2015-1 SOLVED PAPER - 2015

GENERAL APTITUDEQUESTION 1 TO 5 CARRY ONE MARK EACH

1. Ram and Ramesh appeared in an interview for two vacanciesin the same department . The probability of Ram’s selectionis 1/6 and that of Ramesh is 1/8. What is the probability thatonly one of them will be selected?(a) 47/48 (b) 1/4(c) 13/48 (d) 35/48

2. What is the adverb for the given word below?Misogynous(a) Misogyousness (b) Misogynity(c) Misogynously (d) Misogynous

3. An electric bus has onboard instruments that report thetotal electricity consumed since the start of the trip as wellas the total distance covered . During a single day ofoperation, the bus travels on stretches M,N,O and P, in thatorder. The cumulative distances travelled and thecorresponding electricity consumption are shown in the Tablebelow:-

Stretch Cumulative distance (km)

Electricity used (kWh)

M 20 12

N 45 25

O 75 45

P 100 57

The stretch where the electricity consumption per km isminimum is(a) M (b) N(c) O (d) P

4. Choose the appropriate word/phrase, out of the four optionsgiven below, to complete the following sentence :Dhoni , as well as the other team members of Indian team,________ present on the occasion.(a) were (b) was(c) has (d) have

2015SET - 1

Duration: 3 hrs Maximum Marks: 100

INSTRUCTIONS

1. There are a total of 65 questions carrying 100 marks.

2. This question paper consists of 2 sections, General Aptitude (GA) for 15 marks and the subject specificGATE paper for 85 marks. Both these sections are compulsory.

3. The GA section consists of 10 questions. Question numbers 1 to 5 are of 1-mark each, while question numbers 6 to10 are of 2-marks each. The subject specific GATE paper section consists of 55 questions, out of which questionnumbers 11 to 35 are of 1-mark each, while question numbers 36 to 65 are of 2-marks each.

4. Questions are of Multiple Choice Question (MCQ) or Numerical Answer type. A multiple choice question will havefour choices for the answer with only one correct choice. For numerical answer type questions, the answer is a numberand no choices will be given.

5. Questions not attempted will result in zero mark. Wrong answers for multiple choice type questions will result in

NEGATIVE marks. For all 1 mark questions, 13

mark will be deducted for each wrong answer. For all 2 marks questions,

23

mark will be deducted for each wrong answer..

6. There is NO NEGATIVE MARKING for questions of NUMERICAL ANSWER TYPE.

2015 -2 SOLVED PAPER - 2015

5. Choose the word most similar in meaning to the given word:AWKWARD(a) Inept (b) Graceful(c) Suitable (d) DreadfulQUESTION 6 TO 10 CARRY TWO MARKS EACH

6. Lamenting the gradual sidelining of the arts in schoolcurricula, a group of prominent artists wrote to the ChiefMinister last year, asking him to allocate more funds tosupport arts education in schools. However, no suchincrease has been announced in this year’s Budget. Theartists expressed their deep anguish at their request notbeing approved, but many of them remain optimistic aboutfunding in the future.Which of the statement(s) below is/are logically valid andcan be inferred from the above statements?(i) The artists expected funding for the arts to increase

this year.(ii) The Chief Minister was receptive to the idea of

increasing funding for the arts.(iii) The Chief Minister is a prominent artist.(iv) Schools are giving less importance to arts education

nowadays.(a) (iii) and (iv) (b) (i) and (iv)(c) (i) ,(ii) an(iv) (d) (i) and (ii)

7. A tiger is 50 leaps of its own behind a deer. The tiger takes 5leaps per minute to the deer’s 4. If the tiger and the deercover 8 metres and 5 meters per leap respectively, whatdistance in metres will the tiger have to run before it catchesthe deer?

8. If a2 + b2 + c2 = 1 , then ab + bc + ac lies in the interval.

(a) [1,2/3] (b)1 , 12

é ù-ê úë û(c) [–1,1/2] (d) [2, –4]

9. In the following sentence certain parts are underlined andmarked P,Q and R. One of the parts may contain certain erroror may not be acceptable in standard written communication.Select the part containing an error. Choose D as your answerif there is no error.

The student corrected P

all the errors that

Qthe instructor marked on the .

Ranswer book

(a) P (b) Q(c) R (d) No error

10. Given below are two statements followed by two conclusion.Assuming these statements to be true, decide which onelogically follows.Statements:I. All film directors are playback singers.II. All film directors are film stars.Conclusion :I. All film directors are playback singers.II. Some film stars are film directors.(a) Only conclusion I follows.(b) Only conclusion II follows.(c) Neither conclusion I nor II follows.(d) Both conclusions I and II follow.

TECHNICAL SECTION

QUESTION 11 TO 35 CARRY ONE MARK EACH

11. If any two columns of a determinant 4 7 8

P 3 1 59 6 2

é ùê ú= ê úê úë û

are

interchanged, which one of the following statementsregarding the value of the determinant is CORRECT?(a) Absolute value remains unchanged but sign will change.(b) Both absolute value and sign will change.(c) Absolute value will change but sign will not change .(d) Both absolute value and sign will remain unchanged.

12. A swimmer can swim 10km in 2 hours when swimming alongthe flow of a river. While swimming against the flow, shetakes 5 hours for the same distance . Her speed in still water(in km/h) is______

13. Which of the following types of stress strain relationshipbest describes the behaviour of brittle materials, such asceramics and thermosetting plastics,(s stress and e = strain)?

(a)s

e

(b)s

e

(c)s

e

(d)s

e

14. Consider fully developed flow in a circular pipe withnegligible entrance length effects. Assuming the mass flowrate , density and friction factor to be constant, if the lengthof the pipe is doubled and the diameter is halved, the headloss due to friction will increase by a factor of(a) 4 (b) 16(c) 32 (d) 64

15. Which one of the following is the most conservative fatiguefailure criterion?(a) Soderberg (b) Modified Goodman(c) ASME Elliptic (d) Gerber

16. The Blasius equation related to boundary layer theory is a(a) third-order linear partial differential equation(b) third-order nonlinear partial differential equation(c) second -order nonlinear ordinary differential equation(d) third-order nonlinear ordinary differential equation.

2015-3 SOLVED PAPER - 2015

17. Consider a slider crank mechanism with nonzero masses andinertia. A constant torque t is applied on the crank as shownin the figure. Which of the following plots best resemblesvariation of crank angle , q versus time

t

qm

(a)q

time(b)

q

time

(c)q

time(d)

q

time

18. Simpson’s 13

rule is used to integrate the function ( ) 23 9f x x

5 5= +

between x = 0 and x = 1 using the least number of equal sub –intervals. The value of the integral is ___________

19. Consider a stepped shaft subjected to a twisting momentapplied at B as shown in the figure. Assume shear modulus,G = 77 GPa. The angle of twist at C (in degrees) is _____

100 Nm

10 mmf 20 mm

500 mmA

B C

500 mm

20. For an ideal gas with constant values of specific heats, forcalculation of the specific enthalply,(a) it 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 known

21. Air enters a diesel engine with a density of 1.0 kg/m3.Thecompression ratio is 21. At steady state, the air intake is30×10–3 kg/s and the net work output is 15 kW . The meaneffective pressure (in kPa) is ______

22. For flow of viscous fluid over a flat plate, if the fluidtemperature is the same as the plate temperature, the thermalboundary 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 all

23. A wheel of radius r rolls without slipping on a horizontalsurface shown below. If the velocity of point P is 10m/s inthe horizontal direction, the magnitude of velocity of pointQ (in m/s) is ________

P

Q

r

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

ratio of 0.01 kg

kg dry air mixes with a second stream of

superheated water vapour flowing at 0.1 kg/s. Assumingproper and uniform mixing with no condensation, the

humidity ratio of the final stream kgin

kg dry airæ öç ÷è ø is ______.

25. Two identical trusses support a load of 100 N as shown inthe figure. The length of each truss is 1.0m; cross-sectionalarea is 200 mm2, young’s modulus E = 200GPa. The force inthe truss AB (in N) is ______

A

B

C

30°

100N

30°

26. Consider a steel (Young’s modulus E = 200 GPa) columnhinged on both sides. Its height is 1.0 m and cross-section is10mm × 20mm. The lowest Euler critical bucking load (in N)is _______

27. Among the four normal distribution with probability densityfunctions as shown below, which one has the lowestvariance?

–2 –1 0 1 2

IV

IIIII

I

(a) I (b) II(c) III (d) IV

2015 -4 SOLVED PAPER - 2015

28. Given two complex numbers ( )1z 5 5 3 i= + and 2z

z 2i,3

= +

the argument of 1

2

zz in degrees is

(a) 0 (b) 30(c) 60 (d) 90

29. Match the following products with preferred manufacturingprocess:

P Rails 1 Blow molding

Q Engine cranks haft 2 Extrus ion

R Aluminium channels 3 Forging

S PET water bottles 4 Rolling

Product Process

(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

30. A Carnot Engine (CE-1) works between two temperaturereservoirs A and B , where TA = 900K and TB = 500K. Asecond Carnot Engine (CE-2) works between temperaturereservoirs B and C, where Tc = 300 K. In each cycle of CE-1and CE-2 , all the heat rejected by CE-1 to reservoir B is usedby CE-2 . For one cycle operation, if the net Q absorbed byCE-1 from reservoir A is 150 MJ, the net heat rejected toreservoir C by CE-2 (in MJ) is _________

31. Holes of diameter 0.040+0.02025.0+ mm are assembled

interchangeably with the pins of diameter 0.005–0.00825.0+ mm.

The minimum clearance in the assembly will be(a) 0.048 mm (b) 0.015 mm(c) 0.005 mm (d) 0.008 mm

32. The function of interpolator in a CNC machine controller isto(a) control spindle speed(b) coordinate feed rates of axes.(c) control tool rapid approach speed.(d) perform Miscellaneous (M) functions (tool change ,

coolant control etc.)33. Under certain cutting conditions, doubling the cutting speed

reduces the tool life to th

161æ ö

ç ÷è ø of the original. Taylor’s tool

life index (n) for this tool workplace combination willbe ____

34. The value of ( )2

x 0 4

1 cos xlim

2x®

- is

(a) 0 (b)12

(c)14

(d) undefined

35. In a linear arc welding process, the heat input per unit lengthis inversely proportional to(a) welding current(b) welding voltage(c) welding speed(d) duty cycle of the power source

QUESTION 36 TO 65 CARRY TWO MARKS EACH36. A 10 mm diameter electrical conductor is covered by an

insulation of 2 mm thickness. The conductivity of theinsulation is 0.08 W/m-K and the convection coefficient atthe insulation surface is 10 W/m2-K. Addition of furtherinsulation of the same material will(a) increase heat loss continuously(b) decrease heat loss continuously(c) increase heat loss to a maximum and then decrease

heat loss(d) decrease heat loss to a minimum and then increase

heat loss

37. Find the solution of 2

2d y ydx

= which passes through the

origin and the point 3In 2, .4

æ öç ÷è ø

(a) x x1y e e2

-= - (b) ( )x x1y e e2

-= +

(c) ( )x x1y e – e

2-= (d) x x1

y e e2

-= +

38. An orthogonal turning operation is carried out under thefollowing conditions; rake angle = 5°, spindle rotationalspeed = 400 rpm, axial feed = 0.4 m/min and radial depth ofcut = 5mm. The chip thickness , tc, is found to be 3mm. Theshear angle (in degrees) in this turning process is ____

39. A cantilever beam with flexural rigidity of 200 N.m2 is loadedas shown in the figure . The deflection (in mm) at the tip ofthe beam is ____

500 N

50 mm

100 mm40. In the assembly shown below, the part dimensions are;

L1 22.0±.0.001mm, L2 = L3 = 10.0±.0.005mm, Assuming the normaldistributions of part dimensions, the dimension L4 in mm forassembly condition would be,

2015-5 SOLVED PAPER - 2015

L2L1

L3 L4

(a) 2.0±.0.008 (b) 2.0±.0.012

(c) 2.0±.0.016 (d) 2.0±.0.020

41. A pinion with radius r1 , and inertia I1 is driving a gear withradius r2 and inertia I2 . Torque t1 is applied on pinion. Thefollowing are free body diagrams of pinion and gear showingimportant forces (F1 and F2) of interaction . Which of thefollowing relations hold true?

q1

q2

t1

r1 r2F1

F2

Inertia = I1 Inertia = I2

q q1 2, = AngularDisplacements

(a). . . .

11 11 2 1 2 2 2

2

rF F ; I ; F I

r¹ t = q = q

(b)

2 . . . .1 11 11 2 1 1 2 2 2 22 2

r rF F ; I I ; F Ir r

é ùæ öê ú= t = + q = qç ÷è øê úë û

(c). . . .

1 21 2 1 1 2 2 21F F ; I ; F Ir

= t = q = q

(d)

2 . . . .1

1 21 2 1 1 2 2 2 22

r 1F F ; I I ; F Ir r

é ùæ öê ú¹ t = + q = qç ÷ê è ø úë û42. Steam enters a well insulated turbine and expands

isentropically throughout. At an intermediate pressure,20 percent of the mass is extracted for process heating andthe remaining steam expands isentropically to 9 kPa. Inlet totrubine P = 14 MPa, T = 560°C, h = 3846 kJ/kg, s = 6.6 kJ/(kg.K)Intermediate stage: h = 2776 kJ/kgExit of turbine : P = 9kPa, hf = 174 kJ/kg,hg = 2574 kJ/kg, sf = 0.6 kJ/(kg.K);sg = 8.1 kJ/(kg.K)If the flow rate of steam entering he turbine is 100 kg/s, thenthe work output (in MW) is _____

43. Consider a spatial curve in three – dimensional space given

in parametric form by x(t) = cost, y(t) = sint, ( ) 2z t t, 0 t .2p= < £

pThe length of the curve is ___

44. A machine element is subjected to the following bi-axial stateof stress: sx = 80MPa; sy = 20MPa; txy = 40MPa. If the shearstrength of the material is 100 MPa, the factor of safety asper Tresca’s maximum shear stress theory is(a) 1.0 (b) 2.0(c) 2.5 (d) 3.3

45. Consider an ant crawling along the curve (x – 2)2 + y2 = 4 ,where x and y are in meters, The ant starts at the point (4,0)and moves counter – clockwise with a speed of 1.57 metersper second . The time taken by the ant to reach the point(2,2) is (in seconds) _______

46. Match the following pairs:

P I Incompres s ible continuity

Q II Steady flow

R III Irrotational flow

S IV Zero acceleration of flu id particle

Product Process

0Ñ ´ Ñ =

. 0Ñ Ñ =

D0

DtÑ

=

0t

¶ Ñ =¶

(a) P-IV, Q-I, R-II,S-III (b) P-IV,Q-III,R-I,S-II(c) P-III,Q-I, R-IV,S-II (d) P-III,Q-I,R-II,S-IV

47. Following data refers to the activities of a project, where,node 1 refers to the start and node 5 refers to the end of theproject.

A ctivity Duration (days )1-2 22-3 14-3 31-4 32-5 33-5 24-5 4

The critical 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

2015 -6 SOLVED PAPER - 2015

48. Considering massless rigid rod and small oscillations, thenatural frequency (in rad/s) of vibration of the system shownin the figure is

k = 400 N/m

m = 1 kg

r 2r

(a)4001

(b)400

2

(c)400

3(d)

4004

49. A mobile phone has a small motor with an eccentric massused for vibrator mode. The location of the eccentric masson motor with respect to center of gravity (CG) of the mobileand the rest of the dimensions of the mobile phone are shown.The mobile is kept on a flat horizontal surface.

10 cmCG Motor

Eccentric

Q Mass

6 cm 3 cm

P

Given in addition that the eccentric mass =2 grams,eccentricity = 2.19 mm, mass of the mobile = 90 grams ,g = 9.81 m/s2 .Uniform speed of the motor in RPM for whichthe mobile will get just lifted off the ground at the end Q isapproximately(a) 3000 (b) 3500(c) 4000 (d) 4500

50. Temperature of nitrogen in a vessel of volume 2m3 is 288 K.A U-tube manometer connected to the vessel shows areading of 70cm of mercury (level higher in the end open toatmosphere) . The universal gas constant is 8314 J/kmol-K,atmospheric pressure is 1.01325 bar, acceleration due togravity is 9.81 m/s2 and density of mercury is 13600 kg/m3.The mass of nitrogen (in kg) in the vessel is _______

51. For the turss shown in figure, the magnitude of the force inmember PR and the support reaction at R are respectively

100 kN

60° P

Q R

4 m

45°

(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 100kN

52. A horizontal plate has been joined to a vertical post usingfour rivets arranged as shown in the figure. The magnitudeof the load on the worst loaded rivet (in N) is__________

40 mm

500 mm

400 N40 mm

53. A DC welding power source has a linear voltage-current (V-I) characteristic with open circuit voltage of 80V and a shortcircuit current of 300A. For maximum arc power, the current(in Amperes) should be set as_______

54. A well insulated rigid container of volume 1m3 contains 1.0kgof an ideal gas [Cp = 1000 J/(kg.K) and Cv = 800J/(kg.K) at apressure of 105 Pa. A stirrer is rotated at constant rpm in thecontainer for 1000 rotations and the applied torque is 100 N-m. The final temperature of the gas(in K) is _____

55. The velocity field on an incompressible flow is given byV = (a1x + a2y + a3z)i + (b1x + b2y + b3z)j + (c1+ c2y + c3z)k,where a1 = 2 and c3 = –4 . The value of b2 is________

2015-7 SOLVED PAPER - 2015

56. For flow through a pipe of radius R, the velocity andtemperature distribution are as follows :

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

2rC 1 ,R

é ùæ ö-ê úç ÷è øê úë ûwhere C1 and C2 are constants. The bulk mean temperature

is given by ( )R

m 2m 0

2T u r, x TU R

= ò (r, x)rdr,with Um being

the mean velocity of flow . The value of Tm is

(a)2

m

0.5CU (b) (b) 0.5C2

(c) 0.6C2 (d)2

m

0.6CU

57. Air (r=1.2 kg/m3 and kinematic viscosity, v=2×10-5m2/s) witha velocity of 2m/s flows over the top surface of a flat plate oflength 2.5m. If the average value of friction coefficient

is fx

1.328C ,

Re= the total drag force (in N) per unit width of

the plate is _____58. Water (r = 1000kg/m3) flows through a venturimeter with

inlet diameter 80mm and throat diameter 40mm.The inlet andthroat gauge pressures are measured to be 400 kPa and 130kPa respectively . Assuming the venturimeter to be horizontaland neglecting friction , the inlet velocity (in m/s) is_______

59. For a canteen, the actual demand for disposal cups was500units in January and 600 units in February. The forecastfor the month of january was 400 units. The forecast for themonth of March considering smoothing coefficient as 0.75is______

60. A triangular facet in a CAD model has vertices: P1(0,0,0);P2(1,1,0) and P3(1,1,1). The area of the facet is(a) 0.500 (b) 0.707(c) 1.414 (d) 1.732

61. The solidification time of a casting is proportional to 2V ,

Aæ öç ÷è ø

Where V is the volume of the casting and A is the totalcasting surface area losing heat. Two cubes of same materialand size are cast using sand casting process. The top faceof one of the cubes is completely insulated. The ratio of thesolidification time for the cube with top face insulated tothat of the other cube is

(a)2536

(b)3625

(c) 1 (d)65

62. A precision instrument package(m = 1kg) needs to bemounted on a surface vibrating at 60 Hz. It is desired thatonly 5% of the base surface vibration amplitude betransmitted to the instrument .Assume that the isolation isdesigned with its natural frequency significantly lesser than60Hz, so that the effect of damping may be ignored. Thestiffness (in N/m) of the required mounting pad is ________

63. The probability of obtaining at least two ‘SIX’ in throwing afair dice 4 times is(a) 425/432 (b) 19/144(c) 13/144 (d) 125/432

64. A ball of mass 0.1 kg, initially at rest, is dropped from heightof 1m. Ball hits the ground and bounces off the ground.Upon impact with the ground, the velocity reduces by 20%.The height (in m) to which the ball will rise is _____

65. In a slab rolling operation, the maximum thickness reduction(D hmax ) is given by D hmax = m2 R where R is the radius of theroll and m is the coefficient of friction between the roll andthe sheet. If m = 0.1, the maximum angle subtended by thedeformation zone at the centre of the roll (bit angle in degrees)is________

2015 -8 SOLVED PAPER - 2015

GENERAL APTITUDE

1. (b) The Probability of Ram’s selection = 16

The Probability of Ramesh selection = 18

P (Ram not selected) = 1 51

6 6- =

P (Ramesh not selected) = 1 718 8- =

Probability that only one is selected

1 7 1 5 12 16 8 8 6 48 4= ´ + ´ = =

2. (c) The adverb of the word ‘Misogynous’ is‘Misogynously’.

3. (c) For m Þ 12 0.620

=

For n Þ 25 0.55545

=

For o Þ 45 0.675

=

For p Þ 57 0.57100

=

Hence, The stretch where the electricity consumptionper km is minimum is N.

4. (b) Singular verb is used with the word as well as.5. (a) Awkward means difficult to handle or manage.

Similarly,Inept means inappropriate or out of place.

6. (b)7. (b) Distance covered by tiger in 1 minute = 5 × 8 = 40m

Distance covered by deer in 1 minute = 4 × 5 = 20mDistance between tiger and deer = 50 × 8m = 400m

Time taken to catch deer = 400 20 minutes

40 20=

-

Distance covered by tiger in 20 minutes= 20 × 40 = 800 metres.

8. (b) Given, a2 + b2 + c2 = 1

We know that(a + b + c)2 ³ 0

Þ a2 + b2 + c2 + 2ab + 2bc + 2ca ³ 0

Þ 1 + 2 (ab + bc + ca) ³ 0

Þ ab + bc + ca ³ 1

2-

Again,

2 2 2( ) ( ) ( ) 0b c c a a b- + - + - ³

Þ 2 2 2 2 2 22 2 2 0b c bc c a ca a b ab+ - + + - + + - ³

Þ 2 2 22( ) 2( ) 0a b c ab bc ca+ + - + + ³

Þ 2 2 2ab bc ca a b c+ + £ + +

or 1ab bc ca+ + £

Hence,

1 12

ab bc ca- £ + + £

9. (b) ‘The’ is not required in ‘Q’

10. (d) Venn-diagram representation :

Playback singers

Film directors

Film stars

Conclusions :I. TrueII. True

2015-9 SOLVED PAPER - 2015

TECHNICAL SECTION

11. (a)12. 3.5

Let swimmer be ‘A’ and river be ‘B’Then, 2A + 2B = 10 ...(1)5A – 5B = 10 ...(2)on solving eqns (1) and (2), we getA = 3.5, B = 1.5

13. (d)

14. (d) As we know that head loss (hL) = 2L Vf

D 2g

2

L

QfLAh

2Dg

æ öç ÷è ø=

from the above equation, L 5Lh

Dµ

Here, 1L 5Lh

Dµ & ( )2L 5 5

2L Lh 64DD / 2

µ = ´

Ratio 51

52

L D

L D

Lh 1h 64 L 64

= =´

so head loss due to friction will increase by the factor 64.15. (a)16. (d)17. (b)18. (b) 2

Hint: Use Simpson’s 1

3 rule,

( ) ( ) ( )0

0

x xh

0 n 1 3 n 1x

hf x dx [ y y 4 y y .... y3

+

-= + + + + +ò

+ ( )2 4 n 22 y y ..... y ]-+ + +

19. 0.236

Angle of twist at C, (q) = 9TL 10 0.5GJ 77 10 0.024

´=´ ´p´

95 32 0.236

77 3.14 0.024 10´q = =

´ ´ ´

20. (a)21. 525

Mean Effective Pressure

= 3

net work output 151swept volume 30 10 121

-=

æ ö´ -ç ÷è ø

= 315 21 10 525

30 20´ ´ =´

22. (d)23. 20

At point ‘R’, the magnitude of velocity will be as:10 + 10 = 20 m/s

R u

24. 0.01971

The humidity rate of final stream = 1 1 2 2

1 2

M W M WM M

++

= 0.01 10.1 0.1 1

10.1 0.1´ + ´

+ = 0.01971

25. 100As trusses AB & BC are identical so tension will be same,so2T sin 30 = 100

100 100T 10012sin 30 22

= = =´

30

A

B

C

100N

30T T

2015 -10 SOLVED PAPER - 2015

26. 3286.53

Lowest Euler critical buckling load = 2

2EI

Lp

= ( ) ( )2 393.14 200 10 0.02 0.0112 1

´ ´ ´ ´´

= 3286.53

27. (d)

28. (a) arg (Z1) = tan–1 15 3 tan 35

-= = 60°

arg (Z2) = tan–1 2

2 / 3æ öç ÷è ø

= tan–1 ( )3 = 60°

1

2

ZargZæ öç ÷è ø

= arg(Z1) – arg(Z2)

= 60 – 60 = 0

29. (b)

30. 50

21

1

T 5001 1 0.444T 900

h = - = - =

( ) ( )2 1 1Q 1 Q 1 0.444 150 83.4= -h ´ = - ´ =

32

2

T 3001 1 0.4T 500

h = - = - =

( ) ( )3 2 2Q 1 Q 1 0.4 83.4 50= -h = - =

31. (b) Hint: Minimum clearance = minimum hole – maximumshaft= (25 + 0.020) – (25 + 0.005)= 0.015

32. (b)33. 0.25

Hint: Taylor’s tool life expression, VTn = C

V1T1n =

21

1T2V16æ ö´ç ÷è ø

34. (a) Hint: Using L’s Hospital rule

35. (d)

36. (c) rC = 8 mm\ The heat lost increases to maximum then decreases.

37. (c)38. 32.24

Shear angle, tanf = r cos

1 r sina

- a

where r = chip thickness ratio = 35 = 0.6

tan f = 0.6cos5 0.6306

1 0.6sin 5° =

- °

f = tan–1 0.6306 = 32.24°39. 0.26

Hint: Deflection at the tip of the beam =3 2WL WL 0.05

3EI 2EI+ ´

40. (d) L4 = L1 – L2 – L3 = 22 – 10 – 10 = 2 mmTolerance = 0.01 + 2 × 0.005 = 0.02

41. (d)42. 125.56

Here, h1 = 3486 kJ/kg, h2 = 2776 kJ/kgS = 6.6, sf = 0.6s = sf + y (0.1 – sf)h = hf + y(hg – hf)= 174 + 0.8 (2574 – 174)= 2094 kJ/kgw = (h1 – h2) + y (h2 – h)= 1255.6 kJ/kg= 125.56 MW

43. 1.86Hint: Length of the curve is given by

2 2 22

0

dx dy dz dtdt dt dt

p

æ ö æ ö æ ö+ +ç ÷ ç ÷ ç ÷è ø è ø è øò

44. (b) As we known that

2x y x y 2

1 xy2 2s + s s -sæ ö

s = + + sç ÷è ø

= ( )2

280 20 80 20 402 2+ -æ ö+ +ç ÷è ø

2015-11 SOLVED PAPER - 2015

= 50 900 1600+ +

= 50 + 50 = 100

and, s2 = 0

Shear steam (s) = 1 2 100 0 502 2

s -s -= =

Factor of safety = 100 250

=

45. 2

Distance travelled = circumference 4

4 4p= = p

Time taken = 2sec1.57p =

46. (a)

47. (b)

48. (d) Hint: 2

2d x 2rdt= q

49. (b) Hint: Take moments about P and equating it to 0.

50. 4.55Hint: Pressure (P) = rghPV = nRT

51. (c) Taking moment about Q,100 cos 60 × 4 = R × 4R = 50 kN

Force in member PR (FPR) = 100cos60 50

cos45 1/ 2= = 70.72 kN

52. 1840

Shear load = 400

4= 100N

Secondary shear load = 1

2 2 2 21 2 3 4

PeR

R R R R+ + += 1840 N

53. 150

P – V = 80 I – 280 I300

On differentiating, we getI = 150 Amp

54. 628.31CPDT = 2p × (100)2

( )2

p

2 100T 628.31K

Cp

D = =

55. 2

As we know that, 2u 2v 2w 02x 2y 2z

+ + =

then, a1 + b2 + c3 = 02 + b2 – 4 = 0b2 – 2 = 0b2 = 2

56. (c) Given, ( ) ( )R

m 2m 0

2T u r,x T r,x rdrU R

= ò

= R 3

1 22m 0

2 rC C 1 rdrRU R

ì üï ïæ ö-í ýç ÷è øï ïî þò

= R 4

1 22 3

m 0

2C C rr drU R R

ì üï ï-í ýï ïî þò

= 1 2

m

0.6C CU

Tm = 0.6 C2 [Ar (r, x) is constant so, Um = C1]

57. 0.016

Given CF = xx

1.328 vd, ReRe

r=m

(Total drag force) 2F

1F C Av2= r

Here, v = 2m/s, r = 1.2 kg/m3, A = 2.5 × 4mghon putting the above values, we get, F = 0.016 N

58. 6Using the following equation

2 21 1 2 2p v p v

pg 2g pg 2g+ = +

Here, p1 = 400 kpa, p2 = 130 kPa, P = 1000 kg/m3

Putting the values, and after solvingwe get, v1 = 6 m/s

59. 568.75FFeb = 400 + 0.75 (500 – 400)

= 475Fmarch = 475 + 0.75 (600 – 475)

= 568.75

2015 -12 SOLVED PAPER - 2015

60. (b) Hint: Area = 12

× breadth × height

61. (b) Hint: t = 2Vk

Aæ öç ÷è ø

62. 6767.6w = 2pN = 2 × 3.14 × 60 = 376.8 rad/sec

vibration amplitude = 2

2n

5 1100

1=

w-w

2

2n

n

10.05 21

1

æ öw= Þ =ç ÷wè øæ öw- ç ÷wè ø

( )22 2 2

n n376.8

2121

w = w Þ w =

n 82.27rad / secw =

nK 82.27 K 6767.6 N / mm

w = = Þ =

63. (b)64. 0.64

Velocity (v) = 2gh = 2 9.8 1´ ´ = 4.43 m/s

Reduced velocity = 204.43

100´ = 0.885 m/s

Velocity after reduction = 4.43 – 0.885 = 3.545 m/s

Height of rise of ball (h) = ( )22 3.545v 0.64m

2g 2 9.8= =´

65. 5.71

Hint: htan

RDq = = tan–1µ = 5.7106°