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
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.
2
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
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.
3
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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4
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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5
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
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.
6
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
ME-GATE-2015
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7
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
ME-GATE-2015
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8
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)
ME-GATE-2015
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9
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)
ME-GATE-2015
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10
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
ME-GATE-2015
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11
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
ME-GATE-2015
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12
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
ME-GATE-2015
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13
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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14
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
ME-GATE-2015
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15
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
ME-GATE-2015
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16
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
ME-GATE-2015
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17
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
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.
18
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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