Arc Welding (AW) Milling (M)

Dr ill ing (D) Punching is SheetMetal (P)

Laser Cutt ing of Spot Welding (SW)Sheet Metal (LC)

(a) AW, LC and M

(b) AW, D, LC and M

(c) D, LC, P and SW

(d) D, LC, and SW

28. An assembly act i v i t y i s r epr esented on anOperat ion Process Char t by the symbol

(a) L (b) A

(c) D (d) O

29. The sales of a product dur ing the last four yearswere 860, 880, 870 and 890 units. The forecastfor the four th year was 876 units. I f the forecastfor the f i ft h year, using simple exponent i alsmoothing, is equal to the forecast using a threeper i od mov i ng aver age, t he val ue of t heexponent ial smoothing constant is

(a)17

(b)15

(c)27

(d)25

30. Consider a single server queuing model wi thPoisson ar r ivals ( = 4/hour ) and exponent ialservice ( = 4/hour ). The number in the systemis restr icted to a maximum of 10. The probabil i tythat a person who comes in leaves without joiningthe queue is

(a) 111

(b)1

10

(c)19

(d)12

Q. 31 t o Q. 80 car r y t w o mar k s each .

31. Which one of the fol lowing is an eigenvector of

the matr ix

5 0 0 00 5 0 00 0 2 10 0 3 1

?

(a)

1

00

–2L

NMMM

O

QPPP

(b)

0010

L

NMMM

O

QPPP

(c)

100–2

L

NMMM

O

QPPP

(d)

0010

L

NMMM

O

QPPP

32. With a 1 unit change in b, what is the change in xi n t he solut i on of t he syst em of equat i ons x + y = 2, 1.01x + 0.99 y = b?

(a) zero (b) 2 units

(c) 50 units (d) 100 units


6

33. By a change of var iables x(u,) = u, y(u, v) = /uin a double integral, the integrand f(x,y) changesto f (u, u/) (u,). Then, (u,) is

(a) 2u

(b) 2 u

(c) 2 (d) 1

34. The r ight circular cone of largest volume thatcan be enclosed by a sphere of 1 m radius has aheight of

(a) 13

m (b)23

m

(c)2 2

3m (d)

43

m

35. I f xdydx

xylnxx

2 22

, and y (1) = 0, then what

is y(e)?

(a) e (b) 1

(c)1e

(d)12e

36. The l ine integral V.dz r of the vector funct ion

V 2 2 2r xyzi x zj k ykb g fr om the or igin to

the point P(1, 1, 1)

(a) is 1

(b) is zero

(c) is – 1

(d) cannot be determined without specifying thepath

37. Start ing from x0 = 1, one step of Newton-Raphsonmethod in solving the equat ion x3 + 3x – 7 = 0gives the next value (x1) as

(a) x1 = 0.5

(b) x1 = 1.406

(c) x1 = 1.5

(d) x1 = 2

38. A single die is thrown twice. What is theprobabil i ty that the sum is neither 8 nor 9?

(a)19

(b)5

36

(c)14

(d)34

39. Two books of mass 1 kg each are kept on a table,one over the other. The coefficient of fr ict ion onevery pair of contact ing sur faces is 0.3. the lowerbook is pul led with a hor izontal for ce F. Theminimum value of F for which slip occurs betweenthe two books is

(a) zero

(b) 1.06 N

(c) 5.74 N

(d) 8.83 N

40. A shell is fired from a connon. At the instant theshell is just about to leave the bar rel, i ts velocityrelat ive to the bar rel is 3m/s, while the bar rel isswinging upwards with a constant angular velocityof 2 rad/s. The magnitude of the absolute velocityof the shell is

2m

2 rad/s

(a) 3 m/s (b) 4 m/s

(c) 5 m/s (d) 7 m/s

41. An elevator (l ift ) consists of the elevator cage anda counter weight , of mass m each. The cage andthe counterweight are connected by a chain thatpasses over a pulley. The pulley is coupled to amotor. I t is desired that the elevator should havea maximum stopping t ime of t seconds from apeak speed . I f the iner t ias of the pulley and thechain are neglected, the minimum power that themotor must have is

pul ley

m

m

cage

counterweight

v

chainv

(a) 12

2m (b)m

t2

2

(c) m

t2

(d)2 2m

t


7

42. A 1 kg mass of clay, moving with a velocity of 10m/s, st r ikes a stat ionary wheel and st icks to i t .The sol id wheel has a mass of 20 kg and a radiusof 1m. Assuming that the wheel and the groundare both r igid and that the wheel is set into purerol l ing mot ion, the angular velocity of the wheelimmediately after the impact is approximately

1m

10 m/s

1 kg

20 kg

(a) zero (b)13

rad/s

(c) 103

rad/s (d)103

rad/s

43. The two shafts AB and BC, of equal length anddiameter s d and 2d , ar e made of the samemater ial. They are joined at B through a shaftcoupling, while the ends A and C are buil t -in(cant i levered). A twist ing moment T is applied tothe coupling. I f TA and TC represent the twist ingmoments at the ends A and C, respect ively, then

coupling 2dd

A B C

L L

(a) TC = TA

(b) TC = 8TA

(c) TC = 16 TA

(d) TA = 16 TC

44. A beam is made up of two ident ical bars AB andBC, by hinging them together at B. The end A isbuil t -in (cant i levered) and the end C is simply-suppor ted. With the load P act ing as shown, thebending moment at A is

AB C

P

L/2L L

(a) zero (b)PL2

(c)3PL

2(d) indeterminate

45. A canti lever beam carr ies the anti-symmetr ic loadshown, wher e w0 is the peak intensity of thedi st r i but ed l oad. Qual i t at i vel y, t he cor r ectbending moment diagram for this beam is

wo

L LA

B

wo

(a) (b)

(c) (d)

46. A cant i lever beam has the square cross sect ion10 mm 10 mm. I t car r ies a t ransverse load of10 N. Consider ing only the bot tom fibres of thebeam, t he cor r ect r epr esen t at i on of t helongitudinal var iat ion of the bending stress is

1m 1m

10N

10mm

10mm

(a) 60 M Pa

(b) 60 M Pa

(c) 400 MPa

(d) 400 MPa

47. I n a cam-fol lower mechanism, the follower needsto r ise through 20 mm dur ing 60 of cam rotation,the first 30 with a constant acceleration and thenwith a decelerat ion of the same magnitude. Theinit ial and final speeds of the fol lower are zero.The cam rotates at a uniform speed of 300 rpm.The maximum speed of the fol lower is

(a) 0.60 m/s

(b) 1.20 m/s

(c) 1.68 m/s

(d) 2.40 m/s


8

48. A rotat ing disc of 1 m diameter has two eccentr icmasses of 0.5 kg each at radi i of 50 mm and60 mm at angular posi t ions of 0 and 150 ,respect ively. A balancing mass of 0.1 kg is to beused to balance the rotor. what is the r adialposit ion of the balancing mass?

(a) 50 mm

(b) 120 mm

(c) 150 mm

(d) 280 mm

49. I n a spr ing-mass system, the mass is 0.1 kg andt he st i f f ness of t he spr i ng i s 1 k N /m. Byintroducing a damper, the frequency of oscil lationis found to be 90% of the or iginal value. What isthe damping coefficient of the damper?

(a) 1.2 N.s/m

(b) 3.4 N.s/m

(c) 8.7 N.s/m

(d) 12.0 N.s/m

50. The Mohr ’s circle of plane stress for a point in abody is shown. The design is to be done on thebasis of the maximum shear stress theory foryielding. Then, yielding wi l l just begin i f t hedesigner chooses a duct i le mater ial whose yieldstrength is

(M Pa)

(M Pa)

(a) 45 MPa (b) 50 MPa

(c) 90 MPa (d) 100 MPa

51. A weighing machine consists of a 2 kg pan restingon spr ing. In this condition, with the pan rest ingon the spr ing, the length of the spr ing is 200 mm.When a mass of 20 kg is placed on the pan, thelength of the spr ing becomes 100 mm. For thespring, the un-deformed length l0 and the spr ingconstant k (sti ffness) are

(a) l0 = 220 mm, k = 1862 N/m

(b) l0 = 210 mm, k = 1960 N/m

(c) l0 = 200 mm, k = 1960 N/m

(d) l0 = 200 mm, k = 2156 N/m

52. A ventur imeter of 20 mm throat diameter is usedto measure the velocity of water in a hor izontalpipe of 40 mm diameter. I f the pressure differencebetween the pipe and throat sect ions is found tobe 30 kPa then, neglect ing fr ict ional losses, theflow velocity is

(a) 0.2 m/s

(b) 1.0 m/s

(c) 1.4 m/s

(d) 2.0 m/s

53. A U-tube manometer with a small quant ity ofmercury is used to measure the stat ic pressuredifference between two locat ions A and B in aconical section through which an incompressiblefluid flows. At a part icular flow rate, the mercurycolumn appears as shown in the figur e. Thedensi t y of mer cur y i s 13600 kg/m3 andg = 9.81 m/s2. Which of the fol lowing is cor rect ?

AB

150 mm

(a) Flow direct ion is A to B and pA – pB = 20 kPa

(b) Flow direct ion is B to A and pA – pB = 1.4 kPa

(c) Flow direct ion is A to B and pB – pA = 20 kPa

(d) Flow direct ion is B to A and pB – pA = 1.4 kPa

54. A reversible thermodynamic cycle containing onlythr ee pr ocesses and pr oducing wor k is to beconstructed. The constraints are

(i) there must be one isothermal process,

(ii) there must be one isentropic process,

(iii)the maximum and minimum cycle pressuresand the clearance volume are fixed, and

(iv) polytropic processes are not allowed. Then thenumber of possible cycles are

(a) 1

(b) 2

(c) 3

(d) 4


9

55. Nitrogen at an init ial state of 10 bar, 1 m3 and300 K is expanded isothermally to a final volume

of 2 m3. The p-v-T relat ion is pa

FHG

IKJ

2 RT ,

where a > 0. The final pressure

(a) wil l be sl ight ly less than 5 bar

(b) wil l be sl ight ly more than 5 bar

(c) wil l be exact ly 5 bar

(d) cannot be ascer tained in the absence of thevalue of a.

56. Heat flows through a composite slab, as shownbelow. The depth of the slab is 1 m. The k valuesare in W/m.K. the overal l thermal resistance inK/W is

0.5 m 0.25 m

k = 0.02 k = 0.10 0.5 m

1m

k = 0.04

q

(a) 17.2 (b) 21.9

(c) 28.6 (d) 39.2

57. A small copper bal l of 5 mm diameter at 500 K isdropped into an oi l bath whose temperature is300 K . The thermal conduct ivity of copper is400 W/m.K, i ts density 9000 kg/m3 and its specificheat 385 J/kg.K. I f the heat t ransfer coefficient is250 W/m2.K and lumped analysis is assumed tobe val id, the rate of fal l of the temperature of theball at the beginning of cooling wil l be, in K /s,

(a) 8.7

(b) 13.9

(c) 17.3

(d) 27.7

58. A solid cyl inder (sur face 2) is located at the centreof a hollow sphere (sur face 1). The diameter ofthe spher e is 1 m, whi le the cyl inder has adiameter and length of 0.5 m each. The radiationconfigurat ion factor F11 is

(a) 0.375

(b) 0.625

(c) 0.75

(d) 1

59. Hot oi l is cooled from 80 to 50 C in an oi l coolerwhich uses air as the coolant. The air temperaturer ises from 30 to 40 C. The designer uses a LMTDvalue of 26 C. The type of heat exchanger is

(a) paral lel flow

(b) double pipe

(c) counter flow

(d) cross flow

60. The vapour compression refr igerat ion cycle isrepresented as shown in the figure below, withstate 1 being the exi t of the evapor ator. Thecoordinate system used in this figure is

4 1

2

3

(a) p-h (b) T-s

(c) p-s (d) T-h

61. A vapour absorption refr igeration system is a heatpump with three thermal reservoirs as shown inthe figur e. A r efr iger at ion effect of 100 W isrequired at 250 K when the heat source availableis at 400 K. Heat reject ion occurs at 300 K. Theminimum value of heat required (in W) is

(a) 167 (b) 100

(c) 80 (d) 20

62. Various psychrometr ic processes are shown in thefigure below.

45

1

2

W (kg/kg)

T ( C)o

3O


10

Pr ocess i n Name of t he pr ocessFigur e

P. 0-1 1. Chemical dehumidificat ion

Q. 0-2 2. Sensible heat ing

R. 0-3 3. Cooling and dehumidificat ion

S. 0-4 4. Humidificat ion with steaminject ion

T. 0-5 5. Humidification with waterinject ion

The matching pairs are

(a) P-1, Q-2, R-3, S-4, T-5,

(b) P-2, Q-1, R-3, S-5, T-4

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

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

63. I n the velocity diagram shown below, u = bladevel oci t y, C = absol u t e f l u i d vel oci t y andw = relat ive velocity of fluid and the subscr ipts1 and 2 refer to inlet and out let .

C1 w2

w1

C2

u1 = u2

(a) an impulse turbine

(b) a react ion turbine

(c) a centr i fugal compressor

(d) an axial flow compressor

64. A leaf is caught in a whir lpool. At a given instant ,the leaf is at a distance of 120 m from the centreof the whir lpool. The whir lpool can be descr ibedby the fol lowing velocity dist r ibut ion;

Vr = –60 10

2 r

3FHG

IKJ

m/s and V0 = 300 10

2 r

3

m/s,

where r (in metres) is the distance from the centreof the whir lpool. What wil l be the distance of theleaf from the centre when it has moved throughhalf a revolut ion?

(a) 48 m

(b) 64 m

(c) 120 m

(d) 142 m

65. A mould has a downsprue whose length is 20 cmand the cross sect ional area at the base of thedownsprue is 1 cm2. The downspr ue feeds ahor izontal runner leading into the mould cavityof volume 1000 cm3. The t ime required to fi l l themould cavity wil l be

(a) 4.05 s

(b) 5.05 s

(c) 6.05 s

(d) 7.25 s

66. A 2 mm thick metal sheet is to be bent at anangle of one radian with a bend radius of 100 mm.I f the stretch factor is 0.5, the bend al lowance is

1 radian

2 mm

(a) 99 mm (b) 100 mm

(c) 101 mm (d) 102 mm

67. Spot welding of two 1 mm thick sheets of steel(density = 8000 kg/m3) is car r ied out successful lyby passing a cer tain amount of cur r ent for0.1 second through the electrodes. The resultantweld nugget formed is 5 mm in diameter and1.5 mm thick. I f the latent heat of fusion of steelis 1400 kJ/kg and the effect ive resistance in thewelding operat ion in 200 , the cur rent passingthrough the electrodes is approximately

(a) 1480 A

(b) 3300 A

(c) 4060 A

(d) 9400 A

68. A 600 mm 30 mm flat sur face of a plate is to befinish machined on a shaper. The plate has beenfixed with the 600 mm side along the tool t raveldirect ion. I f the tool over -t ravel at each end ofthe plate is 20 mm, average cut t ing speed is8m/min, feed rate is 0.3 mm/stroke and the rat ioof return t ime to cut t ing t ime of the tool is 1:2,the t ime required for machining wil l be

(a) 8 minutes

(b) 12 minutes

(c) 16 minutes

(d) 20 minutes


11

69. The tool of an NC machine has to move along acircular arc from (5,5) to (10,10) while per formingan operation. The centre of the arc is at (10,5).Which one of the following NC tool path commandsper forms the above mentioned operation?

(a) N010 G02 X10 Y10 X5 Y5 R5

(b) N010 G03 X10 Y10 X5 Y5 R5

(c) N010 G01 X5 Y5 X10 Y10 R5

(d) N010 G02 X5 Y5 X10 Y10 R5

70. A component can be produced by any of the fourprocesses I , I I , I I I and IV. Process I has a fixedcost of Rs. 20 and var iable cost of Rs. 3 per piece.Process I I has a fixed cost Rs. 50 and var iablecost of Re. 1 per piece. Process I I I has a fixed costof Rs. 40 and var iable cost of Rs. 2 per piece.Process IV has a fixed cost of Rs. 10 and var iablecost of Rs. 4 per piece. I f the company wishes topr oduce 100 pieces of t he component , fr omeconomic point of view it should choose

(a) Process I

(b) Process I I

(c) Process I I I

(d) Process IV

71. A welding operation is t ime-studied during whichan operator was pace-rated as 120%. The operatortook, on an average, 8 minutes for producing theweld-joint. I f a total of 10% allowances are allowedfor t h i s oper at i on , t he expect ed st andar dproduct ion rate of the weld-joint

(in units per 8 hour day) is

(a) 45 (b) 50

(c) 55 (d) 60

72. The dist r ibut ion of lead t ime demand for an i temis as fol lows:

Lead t ime demand Probabili ty

80 0.20

100 0.25

120 0.30

140 0.25

The reorder level is 1.25 t imes the expected valueof the lead t ime demand. The service level is

(a) 25% (b) 50%

(c) 75% (d) 100%

73. A project has six act ivit ies (A to F) with respectiveact ivity dur at ions 7,5,6,6,8,4 days. The networkhas t hr ee paths A-B, C-D and E-F. Al l t heact ivit ies can be crashed with the same crashcost per day. The number of act ivit ies that needto be crashed to reduce the project durat ion by1 day is

(a) 1

(b) 2

(c) 3

(d) 6

74. A company has two factor ies S1, S2 and twowarehouses D1, D2. The supplies from S1 and S2are 50 and 40 units respect ively. Warehouse D1requires a minimum of 20 units and a maximumof 40 units. Warehouse D2 requires a minimumof 20 units and, over and above, i t can take asmuch as can be suppl i ed. A bal ancedtranspor tat ion problem is to be formulated forthe above situat ion. The number of supply points,the number of demand points, and the total supply(or total demand) in the balanced t ranspor tat ionproblem respect ively are

(a) 2, 4, 90

(b) 2, 4, 110

(c) 3, 4, 90

(d) 3, 4, 110

75. Two tools P and Q have signatures 5-5-6-6-8-30-0 and 5-5-7-7-8-15-0 (bot h ASA)respect ively. They are used to turn componentsunder the same machining conditions. I f hP andhQ denote the peak-to-val ley heights of sur facesproduced by the tools P and Q, the rat io hP/hQ

wil l be

(a) tan8 cot15tan8 cot30

(b)tan15 cot8tan30 cot8

(c)tan cottan cot

15 730 7

(d)tan7 cot15tan7 cot30


12

Common Data Quest i ons

Common Dat a for Quest i ons 76, 77, 78:

An i nst ant aneous con f i gu r at i on of a four -barmechanism, whose plane is hor izontal, is shown inthe figure below. At this instant , the angular velocityand angular accelerat ion of l ink O2 A are = 8 rad/sand = 0, respect ively, and the dr iving torque () iszero. The l ink O2 A is balanced so that i ts centre ofmass fal ls at O2.

90o 90o

60 mm

A

B

O2 O4

160 mm

240 mm

76. Which kind of 4-bar mechanism is O2ABO4 ?

(a) Double-crank mechanism

(b) Crank-rocker mechanism

(c) Double-rocker mechanism

(d) Paral lelogram mechanism

77. At the instant considered, what is the magnitudeof the angular velocity of Q4B?

(a) 1 rad/s (b) 3 rad/s

(c) 8 rad/s (d)643

rad/s

78. At the same instant , if the component of the forceat joint A along AB is 30 N, then the magnitudeof the joint ract ion at O2

(a) is zero

(b) is 30 N

(c) is 78 N

(d) cannot be determined from the given data

Common Dat a for Quest i ons 79, 80:

I n two air standard cycles – one operat ing on theOt to and t he other on t he Br ayton cycle– ai r isisentropical ly compressed from 300 to 450 K . Heatis added to raise the temperature to 600 K in theOtto cycle and to 550 K in the Brayton cycle.

79. I f 0 and B are the efficiencies of the Otto andBrayton cycles, then

(a) 0 = 0.25, B = 0.18

(b) 0 = B = 0.33

(c) 0 = 0.5, B = 0.45

(d) it is not possible to calculate the efficiencies unlessthe temperature after the expansion is given

80. I f W0 and WB are work outputs per unit mass, then

(a) W0 > WB

(b) W0 < WB

(c) W0 = WB

(d) i t is not possible to calculate the work outputsunless the temperature after expansion is given

L ink ed Answer Quest ions: Q,81a t o Q.85b car r yt w o mar k s each .

Statement for Linked Answer Questions 81a and 81b:

The complete solut ion of the ordinary different ial

equat ion d y

dxp

dydx

qy2

2 = 0 is y = c1 e– x + c2e

– 3x

81a. Then, p and q are

(a) p = 3, q = 3 (b) p = 3, q = 4

(c) p = 4, q = 3 (d) p = 4, q = 4

81b. Which of t he fol lowing is a solu t ion of the

differential equat ion d y

dxp

dydx

q y2

2 1 0 b g ?

(a) e– 3x (b) xe– x

(c) xe– 2x (d) x2e– 2x

St at emen t for L i nk ed Answ er Quest i ons 82aand 82 b :

A band brake consists of a lever at tached to one endof the band. The other end of the band is fixed to theground. The wheel has a radius of 200 mm and thewrap angle of the band is 270°. The braking forceapplied to the lever is l imited to 100 N, and thecoefficient of fr ict ion between the band and the wheelis 0.5. No other informat ion is given.

100 N

200 mm

1m 1m


13

82a. The maximum tension that can be generated inthe band dur ing braking is

(a) 1200 N

(b) 2110 N

(c) 3224 N

(d) 4420 N

82b. The max i mum wheel t or que t hat can becompletely braked is

(a) 200 N.m

(b) 382 N.m

(c) 604 N.m

(d) 844 N.m

St at ement for L i nk ed Answ er Quest i ons 83a and83b:

Consider a l inear pr ogr amming problem wi th twovar iables and two constraints. The object ive funct ionis: Maximize X1 + X2. The corner points of the feasibleregion are (0,0), (0,2) (2,0) and (4/3,4/3)

83a. I f an addit ional constraint X1 + X2 5 is added,the opt imal solut ion is

(a)53

53

,FHG

IKJ

(b)43

43

,FHG

IKJ

(c)52

52

,FHG

IKJ

(d) (5, 0)

83b. Let Y1 and Y2 be the decision var iables of thedual and v1 and v2 be the slack var iables of thedual of the given l inear programming problem.The opt imum dual var iables are

(a) Y1 and Y2

(b) Y1 and v1

(c) Y1 and v2

(d) v1 and v2

St at ement for L i nk ed Answ er Quest i ons 84a and84b :

The fol lowing table of proper ties was pr inted out forsaturated liquid and saturated vapour of ammonia. Thet it les for only the first two columns are available. Al lthat we know is that the other columns (columns 3 to8) contain data on specific proper ties, namely, internalenergy (kJ/kg), enthalpy (kJ/kg) and entropy (kJ/kg. K).

t(C) p (kPa)

-20 190.2 88.76 0.3657 89.05 5.6155 1299.5 1418.0

0 429.6 179.69 0.7114 180.36 5.3309 1318.0 1442.2

20 857.5 272.89 1.0408 274.30 5.0860 1332.2 1460.2

40 1554.9 368.74 1.3574 371.43 4.8662 1341.0 1470.2

84a. The specific enthalpy data are in columns

(a) 3 and 7 (b) 3 and 8

(c) 5 and 7 (d) 5 and 8

84b. When saturated l iquid at 40 C is thr ot t ledto – 20 C, the quali ty at exit wil l be

(a) 0.189 (b) 0.212

(c) 0.231 (d) 0.788

St at ement for L i nk ed Answ er Quest i ons 85a and85b:

An un-insulated air condit ioning duct of rectangularcross sect ion 1m × 0.5 m, car rying air at 20C with avelocity of 10 m/s, is exposed to an ambient of 30°C.Neglect the effect of duct construct ion mater ial. Forair n the range of 20-30C, data are as fol lows: thermalconduct ivi t y = 0.025 W/m.K : velocit y = 18 Pa.s;Pr andt l number = 0.73; density = 1.2 kg/m3. Thelaminar flow Nussch number is 3.4 for constant wallt emper at ur e condi t ions and, for t ur bu lent f low,Nu = 0.023 Re0.8Pr0.8

85a. The Reynolds number for the flow is

(a) 444

(b) 890

(c) 4.44 105

(d) 5.33 105

85b. The heat t ransfer per metre length of the duct ,in watts, is

(a) 3.8 (b) 5.3

(c) 89 (d) 769

n n

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