Full Length Practice Test - 08

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GATE - Mechanical Engineering Wednesday, 16 January 2013

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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

Length Practice Test - 08 http://thegateacademy.in/student-login/mod/quiz/review.php?attem

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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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Full Length Practice Test - 08