GATE Mechanical Engineering

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Dura Lion: Three HOtlfS Maxi111tun Ma rks: 100

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4. This Question Book let contains 16 pages incl udi ng bhtnk pa ges for rough work. After you are penniued 10 open 1he seal , please check all pages and report discrepancies, i f any, 10 t he invigilator.

5. There are a total of 65 questions carrying 100 marks.Al l these

)

Q.1- Q.25 carry one n1ark each.

Q.1 1 In abrasi ve jet machini ng.as the discance between t he nozzle tip and the work surface increases.the

111a.leriaJ re1ll0\1al rnle (A) increases conti nuously. (B) decreases conti nuousl y. (C) decreases, becomes stable and then .increases. (0) increases, becomes stable and then decreases.

Q.2 Match the following meml forming processes with thei.r associmed stresses in the workpiece.

Metal rorming process I. Coining

4. Deep Drawing

(AJ 1-S, 2-P, 3-Q. 4-R (Cl 1-P, 2-Q, 3-S, 4-R

Type or stress P. Tensile

Q. Shear

R. Tensile and compressive

S. Compressi ve

(B) 1-S.2-P.3-R. 4-Q (0) 1 -P, 2-R, 3-Q, 4-S

-i().040

Q.3 In an interchangeable assembly, shafts of size 25.0oo 0010 mm mare with holes or si1.c ..o.o:.to

25.000'0 010 rrun. The maximum i nterle' rence (in microns) in the assembly is

(A) 40 (B) 30 (C) 20 (0) 10

Q.4 Duri ng norm.. lizing processof steel, the speci men is heated

(A) between the upper and lower critical temperature and cooled i n sti ll air. (B) above the upper critical temperntu re and cooled in furnace. (C) above the upper crit ical temperature and cooled in still a ir. (0) between the upper and lower cri tical temperatureand cooled in furnace.

Q.5 Oil flows t hrough a 200 mm diameter hori zontal cast iron pi pe (frict i on factor. f = 0.0225) of

length 500 m. The volumetric flow rate i s 0.2 mJ/s. The head loss (in 111) due 10 friction is (assume g = 9.81 mls2

(A) 1 1 6. 1 8 (B) 0.1 1 6 (C) 18.22 (0) 232.36

Q.6 For an opaque surface. the absorptivity (a). transmissivity ('r)and rellectivity (p) are related by Lhe equm ion:

(A) a +p=r (B) p +a+r =O (C) a+p = I (D) a+p =O

Q.7 Steam enters an adi abatic turbi ne operating at steady state with an enthalpy of 3251.0 kJ/kg and leaves as a satu rated mixture at 15 kPa with qual ity (dryness fraction) 0.9.The emhalpies of the saturated liqu id and vapor at 15 kPa are he= 225.94 Id/kg and h8 = 2598.3 Id/kg respectively. The mass llow rate of steam is J O kj;/s. Kinet ic and potential energy changes are negligible. The power output of the turbine in MW is

(A) 6.5 (Bl 8.9 (C) 9. 1 (0) 27.0

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Q.8 The following are the data f9r two crossed hel ical gears used for speed reduct ion: Gear l :Pitch circle diameter in the plane of rotation 80 mm and hel ix angle 30" Gear JI : Pitch circle diameter in the plane of rotation 120 mm and helix angle 22.5 I f the input speed is 1440 rpm, the out put speed in rpm is

(A) 12'

Q.10 A thin walled spherical shell is subjected to an imernal pressure. I f the radius of the shell is increased by I % and the thickness is reduced by I %, with the internal pressu1c remai ning the same, the percentage change in the circumferential (hoop) stress is

(A) 0 (B) I (C) J.08 (0) 2.02

Q.I I The area enclosed between the st raight line y = x and the parabola y = l in the x-y plane is (A) 1/6 (B) 1/4 (C) 1/3 (0) 1/2

Q. I 2 Consider the fu nction f (x) =lxl in the interval -I < x < I. Al the point x = 0. f(x) is

(A) conti nuous and differentiable. (B) non-continuous and differentiable. (C) continuous and non-differentiable. (0) nei ther continuous nor di fferentiable.

Q.13 Which one of the following is NOT a decision taken during the aggregate production planni ng

stage?

(A) Schedul i ng of machines (B) Amount of Jabour 10 be com mitted (C) Rare at which production should happen (0) I nventory to be carried forward

Q.14 .Im(1-cosx ) .IS " ;-0 x2

(A) 1/4 (B) 1/2 (C) I (0)2 Q.15 A CNC venical mi l ling machine has 10 cm a straight slot of 10 mm wi dth and 2 mm depth by a

cutter of 10 mm diameter between points (0, 0) and (100, 100) on the XY plane (dimensions in mm). TI1e feed rate used for mi lling is 50 mm/min. Mill ing t ime for the slor (in seconds) is

(A) 120 (B) 170 (C) 1 80 (0) 240

Q.16 A solid cyl i nder of diameter I 00 mm and height 50 mm i s forged between two fricti onless fl at dies to a height of 25 mm. The percemagecha nge in d iameter is

(A) 0 (B) 2.07 (C) 20.7 (0) 41.4

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Q.17 The velocicy triangles m the inlet and exit of the rotor of a turbomachine arc shown. V denoces the

absolute velocicy of the fluid. W dcnoces the relative velocicy of the fluid and U denotes the blade velocity. Subsc1ipts Iand 2 refer to inlet and outlet respect ively. If V2 = W1 and V1 = w,. then the degree of reaction is

(A) 0 (B) I (C) 0 5 (D) 0.25

Q.18 \Vhich one of the fol lowing configurations has the highest fi n effect iveness?

(A) Thin. closely spaced fins (C) Thick, wideI)'spaced fins

(B)Thin, widely spaced fins (D)Thick, closely spaced fins

Q.19 An ideal gas of mass m

is 1,

t - J

Q.21 A ci rcul ar solid disc of uniform thickness 20 n n. radi us 200 m11 and mass 20 kg. is used as a nywheel. If it rotates a1 600 rpm, the kinetic energy of 1he flywheel , in J oules is

(A) 395 (C) 1580

(B) 790 (0) 3160

Q.22 A cantilever beam of length L is subjected 10 a moment M at the free end. The moment of inertia of ie beam cross section about the neutral axis is I and the Young's modulus is E.The magni tude of the maximum detlccrion is

ML' (A) 2El

. , (B) ML"

ET . ,

(C) 2ML- EI

. , (O) 4ML"

EI

Q.23 For a long slender column of uni form cross sect ion, the ratio of critical buckling load for the case wi th both ends clamped to the case wit h both ends hinged is

(A) I (B) 2 (C) 4 (0) 8

Q.24 At x = 0, the function f (x)= x3 + I has

(A) a maximum val ue (C) a si ngularity

(B) a minimum value (0)a 1>oi n1 of inflection

Q.25 For the spherical surface x- + y+ z = I, the unn'

( JIi , .JI2,0 ) g. 1cn by outward nonnaI vector m the point

(A) I I -i + -j .J2 .J2

. (B) -I . -I . .J2 .J2

I I I (0)-i +-j+ -k (CJ k J3 J3 J3

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Q.26 - Q.55 carry l\VO marks each.

Q.26 1'he homogeneous state of stress for a metal part u ndergoi ng pl ast ic deformation is

10 5 0 T = 5 20 0

0 0 -10 whe1e U1e stress component values are in MPa. Using von Mi ses yield cri terion . the value of estimated shear yield stress, in MPa is

(A) 9.50 (B) 16.07 (C) 28.52 {D) 49.41

Q.27 Details penain i ng lO an orthogonal metal cuu ing process are given below.

Chip thickne ss ratio 0.4 Undeformed thickness 0.6 mm Rake angle + I 0 Cutti ng speed 2.5 m/S Mean thickness of pri mary shear zone 25 microns

1'he shear strain rate in s 1 during the process is (A) 0. J 78Jx l 05 (B) 0.7754x 105 {C) J.0104x J 05 (D) 4.397x l05

Q.28 Tn a si ngle pass drill ing operation , a through hole of 15 mm diameter is to be dri lled i n a steel plate

of 50 mm thickness. Dri ll spindle speed is 500 rpm. feed is 0.2 mm/rev and drill poi ni angle i s I 18.Assuming 2 mm clearance at approach and exi t, 1c total dri ll time (in seconds) is

(A) 35.1 (B) 32.4 (C) 31.2 {D) 30. I

Q.29 Consider two infinitely long thin concentric ru bes of ci rcular cross sect ion as shown i n the figure. If D1 and D2 arc the diameters of the inner and outer tubes respecti vely, then che view factor F22 i s given by

- 1-

2

(B) zero

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Q.30 An i ncompl'essible fluid flows over a flat plate with zero p1essure gradient. The boundary layer thiclme s is I mm at a location where t he Reynolds n umber is 1 000. If the veloci ty of the flu id alone is increased by a factor of 4, then the boundary layel' thickness m the same location, i n nm1 wi ll be

(A) 4 (B) 2 (C) 0.5 (0) 0.25

Q.31 A room contains 35 kg of dry air and 0.5 kg of water vapor. 111e total pressure and temperature of ai r in the room are 100 kPa and 25C l'espectively.Given that the saturation pressu re for water at 25C is 3.17 kPa , the relati ve hui11idity of t he ail' in the room is

(A) 67% (B) 55% (C) 83% (D) 71 %

Q.32 A fi llet welded joint is subjected to transverse loadi ng F as shown in the figure. Both legs or the fillets arc of 1 0 mm size and the wel d length is 30 mm. I f the allowable shear st ress of the weld is 94 M Pa , consi dering the min imum throat area of t he weld , the maximum allowable tra11sverse load in kN is

F o rf

(B) f (t) =e- sin t (0) f (t)= 1-e-t

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Q.36 For the matr ix A = [ ]- ONE of the normalized eigen vectors is given as

I 3 l 2

(A) Jj

(B) ../2. (C) JIO -1 -I (D) JS

2 2 ../2. JIO JS

Q.37 Calculate the punch size i n mm,for a circular blanking ope111tion for which detai ls are given below.

Size of the bl ank 25 mm

Thickness of the sheet 2 mm

Radial clearance between pu nch and die 0.06 mm

Die allowance 0.05 mm

(A) 24.83 (B) 24.89 (C) 25.01 (D) 25. 17

Q.38 In a single pass rolling process using 410 mm diameter steel rollers, a stri p of width 140 mm and thickness 8 mm undergoes 10% reduction of thickness. The angle of bite i n radia ns is (A) 0.006 (B) 0.03 1 (C) 0.062 (D) 0.600

Q.39 In a DC arc welding operntion. the voltage-arc lengtl1 characterist ic was obtained as V: c = 20+51 where the arc length I wa. varied between 5 mm and 7 nun. Hecc V,,.c denotes the arc voltage in Volts. The arc current was varied from 400 A to 500 A Assumi ng linear power source chioracteristic, the open circui1 voltage and the short circuil Curren! for the weldi ng oper,ltion are

(A) 45 V,450 A (B) 75 V,750 A (C) 95 V.950 A (D) 150 V, 1500 A Q.40 A large tank with a nozzle anached comains three immiscible.inviscid fluids as shown . Assuming

1hat 1he changes in h 1, h2 and h3 are negligible, 1he insianraneous discharge veloci1y is

(A)

(C)

(D)

hi P2

h, p,

h, Pl ......._ ---------,.,...-.. --

2g(p,h, + P 2 h2 + p3h,)

p, +p,+p 3

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Conunon Data Questions

Common Data for Questions 48 and 49:

Two srccl t russ members, AC and BC, each havi ng cross sccrional area of 1 00 mm'. are subjected ro a horizonral force F as shown i n figure. Al l the jo i nts are hinged.

?t=C; -F

Q.48 If F = I kN, rhe magnitude of the vertical reaction force developed at the poi nt B i n kN is

(A) 0.63 (B) 0.32 (C) 1.26 (D) 1.46

Q.49 The maximu m force F in kN that can be applied at C such that the axial stress in any of the rruss members DOES NOT exceed J OO MPa i s

(A) 8. 17 (B) I 1.15 (C) 14.14 (0) 22.30

Common Oata (or Questions 50 and 51:

A refrigerator operates between 120 kPa and 800 kPa in an ideal vapor compression cycle with R- 1 34a as the rcf1igeram. The refrigerant enters the c.ompressor as saturated vapor and leaves the condenser as samrJtcd li quid. The mass now rate of the refrigeram is 0.2 kg/s.Propenies for R-134a are as follows:

Saturated R-134a

P (kPa) T (C) hr (kJ/kg) 11 (kl/kg) Sr (kJ/kg.K) ss (kl/kg.K) 1 20 -22.32 ?_?....,.-) 237 0.093 0.95 800 31.31 95.5 267.3 0.354 0.918

Superheated R-J 34a

P (kPa)

800

T (C)

40

h (kl/kg)

276.45

s (kJ/kg.K)

0.95

Q.50 The rate at which heat is extracted, in kJ/s from the refrigernted space is (A) 28.3 (B) 42.9 (C) 34.4 (D) 14.6

Q.51 The power required for the compressor in kW is

(A) 5.94 (B) 1.83 (C) 7.9 (0) 39.5

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Linked Answer Questions

Statcntent for Linked Answer Questions52 and 53:

Air enters an adiabatic nozzle at 300 kPa, 500 K with a veloci ty of 10 mis. IL leaves the nozzle at 100 kPa with a velocity of 1 80 mis.The in let area is 80 cm2 TI1e specific heat of air C ,is I 008J /kg.K.

Q."? The exi t tempera ture of the a ir i s (A) 5 16 K (B) 532 K (C) 484 K (D)468 K

Q.53 The exi t area of the nozzle in cm2 is

(A) 90.I (B) 56.3 (C) 4.4 (D) 12.9

Statement for Linked Answer Questions 54 and 55:

For a particular project, eight activities are to be carried out. Thei r relationships witb other acti vities and expected durations are mentioned in the wbl e below.

Activity Predecessors

b a

Duration (days) 3 4

c d e f g h

Q.54 The critical path for the project is

(A) a -b -e-g -h (C) a -d - f -h

a

b d

c.e f'

General Aptitude (GA) Questions

Q.56-Q. 60 carry one 1nark each.

Q.56 Choose the most appropriate al1ernative from 1he options given below 10 complete Lhe followi ng se11re11ce:

Surcsh's dog is the one----was hurt in the stampede.

(A) thal (B) which (C) who (D) whom

Q.57 The cost function for a product in a fi rm is given by Sq', where q is the amount of production.The firm can sell the product at a marke1 price of {SO per unit. The number of un its to be produced by 1he firm such that the profit is maximi zed is

(A) 5 (B) 10 (C) 15 (D) 25

Q.58 Choose the most appropriate alternative from the options given below to complete the followi ng sente11ce:

Despite several the n1issio11 succeeded in its at1empt to resolve the conflict.

(A) attempts (B) setbacks (C) meetings (D) delegations

Q.59 Which one of the following opt ions is the closest in meaning to the word given bel ow?

Mitigate

(A) Dimi nish (B) Divu lge (C) Dedicate (D) Denote

Q.60 Choose the grammat ically INCORRECT sentence: (A) They gave us the money back less the service charges of Three Hund1ed rupees. (B) This counby's expenditure is not less tlian Uiat of Bangladesh. (C) ll1e commiuee initially asked for a fund ing of Fifty Lakh rupees. but later se11led for a lesser

Sllnl. (D) TI1i s country 's expendi rure on educational refonns is very less.

Q.61 - Q.65 carry tvo marks each.

Q.61 1 Given t he sequence of terms, AO CG FK J P.the next term is

(A) OV (B) OW (C) PV (D) PW

Q.62 Wanted Temporary, Part-time persons for the post of Field Interviewer to cond uct personal interviews to collect and collate economic data. Rec1uireme11ts: High Schoolpass, must be available for Day, Evening and Saturday work. Tra nsportation paid, expenses reimbursed.

Which one of the followi ng is the best inference from the above advertisement?

(A) Gender-discrimi nawry (B) Xenophobic (C) Not designed to make the post a11ractive (D) Not gender-d iscrimi natory

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Q.63 A poli tical party orders an arch for the cnuancc to Lhe ground in which the annual convent ion is being held. The profile of the arch follows the equation y = 2x -0.Ix2 where y is the height of the arch i n meters. The maximum possi ble height of the arch is

(A) 8 meters (B) 10 meters (C) I2 meters (D) 14 meters

Q.64 An automobi le plan t contracted to buy shock absorbers from two suppliers X and Y. X supplies 60% and Y suppl ies 40% of the shock absorbers.All shock absorbers are subjecte d co a quality test. '111e ones cbat pass the quali ty test arc considered reliable. Of X 's shock absorbers, 96% are reliable. Of Y 's shock absorbers. 72% arc rliablc.

The probabili ty thac a randomly chosen shock absorber, which is found to be reliable. is made by Y is

(A) 0.288 (B) 0.334 (C) 0.667 (D) 0.720

Q.65 Which of the following assert ions are CORRECT?

P: Addi ng 7 to each entry i n a lisc adds 7 to the mean of Lhe li st Q: Adding 7 to each entry in a list adds 7 to the standard deviation of the list R: Doubl ing each entry i n a l ist doubles I.he mean of the list S: Doubling each entry in a l i st leaves the standard deviation of the list unchanged

(A) P.Q (B) Q, R (C) P, R (D) R. S

END OF THE QUESTION PAPER

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Q.8 The following are the data f9r two crossed helical gears used for speed reduction: Gear l :Pitch circle diameter in the plane of rotation 80 mm and hel ix angle 30" Gear JI : Pitch circle diameter in the plane of rotation 120 mm and helix angle 22.5Q.9 A solid disc of radius r rolls without slipping on a horizontal floor with angular velocity w and angu lar acceleration cz. The mag!litud e of the acceleration of the point of conract on the disc isQ.10 A thin walled spherical shell is subjected to an imernal pressure. I f the radius of the shell is increased by I % and the thickness is reduced by I %, with the internal pressu1 c remai ning the same, the percentage change in the circumferential ...Q.I I The area enclosed between the straight line y = x and the parabola y = l in the x-y plane is(A) continuous and differentiable.(A) Schedul i ng of machines (B) Amount of Jabour 10 be com mittedQ.15 A CNC venical milling machine has 10 cm a straight slot of 10 mm width and 2 mm depth by a cutter of 10 mm diameter between points (0, 0) and (100, 100) on the XY plane (dimensions in mm).(A) 2ElET(C) 2ML

.J2 .J2.

.J2 .J2I I I(CJ k

Q.26 1'he homogeneous state of stress for a metal part u ndergoing plastic deformation isQ.27 Details penain ing lO an orthogonal metal cuu ing process are given below.Q.28 Tn a si ngle pass drilling operation , a through hole of 15 mm diameter is to be dri lled i n a steel plate of 50 mm thickness. Dri ll spindle speed is 500 rpm. feed is 0.2 mm/rev and drill poini angle i s I 18 .Assuming 2 mm clearance at approa...Q.29 Consider two infinitely long thin concentric ru bes of ci rcular cross sect ion as shown i n the figure. If D1 and D2 arc the diameters of the inner and outer tubes respecti vely, then che view factor F22 i s given by2

Q.30 An incompl'essible fluid flows over a flat plate with zero p1 essure gradient. The boundary layer thiclme s is I mm at a location where t he Reynolds n umber is 1 000. If the velocity of the flu id alone is increased by a factor of 4, then the bo...Q.31 A room contains 35 kg of dry air and 0.5 kg of water vapor. 111e total pressure and temperature of air in the room are 100 kPa and 25 C l'espectively.Given that the saturation pressu re for water at 25 C is 3.17 kPa , the relati ve hui11idity of ...Q.32 A fi llet welded joint is subjected to transverse loading F as shown in the figure. Both legs or the fillets arc of 10 mm size and the weld length is 30 mm. I f the allowable shear stress of the weld is 94 MPa , consi dering the min imum throat a...Q.33 A concentr-dtcd mass 111 is attached at the cenrrc of a 1 od of length 2L as shown in the figure. The rod is kept i n a horizomal equilibri um position by a spring of stiffness k. For very small amplitude of vibration. neglecting the weights of t...Q.34 111e state of stress at a point u nder plane stress condition is111e radius of the !\llohr's circle representing the given state of stress in MPa isQ.35 The i nverse Laplace transform of the function F(s) = 1 is given by-1 -I2(l-2v)(l-2v). .......

Conunon Data QuestionsCommon Data for Questions 48 and 49:Common Oata (or Questions 50 and 51:Saturated R-134aT ( C)0.95

Linked Answer Questions3b d6

General Aptitude (GA) QuestionsQ.61 - Q.65 carry tvo marks each.Space for Rough Work

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