ME Forenoon New

ME-GATE-2015

Disclaimer – This paper analysis and questions have been collated based on the memory of some students who appeared in the paper and should be considered only as guidelines. GATEFORUM does not take any responsibility for the correctness of the same.

1

GATE 2015 – A Brief Analysis

(Based on student test experiences in the stream of ME on 1st

February, 2015 – Forenoon Session)

Section wise analysis of the paper

Section

Classification 1 Mark 2 Marks

Total No of

Questions

Engineering

Mathematics 5 4 9

Engineering Mechanics 0 1 1

Strength of Materials 3 5 8

Design of Machine

Elements 2 2 4

Theory of Machines 1 2 3

Vibrations 2 1 3

Fluid Mechanics 3 2 5

Thermal Science 3 4 7

Heat Transfer 1 2 3

Manufacturing Science 2 5 7

Industrial Engineering 3 2 5

Verbal Ability 3 3 6

Numerical Ability 2 2 4

30 35 65

ME-GATE-2015


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Questions from the Paper

1. A, CD, GHI, ____, UVWXY

(A) MNOP (B) QRST (C) KLMN (D) LMNO

Key: (A)

Exp:

2. Let us _____________.

(A) Introvert (B) Alternate (C) Atheist (D) Altruist

Key: (B)

Exp: Blank suggests action, therefore choose verb. B is the only verb.

3. If the Athlete had wanted to come first in the race, he ___________ several hours

everyday

(A) should practice (B) should have practiced

(C) practiced (D) should be practice

Key: (B)

Exp: For condition regarding something which already happened, should have practiced is the

correct choice.

4. Connotation of a road or way

(A) Pertinacious (B) Viaticum (C) Clandestine (D) Ravenous

Key: (A)

Exp: No word is relevant. Least irrelevant word is pertinacious.

5. x>y>1, which of the following must be true?

(i) lnx > lny (ii) ex > e

y (iii) y

x > x

y (iv) cosx > cosy

(A) i and ii (B) i and iii (C) iii and iv (D) ii and iv

Key: (A)

Exp: For whole numbers, greater the value greater will be its log.

Same logic for power of e.

6. From a circular sheet of paper of radius 30 cm, a sector of 10% area is removed. If the

remaining part is used to make a conical surface, then the ratio of the radius and height of

the cone is ____________.

Key: 13.08

Exp: 90% of area of sheet = Cross sectional area of cone

A, C D, G H I, U V W X YM N O P,

B1

E,F2

JKL3

QRST4

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1

1

0.9 30 30 r 30

27 cm r

height of the cone 2 230 27

13.08 cm

7. Question on Para jumbling.

8. Ms. X will be in Bagdogora from 1/5/14 to 20/5/14 and from 22/5/14 to 31/5/14. On the

morning of 21/5/14, she will reach Kochi via Mumbai.

(A) Ms. X will be in Kochi for only one day in May

(B) Ms. X will be in Kochi for one day only in May

(C) Ms. X will be only in Kochi for one day in May

(D) Ms. X will be in Kochi for one day in only May

Key: (A)

Exp: Second sentence says that Ms. X reaches Kochi on 21/05/2014. Also she has to be in

Bagdogora on 22/05/2014.

She stays in Kochi for only one day in may.

9. log tan1°+log tan2°+------+ log tan89° is _________.

(A) 1 (B) 1 2 (C) 0 (D) -1

Key: (C)

Exp:

o o o o

o o

log tan1 log tan89 log tan1 tan89

log tan1 cot1

log1

0

Using the same logic total sum is ‘0’.

10. Two friends would like to keep a secret between themselves. As per standard English, one

of them will say

(A) It would remain between you and me

(B) It would remain between me and you

(C) It would remain between you and I

(D) It would remain between I and you

Key: (A)

11. The cylindrical Uranium fuel rod of radius 5 mm in a nuclear reactor is generating

heat at the rate of 4×107 W/m

3. The rod is cooled by a liquid (convective heat

transfer coefficient 21000 W / m K ) at o25 C. At steady state the surface

temperature (in K) of the rod is

(A) 308 (B) 398 (C) 418 (D) 448

ME-GATE-2015


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Key: (B)

Exp: The surface temp.g

w a

q(T ) T R

2h

734 10

298 5 102 1000

wT 398 K

12. A cantilever beam with square cross section of 6mm side is subjected to a load of 2

kN normal to the top surface as shown in the figure. The young’s modulus of

elasticity of the material of the beam is 210 GPa. The magnitude of slope (in

radian) at Q is ________.

Key: 0.1587

Exp: Slope. Q

Px(2L x)

2EI

where x is measured from the fixed end

Q 49

2000(0.02)(2 0.1 0.02)

(0.006)2 210 10

12

=-0.1587

The magnitude of slope is 0.1587 radian

13. The surface integral i j

s

19x 3y nds

over the sphere given by

2 2 2x y z 9 is ____ .

Key: 216

Exp: By Gauss divergence theorem,

S V

F.n ds divFdV

Here F 9x i 3y

div F 9 3 6

V

s

1 1 19x i 3yj .nds 6 dV 6V

100 mm

20 mm2kN

Q

ME-GATE-2015


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3

3

1 46 r

3

8(3)

216.

14. In a certain slider crank mechanism, length of the crank and connecting rod is

equal. If the crank rotates with the uniform angular speed of 14 rad/sec and the

crank length is 300 mm, the maximum acceleration of the slider (in m/s2) is

_______.

Key: 117.6

Exp: 2

maxa 2r (when 0) i.e at Inner dead centre

22 0.3 14

2

maxa 117.6 m / s

15. For a fully developed laminar flow of water (dynamic viscosity 0.001 Pa-s) through

a pipe of radius 5 cm, the axial pressure gradient is -10Pa/m. The magnitude of

axial velocity (in m/s) at the radial location of 0.2cm is ________.

Key: 6.24

Exp: 2 21 PG R r

4 x

2 21( 10) (0.05) (0.002)

4 0.001

u 6.24m / s

16. A single degree freedom springs mass system is subjected to a sinusoidal force of

10N amplitude and frequency ω along the axis of the springs. The stiffness of the

springs is 150 N/m, damping factor is 0.2 and the undamped natural frequency

10ω. At steady state, the amplitude of vibration (in m) is approximately

(A) 0.05 (B) 0.07 (C) 0.7 (D) 0.9.

Key: (B)

Exp: Amplitude of vibration A= 0

2 2

n n

f / s

21

2

2 2

10 /150

1 11 2 0.2

10 10

= 0.06605 ≃ 0.07

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17. In a two stage wire drawn operation the fractional reduction (ratio of change in

cross sectional area to initial cross sectional area) in the first stage 0.3. Overall

reduction is _______.

(A) 0.24 (B) 0.58 (C) 0.6 (D) 1

Key: (A)

Exp: Since only option (A) is less then 0.3. (A) is the correct ans as overall reduction will be

less then the reduction in the first stage.

18. The values of function f(x) at 5 discrete points are given below:

x 0 0.1 0.2 0.3 0.4

f (x) 0 10 40 90 160

Using trapezoidal rule with step size of 0.1, the value of 0.1, the value of

0.4

0f (x) dx is ________ .

Key: 22

Exp:

0 1 2 3 4

x 0 0.1 0.2 0.3 0.4

y f (x) 0 10 40 90 160

y y y y y

0.4 0.4

0 4 1 2 30 0

hf (x)dx ydx (y y ) 2(y y y )

2

0.1(0 160) 2(10 40 90)

2

22

19. Which of the following statements are true regarding electrochemical machining?

(A) An electrolytic material removal process

(B) There is a tool wear

(C) Thermal or mechanical stresses will be transferred to the part

(D) None

Key: (A)

Exp: ECM is an electrolytic material removal process.

20. The initial velocity of an object is 40 m/s. The acceleration of the object is given by

the following expression a=-0.1V. Where V is instantaneous velocity of the object.

The velocity of the object after 3 seconds will be ________.

Key: 29.632

Exp: a=-0.1v

dv0.1v

dt

lnv 0.1t ln k

http://en.wikipedia.org/wiki/Electrolyte

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0.1t

0.1t

0.1 3

v ke

at t 0 ; v 40

k 40

v 40e

at t 3 seconds

v 40 e 29.6327 m / s

21. The flow stress (in MPa) of a material is given by 0.1500 . where is true

strain. The young’s modulus of elasticity of the material is 200 GPa. A block of

thickness 100 mm made of this material is compressed to 95mm thickness and then

the load is removed. The final dimension of the block (in mm) is __________.

Key: 95.18

Exp:

.1

100Truestrain ln 0.5129

95

500 0.5129 371.5147523

Upto elastic limits using hooks law

69

E

371.5147523 10 100200 10

0.18575mm considering thisfor elastic recovery

l

l

l

l

∴ This will be added to 95 mm

Final dimension 95.18575 mm

22.

C is midpoint of PQ. The magnitude of bending moment (in kN-m) at fixed end O

is __________.

(A) 2.5 (B) 5 (C) 10 (D) 25

Key: (B)

Exp:

P-being internal hinge

Mp = 0 _______(1)

Condition ‘PQ’, reaction at Q = 10 kN

Now from (1)

Mp = 0 M0-RQ×1+Rc×0.5 = 0

2 m

10kN

1 m

0P Q

C

2m

2m

C

PQ

10kN

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M0 = 5kN

23. A hollow shaft (d0 = 2d1, where 0d & d1 are the outer and inner diameter

respectively) needs to transmit 20kW power at 3000 rpm. If the maximum

permissible shear stress is 30 Mpa, 0d is _______.

(A) 11.29mm (B) 22.58mm (C) 33.87mm (D) 45.16mm

Key: (B)

Exp: P T

3

6

04p 11

1

2 300020 10 T

60

T 63.662 N m

T 63.662 30 10, So, (r d),

I r d(15d )

32

d 11.295 mm

0 1d 2d 22.59 mm

24. Work is done on adiabatic system due to which its velocity changes from 10m/s to

20m/s, elevation increases by 40 m and temperature increases by 1K. The mass of

the system is 10 kg, pC 100 J / (kg.K) and gravitational acceleration is 210m / s .

If there is no change in any other component of the energy of the system, the

magnitude of total work done (in kJ) on the system is ________ .

Key: 6.5

Exp: Using SFEE

2

2

1 21 2 1 2

v vm z z g h h W

2 2

2 210 2010 ( 40) 10 100 1 W

2 20

W 6.5kJ

Work done on the system is 6.5 kJ.

25. In a plane stress condition, the components of stress at a point are

x y xy20MPa, 80MPa and T 40MPa. The maximum shear stress (in MPa)

at the point is ________.

(A) 20 (B) 25 (C) 50 (D) 100

Key: (C)

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Exp:

2

x y 21 2max xy

2 2

2

280 2040

2

50MPa

26. One kg of air (R=287J/kg.K) undergoes an irreversible process between

equilibrium state o 31(20 C, 0.9m ) and equilibrium state o 32(20 C, 0.6m ) the change

in entropy S2-S1 (in J / kg.K) is ________.

Key: -116.36

Exp: 22 1

1

Vs s mR ln

V

0.6

287ln 116.368J / kgK0.9

27 A cube and a sphere made of cast iron (each of volume 1000 cm3) were cast under

identical conditions. The time taken for solidifying the cube was 4seconds. The

solidification time (in seconds) for the sphere is ________.

Key: 6.15

Exp:

2

s

Vt k

A

2

cubesphere cube 2

sphere

At t

A

2 3

2 2

sphere

3 3

2 2

cube

2

sphere 2

4r 1000cm r 6.2035cm

3

A 4 r 483.597cm

a 1000 cm a 10 cm

A 6a 600 cm

(600)t 4

(483.597)

6.157sec

28. The head loss for a laminar incompressible flow through a horizontal circular pipe

is h1. Pipe length and fluid remaining the same, if the average flow velocity doubles

and the pipe diameter reduces to half its previous value, the head loss is h2. The

ratio h2/h1 is

(A) 1 (B) 4 (C) 8 (D) 16

Key: (C)

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Exp: head loss avg

2

uh

D

2

avg,22 1

1 2 avg,1

2

2

1

uh D

h D u

2 2

h8

h

29. A manufacturer has the following date required a produces Fixed cost is 50000 Rs,

variable cost is 200 Rs, Selling price is 300 Rs production capacity =1500 units per

month. If the production is carried by at 80% of the rated capacity, the monthly

profit (in Rs) is _____ .

Key: 70000

Exp: Profit per month = 0.8 ×1500 × (300-200) – 50000

= 120000-50000

= 70000

30. The chance of a student passing in a exam is 20%. The chance of a student passing

in a exam and getting above 90% marks in it is 5%. Given that student passes the

exam, the probability that student gets above 90% marks is

(A) 1/18 (B) 1/4 (C) 2/9 (D) 5/18

Key: (B)

Exp: Given that the student is passing exam, i.e., if only 20 students (out of 100) are

considered, of the 5 students get more than 90%

∴ 5 out of 20 is the probability

or 1/4 is the answer.

31. A single point cutting tool with 00 rake angle is used in an orthogonal machining

process. At a cutting speed of 180m/min, the thrust force is 490N. If the coefficient

of friction between the tool and the chip is 0.7, then the power consumption (in

kW) for the machine operation is ________.

Key: 2.1

Exp: C T

C T

F sin F cosF

N F cos F sin

T

C

C

C

Given : 0

F

F

4900.7

F

F 700 N

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c c

180 1Powerconsumption,P F V 700 kW

60 1000

P 2.1kW

32. In a rankine cycle, the enthalpies at turbine entry and outlet are 3159 kJ/kg and

2187 kJ/kg respectively. If the specific pump work is 20 kJ/kg, the specific stream

consumption in (kg/kW-h) of the cycle based on the net output is ___

Key: 3.78

Exp: Specific steam consumption T P

3600

W W

WT = 2 1h h = 3159-2187 kJ/kg

WT = 972 kJ/kg

WP = 20 kJ/kg

Thus specific steam consumption 3600

kg kW h972.20

3.7815kg kW.h

33. A hollow shaft of 1m length is designed to transmit power of 30 kW at 700 rpm.

The maximum permissible angle of twist in the shaft is 1o. The inner diameter of

the shaft is 0.7 times the outer diameter. The modulus of rigidity is 80 GPa. The

outside diameter (in mm) of the shaft is ________.

Key: 44.52

Exp: P = T

P

2 70030 1000 T

60

T 409.256 N m

T G

I

l

9

4 40

1m409.256 80 10

1 180 radians1 0.7 d 18032

l

Solving, we get

d0 = 44.5213 mm

34. The total emissive power of a surface is 500W/m2 at a temperature

2

1T and1200 W / m at a temperature T2, where the temperatures are in kelvin.

Assume the emissivity of the surface to be constant, the ratio of the temperatures

1

2

Tis

T _______.

(A) 0.308 (B) 0.416 (C) 0.8030 (D) 0.0874

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Key: (C)

Exp: Emissive power ∝ T4

4

1

2

1

2

T500

1200 T

T0.8034

T

35. At x=0, the function f (x) x has _______.

(A) minimum (B) maximum

(C) point of inflection (D) neither minimum nor maximum.

Key: (A)

Exp: For negative values of x, f(x) will be positive

For positive values of x, f(x) will be positive

∴ minimum value of f(x) will occur at x = 0

36. In the laminar flower of air (Pr=0.7) over a heated plate, if tand denotes

hydrodynamic and thermal boundary layer thickness respectively, then ________.

(A) t (B) t

(C)

t (D) t0, 0

Key: (C)

Exp: When Pr < 1 δt > δ

Pr > 1 δt < δ

Pr = 1 δt = δ

37. A gas is stored in a cylindrical tank of inner radius 7m and wall thickness 5cm. The

gauge pressure of the gas is 2MPa. The maximum shear stress (in MPa) in the wall

is ________.

(A) 35 (B) 70 (C) 140 (D) 280

Key: (B)

Exp: c

l

2 cmax

pd 2 14280MPa

2t 2 0.05

pd 2 14140MPa

4t 4 0.05

Maximumshearstress 70MPa2 2

l l

Note: This stress τmax is the maximum In-plane shear stress.

Absolute τmax will be c 140MPa2

38. Laplace transform of i5te where i 1 is

(A) 1

s 5i (B)

1

s 5i (C)

1

s 5i

(D)

1

s 5i

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Key: (A)

Exp:

at

i5t

1L e

s a

1L e

s 5i

39.

The minimum time for completion of the project is _______.

Key: 40

Exp: Time taken for 3 paths are as follows

Path 1 = 12+11+10

Path 2 = 14+12+10

Path 3 = 14+7+9+10

∴ Path3 is longest i.e. path 3 is critical path

∴ Project duration = 40 days

40. dy

5y; y 2; at t 0. If t 3;y ?dt

(A) -5e-10

(B) 2e-10

(C) 2e-15

(D) -15e-2

e-x

Key: (C)

Exp: dy

5y y 2 at t 0dt

5t

5t

y k e

at t 0 y 2

y 2e

at t = 3

y = 2e-15

41. A resistance capacitance relaxation circuit is used in an electrical discharge machining

process. The discharge voltage is 100V. At a spark cycle time of 25μs, the average power

input required is 1 kW. The capacitance in μF in the circuit is_______.

(A) 2.5 (B) 5 (C) 7.5 (D) 10

Key: (B)

Exp:

2d

av

1CV

2Wt

is the average power required

1 3 5 6

2 4

12 11 10

7

14 129

ME-GATE-2015


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6

6

1C 100

2100025 10

C 5 10 F

i.e.,C 5 F

42. Find the magnitude of the force in (kN) in the member SR is

(A) 10 (B) 14 (C) 20 (D) 28

Key: (C)

Exp:

Rp + Rx = 30000

Mp = 0

Rx×3 = 2×3000

Rx = 20kN

and Rp = 10 kN

for balance at ‘x’ FRx = 20kN

at ‘RT’ FRT cos45 = 20

RT

20F

cos45 ____ (1)

Also FSR = FRTcos45 ____ (2)

from (1) and (2)

FSR = 20 kN

1m 1m 1m

30kN

V RSW

1m

P

U T

S R

20

20

xT

1m

W V S R

XPU T

3m

2m

1mpR

xR

30kN

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43. During a TIG welding process, the arc current and arc voltage were 50A and 60V,

respectively, when the welding speed was 150 mm/min. In another process, the TIG

welding is carried out at a welding speed of 120 mm/min at the same arc voltage and heat

input to the material so that weld quality remains the same. The welding current (in A) for

this process is

(A) 40 (B) 44.72 (C) 55.9 (D) 62.65

Key: (A)

Exp: Total heat input = VIt

time t is inversely proportional to weld speed (S)

2 2 1 1

2 1

2

2

V I V I

S S

120I 50

150

I 40A

44. For the same values of peak pressure, peak temperature and heat rejection, the correct

order of efficiency for otto, dual and diesel cycles is

(A) otto>dual>diesel (B) otto<dual> diesel

(C) otto<dual< diesel (D) otto>dual< diesel

Key: (C)

Exp: For same values of peak pressure and temperature. Diesel cycle is most efficient and Otto

cycle is least. Efficiency of dual cycle lies in between.

diesel > dual > otto

45. The vendors were asked to supply a very high precision component. The respective

probabilities of meeting the strict design specifications are 0.8, 0.7 and 0.5. Each vendor

supplies one component. The probability that out of total three components supplied by

the vendors, at least one will meet the design specifications is _________.

Key: 0.97

Exp: Probability (at least one will meet specification) = 1-probability(none will meet

specification)

= 1-(1-0.8)×(1-0.7)×(1-0.5)

= 1-0.2×0.3×0.5

= 1-0.03

= 0.97

46. Which one of the following statement is true?

(A) GO gauge represents lower control limit in hole

(B) NOGO gauge represents lower control limit in hole

(C) GO gauge represents lower control limit in shaft

(D) NOGO gauge represents upper control limit in shaft

Key: (A)

Exp: Go gauge represents lower limit in hole

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47. If the velocity for a potential flow is given by x,y x,y

v u if x,y

V with usual notation

then the slope of the potential line at (x, y) is ______

(A) v/x (B) -u/v (C) v2/u

2 (D) u/v.

Key: (B)

48. At least one eigen value of a singular matrix is

(A) positive (B) zero (C) Negative (D) imaginary

Key: (B)

49. A rope brake dynamometer attached for the crank shaft IC engine measures a brake

power of 10kW. When the speed of rotation of the shaft is 400 rad/s, the shaft torque (in

N-m) sensed by the dynamometer is ________.

Key: 25

Exp: P = T

10000

T 25N m400

50. The number of degrees of freedom of the planetary gear train is __________.

(A) 0 (B) 1 (C) 2 (D) 3

Key: (C)

Exp: A planetary gear train has 2 DOF and hence requires too input to get desired output.

51. COP of a Carnot heat pump operating between temperatures o o6 C &37 C is ________.

Key: 10

Exp: 1

c.p.1 2

T 310COP 10

T T 31

52. In a spring mass system, the mass is ‘m’ and spring constant is K. The critical damping

coefficient the system is to 0.1 kg/s. In another spring mass system, the mass is ‘2m’ and

the spring constant is 8K. The critical damping coefficient of the system (in kg/s) of this

system is ________.

Key: 1.6

20 teeth gear

arm

50 teeth gear

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Exp:

C

n

2 2

C C2 11 1

C 2

2SC 2 Sm

S mC C

S m

0.4 8 2

C 1.6

53. For Rankine cycle with reheat, which of the following is true?

(i) increase in average temperature

(ii) reduction in thermal efficiency

(iii) drier steam at turbrine exit

(A) only i, ii (B) ii, iii (C) only I, iii (D) i, ii, iii

Key: (C)

Exp: With reheat average temperature of heat addition increases. Hence, efficiency of cycle

also increases. Further, the quality of steam is higher at turbine exit.

54. Vander walls is equation of state is 2

ap V b RT.

v

SI unit of a is _______.

(A)

22 3

2

kg m s m

molm

(B)

222 3

2

kg m s m

molm

(C)

22 3kg m s m

m mol

(D)

2 3

2

kg m s m

molm

Key: (A)

Exp: SI unit of a is

23

23

22 3

2

mbar

kmol

or

mPascal

mol

or

kg m s m

molm

55. The table represents number of units of demand.

Month Jan Feb Mar Apr May

Number 10 11 16 19 25

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Which of the following statements for sixth period estimated number of units is true?

(A) Regression value will be more than moving average value

(B) As the number of periods increase, the moving average will give a greater value

(C) Simple exponential smoothing will give more value than moving average

(D) Regression value will be less than moving average value

Key: (B)

Exp: In case of increasing trend, regression will give increasing value than moving average.

56. Annual demand of a product is 50000 and ordering cost is 7000 Rs per order and EOQ is

10000 units. At optimum annual inventory cost, annual inventory holding cost is

_________Rs.

Key: 35000

Exp: At optimum total inventory cost (TIC), annual inventory hold is cost is equal to annual

inventory ordering cost

= Number of orders × ordering cost per order

500007000

10000

5 7000

35000

57. A manufacturing technique in which the parts having similarities in Geometry,

manufacturing process and/or functions are assembled together is

(A) Group Technology (B) Cellular Layout

(C) Agile manufacturing (D) Line Balancing

Key: (A)

Exp: Group technology takes full advantage of similarity between parts, through

standardization and common processing.

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