gate – 2015 - career launchermedia.careerlauncher.com/gate-exams/gate actual paper-...

Q. No. 1 – 5 Car r y One M ar k Each1. What is the adverb for the given word below?

Misogynous(a) Misogynousness (b) Misogynity

(c) Misogynously (d) Misogynous2. Ram and Ramesh appeared in an interview for

two vacancies in the same depar tment . Theprobabil i ty of Ram’s select ion is 1/6 and that ofRamesh is 1/8. What is the probabil i ty that onlyone of them wil l be selected?

(a)4748

(b) 14

(c) 1348

(d) 3548

3. Choose the appropr iate word/phrase, out of thefour options given below, to complete the followingsentence:Dhoni , as wel l as the other team members ofIndian team, _____ present on the occasion.(a) were (b) was(c) has (d) have

4. An electr ic bus has onboard instr uments thatrepor t the total electr ici ty consumed since thestar t of the t r ip as wel l as the total distancecovered. During a single day of operation, the bustravels on stretches M , N , O and P, in that order.The cumulat ive distances t r avel led and thecor responding electr icity consumption are shownin the table below.

St retch Comulat ive Electr ici t ydistance(km) used (kWh)

M 20 12N 45 25O 75 45

P 100 57

The stretch where the electr ici ty consumpt ionper km is minimum is(a) M (b) N(c) O (d) P

5. Choose the word most similar in meaning to thegiven word:Awkward(a) Inept (b) Graceful(c) Suitable (d) Dreadful

6. I n t he fol lowing sentence cer tain par ts ar eunder l ined and marked P, Q and R. One of thepar ts may contain cer tain er ror or may not beacceptable in standard wr it ten communicat ion.Select the par t containing an er ror. Choose D asyour Answer : i f there is no er ror.

The student cor rected all t heerrorsP

that

theinst ructor markedQ

on the answer bookR

(a) P (b) Q

(c) R (d) No Er ror

7. Given below are two statements fol lowed by twoconclusions. Assuming these statements to betrue, decide which one logical ly fol lows.

Stat ement :I . Al l fi lm stars are playback singers.

I I . Al l fi lm directors are fi lm stars.Conclusions:I . Al l fi lm directors are playback singers.

I I . Some fi lm stars are fi lm directors.

(a) Only conclusion I fol lows

(b) Only conclusion I I fol lows

(c) Neither conclusion I nor I I fol lows

(d) Both conclusions I and I I fol low

8. Lament ing the gradual sidel ining of the ar ts inschool cur r icula, a group of prominent ar t istswrote to the Chief M inister last year, asking himto al locate more funds to suppor t ar ts educat ionin schools. However, no such increase has beenannounced in this year ’s Budget. The ar t istsexpressed their deep anguish at their request notbeing appr oved, but many of them r emainopt imist ic about funding in the future.Which of the statement(s) below is/are logical lyval i d and can be i n fer r ed f r om t he abovestatements?

i . The ar t ists expected funding for the ar ts toincrease this year.

i i . The Chief M inister was recept ive to the ideaof increasing funding for the ar ts.

GATE – 2015 M E : M ECH ANI CAL ENGI NEERI NG

Set - 1N o. of Quest i ons : 65 Maxi mum Mar k s : 100

GENERAL APTI TUDE

2 SOLVED PAPER – 2015 (SET - 1)

i ii . The Chief M inister is a prominent ar t ist .iv. Schools are giving less impor tance to ar ts

education nowadays.(a) i i i and iv (b) i and i v(c) i , i i and i v (d) i and i i i

9. I f a2 + b2 + c2 = 1, then ab + bc + ac l ies in theinterval

(a)2

1,3

(b)1

,12

(c)1

1,2

(d) [2,– 4]

10. A t iger is 50 leaps of i ts own behind a deer. Thet iger takes 5 leaps per minute to the deer ’s 4. I fthe t iger and the deer cover 8 metre and 5 metreper leap respectively, what distance in meters willthe t iger have a run before i t catches the deer?

MECHANI CAL ENGI NEERI NG

1. I f any two columns of a determinant P =

4 7 8

3 1 5

9 6 5ar e interchanged, which one of the fol lowingst at emen t s r egar di ng t he val ue of t hedeterminant is CORRECT?(a) Absolute value remains unchanged but sign

wil l change(b) Both absolute value and sign wil l change(c) Absolute value wil l change but sign wil l not

change

(d) Both absolute value and sign wil l remainunchanged

2. A wheel of radius r rol ls without sl ipping on ahor izontal sur face shown below. I f the velocity ofpoint P is 10 m/s in the hor izontal direct ion, themagnitude of velocity of point Q (in m/s) is ______.

3. Which one of the fol lowing types of st ress-strainrelat ionship best descr ibes the behavior of br i t t lemater ials, such as ceramics and thermosett ingplast ics, (= stress and = st rain)?

(a)

(b)

(c)

(d)

4. The funct ion of interpolator in a CNC machinecontrol ler is to(a) control spindle speed(b) coordinate feed rates of axes

(c) control tool rapid approach speed(d) per for m Miscel laneous (M) funct ions (tool

change, coolant control etc.)

5. Holes of diameter 0.0400.02025.0 mm are assembled

inter changeabl y wi t h t he pins of di amet er0.0050.00825.0 mm. The minimum clearance in the

assembly wil l be(a) 0.048 mm (b) 0.015 mm(c) 0.005 mm (d) 0.008 mm

6. Simpson’s 13

rule is used to integrate the function

f(x) = 23 95 5

x between x = 0 and x = 1 using the

least number of equal sub-intervals. The value ofthe integral is ___________

7. Consider ful ly developed flow in a circular pipewith negligible entrance length effects. Assumingthe mass flow rate, density and fr ict ion factor tobe constant , i f the length of the pipe is doubledand the diameter is halved, the head loss due tofr ict ion wil l increase by a factor of(a) 4 (b) 16(c) 32 (d) 64

SOLVED PAPER – 2015 (SET - 1) 3

8. For an ideal gas with constant values of specificheats, for calculat ion of the specific enthalpy,(a) i t is sufficient to know only the temperature(b) both temperature and pressure are required

to be known(c) both temperature and volume are required to

be known(d) both temperature and mass are required to

be known9. A Car not engine (CE-1) wor ks between two

temperature reservoirs A and B, where TA = 900K and TB = 500 K. A second Carnot engine (CE-2)works between temperature reservoirs B and C,where TC = 300 K. In each cycle of CE-1 andCE-2, al l the heat rejected by CE-1 to reservoir Bis used by CE-2. For one cycle of operat ion, i f thenet Q absorbed by CE-1 fr om r eser voi r A is150 MJ, the net heat rejected to reservoir C byCE-2 (in MJ) is _________.

10. A stream of moist air (mass flow rate = 10.1 kg/s)

with humidity rat io of kg

0.01kgdry air

mixes with

a second stream of superheated water vapourflowing at 0.1 kg/s. Assuming proper and uniformmixing with no condensat ion, the humidity rat io

of the final st ream kg

inkg dry air

is _________.

11. Consider a steel (Young's modulus E = 200 GPa)column hinged on both sides. I ts height is 1.0mand cross-sect ion is 10 mm 20 mm. The lowestEuler cr i t ical buckl ing load (in N) is ______.

12. Air enter s a diesel engine wi th a densi t y of1.0 kg/m3. The compression rat io is 21. At steadystate, the air intake is 30 10– 3 kg/s and the networ k out put i s 15 k W. The mean ef fect i vepressure (kPa) is _______.

13. M atch the fol lowing pr oducts wi th pr efer redmanufactur ing processes:

Product ProcessP Rails (1)Blow

molding

Q Enginecrankshaft (2)ExtrusionR Aluminium channels (3) Forging

S PET water bot t les (4)Roll ing

(a) P – 4, Q – 3, R – 1, S – 2

(b) P – 4, Q – 3, R – 2, S – 1

(c) P – 2, Q – 4, R – 3, S – 1

(d) P – 3, Q – 4, R – 2, S – 1

14. Under cer tain cut t ing condit ions, doubling the

cut t ing speed reduces the tool l i fe to t h

116

of

the or iginal. Taylor ’s tool li fe index(n) for this tool-workpiece combinat ion wil l be _______

15. Consider a sl ider crank mechanism with nonzeromasses and iner tia. A constant torque is appliedon the crank as shown in the figure. Which ofthe fol lowing plots best resembles var iat ion ofcrank angle, versus t ime

(a)

(b)

(c)

(d)


16. The value of 2

4

1 cos( )l im is

2x

xx

(a) 0 (b)12

(c)14

(d) undefined

17. Two identical trusses support a load of 100 N as shownin the figure. The length of each truss is 1.0 m, cross-sectional area is 200 mm2; Young's modulus E = 200GPa. The force in the truss AB (in N) is __________

18. Among t he four nor mal di st r i but i ons wi t hprobabi l i ty density funct ions as shown below,which one has the lowest var iance?

–1–2 0 1 2

IV

I I I

I I

I

(a) I (b) I I (c) I I I (d) IV19. Given two complex numbers Z1 = 5 ( 3)i and z2

=2

2 ,3

i the argument of 1

2

zz in degrees is

(a) 0 (b) 30 (c) 60 (d) 9020. The Blasius equat ion related to boundary layer

theory is a(a) third-order linear part ial differential equation(b) third-order nonlinear partial differential equation(c) second-order nonlinear ordinary different ial

equat ion

(d) thi rd-order nonlinear or dinary different ialequat ion

21. A swimmer can swim 10 km in 2 hours whenswimming along the flow of a river. While swimmingagainst the flow, she takes 5 hours for the samedistance. Her speed in still water (in km/h) is _______.

22. For flow of viscous fluid over a flat plate, i f thef lu id t emper at ur e is t he same as the plat etemperature, the thermal boundary layer is(a) thinner than the velocity boundary layer(b) thicker than the velocity boundary layer(c) of the same thickness as the velocity boundary

layer(d) not formed at al l

23. Whi ch one of t he fol l ow i ng i s t he mostconservat ive fat igue fai lure cr iter ion?(a) Soderberg (b) Modified Goodman(c) ASME Elliptic (d) Gerber

24. I n a l inear arc welding process, the heat inputper unit length is inversely propor t ional to(a) welding cur rent(b) welding voltage(c) welding speed

(d) duty cycle of the power source25. Consider a stepped shaft subjected to a twist ing

moment applied at B as shown in the figure.Assume shear modulus, G = 77 GPa. The angleof twist at C (in degrees) is _____

26. A 10 mm diameter electr ical conductor is coveredby an i nsu l at i on of 2 mm t h i ck ness. Theconduct ivity of the insulat ion is 0.08 W/m-K andthe convect ion coefficient at the insulat ion surfaceis 10 W/m2-K . Addit ion of fur ther insulat ion ofthe same mater ial wil l(a) increase heat loss cont inuously(b) decrease heat loss cont inuously(c) increase heat loss to a maximum and then

decrease heat loss

(d) decrease heat loss to a minimum and thenincrease heat loss

27. A machine element is subjected to the fol lowingbi-axial state of st ress; x = 80 MPa; y = 20 MPa;xy = 40MPa. I f the shear st rength of the mater ialis 100 MPa, the factor of safety as per Tresca’smaximum shear stress theory is(a) 1.0 (b) 2.0(c) 2.5 (d) 3.3

28. The probabil i ty of obtaining at least two ‘‘SIX’’ inthrowing a fair dice 4 t ime is(a) 425/432 (b) 19/144(c) 13/144 (d) 125/432

29. A hor izontal plate has been joined to a ver t icalpost using four r ivets arranged as shown in figure.The magnitude of the load on the worst loadedr ivet (in N) is ________


30. Temperature of nit rogen in a vessel of volume2 m3 is 288 K. A U-tube manometer connected tothe vessel shows a reading of 70 cm of mercury(level higher in the end open to atmosphere). Theuni ver sal gas const ant i s 8314 J /k mol -K ,atmospher ic pressure is 1.01325 bar, accelerat iondue to gravity is 9.81 m/s2 and density of mercuryis 13600 kg/m3. The mass of nit rogen (in kg) inthe vessel is _______.

31. The solidification t ime of a casting is proport ional

to

2V

,A

where V is the volume of the cast ing

and A is the total casting sur face area losing heat.Two cubes of same mater ial and size are castusing sand casting process. The top face of one ofthe cubes is completely insulated. The rat io ofthe sol idificat ion t ime for the cube with top faceinsulated to that of the other cube is

(a)2536

(b)3625

(c) 1 (d)65

32. Match the fol lowing pairs:

(P) V 0 (I ) I ncompressible cont inuity equat ion

(Q) .V 0 (I I ) Steady flow

DV(R) 0 (I I I ) I r rotat ional flow

DV

(S) 0 (IV) Zero accelerat ion of fluid part icle

t

t

Equ at i on Ph ysi cal I n t er pr et at i on

(a) P – IV, Q – I , R – I I , S – I I I (b) P – IV, Q – I I I , R – I , S – I I

(c) P – I I I , Q – I , R – IV, S – I I (d) P – I I I , Q – I , R – I I , S – IV

33. Steam enters a well insulated turbine and expands isentropically throughout. At an intermediate pressure,20 percent of the mass is extracted for process heat ing and the remaining steam expands isentropical ly to9 kPa.

Inlet to turbine: P = 14 MPa, T = 560C, h = 3486 kJ/kg, s = 6.6 kJ/(kg.K)

Intermediate stage: h = 27776 kJ/kgExit of turbine: P = 9 kPa, h f = 174 kJ/kg, hg = 2574 kJ/kg,

sf = 0.6 kJ/(kg.K), sg = 8.1 kJ/(kg.K)I f the flow rate of steam enter ing the turbine is 100 kg/s, then the work output (in MW) is _______.

34. Wat er ( = 1000 k g/m 3) f l ows t h r ough aventur imeter with inlet diameter 80 mm andthr oat diameter 40 mm. The inlet and thr oatgauge pressures are measured to be 400 kPa and130 kPa respectively. Assuming the ventur imeterto be hor izontal and neglect ing fr ict ion, the inletvelocity (in m/s) is ________.

35. For a canteen, the actual demand for disposablecups was 500 units in January and 600 units inFebruary. The forecast for the month of Januarywas 400 uni ts. The forecast for the month ofMarch consider ing smoothing coefficient as 0.75is _______.

36. Consider a spat ial curve in three-dimensionalspace given in parametr ic form by

x(t) = cos t, y(t) = sin t, z(t) =2

,02

t t

The length of the curve is ______

37. Consi der i ng massless r i gi d r od and smal losci l lat ions, the natural frequency (in rad/s) ofvibrat ion of the system shown in the figure is

(a)4001

(b)4002

(c)4003

(d)4004

38. A tr iangular facet in a CAD model has ver t ices:P1(0, 0, 0); P2(1, 1, 0) and P3(1, 1, 1). The area ofthe facet is(a) 0.500 (b) 0.707(c) 1.414 (d) 1.732


39. I n a sl ab r ol l i ng oper at i on, t he max imumthickness reduction (hmax) is given by (hmax) µ

2R,where R is the radius of the rol l and µ is thecoefficient of fr ict ion between the rol l and thesheet. I f µ = 0.1, the maximum angle subtendedby the deformat ion zone at the centre of the rol l(bite angle in degree) is ______.

40. Fine the solu t i on of 2

2

d yy

dx whi ch passes

through the or igin and the point 3

in 2, ,4

(a)12

x xy e e (b)1

( )2

x xy e e

(c)1

( )2

x xy e e (d)12

x xy e e

41. For the t russ shown in figure, the magnitude ofthe force in member PR and the suppor t reactionat R are respect ively(a) 122.47 kN and 50 kN

(b) 70.71 kN and 100 kN

(c) 70.71 kN and 50 kN(d) 81.65 kN and 100 kN

42. A ball of mass 0.1 kg, init ial ly at rest , is droppedfrom height of 1 m. Ball hits the ground andbounces off the ground. Upon impact with theground, the velocity reduces by 20%. The height(in m) to which the ball wi l l r ise is ______

43. A DC welding power source has a l inear voltage-cur rent (V-I ) character ist ic with open ci rcui tvoltage of 80 V and a shor t circuit cur rent of300 A. For maximum arc power, the cur rent (inAmperes) should be set as _____.

44. A well insulated r igid container of volume 1 m3

contains 1.0 kg of an ideal gas [Cp = 1000 J/(kg.K)and Cv = 800 J/(kg.K)] at a pressure of 105 Pa. Astirrer is rotated at constant rpm in the containerfor 1000 rotat ions and the applied torque is 100N-m. The final temperature of the gas (in K) is_________.

45. A pinion with radius r 1, and iner t ia I 1 is dr iving agear with radius r 2 and iner t ia I 2. Torque 1 isapplied on pinion. The fol lowing are free bodydiagrams of pinion and gear showing impor tantforces (F1 and F2) of interact ion. Which of thefol lowing relations hold t rue?

(a) 11 2 1 1 1 2 2 12

2

F F ; I : F Irr

(b)2

1 11 2 1 1 2 1 2 2 12

2 2

F =F ; = I I : F =Ir rr r

(c) 1 2 1 1 1 2 2 22

1F =F ; = I : F =I

r

(d)2

11 2 1 1 2 1 2 2 2

2 2

1F F ; = I I ;F =I

rr r

46. A cant i lever beam with flexural r igidity of 200Nm 2 is l oaded as shown i n t he f igur e. Thedeflect ion (in mm) at the t ip of the beam is _____.

47. In the assembly shown below, the part dimensionsare:

L 1 = 22.0 0.01 mm,L 2 = L 3 = 10.00.005 mm,Assumi ng t he nor mal di st r i but i on of par tdimensions, the dimension L 4 in mm for assemblycondit ion would be:

(a) 2.00.008 (b) 2.00.012

(c) 2.00.016 (d) 2.00.020

48. A mobile phone has a small motor with an eccentr icmass used for vibrator mode. The locat ion of theeccentr ic mass on motor with respect to center ofgravity (CG) of the mobile and the rest of thedimensions of the mobile phone are shown. Themobile is kept on a flat hor izontal sur face.

Given in addit ion that the eccentr ic mass = 2grams, eccentr icty = 2.19 mm, mass of the mobile= 90 grams, g = 9.81 m/s2. Uniform speed of themotor in RPM for which the mobile wil l get justli fted off the ground at the end Q is approximately(a) 3000 (b) 3500(c) 4000 (d) 4500


49. A precision instrument package (m = 1 kg) needsto be mounted on a sur face vibrat ing at 60 Hz. I tis desi r ed t hat on ly 5% of t he base sur facevibr at i on ampl i t ude be t r ansmi t t ed t o t heinst r ument . Assuming that the isolat i on i sdesigned with i ts natural frequency significant lylesser than 60 Hz, so that the effect of dampingmay be ignored. The st i ffness (in N/m) of therequired mount ing pad is ________.

50. Following data refers to the act ivit ies of a project ,where, node 1 refers to the star t and node 5 refersto the end of the project

)

1-2 22-3 1

4-3 31-4 3

2-5 3

3-5 24-5 4

Act i v i t y Du r at i on (days

The cr it ical path (CP) in the network is

(a) 1-2-3-5 (b) 1-4-3-5

(c) 1-2-3-4-5 (d) 1-4-5

51. For flow through a pipe of radius R, the velocityand temperature dist r ibut ion are as fol lows:

u(r,x) = C1, and T(r ,x) = 3

2C 1 ,Rr

where C1

and C2 are constantsThe bul k mean temper atur e is given by Tm

=R

2 0

2( , )T ( , ) ,

Rm

u r x r x rdru

with Um bing the mean velocity of flow. The valueof Tm is

(a) 20.5CU m

(b) 0.5C2

(c) 0.6C2 (d) 20.6CU m

52. Consider an ant crawling along the curve (x – 2)2

+ y2 = 4, where x and y are in meters. The antstar ts at the point (4, 0) and moves counter -clockwise with a speed of 1.57 meters per second.The t ime taken by the ant to reach the point(2, 2) is (in seconds) _______.

53. Air ( = 1.2 kg/m3 and kinemat ic viscosity, v = 2 10– 5 m2/s) with a velocity of 2 m/s flows over thetop sur face of a flat plate of length 2.5 m. I f the

average value of fr ict ion coefficient is Cr =1.328

,Rex

the total drag force (in N) per unit width of theplate is ________.

54. The velocity field of an incompressible flow isgiven by

V = (a1x + a2y + a3z)i + (b1x + b2y + b3z)j + (c1x + c2y+ c3z)k, where a1 = 2 and c3 = – 4. The value of b2

is ________.

55. An or thogonal turning operat ion is car r ied outunder the fol lowing condit ions: rake angle = 5,spindle rotat ional speed = 400 rpm; axial feed =0.4 m/min and radial depth of cut = 5 mm. Thechip thickness tc, is found to be 3 mm. The shearangle (in degrees) in this tur ning pr ocess is________.

ANSWERS

GENERAL APTI TUDE

1. (c) 2. (b) 3. (b) 4. (b) 5. (a) 6. (b) 7. (d)

8. (b) 9. (b) 10. (800)

MECHANI CAL ENGI NEERI NG

1. (a) 2. (20) 3. (d) 4. (b) 5. (b) 6. (2) 7. (d)

8. (a) 9. (50) 10. (0.02) 11. 3285-3295 12. (525) 13. (b) 14. 0.25

15. (d) 16. (c) 17. 100 18. (d) 19. (a) 20. (d) 21. (3.5)

22. (d) 23. (a) 24. (c) 25. 0.236 26. (c) 27. (b) 28. (b)

29. 1839.83 30. 4.55 31. (b) 32. (c) 33. 125.56 34. (6) 35. 568-570

36. 1.86 37. (d) 38. (b) 39. 5.71 40. (c) 41. (c) 42. 0.64

43. 150 44. 1283.4-1287.4 45. (b) 46. 0.26 47. (b) 48. (b) 49. 6767.6

50. (b) 51. (c) 52. (2) 53. 0.0159 54. (2) 55. 18.5-19.0


2. P (Ram) = 1/6; p(Ramesh) = 1/8p(only at) = p (Ram) × p (not ramesh) + p(Ramesh)

× p(n0 × Ram)

= 7 1 516 8 8 6

12 1

440

4. For M 1220

= 0.6

N 1325

= 0.52

O 2030

= 0.66

P 1225

= 0.48

6. The is not required in ‘Q’.10. Tiger – 1 leap 8 meter

Speed = 5 leap/hr = 40m/minDeer 1 leap = 5 meterspeed = 4hr = 20m/minLet at time ‘t’ the tiger catches the deer. Distance travelled by deer + initial distance

between them50 × 8 400m = distance covered by tiger. 40 × t = 400 + 20t

400200

t = 20 min

total distance 400 + 20 × t = 800 msMECHANICAL ENGINEERING

2. At pt ‘A’, the velocity 10 + 10 = 20 m/s

AV

V

V = 0

5. Minimum clearance minimum m hole – maxium shaft

= 25 + .020 – 25 + .005= 0.015 mm

6.

2

10 1

23 9 9 39 12

( )5 5 5 20 5

x

y f x x

EXPL ANATI ONS

1

0

ydx =

19 12 392 4

2 5 5 20

= 2

7. head loss =

2

2Q

L A2 2

flf v

gd gd

head loss 5

Ld

*1 5

Lh

d

*2 5

2.L

2

hd

= 5

L64

d

1

2

hh

= 2

1

1 6464hh

9. 900

HE

500

HE

300Q3

Q2

Q2

Q1

W

W

1 = 1

1

1 T 1 500 4.44T 900

Q2 = (1 – 1) × Q1

= 53.33 MJ

2 = 3

2

1 T 3001 0.4

T 500

Q3 = (1 – 2) × Q2

= 50 MJ

10. new = 1 1 2 2

1 2

m mm m

0.1 10.1 .1 1

10.1 .1

= 0.02 kg/kg dry air

11. Euler’s critical load = 2

2

EI1

2 9 3200 10 .02 .01

12

= 3289.8681 N


12. mep =work output

swept volume

=3

121

30 10 121

= 525 kPa14. VTn = C

1 1V Tn = 21

1T2V 16 on solving we get

n = 0.25

16.2

40

1 cos( )lim

2x

xx

=

00

Using L Hospital Rule

2

30

(sin )2lim

8x

x xx

= 00

2 2

20

(cos )2 2 (sin )2lim

24x

x x x xx

2 2 2

20

(cos )4 2sinlim

24x

x x xx

= 2 2 2 2

0

( sin )4 cos (8 ) 2(cos )2lim

48x

x x x x x xx

=

2 2 2 2

2 2

0

( cos )2 (4 ) ( sin )(8 ) ( sin )(2 )(8 )

12cos ( sin )(2 )4lim

48x

x x x x x x x x

x x x x

= 12 148 4

17. 2f sin 30 = 100 f = 100 N

FF

100

2F sin 30

18. We have Probability distribution function ofNormal Distribution

f(x) =2

2( )

21 x

ex

...(1)

Variance = 2 is lowest also lowest If decreases f(x) increases ( from (1)) Curve will have highest peak

19. z1 = 5 5 3 i

arg z1 = tan–1 15 3tan 3 60º

5

z2 =2

23

i

arg z2 = 1 12tan tan 3 60º

23

1

2

argzz

= arg(z1) – arg(z2)

= 60º – 60º = 021. Let Swimmer = x

River = y

2 =10

x y

5 =10

x y

On solving we get x = 3.5 km/h25. Angle of twist at (C) = Angle of twist at (B)

= T LG J

9

10 0.5 3277 10 .024

0.23605026. rc = 8mm

the heat lost increases to maximum and thendecreases.

27. 1 =2

280 20 80 2040

2 2

= 250 50 = 1002 = 0

= 1 2 507

FOS =100

250

28. n = 4; p = 16

q = 1 1 56 6

p(x 2) = 1 – p (x < 2)

= 1 [ ( 0) ( 1)]p x p x

= 0 4 1 3

0 1

1 5 1 5 191 4C 4C

6 6 6 6 144


29. Shear load on all rivets 400100N

4

Secondary shear load, due to bending moment

1

2 2 2 21 1 3 4

Pe rr r r r

2

400 .5 .02 2

.02 2 4

1767.766953 NP = 1839.837 N.

30. p = gh= 0.7 × 1360 × 9.81= 9339.12pa

Actual pressure = atmospheric pressure= 110664.12 pa

pv = mrT m pv/RT

=110664.12 2

288 8314

4.5539kg

31. tmin = 2VAk

t1 =293

502k

t2 =935

k

1

2

tt = 36

2533. h1 = 3486 kJ/kg

h2 = 2776 kJ/kgs1 = s3 = 6.6

6.6 = .6 + x(0.1 – .6)x = 0.8

15

220%

4 31 – m

m

h = 174 + .8(2574 – 174)= 2094 kJ/kg

w = (3486 – 2776) + .8 (2776 – 2094)= 1255.6 kJ/kg= 125.56 MW

34.2

1 1

2p vg g

=

212 2

2

4000001300002

pp vpg g

v1 × 802 = v2 × 402

v2 = 4v1

Substituting v2 and solving for v1 we getv1 = 6m/s

35. Forecast for Feb= 400 + (500 – 400)= 400 + .25 × 100 = 475

Forecast for march = 475 + (600 – 475)= 560.75

36. The length of the curve

=2 2 2/ 2

0

dx dy dzdt

dt dt dt

=2/ 2

2 2

0

2( sin ) (cos )t t dt

=/ 2

2 22

0

4sin cost t dt

=/ 2

20

41 dt

=/ 2

2 0

41 t

=4

1 1.86222 2

37.Form dx = 2r2

2

d xdt

= ..2 .r

Taking moments2r .m. 2r... + 400 × (r) × r = 0

4m... + 400 × = 0

= 4004

38. Area = 12

b h

=1

22

a a

a = 1

12

= 0.7071

y

x

z


39. = tan–1 1tanRh

5.7106º

40.2

2

d ydx

= y (D2 – 1) y = 0

D2 – 1 = 0 D = ± 1

y = c1 ex + c2 e

–x

Passes through (0, 0) and 3142,

4

(0, 0)

0 = C1 + C2 ...(1)

3142,

4

34

= C1 e142 + C2 e

–142 = C1 2 + 2C2

2C1 + 2

1C

2 =

34

...(2)

solving (1) and (2)

C1 =12

C2 = – 12

y = 1 12 2

x xe e

= 1( )

2x xe e

41. MQ = 0100 × cos 60 × 4 = Ra × 4

Ra = 50 kNFPR × cos 45 = 100 cos 60

FPR = 70.71 kN100 sin 60

100 cos 60FPR

Q

36.6 50

42. v = 2 2 9.01 1 4.4294 m/sgh

v = 0 × v = 3.5432 m/s

h =2

2vg

= 0.64m

43. v = 8080 I

300

p – v7 = 80I – 280I

300Differentiating and equating to ‘0’

I = 150A45. F1 = F2 [Vertical equilibrium]

For Gear 1For Gear 2

1 1 1 1 1F Ir 2 2 2 2F Ir

11 2 2

2

Irr

= I1 1 ... using F2 = 2 2

2

Ir

and F1=

1 = 11 1 2

2

I Irr

= 2 11 2 1

1 2

I Irr

1 =2

1 1 21 2 1

2 12

I I ......r rr r

and clearly F2 =2 1 1

2

I rr

46. Deflection = Deflection at load + Slope × Distance

3 2W1 W1

.053EI 2EI

W = 5001 = .05

EI = 200 = 0.2604 mm

47. Since all dimensions have bilateral tolerancesL4 = L1 – L2 – L3

= 22 – 10 – 10L4 = 2 mm

Tolerance = 0.01 + 0.0015 + 0.0005= 0.012

L4 = 2.0±0.02 mmTolerance is calculated assuming L4 to be sinkand tolerance of sink will be cumulative sum ofall tolerances

48. When lifted from ground at QReaction = 0 taking moments about ‘p’ and equating to 0

.09 × .06 = mr 2 × .099.01 × .09 × .06 = .002 × 2.19 × 10–3 × 2 × .09 = 366.50 rad/s

= 3500 rpm


49. = 2N = 2 × × 60 = 376.99 rad/second

.05 = 2

1

1n

2 2

20 1 21n n

2 =221 n

n = 82.266 rad/s

n = 82.266km

1 = 6767.6005 N/m

50.

1

4

2

3

50 22 5

0 3 3 6

3 7

6 832

Critical path – 1 – 4 – 3 – 5Time taken = 8 days

51. Tm =3R

1 220

2C C 1

R Rm

rr dr

u

=R 4

1 22 3

0

2C CR Rm

rr dr

u

=21 2

2

2C C 3R

R 10mu

=1 20.6C C

mu

Since u(r, x) is constant, um = C1

tm = 0.6C2

52.

(0, 0) (2, 0) (4, 0)

14

×circumference

14

× × 4

time = 2sec1.5

53. Cf =1.320

Rex

Rex =.vd vd

v

v = 2m/s1 = 2.5m = 2 × 10–5 m2/s

F = 21C A

2 f v

A = 2.5 × 1On substituting we get

F = 0.0159N

54.u v wx y z

= 0

a1 + b2 + c3 = 02 – 4 + b2 = 0

b2 = 2

gate – 2015 - career launchermedia.careerlauncher.com/gate-exams/gate actual paper-...

Documents