GATE ME 2018: Mechanical Engineering Session 2
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GATE 2018 General Aptitude (GA) Set-2
Q. 1 – Q. 5 carry one mark each.
Q.1 “The dress _________ her so well that they all immediately _________ her on her
appearance.”
The words that best fill the blanks in the above sentence are
(A) complemented, complemented (B) complimented, complemented
(C) complimented, complimented (D) complemented, complimented
Q.2 “The judge’s standing in the legal community, though shaken by false allegations of
wrongdoing, remained _________.”
The word that best fills the blank in the above sentence is
(A) undiminished (B) damaged (C) illegal (D) uncertain
Q.3 Find the missing group of letters in the following series:
BC, FGH, LMNO, _____
(A) UVWXY (B) TUVWX (C) STUVW (D) RSTUV
Q.4 The perimeters of a circle, a square and an equilateral triangle are equal. Which one of the
following statements is true?
(A) The circle has the largest area.
(B) The square has the largest area.
(C) The equilateral triangle has the largest area.
(D) All the three shapes have the same area.
Q.5 1 1 1
The value of the expression + + is _________.
1+logu vw 1+logv wu 1+logw uv
(A) -1 (B) 0 (C) 1 (D) 3
Q. 6 – Q. 10 carry two marks each.
Q.6 Forty students watched films A, B and C over a week. Each student watched either only
one film or all three. Thirteen students watched film A, sixteen students watched film B
and nineteen students watched film C. How many students watched all three films?
(A) 0 (B) 2 (C) 4 (D) 8
GA 1/3
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GATE 2018 General Aptitude (GA) Set-2
Q.7 A wire would enclose an area of 1936 m2, if it is bent into a square. The wire is cut into
two pieces. The longer piece is thrice as long as the shorter piece. The long and the short
pieces are bent into a square and a circle, respectively. Which of the following choices is
closest to the sum of the areas enclosed by the two pieces in square meters?
(A) 1096 (B) 1111 (C) 1243 (D) 2486
Q.8 A contract is to be completed in 52 days and 125 identical robots were employed, each
operational for 7 hours a day. After 39 days, five-seventh of the work was completed. How
many additional robots would be required to complete the work on time, if each robot is
now operational for 8 hours a day?
(A) 50 (B) 89 (C) 146 (D) 175
Q.9 A house has a number which needs to be identified. The following three statements are
given that can help in identifying the house number.
i. If the house number is a multiple of 3, then it is a number from 50 to 59.
ii. If the house number is NOT a multiple of 4, then it is a number from 60 to 69.
iii. If the house number is NOT a multiple of 6, then it is a number from 70 to 79.
What is the house number?
(A) 54 (B) 65 (C) 66 (D) 76
GA 2/3
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GATE 2018 General Aptitude (GA) Set-2
Q.10 An unbiased coin is tossed six times in a row and four different such trials are conducted.
One trial implies six tosses of the coin. If H stands for head and T stands for tail, the
following are the observations from the four trials:
(1) HTHTHT (2) TTHHHT (3) HTTHHT (4) HHHT__ __.
Which statement describing the last two coin tosses of the fourth trial has the highest
probability of being correct?
(A) Two T will occur.
(B) One H and one T will occur.
(C) Two H will occur.
(D) One H will be followed by one T.
END OF THE QUESTION PAPER
GA 3/3
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GATE 2018 Mechanical Engineering (Set 2)
Q. 1 – Q. 25 carry one mark each.
Q.1 The Fourier cosine series for an even function f ( x) is given by
f ( x ) a0 an cos(nx ) .
n 1
The value of the coefficient a 2 for the function f ( x) cos ( x) in [0, ] is
2
(A) 0.5 (B) 0.0 (C) 0.5 (D) 1.0
Q.2
The divergence of the vector field u e x cos y iˆ sin y ˆj is
(A) 0 (B) e x cos y e x sin y
(C) 2e x cos y (D) 2e x sin y
Q.3 Consider a function u which depends on position x and time t. The partial differential
equation
u 2u
t x 2
is known as the
(A) Wave equation
(B) Heat equation
(C) Laplace’s equation
(D) Elasticity equation
x 3 0 , y0 1 , the value of y 1
Q.4 dy
If y is the solution of the differential equation y 3
dx
is
(A) −2 (B) −1 (C) 0 (D) 1
Q.5 The minimum axial compressive load, P, required to initiate buckling for a pinned-pinned
slender column with bending stiffness EI and length L is
2 EI 2 EI 3 2 EI 4 2 EI
(A) P (B) P (C) P (D) P
4 L2 L2 4 L2 L2
ME 1/15
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GATE 2018 Mechanical Engineering (Set 2)
Q.6 A frictionless gear train is shown in the figure. The leftmost 12-teeth gear is given a torque
of 100 N-m. The output torque from the 60-teeth gear on the right in N-m is
12 Teeth
T =100 N-m 48 Teeth
60 Teeth
12 Teeth
(A) 5 (B) 20 (C) 500 (D) 2000
Q.7 In a single degree of freedom underdamped spring-mass-damper system as shown in the
figure, an additional damper is added in parallel such that the system still remains
underdamped. Which one of the following statements is ALWAYS true?
M
K C
(A) Transmissibility will increase.
(B) Transmissibility will decrease.
(C) Time period of free oscillations will increase.
(D) Time period of free oscillations will decrease.
Q.8 Pre-tensioning of a bolted joint is used to
(A) strain harden the bolt head (B) decrease stiffness of the bolted joint
(C) increase stiffness of the bolted joint (D) prevent yielding of the thread root
Q.9 The peak wavelength of radiation emitted by a black body at a temperature of 2000 K is
1.45 µm. If the peak wavelength of emitted radiation changes to 2.90 µm, then the
temperature (in K) of the black body is
(A) 500 (B) 1000 (C) 4000 (D) 8000
ME 2/15
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GATE 2018 Mechanical Engineering (Set 2)
Q.10 For an ideal gas with constant properties undergoing a quasi-static process, which one of
the following represents the change of entropy (s) from state 1 to 2?
T P
(A) s C p ln 2 R ln 2
T1 P1
T V
(B) s CV ln 2 C p ln 2
T1 V1
T P
(C) s C P ln 2 CV ln 2
T1 P1
T V
(D) s CV ln 2 R ln 1
T1 V2
Q.11 Select the correct statement for 50% reaction stage in a steam turbine.
(A) The rotor blade is symmetric.
(B) The stator blade is symmetric.
(C) The absolute inlet flow angle is equal to absolute exit flow angle.
(D) The absolute exit flow angle is equal to inlet angle of rotor blade.
Q.12 Denoting L as liquid and M as solid in a phase-diagram with the subscripts representing
different phases, a eutectoid reaction is described by
(A) M 1 M 2 M 3
(B) L1 M 1 M 2
(C) L1 M 1 M 2
(D) M 1 M 2 M 3
Q.13 During solidification of a pure molten metal, the grains in the casting near the mould wall
are
(A) coarse and randomly oriented
(B) fine and randomly oriented
(C) fine and ordered
(D) coarse and ordered
Q.14 Match the following products with the suitable manufacturing process
Product Manufacturing Process
P Toothpaste tube 1 Centrifugal casting
Q Metallic pipes 2 Blow moulding
R Plastic bottles 3 Rolling
S Threaded bolts 4 Impact extrusion
(A) P-4, Q-3, R-1, S-2 (B) P-2, Q-1, R-3, S-4
(C) P-4, Q-1, R-2, S-3 (D) P-1, Q-3, R-4, S-2
ME 3/15
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GATE 2018 Mechanical Engineering (Set 2)
Q.15 Feed rate in slab milling operation is equal to
(A) rotation per minute (rpm)
(B) product of rpm and number of teeth in the cutter
(C) product of rpm, feed per tooth and number of teeth in the cutter
(D) product of rpm, feed per tooth and number of teeth in contact
Q.16 Metal removal in electric discharge machining takes place through
(A) ion displacement
(B) melting and vaporization
(C) corrosive reaction
(D) plastic shear
Q.17 The preferred option for holding an odd-shaped workpiece in a centre lathe is
(A) live and dead centres (B) three jaw chuck
(C) lathe dog (D) four jaw chuck
Q.18 A local tyre distributor expects to sell approximately 9600 steel belted radial tyres next
year. Annual carrying cost is Rs. 16 per tyre and ordering cost is Rs. 75. The economic
order quantity of the tyres is
(A) 64 (B) 212 (C) 300 (D) 1200
Q.19 1 2 3
If A = 0 4 5 then det(A-1) is __________ (correct to two decimal places).
0 0 1
Q.20 A hollow circular shaft of inner radius 10 mm, outer radius 20 mm and length 1 m is to be
used as a torsional spring. If the shear modulus of the material of the shaft is 150 GPa, the
torsional stiffness of the shaft (in kN-m/rad) is ________ (correct to two decimal places).
Q.21 Fatigue life of a material for a fully reversed loading condition is estimated from
a 1100 N 0.15 ,
where a is the stress amplitude in MPa and N is the failure life in cycles. The maximum
allowable stress amplitude (in MPa) for a life of 1 105 cycles under the same loading
condition is ________ (correct to two decimal places).
ME 4/15
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GATE 2018 Mechanical Engineering (Set 2)
Q.22 The viscous laminar flow of air over a flat plate results in the formation of a boundary
layer. The boundary layer thickness at the end of the plate of length L isL. When the plate
length is increased to twice its original length, the percentage change in laminar boundary
layer thickness at the end of the plate (with respect to L) is ________ (correct to two
decimal places).
Q.23 An engine operates on the reversible cycle as shown in the figure. The work output from
the engine (in kJ/cycle) is ______ (correct to two decimal places).
Q.24 The arrival of customers over fixed time intervals in a bank follow a Poisson distribution
with an average of 30 customers/hour. The probability that the time between successive
customer arrival is between 1 and 3 minutes is _______ (correct to two decimal places).
ME 5/15
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GATE 2018 Mechanical Engineering (Set 2)
Q.25 A ball is dropped from rest from a height of 1 m in a frictionless tube as shown in the
figure. If the tube profile is approximated by two straight lines (ignoring the curved
portion), the total distance travelled (in m) by the ball is __________ (correct to two
decimal places).
ME 6/15
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GATE 2018 Mechanical Engineering (Set 2)
Q. 26 – Q. 55 carry two marks each.
Q.26 Let z be a complex variable. For a counter-clockwise integration around a unit circle C ,
centred at origin,
1
∮C 5z−4 dz = Aπi ,
the value of A is
(A) 2/5 (B) 1/2 (C) 2 (D) 4/5
Q.27 Let X1 and X2 be two independent exponentially distributed random variables with means
0.5 and 0.25, respectively. Then Y = min (X1, X2) is
(A) exponentially distributed with mean 1⁄6
(B) exponentially distributed with mean 2
(C) normally distributed with mean 3⁄4
(D) normally distributed with mean 1⁄6
Q.28 For a position vector r x i y j z k the norm of the vector can be defined as
r x 2 y 2 z 2 . Given a function ln r , its gradient is
r⃗ r⃗ r⃗
(A) r⃗ (B) (C) (D)
|r⃗| r⃗∙r⃗ |r⃗|3
Q.29 In a rigid body in plane motion, the point R is accelerating with respect to point P at
10∠180 m/s2. If the instantaneous acceleration of point Q is zero, the acceleration (in
m/s2) of point R is
(A) 8∠233 (B) 10∠225 (C) 10∠217 (D) 8∠217
ME 7/15
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GATE 2018 Mechanical Engineering (Set 2)
Q.30 A rigid rod of length 1 m is resting at an angle 45o as shown in the figure. The end P is
dragged with a velocity of U 5 m/s to the right. At the instant shown, the magnitude of
the velocity V (in m/s) of point Q as it moves along the wall without losing contact is
(A) 5 (B) 6 (C) 8 (D) 10
Q.31 A bar of circular cross section is clamped at ends P and Q as shown in the figure. A
torsional moment T = 150 Nm is applied at a distance of 100 mm from end P. The
torsional reactions (TP , TQ ) in Nm at the ends P and Q respectively are
(All dimensions are in mm)
(A) (50, 100) (B) (75, 75) (C) (100, 50) (D) (120, 30)
ME 8/15
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GATE 2018 Mechanical Engineering (Set 2)
Q.32 In a cam-follower, the follower rises by h as the cam rotates by (radians) at constant
angular velocity (radians/s). The follower is uniformly accelerating during the first half
of the rise period and it is uniformly decelerating in the latter half of the rise period.
Assuming that the magnitudes of the acceleration and deceleration are same, the maximum
velocity of the follower is
4ℎ 2ℎ
(A) (B) ℎω (C) (D) 2ℎ
Q.33 A bimetallic cylindrical bar of cross sectional area 1 m2 is made by bonding Steel
(Young’s modulus = 210 GPa) and Aluminium (Young’s modulus = 70 GPa) as shown in
6
the figure. To maintain tensile axial strain of magnitude 10 in Steel bar and compressive
6
axial strain of magnitude 10 in Aluminum bar, the magnitude of the required force P (in
kN) along the indicated direction is
(A) 70 (B) 140 (C) 210 (D) 280
Q.34 Air flows at the rate of 1.5 m3/s through a horizontal pipe with a gradually reducing cross-
section as shown in the figure. The two cross-sections of the pipe have diameters of
400 mm and 200 mm. Take the air density as 1.2 kg/m3 and assume inviscid
incompressible flow. The change in pressure p2 p1 (in kPa) between sections 1 and 2
is
200 mm
Air Flow 1
400 mm 2
1.5 m3/s
(A) 1.28 (B) 2.56 (C) 2.13 (D) 1.28
ME 9/15
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GATE 2018 Mechanical Engineering (Set 2)
Q.35 The problem of maximizing z x1 x2 subject to constraints x1 x2 10, x1 0, x2 0
and x2 5 has
(A) no solution
(B) one solution
(C) two solutions
(D) more than two solutions
Q.36 Given the ordinary differential equation
d 2 y dy
6y 0
dx 2 dx
dy
with y(0) 0 and (0) 1 , the value of y(1) is _________ (correct to two decimal
dx
places).
Q.37 A thin-walled cylindrical can with rigid end caps has a mean radius R 100 mm and a
wall thickness of t 5 mm. The can is pressurized and an additional tensile stress of
50 MPa is imposed along the axial direction as shown in the figure. Assume that the state
of stress in the wall is uniform along its length. If the magnitudes of axial and
circumferential components of stress in the can are equal, the pressure (in MPa) inside the
can is ___________ (correct to two decimal places).
Q.38 A bar is subjected to a combination of a steady load of 60 kN and a load fluctuating
between10 kN and 90 kN. The corrected endurance limit of the bar is
150 MPa, the yield strength of the material is 480 MPa and the ultimate strength of the
material is 600 MPa. The bar cross-section is square with side a. If the factor of safety is 2,
the value of a (in mm), according to the modified Goodman’s criterion, is ________
(correct to two decimal places).
ME 10/15
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GATE 2018 Mechanical Engineering (Set 2)
Q.39 A force of 100 N is applied to the centre of a circular disc, of mass 10 kg and radius 1 m,
resting on a floor as shown in the figure. If the disc rolls without slipping on the floor, the
linear acceleration (in m/s2) of the centre of the disc is ________ (correct to two decimal
places).
100N
Q.40 A frictionless circular piston of area 10 2 m2 and mass 100 kg sinks into a cylindrical
container of the same area filled with water of density 1000 kg/m3 as shown in the figure.
3
The container has a hole of area 10 m2 at the bottom that is open to the atmosphere.
Assuming there is no leakage from the edges of the piston and considering water to be
incompressible, the magnitude of the piston velocity (in m/s) at the instant shown is _____
(correct to three decimal places).
patm
g = 10 m/s2
100 kg
0.5 m
ME 11/15
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GATE 2018 Mechanical Engineering (Set 2)
Q.41 A 0.2 m thick infinite black plate having a thermal conductivity of 3.96 W/m-K is exposed
to two infinite black surfaces at 300 K and 400 K as shown in the figure. At steady state,
the surface temperature of the plate facing the cold side is 350 K. The value of Stefan-
Boltzmann constant, , is 5.67 × 10-8 W/m2 K4. Assuming 1-D heat conduction, the
magnitude of heat flux through the plate (in W/m2) is ________ (correct to two decimal
places).
0.2 m
vacuum vacuum 400 K
300 K
Q.42 Air is held inside a non-insulated cylinder using a piston (mass M=25 kg and area A=100
cm2) and stoppers (of negligible area), as shown in the figure. The initial pressure Pi and
temperature Ti of air inside the cylinder are 200 kPa and 400C, respectively. The ambient
pressure P and temperature T are 100 kPa and 27C, respectively. The temperature of the
air inside the cylinder (C) at which the piston will begin to move is _________ (correct to
two decimal places).
ME 12/15
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GATE 2018 Mechanical Engineering (Set 2)
Q.43 A standard vapor compression refrigeration cycle operating with a condensing temperature
of 35 o C and an evaporating temperature of 10 o C develops 15 kW of cooling.
The p-h diagram shows the enthalpies at various states. If the isentropic efficiency of the
compressor is 0.75, the magnitude of compressor power (in kW) is _________ (correct to
two decimal places).
Q.44 Ambient air is at a pressure of 100 kPa, dry bulb temperature of 30 o C and 60% relative
humidity. The saturation pressure of water at 30 o C is 4.24 kPa. The specific humidity of
air (in g/kg of dry air) is ________ (correct to two decimal places).
Q.45 A test is conducted on a one-fifth scale model of a Francis turbine under a head of
2 m and volumetric flow rate of 1 m3/s at 450 rpm. Take the water density and the
acceleration due to gravity as 103 kg/m3 and 10 m/s2, respectively. Assume no losses both
in model and prototype turbines. The power (in MW) of a full sized turbine while working
under a head of 30 m is _______ (correct to two decimal places).
ME 13/15
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GATE 2018 Mechanical Engineering (Set 2)
Q.46 The true stress (in MPa) versus true strain relationship for a metal is given by
1020 0.4 .
The cross-sectional area at the start of a test (when the stress and strain values are equal to
zero) is 100 mm2. The cross-sectional area at the time of necking (in mm2) is ________
(correct to two decimal places)
Q.47 A steel wire is drawn from an initial diameter (di) of 10 mm to a final diameter (df) of 7.5
mm. The half cone angle () of the die is 5 and the coefficient of friction () between the
die and the wire is 0.1. The average of the initial and final yield stress [(Y)avg] is 350
MPa. The equation for drawing stress f , (in MPa) is given as:
2μ cotα
1 df
f = (σY )avg {1 + } [1 − ( ) ]
μ cot α di
The drawing stress (in MPa) required to carry out this operation is _________ (correct to
two decimal places).
Q.48 Following data correspond to an orthogonal turning of a 100 mm diameter rod on a lathe.
Rake angle: 15o ; Uncut chip thickness: 0.5 mm; nominal chip thickness after the cut: 1.25
mm. The shear angle (in degrees) for this process is _______ (correct to two decimal
places).
Q.49 Taylor’s tool life equation is used to estimate the life of a batch of identical HSS twist drills
by drilling through holes at constant feed in 20 mm thick mild steel plates. In test 1, a drill
lasted 300 holes at 150 rpm while in test 2, another drill lasted 200 holes at 300 rpm. The
maximum number of holes that can be made by another drill from the above batch at 200
rpm is ______ (correct to two decimal places).
Q.50 For sand-casting a steel rectangular plate with dimensions 80 mm × 120 mm × 20 mm, a
cylindrical riser has to be designed. The height of the riser is equal to its diameter. The total
solidification time for the casting is 2 minutes. In Chvorinov’s law for the estimation of the
total solidification time, exponent is to be taken as 2. For a solidification time of 3 minutes
in the riser, the diameter (in mm) of the riser is __________ (correct to two decimal
places).
ME 14/15
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GATE 2018 Mechanical Engineering (Set 2)
Q.51 The arc lengths of a directed graph of a project are as shown in the figure. The shortest path
length from node 1 to node 6 is _______.
Q.52 A circular hole of 25 mm diameter and depth of 20 mm is machined by EDM process. The
material removal rate (in mm3/min) is expressed as
4 104 I T 1.23 ,
where I 300 A and the melting point of the material, T 1600 C . The time (in minutes)
for machining this hole is ________ (correct to two decimal places)
Q.53 A welding operation is being performed with voltage = 30 V and current = 100 A. The
cross-sectional area of the weld bead is 20 mm2. The work-piece and filler are of titanium
for which the specific energy of melting is 14 J/mm3. Assuming a thermal efficiency of the
welding process 70%, the welding speed (in mm/s) is __________ (correct to two decimal
places).
Q.54 Steam in the condenser of a thermal power plant is to be condensed at a temperature of
30C with cooling water which enters the tubes of the condenser at 14C and exits at 22C.
The total surface area of the tubes is 50 m2, and the overall heat transfer coefficient
is 2000 W/m2 K. The heat transfer (in MW) to the condenser is ______ (correct to two
decimal places).
Q.55 A vehicle powered by a spark ignition engine follows air standard Otto cycle (=1.4). The
engine generates 70 kW while consuming 10.3 kg/hr of fuel. The calorific value of fuel is
44,000 kJ/kg. The compression ratio is _______ (correct to two decimal places).
END OF THE QUESTION PAPER
ME 15/15
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Q.No. Type Section Key/Range Marks 1 MCQ GA D 1 2 MCQ GA A 1 3 MCQ GA B 1 4 MCQ GA A 1 5 MCQ GA C 1 6 MCQ GA C 2 7 MCQ GA C 2 8 MCQ GA Marks to All 2 9 MCQ GA D 2 10 MCQ GA B 2 1 MCQ ME C 1 2 MCQ ME C 1 3 MCQ ME B 1 4 MCQ ME C 1 5 MCQ ME B 1 6 MCQ ME D 1 7 MCQ ME C 1 8 MCQ ME C 1 9 MCQ ME B 1 10 MCQ ME A 1 11 MCQ ME D 1 12 MCQ ME A (or) D 1 13 MCQ ME B 1
Text of page 20
Q.No. Type Section Key/Range Marks 14 MCQ ME C 1 15 MCQ ME C 1 16 MCQ ME B 1 17 MCQ ME D 1 18 MCQ ME C 1 19 NAT ME 0.25 to 0.25 1 20 NAT ME 35.24 to 35.44 1 21 NAT ME 190.00 to 200.00 1 22 NAT ME 41.30 to 41.50 1 23 NAT ME 62.00 to 63.00 1 24 NAT ME 0.36 to 0.40 1 25 NAT ME Marks to All 1 26 MCQ ME A 2 27 MCQ ME A 2 28 MCQ ME C 2 29 MCQ ME D 2 30 MCQ ME A 2 31 MCQ ME C 2 32 MCQ ME C 2 33 MCQ ME D 2 34 MCQ ME A 2 35 MCQ ME B 2 36 NAT ME 1.45 to 1.48 2
Text of page 21
Q.No. Type Section Key/Range Marks 37 NAT ME 4.80 to 5.20 2 38 NAT ME 31.60 to 31.65 2 39 NAT ME 6.60 to 6.70 2 40 NAT ME 1.400 to 1.500 2 41 NAT ME 385.00 to 395.00 2 42 NAT ME 145.00 to 150.00 2 43 NAT ME 9.50 to 10.50 2 44 NAT ME 16.00 to 16.50 2 45 NAT ME 28.85 to 29.25 2 46 NAT ME 65.00 to 70.00 2 47 NAT ME 315.00 to 317.00 2 48 NAT ME 22.00 to 24.00 2 49 NAT ME 252.00 to 254.00 2 50 NAT ME 42.00 to 52.00 2 51 NAT ME 7 to 7 (or) 11 to 11 2 52 NAT ME 7.00 to 7.30 2 53 NAT ME 7.49 to 7.51 2 54 NAT ME 1.14 to 1.16 2 55 NAT ME 7.40 to 7.80 2
Official key not published for this paper.
Page 1 of 21
Source: GATE. Question paper published by GATE.