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GATE 2019
MEnd2 Feb 2019
Forenoon Session
Note:-Don't forget to predict your rank using our rank predictor tool
BY
KREATRYX
Detailed Solutions
R
Klassroom 2020 Program for GATE-EE in Kalu Sarai, New Delhi
Click here
ME Set-1 (Solutions)
© Kreatryx. All Rights Reserved. 1 www.kreatryx.com
Aptitude
Q.1 _______ I permitted him to leave, I wouldn't have had any problem with him being absent, ______ I?
(a) Had, would (b) Have, would
(c) Had, wouldn't (d) Have, wouldn't
Answer: (a)
Solution:
Had I permitted him to leave, I wouldn’t have had any problem with him being absent, would I?
Q.2 The minister avoided any mention of the issue of women's reservation in the private sector. He
was accused of ________ the issue.
(a) Belting (b) Skirting
(c) Collaring (d) Tying
Answer: (b)
Solution:
Skirting means going around or avoiding any direct issue
Q.3 A worker noticed that the hour hand on the factory clock had moved by 225 degrees during her
stay at the factory. For how long did she stay in the factory?
(a) 4 hours and 15 min (b) 3.75 hours
(c) 8.5 hours (d) 7.5 hours
Answer: (d)
Solution:
Each number on clock has 036030
12
Shifting by 0225 implies225
7.530
number
Since hour hand moves by 7.5 numbers, the stay in factory was 7.5 hours
Q.4 John Thomas, an_________ writer, passed away in 2018.
(a) Eminent (b) Prominent
(c) Dominant (d) Imminent
Answer: (a)
Solution:
John Thomas, an eminent writer passed away in 2018
Q.5 The sum and product of two integers are 26 and 165 respectively. The difference between these
two integers is__________
(a) 3 (b) 6
(c) 2 (d) 4
Answer: (d)
Solution:
Let two numbers be x & y
x+y= 26
ME Set-1 (Solutions)
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xy= 165
165y
x
165x 26
x
2x 26x 165 0
x 11 x 15 0
x= 11 or 15
Hence, the difference= x y 4
Q.6 Congo was named by Europeans. Congo's dictator Mobuto later changed the name of the country
and the river to Zaire with the objective of Africanising names of persons and spaces, However, the
name Zaire was a Portuguese alteration of Nzadi o Nzere, a local African tern" meaning 'River that
swallows Rivers', Zaire was the Portuguese name for the Congo river in the 16th and 17th centuries.
Which one of the following statements can be inferred from the paragraph above?
(a) As a dictator Mobuto ordered the Portuguese to alter the name of the river to Zaire
(b) Mobuto's desire to Africanise names was prevented by the Portuguese
(c) Mobuto was not entirely successful in Africanising the name of his country
(d) The term Nzadi o Nzere was of Portuguese origin
Answer: (c)
Solution:
Mobuto was not entirely successful in his effort because he used Portuguese alteration of an African
term
Q.7 A person divided an amount of Rs. 100,000 into two parts and invested in two different schemes.
In one he got 10% profit and in the other he got 12%. Tithe profit percentages are interchanged with
these investments he would have got Rs.120 less. Find the ratio between his investments in the two
schemes.
(a) 11 : 14 (b) 9 : 16
(c) 37 : 63 (d) 47 : 53
Answer: (d)
Solution:
Let first part=x
Second part 100000 x
Amount obtained 10 12
1 x 1 100000 x100 100
= 1.1x+ 112000- 1.12x
= (112000- 0.02x)
Exchanging profit percentage, amount obtained
12 10
1 x 1 100000 x100 100
=110000+ 0.02x
Since now he get 120 less
(112000- 0.02x)- (110000+ 0.02x)= 120
2000- 120= 0.04x
ME Set-1 (Solutions)
© Kreatryx. All Rights Reserved. 3 www.kreatryx.com
188000x 47000
4
Ratio 47000
47 : 5310000 47000
Q.8 Under a certain legal system, prisoners are allowed to make one statement. If their statement
turns out to be true then they are hanged. If the statement turns out to be false then they are shot.
One prisoner made a statement and the judge had no option but to set him free. Which one of the
following could be that statement?
(a) I will be shot
(b) You committed the crime
(c) I did not commit the crime
(d) I committed the crime
Answer: (a)
Solution:
If prisoner says, I will be shot & he is shot then statement is true & hence he must be hanged but if he
hanged then his statement becomes false & he must be shot
So, both outcomes are impossible
Q.9 M and N had four children P, Q, R and S. Of them, only P and R were married. They had children X
and Y respectively. If Y is a legitimate child of W, which one of the following statements is necessarily
FALSE?
(a) W is the wife of P
(b) R is the father of Y
(c) M is the grandmother of Y
(d) W is the wife of R
Answer: (a)
Solution:
Since P & R have children X & Y respectively.
So, X is a child of P & Y is a child of R
Since Y is legitimate child of W
So, W is married to R
Hence 1st statement is false
Q.10 A firm hires employees at five different skill levels P, Q, P, S, T. The shares of employment at
these skill levels of total employment in 2010 are given in the pie chart as shown. There were a total of
600 employees in 2010 and the total employment increased by 15% from 2010 to 2016. The total
employment at skill levels P, Q and R remained unchanged during this period. If the employment at
skill level S increased by 40% from 2010 to 2016, how many employees were there at skill level T in
2016?
ME Set-1 (Solutions)
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(a) 60 (b) 30
(c) 35 (d) 72
Answer: (a)
Solution:
Number of employees in 2016=1.15 600=690
Employment at P, Q & R leave=20+25+25= 70%
Number of employees at P, Q, R
70600 420
100
This remains same in 2016= 420
Employees at S level in 201025
600 150100
Employees at S level in 2016= 1.40 150= 210
Employees at T level in 2016= 690- (420+210) =60
ME Set-1 (Solutions)
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Technical
Q.1 A spur gear with 20° full depth teeth is transmitting 20kW at 200rad/s. The pitch circle diameter of
the gear is 100 mm. The magnitude of the force applied on the gear in the radial direction is
(a) 0.36kN (b) 0.73kN
(c) 1.39kN (d) 2.78kN
Answer: (b)
Solution:
P T 320 10 T 200
T 100 N-m
NF cos r T
NF cos20 0.05 100
NF 2128.355 N
Radial load, R N
F F sin
RF 2128.355 sin20 727.94 N 0.727 kN
Q.2 A slender rod of length L, diameter d (L>>d) and thermal conductivity1
k is joined with another rod
of identical dimensions, but of thermal conductivity2
k , to form a composite cylindrical rod of length
2L. The heat transfer in radial direction and contact resistance are negligible. The effective thermal
conductivity of the composite rod is
(a) 1 2
1 2
2k k
k k (b)
1 2k k
(c) 1 2
1 2
k k
k k (d)
1 2k k
Answer: (a)
Solution:
1 2 eq
L L 2L
k A k A k A
2 1
1 2 eq
k k 2
k k k
1 2
eq
1 2
2k kk
k k
ME Set-1 (Solutions)
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Q.3 During a high cycle fatigue test, a metallic specimen is subjected to cyclic loading with a mean
stress of +140MPa, and a minimum stress of -70MPa. The R-ratio (minimum stress to maximum stress)
for this cyclic loading is_________ (round off to one decimal place)
Answer: -0.2
Solution:
max min
mean 2
min70 MPa (given), mean
140 MPa given
max
max max
70140 280 70 350 MPa
2
min
max
70R 0.2 R 0.2
350
Q.4 4 A block of mass 10kg rests on a horizontal floor. The acceleration due to gravity is 29.81m s . The
coefficient of static friction between the floor and the block is 0.2. A horizontal force of 10N is applied
on the block as shown in the figure. The magnitude of force of friction (in N) on the block is ________
Answer: 10
Solution:
Limiting force L sF N
Required to move the block 0.2 10 9.81 N mg
19.62 N
The force applied is less than the limiting force, the magnitude of force of friction acting on the block
will be equal to the force applied.
Friction force = 10 N
Q.5 The position vector OP of point P (20, 10) is rotated anti-clockwise in X-Y plane by an angle 030
such that point P occupies position Q, as shown in the figure. The coordinates (x, y) of Q are
(a) (12.32, 18.66)
(b) (18.66, 12.32)
(c) (22.32, 8.26)
(d) (13.40, 22.32)
Answer: (a)
Solution:
x cos sin 20
y sin cos 10
ME Set-1 (Solutions)
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cos30 sin30 2030
sin30 cos30 10
17.32 5 12.32
10 8.66 18.66
Q.6 The lengths of a large stock of titanium rods follow a normal distribution with a mean of
440mm and a standard deviation of 1mm. What is the percentage of rods whose lengths lie
between 438mm and 441mm?
(a) 99.75% (b) 86.64%
(c) 81.85% (d) 68.4%
Answer: (c)
Solution:
440 mm
1mm
Upper limit 441 440
11
Lower limit 438 440
21
So total will be 81.85%
Q.7 Consider an ideal Vapor compression refrigeration cycle. If the throttling process is replaced by an
isentropic expansion process, keeping all the other processes unchanged, which one of the following
statements is true for the modified cycle?
(a) Coefficient of performance is the same as that of the original cycle.
(b) Coefficient of performance is higher than that of the original cycle.
(c) Refrigerating effect is lower than that of the original cycle.
(c) Coefficient of performance is lower than that of the original cycle.
Answer: (b)
Solution:
In case of isentropic expansion, we get more refrigerating effect.
Refrigerating effectCOP
Work supplied
So, original cycle
COP COP
ME Set-1 (Solutions)
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Q.8 The table presents the demand of a product. By simple three-months moving average method,
the demand-forecast of the product for the month of September is
Month Demand
January 450
February 440
March 460
April 510
May 520
June 495
July 475
August 560
(a) 510 (b) 490
(c) 536.67 (d) 530
Answer: (a)
Solution:
By moving average method, we get
Forecast for month of September 495 475 560
5103
Q.9 A parabola 2x y with 0 x 1 is shown in the figure. The volume of the solid of rotation obtained
by rotating the shaded area by 360° around the x-axis is
(a)2
(b)
(c) 2
(d)4
Answer: (a)
Solution:
Assume a disc of width ‘dx’ & radius f (x)
2
2Volume of disc f x dx y dx x dx
1
0
Volume xdx2
Q.10 A flat-faced follower is driven using a circular eccentric cam rotating at a constant angular
velocity . At time t=0, the vertical position of the follower is y(0) =0, and the system is in the
configuration shown below.
The vertical position of the follower face, y(t) is given by
(a) e 1 cos2 t
(b) esin2 t
(c) e 1 cos t
(d) esin t
ME Set-1 (Solutions)
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Answer: (c)
Solution:
y OB OB CD OB
AC AD OB
R ecos R e
e 1 cos
e 1 cos t
Q.11 For a hydrodynamically and thermally fully developed laminar flow through a circular pipe of
constant cross-section, the Nusselt number at constant wall heat flux qNu and that at constant wall
temperature TNu are related as
(a)q T
Nu Nu (b)q T
Nu Nu
(c)q T
Nu Nu (d) 2
q TNu Nu
Answer: (c)
Solution:
q
Nu 4.36
T
Nu 3.36
q T
Nu Nu
Q.12 The length, width and thickness of a steel sample are 400mm, 40mm and 20mm, respectively. Its
thickness needs to be uniformly reduced by 2mm in a single pass by using horizontal slab milling. The
milling cutter (diameter: 100mm, width: 50mm) has 20 teeth and rotates at 1200rpm. The feed per
tooth is 0.05mm. The feed direction is along the length of the sample. If the over-travel distance is the
same as the approach distance, the approach distance and time taken to complete the required
machining task are
(a) 14mm, 18.4s (b) 14mm, 21.4s
(c) 21mm, 28.9s (d) 21mm, 39.4s
Answer: (b)
Solution:
Diameter of milling with (D) = 100 mm, length (L) = 400 mm
tf 0.05 mm
N 1200 rpm
Z 20 teeth
Depth of cut (d) = 2 mm
Approach d D d 2 100 2 14 mm
Time taken m
L 2A
f
where
m tf f N Z
Time taken 400 2 14
21.41200
0.5 2060
seconds
ME Set-1 (Solutions)
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Q.13 Water flows through a pipe with a velocity given by4 ˆV x y jm st
, where j is the unit
vector in the y direction, t (>0) is in seconds, and x and y are in meters. The magnitude of total
acceleration at the point (x, y)= (1,1) at t = 2s is _______ 2m s
Answer: 3
Solution:
x
u u ua u v
x y t
y
v v va u v
x y t
So, x
u u ua u v 0
x y t
y y2
v v v 4 4a u v x y 1 a
x y t t t
ya at (1, 1) and t = 2 is 24 1 3 m/s and this will be equal to total acceleration.
Q.14 In a casting process, a vertical channel through which molten metal flows downward from
pouring basin to runner for reaching the mold cavity is called
(a) Blister (b) Sprue
(c) Pin hole (d) Riser
Answer: (b)
Solution:
The vertical channel through which molten metal flows downward from pouring basin to runner for
reaching the mold cavity is called sprue.
Q.15 Consider the stress-strain curve for an ideal elastic-plastic strain hardening metal as shown in the
figure.
The metal was loaded in uniaxial tension starting from O. Upon loading, the stress-strain curve passes
through initial yield point at P, and then strain hardens to point Q, where the loading was stopped,
From point Q, the specimen was unloaded to point R. where the stress is zero.
If the same specimen is reloaded in tension from point R, the value of stress at which the material
yields again is _______ MPa.
Answer: 210
Solution:
Value of the stress at which material will yield again is 210 MPa as seen from the figure.
ME Set-1 (Solutions)
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Q.16 During a non-flow thermodynamic process (1-2) executed by a perfect gas, the heat interaction
is equal to the work interaction 1 2 1 2Q W
when the process is
(a) Isothermal (b) Adiabatic
(c) Isentropic (d) Polytropic
Answer: (a)
Solution:
From fist law
Q U W
Q W when U 0 which means process is isothermal.
Q.17 A cylindrical rod of diameter 10mm and length 1.0m is fixed at one end. The other end is twisted
by an angle of 10° by applying a torque. If the maximum shear strain in the rod is 3p 10 , then p is
equal to________ (round off to two decimal places),
Answer: 0.85 to 0.90
Solution:
Using maxT G
J R L
max maxG R
R L G L
max
maxG
3
max
0.005 100.872 10
1 180
P 0.872
Q.18 Consider the matrix
1 1 0
P 0 1 1
0 0 1
The number of distinct Eigen values of P is
(a) 3 (b) 1
(c) 2 (d) 0
Answer: (b)
Solution:
The given matrix is upper triangular & hence eigen values are diagonal elements which are all 1.
Hence, there is only 1 distinct eigenvalue.
Q.19 Which one of the following welding methods provides the highest heat flux 2W mm ?
(a) Tungsten inert gas welding
ME Set-1 (Solutions)
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(b) Oxy-acetylene gas welding
(c) Plasma arc welding
(d) Laser beam welding
Answer: (d)
Solution:
Laser Beam welding provides a high heat flux on the order of 9 210 W/ mm and above
Q.20 A solid cube of side 1m is kept at a room temperature of 032 C . The coefficient of linear thermal
expansion of the cube material is 5 01 10 C and the bulk modulus is 200MPa. If the cube is
constrained all around and heated uniformly to 042 C , then the magnitude of volumetric (mean) stress
(in MPa) induced due to heating is ______
Answer: 60
Solution:
Block is heated from all the direction, is countsained from all sides, fo we can else, V
V3 T
k
because it become a case of hydrostatic stress.
V3k T
9 53 200 10 1 10 10 660 10 Pa
60 MPa
Q.21 The natural frequencies corresponding to the spring-mass systems I and II areI
andII
respectively. The ratio I
II
is
(a) 2
(b) 4
(c) 1
2
(d)1
4
Answer: (c)
Solution:
eq
1 1 1
k kk
ME Set-1 (Solutions)
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eq 1
kk
2 and eq 2
k 2k
1
k 2k and
2m m
1
2
k
1 12m
4 22k
m
Q.22 Air of mass 1kg, initially at 300K and 10bar, is allowed to expand isothermally till it reaches a
pressure of 1bar. Assuming air as an ideal gas with gas constant of 0.287kJ/kg.K, the change in entropy
of air (in kJ/kg.K, round off to two decimal places) is _________
Answer: 0.65 to 0.68
Solution:
Isothermal expansion takes place
2 2
P 2 1
1 1
T Ps c ln Rln T T
T P
10.87 ln kJ/kgk
10
s 0.66 kJ/kgk
Q.23 Evaluation of4
3
2
x dx using a 2-equal-segment trapezoidal rule gives a value of _____
Answer: 63
Solution:
For 2 equal segment, we consider a point x = 3 between 2 & 4.
4
3
2
1 1x dx f 2 2f 3 f 4 8 2 27 64 63
2 2
Q.24 For the equation 2dy7x y 0
dx , if 3y 0
7 , then the value of y(1) is
(a)3
73
e7
(b)3
77
e3
(c)7
33
e7
(d)7
37
e3
Answer: (c)
Solution:
This is a linear differential equation
Integrating Factor = 32
7x7x dx
3e e 3 37 7
x x23 3
dye 7x e y 0
dx
37x
3d
e y 0dx
ME Set-1 (Solutions)
© Kreatryx. All Rights Reserved. 14 www.kreatryx.com
3 37 7
x x3 3e y c y c e
Since y (0) = 3
7
3c
7
37x
33
y e7
7
33
y 1 e7
Q.25 As per common design practice, the three types of hydraulic turbines, in descending order of
flow rate, are
(a) Pelton, Francis, Kaplan
(b) Francis, Kaplan, Felton
(c) Kaplan, Francis, Felton
(d) Felton, Kaplan, Francis
Answer: (c)
Solution:
In descending order of flow rate, the three types of hydraulic turbines can be arranged in the following
way
Kaplan > Francis > Pelton
Q.26 A gas turbine with air as the working fluid has an isentropic efficiency of 0.70 when 6 operating
at a pressure ratio of 3. Now, the pressure ratio of the turbine is increased to 5, while maintaining the
same inlet conditions. Assume air as a perfect gas with specific heat ratio 1.4 . If the specific work
output remains the same for both the cases, the isentropic efficiency of the turbine at the pressure
ratio of 5 is _______ (round off to two decimal places)
Answer: 0.50 to 0.55
Solution:
1 2
isen
1 2
T T0.7
T T
and
1/
1 1
2 2
T p
T p
isen for case 2 1 3
1 3
T T
T T
ME Set-1 (Solutions)
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Given, inlet conditions is same
1 2 2
1 1 2
12
1
1
T T T0.7 0.7T 1 T T
TTT 1
T
Similarly, 3
2 1 1 3
1
TT 1 T T
T
Equating the above equation [1 2 1 3
T T T T it is given specific work output is equal]
1 2 10.2857 0.2857
1 10.7T 1 T 1
3 5
20.5114,
Q.27 In ASA system, the side cutting and end cutting edge angles of a sharp turning tool are 45° and
10°, respectively. The feed during cylindrical turning is 0.1mm/rev. The centre line average surface
roughness (in µm, round off to one decimal place) of the generated surface is _______
Answer: 3.7 to 3.8
Solution:
Center line avg surface roughness h
4
where s e
f 0.1h
tanC cotC tan45 cot10
0.1h 0.01498 mm
1 5.6712
h 14.989 m
Center line roughness h 14.989
3.747 m4 4
Q.28 A car having weight W is moving in the direction as shown in the figure. The centre of gravity
(CG) of the car is located at height h from the ground, midway between the front and rear wheels. The
distance between the front and rear wheels is I. The acceleration of the car is a. and acceleration due
to gravity is g. The reactions on the front wheels fR and rear wheels r
R are given by
ME Set-1 (Solutions)
© Kreatryx. All Rights Reserved. 16 www.kreatryx.com
(a)f
W W hR a
2 g l
;
r
W W hR a
2 g l
(b)f r
W W hR R a
2 g l
(c)f r
W W hR R a
2 g l
(d)f
W W hR a
2 g l
;
r
W W hR a
2 g l
Answer: (d)
Solution:
V r fF 0 R R W …… (1)
Taking moment about P.
fR ma h w 0
2
f
WR mah
2
f
W W hR a
2 g
From (1), r
W W hR a
2 g
Q.29 If one mole of2
H gas occupies a rigid container with a capacity of 1000 litres and the temperature
is raised from 27°C to 37°C, the change in pressure of the contained gas (round off to two decimal
places), assuming ideal gas behaviour, is ______Pa. (R=8.314J/mol-K)
Answer: 80 to 85
Solution:
1P V nRT,
1P 1 1 8.314 300 31000 1m
1P 2494.2 pa
Now, 2 2
P V nRT
2P 1 1 8.314 310 1 2
1 2
V V
n n
2P 2577.34 pa
Change in pressure 2 1
P P 2577.34 2494.2 Pa
83.14 Pa
Q.30 Five jobs (J1, J2, J3, J4 and J5) need to be processed in a factory. Each job can be assigned to any
of the five different machines (M1, M2, M3, M4 and M5). The time durations taken (in minutes) by the
machines for each of the jobs, are given in the table. However, each job is assigned to a specific
machine in such a way that the total processing time is minimum.
The total processing time is __________minutes.
ME Set-1 (Solutions)
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M1 M2 M3 M4 M4
J1 40 30 50 50 58
J2 26 38 60 26 38
J3 40 34 28 24 30
J4 28 40 40 32 48
J5 28 32 38 22 44
Answer: 146
Solution:
40 30 50 50 58
26 38 60 26 38
40 34 28 24 30
28 40 40 32 48
28 32 38 22 44
Subtracting lowest element of each row from corresponding row
10 0 20 20 28
0 12 34 0 12
16 10 4 0 6
0 12 12 4 20
6 10 16 0 22
Subtracting lowest element of each column from corresponding column
ME Set-1 (Solutions)
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min cost 28 30 28 22 38 146
Q.31 In orthogonal turning of a cylindrical tube of wall thickness 5mm, the axial and the tangential
cutting forces were measured as 1259N and 1601N. respectively. The measured chip thickness after
machining was found to be 0.3mm. The rake angle was 10° and the axial feed was 100mm/min. The
rotational speed of the spindle was 1000rpm. Assuming the material to be perfectly plastic and
Merchant's first solution, the shear strength of the material is closest to
(a) 920MPa
(b) 722MPa
(c) 875MPa
(d) 200MPa
Answer: (b)
Solution:
Orthogonal turning (given)
t f sin 90
t f …… (1)
Now, mf f N
mm rev min100 f 1000 f 0.1
min min rev
From (1), t 0.1
and ct 0.3 mm given
c
t 0.1r 0.33
t 0.3
Axial force x T
F F sin
T1259 N F
and cF 1601 N given
Shear strength s
s
F
bt / sin
…… (2)
Now, s c T
F F cos F sin …… (3)
For finding , use r cos 0.33cos10
tan tan1 rsin 1 0.33sin10
19.021
Put 19.021 in (3)
ME Set-1 (Solutions)
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s c TF F cos 19.021 F sin 19.021 1103.2533 N
Using (2) s
1103.2533719.132 MPa
5 0.1 / sin19.021
Q.32 A circular shaft having diameter 0.01
0.0565.00 mm
is manufactured by turning process. A 50µm thick
coating of TiN is deposited on the shaft. Allowed variation in TiN film thickness is 5 m . The minimum
hole diameter (in min) to just provide clearance fit is
(a) 65.01 (b) 65.12
(c) 64.95 (d) 65.10
Answer: (b)
Solution:
Minimum hole diameter just to provide clearance fit is equal to the maximum diameter of shaft
possible which is equal to 65.01 2 0.05 2 0.005 mm
maximum diameter of shaft 65.12 mm
Q.33 Two immiscible, incompressible, viscous fluids having same densities but different viscosities are
contained between two infinite horizontal parallel plates, 2 in apart as shown below. The bottom plate
is fixed and the upper plate moves to the right with a constant velocity of 3m/s. With the assumptions
of Newtonian fluid steady and fully developed laminar flow with zero pressure gradients in all
directions, the momentum equations simplify to
2
2
d u0
dy
If the dynamic viscosity of the lower fluid2
,
is twice that of the upper fluid,1
then the velocity
at the interface (round off to two decimal places) is _______ m/s
Answer: ()
Solution: 2
2
d u0
dy
1
duC
dy
1 2u C y C
The velocity profile is linear
Shear stress at interface will be same
1 2
1 2
1 2
du du
dy dy
i i
1 1
3 V V 02
1 1
ME Set-1 (Solutions)
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i i3 V 2V
iV 1 m/s
Q.34 The rotor of a turbojet engine of an aircraft has a mass 180kg and polar moment of inertia 10
kg.m2 about the rotor axis. The rotor rotates at a constant speed of 1100 racks in the clockwise
direction when viewed from the front of the aircraft. The aircraft while flying at a speed of 800km per
hour takes a turn with a radius of 1.5km to the left. The gyroscopic moment exerted by the rotor on
the aircraft structure and the direction of motion of the nose when the aircraft turns, are
(a) 162.9N.m and the nose goes down
(b) 162.9N.m and the nose goes up
(c) 1629.6N.m and the nose goes up
(d) 1629.6N.m and the nose goes down
Answer: (d)
Solution:
Gyroscopic couple p pI 10 1100
p
V
R where
5V 800
18 and R 1500 m
Gyroscopic couple 5 1
10 1100 80018 1500
1629.629 Nm
the engine rotates in the clockwise direction and the aeroplane takes a left turn, the nose will go
down.
Q.35 In a four bar planar mechanism shown in the figure, AB =5cm. AD =4cm and DC =2cm. In the
configuration shown, both AB and DC are perpendicular to AD. The bar AB rotates with an angular
velocity of 10rad/s. The magnitude of angular velocity (in rad/s) of bar DC at this instant is
(a) 15
(b) 25
(c) 0
(d) 10
Answer: (b)
Solution:
This is a previous year GATE question on the same concept.
for this case, B c
V V
AB CD5 2
CD
10 5
2
2
CD25 rad / s
ME Set-1 (Solutions)
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Q.36 The value of the following definite integral is _______ (round off to three decimal places)
e
1
xlnx dx
Answer: 2.0 to 2.2
Solution:
e
e 2 2 2 2 2 2 2
1 1
x 1 x x x e e 1 e 1x ln x dx ln x dx ln x ln 2.097
2 x 2 2 4 2 4 4 4 4
Q.37 A steam power cycle with regeneration as shown below on the T-s diagram employs a single
open feed water heater for efficiency improvement. The fluids mix with each other in an open feed
water heater. The turbine is isentropic and the input (bleed) to the feed water heater from the turbine
is at state 2 as shown in the figure. Process 3-4 occurs in the condenser. The pump work is negligible.
The input to the boiler is at state 5. The following information is available from the steam tables:
State 1 2 3 4 5 6
Enthalpy (kJ/kg) 3350 2800 2300 175 700 1000
The mass flow rate of steam bled from the turbine as a percentage of the total mass flow rate at the
inlet to the turbine at state 1 is _______
Answer: 20
Solution:
Using energy balance
2 4 5mh 1 m h h
in 2800 1 m 175 700
2625 m 525
m 0.2 i.e. 20%
ME Set-1 (Solutions)
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Q.38 A harmonic function is analytic if it satisfies the Laplace equation.
If 2 2u x,y 2x 2y 4xy is a harmonic function, then its conjugate harmonic function v(x, y) is
(a) 2 24xy 2y 2x Constant
(b) 2 22x 2y xy Constant
(c) 2 24xy 2x 2y Constant
(d) 24y 4xy Constant
Answer: (c)
Solution:
x
uu 4x 4y
x
By Cauchy – Riemann equation
x yu u
v
4x 4yx
2v 4xy 2y f x
'
x
uv 4y f x
x
Since, x y
uv u
y
'4y f x 4y 4x
'f x 4x
2f x 2x c
2 2v 4xy 2y 2x c
Q.39 At a critical point in a component, the state of stress is given asxx
100MPa ,xy
220MPa ,
xy yx80MPa and all other stress components are zero. The yield strength of the material is
468MPa. The factor of safety on the basis of maximum shear stress theory is ________ (round off to one
decimal place).
Answer: 1.8
Solution:
Finding 1,2
from the given data
2
x y x y 2
1,2 xy2 2
2
2100 220 100 22080
2 2
160 100
1 2260 MPa, 60 MPa
On the basis of maximum shear stress theory
ME Set-1 (Solutions)
© Kreatryx. All Rights Reserved. 23 www.kreatryx.com
Maximum of yt1 2 1 2
S, ,
2 2 2 2N
Maximum of 468
100, 130, 302N
468130
2N
N 1.8
Q.40 A single block brake with a short shoe and torque capacity of 250N.m is shown. The cylindrical
brake drum rotates anticlockwise at 100rpm and the coefficient of friction is 0.25.
The value of a, in mm. (round off to one decimal place), such that the maximum actuating force P is
2000 N, is _______
Answer: 210 to 215
Solution:
f N 0.25 N
Taking moment about A
aP 2.5a N a f 0
4
0.25N
P 2.5 N4
2000 2.5 1.0625 N
N 4705.88 N
T 250 N-m N a
a 0.2125 m 212.5 mm
Q.41 The set of equations
x y z 1
ax ay 3z 5
5x 3y az 6
Has infinite solutions, if a=
ME Set-1 (Solutions)
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(a) -4 (b) -3
(c) 4 (d) 3
Answer: (c)
Solution:
Equation can be expressed in matrix form as
1 1 1 x 1
a a 3 y 5
5 3 a z 6
Equations have infinite solution if A 0
1 1 1
a a 3 0
5 3 a
2 21 a 9 1 a 15 1 3a 5a 0
22a 24 2a 0 2a a 12 0
a 4 and a 3
Out of this only a = 4 gives infinite solution because then
(i) + (ii) = (iii)
Hence equations becomes linearly dependent & number of linearly independent equations are less
than number of variables.
Q.42 In a UTM experiment, a sample of length 100mm was loaded in tension until failure. The failure
load was 40kN. The displacement, measured using the cross-head motion, at failure, was 15mm; the
compliance of the UTM is constant and is given by 85 10 m N . The strain at failure in the sample is
________ %.
Answer: 2
Solution:
L 100 mm 0.1m
P 40 kN
Compliance 2
2
L mm/N
NAEm
m
Given compliance 85 10 m/N
3 8PL40 10 5 10
AE
m
3 840 10 5 100.02
L 0.1
% 0.02 100% 2%
Q.43 A uniform thin disk of mass 1kg and radius 0.1m is kept on a surface as shown in the figure. A
spring of stiffness 1
k 400N m is connected to the disk centre A and another spring of stiffness
2k 100N m is connected at point B just above point A on the circumference of the disk. Initially, both
the springs are un-stretched. Assume pure rolling of the disk. For small disturbance from the
ME Set-1 (Solutions)
© Kreatryx. All Rights Reserved. 25 www.kreatryx.com
equilibrium, the natural frequency of vibration of the system is __________rad/s (round off to one
decimal place).
Answer: 22.5 to 23.5
Solution:
Moment of inertia of thin disc about 2 2
2mR 3mRC mR
2 2
Using conservation of energy method.
2 2 2
1 2
1 1 1I k x k y C
2 2 2
Relation between x and y, x y
2x yR 2R
and x R x R 2
2 2 2
1 22
1 3 x 1 1mR k x k 4x C
2 2 2 2k
Differentiating
1 2
3m xx k xx k 4xx 0
2
3
1 x 400x 400x 02
800 2x x 0
3
2
n n
160023.094 rad/sec
3
Q.44 A cube of side 100 mm is placed at the bottom of an empty container on one of its faces. The
density of the material of the cube is 3800kg m . Liquid of density 31000kg m is now poured into the
container. The minimum height to which the liquid needs to be poured into the container for the cube
to just lift up is ________mm.
Answer: 80
Solution:
Let, the height of the fluid be ‘h’, when cube just lifts up.
BF mg
f submerged b bodyV g V g
31000 a a h 800 a
h 0.8 100 mm
h 80 mm
ME Set-1 (Solutions)
© Kreatryx. All Rights Reserved. 26 www.kreatryx.com
Q.45 Consider an elastic straight beam of length L=10πm, with square cross-section of side a = 5mm,
and Young's modulus E =200GPa. This straight beam was bent in such a way that the two ends meet,
to form a circle of mean radius R. Assuming that Euler-Bernoulli beam theory is applicable to this
bending problem, the maximum tensile bending stress in the bent beam is _________MPa.
Answer: 100
Solution:
Using
M E
J Y R
L 10 2 R R 5m
So, E
a / 2 R
9200 10 0.005
5 2
100 MPa
Q.46 The wall of a constant diameter pipe of length 1m is heated uniformly with flux q" by wrapping a
heater coil around it. The flow at the inlet to the pipe is hydrodynamically fully developed. The fluid is
incompressible and the flow is assumed to be laminar and steady all
through the pipe. The bulk temperature of the fluid is equal to 0°C at the inlet and 50°C at the exit.
The wall temperatures are measured at three locations, P, Q and R, as shown in the figure. The flow
thermally develops after some distance from the inlet. The following measurements are made:
Point P Q R
Wall temp C 50 80 90
Among the locations P, Q and R. the flow is thermally developed at
(a) P and Q only
(b) P, Q and R
(c) R only
(d) Q and R only
Answer: (d)
Solution:
For constant wall flux
ME Set-1 (Solutions)
© Kreatryx. All Rights Reserved. 27 www.kreatryx.com
T remains same after the flow is developed.
P QT | 30 C, T | 50 C ,
RT | 50 C
So flow is thermally developed at Q and R,
Q.47 A plane-strain compression (forging) of a block is shown in the figure. The strain in the direction
is zero. The yield strength yS in uniaxial tension/compression of the material of the block is 300MPa
and it follows the Tresca (maximum shear stress) criterion. Assume that the entire block has started
yielding. At a point where x
40MPa (compressive) and,xy
0 the stress componenty
is
(a) 340MPa (tensile)
(b) 340MPa (compressive)
(c) 260MPa (tensile)
(d) 260MPa (compressive)
Answer: (b)
Solution:
1 2 1 2 SytMax , , ,
2 2 2 2 N
2
2
x y x y
1, 2 xy2 2
x y x y
2 2
x y x y
1 x2 2
x y x y
2 y2 2
ME Set-1 (Solutions)
© Kreatryx. All Rights Reserved. 28 www.kreatryx.com
x y yx SytMax , , , N 1
2 2 2 2 N
y y yt40 S300
and2 2 2 2
y y340 MPa 300 MPa
Larger of the 2 values will the y
y340 MPa
Q.48 A gas is heated in a duct as it flows over a resistance heater. Consider a 101kW electric heating
system. The gas enters the heating section of the duct at 100kPa and 27 °C with a volume flow rate of315m s . If heat is lost from the gas in the duct to the surroundings at a rate of 51kW, the exit
temperature of the gas is
(Assume constant pressure, ideal gas, negligible change in kinetic and potential energies and constant
specific heatP
C 1kJ kg ;R 0.5kJ kg.K )
(a) 037 C (b) 053 C
(c) 032 C (d) 076 C
Answer: (c)
Solution:
k.e. p.e 0
From SFEE
1 2mh Q mh W i
Finding m
PV mRT 3100 10 V mx500 300
m 10 kg / s
So putting in equation (i)
1 2m h h W Q
3
p 1 210 c T T 50 10
3 3
210 1 10 300 T 50 10
2
2
300 5 T
T 305 K 32 C
Q.49 Match the following sand mold casting defects with their respective causes.
Defect Cause
P Blow hole 1 Poor collapsibility
Q Misrun 2 Mold erosion
R Hot tearing 3 Poor permeability
S Wash 4 Insufficient fluidity
ME Set-1 (Solutions)
© Kreatryx. All Rights Reserved. 29 www.kreatryx.com
(a) P-3, Q-4, R-2, S-1 (b) P-3, Q-4, R-1, S-2
(c) P-2, Q-4, R-1, S-3 (d) P-4, Q-3, R-1, S-2
Answer: (b)
Solution:
Blow hole poor permeability
Misrun Insufficient fluidity
Hot tearing poor collapsibility
Wash Mold erosion
Q.50
A project consists of six activities. The immediate predecessor of each activity and the estimated
duration is also provided in the table below:
Activity Immediate
predecessor
Estimate duration
(week)
P - 5
Q - 1
R Q 2
S P, R 4
T P 6
U S, T 3
If all activities other than S take the estimated amount of time, the maximum duration (in weeks) of
the activity S without delaying the completion of the project is _________
Answer: 6
Solution:
Max duration of S = 6 weeks
Q.51
Taylor's tool life equation is given by nVT C , where V is in m/min and T is in min. In a turning
operation, two tools X and Y are used. For tool X. n =0.3 and C=60 and for tool Y, n=0.6 and C=90.
Both the tools will have the same tool life for the cutting speed (in m/min, round off to one decimal
place) of _________
Answer: 38 to 41
Solution: nVT C
ME Set-1 (Solutions)
© Kreatryx. All Rights Reserved. 30 www.kreatryx.com
For X: 0.3VT 60 …… (1)
For Y: 0.6VT 90 …… (2)
From (1), we get,
1/0.3
0T
V
…… (3)
From (2), we get,
1/0.6
90T
V
…… (4)
Equating (3) & (4), we get 1/0.3 1/0.6
60 90
V V
2
60 90
V V
260V
90
V 40 m/min
Q.52 Consider a prismatic straight beam of length L=πm, Pinned at the two ends as shown in the
figure.
The beam has a square cross-section of side p =6mm.
The Young's modulus E = 200GPa, and the coefficient of thermal expansion 6 13 10 K . The
minimum temperature rise required to cause Euler buckling of the beam is _______ K.
Answer: 1
Solution:
2 min
2
e
EIP
L
For hinged beam e
L L m
4
92
2
0.006200 10P
12
And P
E TA
4
99 6
2
0.006200 10200 10 3 10 T
120.006
T 1K
ME Set-1 (Solutions)
© Kreatryx. All Rights Reserved. 31 www.kreatryx.com
Q.53
Three slabs are joined together as shown in the figure. There is no thermal contact resistance at the
interfaces. The center slab experiences a non-uniform internal heat generation with an average value
equal to 31000Wm , while the left and right slabs have no internal heat generation. All slabs have
thickness equal to 1 m and thermal conductivity of each slab is equal to 1 15Wm K . The two extreme
faces are exposed to fluid with heat transfer coefficient 2 1100Wm K and bulk temperature 30 °C as
shown. The heat transfer in the slabs is assumed to be one dimensional and steady, and all properties
are constant. If the left extreme face temperature1
T is measured to be 100 °C, the right extreme face
temperature2
T is __________°C.
Answer: 60
Solution:
1q (through conduction) q through convection on LHS
hA T
100 A 70
7000 A W
2q (through conduction) q through convection on RHS
hA T
3100 A T 30
Now, 1 2
q q 10000 1 A
37000 A 100 A T 30 10000 1 A
37000 100T 3000 10000
3T 60 C
Q.54 The variable x takes a value between 0 and 10 with uniform probability distribution. The variable
y takes a value between 0 and 20 with uniform probability distribution. The probability of the sum of
variables (x +y) being greater than 20 is
(a) 0.25
(b) 0.50
(c) 0
(d) 0.33
ME Set-1 (Solutions)
© Kreatryx. All Rights Reserved. 32 www.kreatryx.com
Answer: (a)
Solution:
If we plot both variables on each axis
Since y x 20, we plot a line y x 20 & shaded area gives probability
x yP x y 20 f x f y dx dy
10 20
0 20 x
1 1dy dx
10 20
10
0
120 20 x dx
200
102
0
1 x 10.25
200 2 4
Q.55 A truss is composed of members AB. BC. CD. AD and BD. as shown in the figure. A vertical 5 load
of 10kN is applied at point D. The magnitude of force (in kN) in the member BC is ________
Answer: 5
Solution:
Taking moment about A.
cR 2a 10 a
cR 5 kN
By lami’s theorem
BC cF R
sin135 sin135
BCF 5 kN
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