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GATE - Mechanical Engineering Wednesday, 16 January 2013
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Home ► My courses ► ME ► Full Length Practice Tests ► Full Length Practice Test - 08
Q 1
Q.1 – 25 Carry One Mark Each.
The efficiency of riveted double cover bolt joint 62.5%. Each plate has thickness 20mm with 25 mm
diameter rivets the allowable stress of plate material is 120 Mpa .Determine pitch of rivets if shearing.
Resistance and crushing resistance of the rivets are 196.375 KN and 150.0 KN respectively.
Select one:
A. 50 mm
B. 100 mm
C. 125 mm
D. 130 mm
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Q 2 (S + 1)-2
is the Laplace transform of
Q 3 The magnitude of the radiant of f = xyz3 at (1, 0, 2) is
Q 4 If is the cube root of -1, then the value of is
Q 5
Q 6
A triangle ABC consists of vertex points A (0, 0), B(1, 0) and C(0, 1). The value of the integral
∬2xdxdy over the triangle is
Select one:
A. tr
B. t3
C. e-2t
D. t
e-t
Select one:
A. 0
B. 3
C. 8
D. ∞
Select one:
A. 1
B. 0
C.
D. None
Select one:
A. an even multiplication of
B. an odd multiplication of
C. an even multiplication of
D. an odd multiplication of
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Q 7 The probability that two friends share same birth month is
Q 8 In axial flow compressor, exit flow angle deviation from the blade angle is a function of
Q 9
For evaporators and condensers, for the given conditions, the logarithmic mean temperature difference
(LMTD) for parallel flow is
Select one:
A. 1
B. 1/3
C. 1/8
D. 1/6
Select one:
A. 1/6
B. 1/12
C. 1/144
D. 1/24
Select one:
A. blade camber
B. space- chord ratio
C. both blade camber and space- chord ratio
D. blade camber and incidence angle
Select one:
A. equal to that for counter flow
B. greater than that for counter flow
C. smaller than that for counter flow
D. very much smaller than that for counter flow
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Q 10 In the assembly of pulley, key and shaft,
Q 11 For an involute gear, the ratio, pitch circle radius/ base circle radius is ( is the pressure angle)
Q 12
For air- conditioning the operation theatre in a hospital, the percentage of outside air in the air supplied is
Q 13
When there are ‘m’ rows and ‘n’ columns in a transportation problem, degeneracy is said to occur when
the number of allocations is
Q 14 At constant efficiency, the horse power of a fan is
Select one:
A. pulley is made the weakest
B. key is made the weakest
C. key is made the strongest
D. all the 3 are designed for equal strength
Select one:
A.
B.
C.
D. co\sec \,\,\phi
Select one:
A. Zero
B. 20
C. 50
D. 100
Select one:
A. less than (m+n-1)
B. greater than (m+n-1)
C. equal to (m-n-1)
D. less than (m-n-1)
Select one:
A. proportional to rpm
B. proportional to rpm2
C. proportional to rpm3
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Q 15 Solar energy can be directly used in
Q 16
If a spring- mass- dashpot system is subjected to excitation by a constant harmonic force, then at
resonance, its amplitude of vibration will be
Q 17
A seamless steel pipe of 100mm internal diameter, is subjected to internal pressure of 12 MPa. It is made
of steel ( Svt=230N/mm2 and µ=0.27) and the factor of safety is 2.5. The thickness of the pipe is
Q 18 The indexing of the turret in a single spindle automatic lathe is done using
Q 19
The ratio of the clearance volume to the displacement volume of a R12 reciprocating compressor is 0.05.
Specific volume at inlet and outlet of compressor are 0.04 and 0.02 m3/kg respectively. Volumetric
efficiency of the compressor is
D. a polynomial function of rpm
Select one:
A. vapour compression refrigeration syatem
B. vapour absorbtion refrigeration system
C. air refrigeration system
D. jet refrigeration system
Select one:
A. infinity
B. inversely proportional to damping
C. directly proportional to damping
D. decreasing exponentially with time
Select one:
A. 8mm
B. 12mm
C. 17mm
D. 22mm
Select one:
A. Geneva mechanism
B. Ratchet and Pawl mechanism
C. Rack and pinion mechanism
D. Whitworth mechanis
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Q 20
A side and face cutter 125mm diameter has 10 teeth. It operates at a cutting speed of 14mm/min with a
table traverse 100mm/min. The feed per tooth of the cutter is
Q 21
Q 22
A shaft of 100mm diameter and 1 m long has one of its end fixed and other end carries a disc of mass
500 kg at a radius of gyration of 450mm. The modulus of rigidity for the shaft material is 80GN/m2. The
frequency of torsional vibrations
Q 23
In a laboratory experiment, the following data were recorded with rope brake: Diameter of the flywheel
1.2m, diameter of the rope 12.5mm, speed of the engine 200rpm, dead load an the brake 600N, spring
balance reading 150N. The brake power of the engine is
Select one:
A. 95.0%
B. 47.5%
C. 38.0%
D. 19.0%
Select one:
A. 10mm
B. 2.86mm
C. 0.286
D. 0.8mm
Select one:
A.
B.
C.
D.
Select one:
A. 14Hz
B. 20Hz
C. 32Hz
D. 56Hz
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Q 24 The integrating factor of the differential equation \sin \frac{{dy}}{{dx}} + 3y = \cos \,x is
Q 25
The Euler’s crippling load for a 2m long slender steel rod of uniform cross section hinged at both the ends
in 1Kn. The Euler’s cripling load for a 1m long steel rod of the same cross section and hinged at both
ends will be
Q 26
A specimen has a fatigue life of N when subjected to mean stress and stress amplitude S. Now as mean
Stress is increases keeping stress amplitude S constant , which of the following holds good for N
Q 27
A domestic food freezer maintains a temperature of -15 C. The ambient air temperature is 30 C. If heat
leaks into the freezer at the continuous rate of 1.75 KJ/s, then the least power necessary to pump this
heat out continuously is
Select one:
A. 2.716Kw
B. 3.529Kw
C. 4.992Kw
D. 5.715Kw
Select one:
A. {e^{{{\tan }^3}\frac{x}{2}}}
B. \log \,\,\tan \,\frac{x}{2}
C. \tan \,{\,^3}\,\frac{x}{2}
D. \tan \,\,\frac{x}{2}
Select one:
A. 0.25Kn
B. 0.5Kn
C. 2Kn
D. 4Kn
Select one:
A. Decreases
B. Increases
C. Remains constant
D. depends on endurance limit
Select one:
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Q 28
An IC engine has a bore and stroke of Z units each. The area to calculate heat loss can be taken as
Q 29
Air (Cp = 1 kJ/Kg, r = 1.4) enters a compressor at a temperature of 2700c.
The compressor pressure ratio is 4. Assuming an efficiency of 80%, the compressor work required in
KJ/Kg is
Q 30
A double riveted lap joint is made between 15mm thick plates. The rivet diameter and pitch are 25mm
and 75mm respectively. If ultimate stresses in shear is 320Mpa and 640Mpa crushing, find minimum
force per pitch which will rupture the joints
Q 31
An impulse turbine produces 100Kw of power when the blade mean speed is 500m/s. The rate of change
of momentum tangential to the rotor is
A. 0.19Kw
B. 0.24Kw
C. 0.31Kw
D. 0.56Kw
Select one:
A. 4π
B. 5π
C. 6π
D. 8π
Select one:
A. 160
B. 172
C. 182
D. 225
Select one:
A. 314.2 KN
B. 300 KN
C. 480 KN
D. 500 KN
Select one:
A. 200N
B. 175N
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Q 32
Viscosity of a fluid is to be determined by a viscometer constructed of two 40-cm long concentric cylinder.
The outer diameter of the inner cylinder is 12 cm, and gap between the 2 cylinders is 0.15 cm. Inner
cylinder is rotated at 300 rpm and torque is measured to be 1.8 N-m. Determine the viscosity of the fluid.
Q 33
Total strain energy stored in a simply supported beam of span ‘L’ and flexural rigidity ‘EI’ subjected to a
concentrated load ‘W’ at the centre is equal to
Q 34 The best fit line using least squares for the data (0, 0), 10, 24), (20, 36) and (30, 60) is
Q 35
C. 150N
D. 125N
Select one:
A. 0.815 N.S/m2
B. 0.518 N.S/m2
C. 15.8 N.S/m2
D. 0.158 N.S/m2
Select one:
A. \frac{{{W^2}{L^3}}}{{40EI}}
B. \frac{{{W^2}{L^3}}}{{60EI}}
C. \frac{{{W^2}{L^3}}}{{96EI}}
D. \frac{{{W^2}{L^3}}}{{240EI}}
Select one:
A. 2x – y = 0
B. 2x – y + 4 = 0
C. 2x – y – 4 = 0
D. None
Select one:
A. 4.015
B. 5.2
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Q 36
An air standard OH° cycle has a compression ratio of 8 , The maximum temperature occurring in the
cycle is 2200 K .volume of cylinder at beginning of compression P1 = 1 bar , V
1= 400 cm
3 network done
in the cycle is
Q 37
The equation of a velocity distribution over a plate is given by u=2y-y2 where u is the velocity in m/s at a
point y meter from the plate measured perpendicularly. Assuming =8.60 poise, he shear stress at a point
15 cm from the boundary is
Q 38
A system undergoes a power cycle while receiving energy by heat transfer from a body initially at TH and
discharging energy by heat transfer to a similar body initially at TC
. Work is developed until the
temperature of each body isT'. Find expression for minimum possible T
'.
Q 39
A square key of side d / 4 is to be fitted on a shaft of diameter d and In the hub of pulley If the material of
The key and shaft is same and two to be equally strong in shear what is length is length of key
C. 0.0916
D. Need more data
Select one:
A. 0. 6715 KJ
B. 0.3397 KJ
C. 0
D. 1.091 KJ
Select one:
A. 1.72N/m2
B. 1.46N/m2
C. 14.62N/m2
D. 17.20N/m2
Select one:
A. \frac{{{{\rm{T}}_{\rm{H}}}{{\rm{T}}_{\rm{C}}}}}{2}
B. \frac{{{{\rm{T}}_{\rm{H}}}{{\rm{T}}_{\rm{C}}}}}{{{{\rm{T}}_{\rm{H}}}{{\rm{T}}_{\rm{C}}}}}
C. \frac{{{{\rm{T}}_{\rm{H}}}}}{{{{\rm{T}}_{\rm{C}}}}}({{\rm{T}}_{\rm{H}}} + {{\rm{T}}_{\rm{C}}})
D. {({{\rm{T}}_{\rm{H}}} + {{\rm{T}}_{\rm{C}}})^{\frac{1}{2}}}
Select one:
A. π d⁄2
B. 2 π d⁄3
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Q 40
Compare the weight of two solid shafts of same length ; one of steel and other of aluminum alloy ;both
Designed for same torsional stiffness Take Ga = 0.27 x 10
5 Mpa , G
S = 0.8 x 10
5 Mpa density of steel is
7600 kg ⁄ m
3
, density of Aluminium is 2600 kg ⁄ m
3
Q 41
The 8mm gap between two large vertical parallel plane surfaces is filled with a liquid of dynamic viscosity
2x10-2
Ns/m2. A thin sheet of 1 mm thickness and 150mmx150mm size, when dropped vertically between
the two plates the two planes attains a steady velocity of 4m/s. Assume that the plate moves centrally.
The weight of the plate is
Q 42
A five stage centrifugal pump with blades radial at outlet runs at 500 rpm deliver ing 0.25 m3/s against a
total head of 100m. The diameter of the impellers is 0.6 m and the flow velocity is 5m/s. The manometric
efficiency is
Q 43 Natural frequency of the system is
C. 3 π d⁄4
D. 4 π d⁄5
Select one:
A. \frac{{{{\rm{W}}_{\rm{S}}}}}{{{{\rm{W}}_{\rm{a}}}}} = 1.014
B. \frac{{{{\rm{W}}_{\rm{S}}}}}{{{{\rm{W}}_{\rm{a}}}}} = 1.698
C. \frac{{{{\rm{W}}_{\rm{S}}}}}{{{{\rm{W}}_{\rm{a}}}}} = 1.9865
D. \frac{{{{\rm{W}}_{\rm{S}}}}}{{{{\rm{W}}_{\rm{a}}}}} = 0.1154
Select one:
A. 1.02N
B. 2.52N
C. 3.09N
D. 4.13N
Select one:
A. 56.1%
B. 69.7%
C. 79.5%
D. 87.8%
Select one:
A. sqrt ( k/ (M+m))
B. sqrt ( k/ (2M+m))
C. sqrt ( k/ (4M+m))
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Q 44 A journal bearing 60mm in diameter and 90mm long runs at 450rpm.
D. sqrt ( k/ (M+2m))
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