Full Length Practice Test - 01

GATE - Mechanical Engineering Wednesday, 16 January 2013

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Q 1If A, B, C and D are angles of a cyclic quadrilateral, then the value of cosA + cosB + cosC + cosD is equalto

Select one:

A. 0

B.

C.

D. 1

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Full Length Practice Test - 01 http://thegateacademy.in/student-login/mod/quiz/review.php?attempt=72437

1 of 20 1/16/2013 9:00 PM

Q 2 The period of the function is:

Q 3 is equal to

Q 4If the probabilities that A and B will die within a year are p and q respectively, then the probability that onlyone of them will be alive at the end of the year is:

Q 5Suns surface at 5800 K emits radiation at a wave-length of 0.5. A furnace at 300oC will emit through asmall opening, radiation at a wavelength of nearly

Q 6 A long semi-circular duct is shown in the figure. What is the shape factor F22

for this case?

Select one:

A.

B.

C.

D. None of these

Select one:

A.

B.

C.

D.

Select one:

A. Pq

B.

C.

D.

Select one:

A. 10

B. 5

C. 0.25

D. 0.025

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Q 7A rectangular water tank, full to the brim, has its length, breadth, and height in the ratio of 2:1:2. The ratioof hydrostatic forces at the bottom to that at any larger vertical surface is:

Q 8A counter flow heat exchanger is used to heat water from 20oC to 80oC by using hot exhaust gas enteringat 140oC and leaving at 80oC. The log mean temperature difference far the heat exchanger is:

Q 9The following data refer to an axial flow turbine stage: Relative velocity of steam at inlet to the rotor = 79.0m/s, relative velocity at the rotor exit = 152 m/s, rotor mean peripheral velocity = 68.4 m/s, work output perkg. of steam = 14100 J. What is the approximate degree of reaction?

Q 10A piece of metal of specific gravity 7 floats in mercury of specific gravity 13.6. What fraction of its volume

Select one:

A. 1.36

B. 0.73

C. 0.56

D. 0.36

Select one:

A. 1/2

B. 1

C. 2

D. 4

Select one:

A. 80C

B. 60C

C. 110C

D. not determinable

Select one:

A. 0.9

B. 0.8

C. 0.7

D. 0.6

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3 of 20 1/16/2013 9:00 PM

is under mercury?

Q 11The discharge over a sharp-edge triangular notch having included angle of 2 and depth of h is given by

Q 12The equivalent length of the stepped pipeline shown in the figure, can be expressed in terms of thediameter D as

Q 13In orthogonal cutting, the depth of cut is 0.5mm at a cutting speed of 2 m/s. If the chip thickness is 0.75mm, the chip velocity is

Select one:

A. 0.5

B. 0.4

C. 0.515

D. 0.5

Select one:

A.

B.

C.

D.

Select one:

A. 5.25 L

B. 9.5 L

C.

D.

Select one:

A. 1.33m/s

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Q 14The barge shown in figure, is 10m long, 2.5m wide and 2 m high, and weighs 196200 N. The minimumdepth of water way necessary to carry it will be

Q 15 A 3 m wide rectangular channel carries 15 m3/sec of water. Its critical depth is equal to

Q 16 The sensitivity of an isochronous governor is

Q 17In a long cylindrical rod of radius R and a surface heat flux of the uniform internal heat generationrate is:

B. 2m/s

C. 2.5m/s

D. 3m/s

Select one:

A. 2 m

B. 1 m

C. 0.8 m

D. 1.2 m

Select one:

A. 1 m

B. 1.5 m

C. 1.6 m

D. 2 m

Select one:

A. Zero

B. One

C. two

D. infinity

Select one:

A.

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Q 18 In power metallurgy, the operation carried out to improve the bearing property of a bush is called

Q 19If a mass m oscillates on a spring having a mass m

s and stiffness K, then the natural frequency of the

system is given by

Q 20A straight teeth slab milling cutter of 100 mm diameter and 10 teeth rotating at 200 rpm is used to removea layer of 3 mm thickness from a steel bar. If the table feed is 400 mm/min, the feed per tooth in thisoperation will be

Q 21The area bounded by the parabola , x-axis and the ordinates is given by

B.

C.

D.

Select one:

A. Infiltration

B. Impregnation

C. Plating

D. heat treatment

Select one:

A.

B.

C.

D.

Select one:

A. 0.2 mm

B. 0.4 mm

C. 0.5 mm

D. 0.6 mm

Select one:

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Q 22 The function, will be continuous

at x = 3 when is equal to

Q 23 If , are roots of the equation

Q 24 The tangent to the curve at the point

Q 25 The set of all points when the function is differentiable, is:

A.

B.

C.

D. None of these

Select one:

A. 3

B. 2

C. 1

D. -1

Select one:

A. 1/4

B. 1/3

C. -1

D. 1

Select one:

A. makes an angle 30 with x-axis

B. is parallel to x-axis

C. is perpendicular to x-axis

D. makes an angle 45 with x-axis

Select one:

A.

B.

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Q 26 Q.26 55 Carry Two Marks Each.

Consider the matrix,

Q 27 An inventor claims that his heat engine has the following specification:

Power developed : 50 KW

Fuel burned per hour : 3 Kg

Heating value of fuel : 75,000 kJ per Kg

Temperature limits : 627 and 27oC

His heat engine is:

Q 28An electric furnace has a laminated wall composed of 0.2 m of refractory brick (K=2) 0.15m of insulation(K=0.15) and 0.15m of brick having (K=1.5) Inner and outer temperatures of wall are 1027oC and 27oCrespectively. Units of K are Kcal-m/hr.m2C. If surface area of the wall is 1.2m2, heat transfer rate will be

C.

D.

Select one:

A.

B.

C.

D.

Select one:

A. Reality

B. Impossible

C. costly

D. cheaper

Select one:

A. 10 Kcal/hr

B. 100 Kcal/hr

C. 1000 Kcal/hr

D. 10,000 Kcal/hr

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Q 29A body weighing 1000 Kg falls 8 cm and strikes a 500 Kg/cm spring. The deformation of spring will be

Q 30A rotating mass having moment of inertia of 30 Kg-m2 rotates at 800 rpm and is travelling in a curve of170 metres radius at a speed of 240 Km/hr. It will experience a gyroscopic reaction of

Q 31A brass pin is of 500 mm length and 40 mm diameter. The turning time to reduce the pin to 38.8 mm inone pas, when cutting speed is 60 metres/mm and feed is 0.8 mm/min is:

Q 32 For the network shown in figure, the variance along the critical path is 4.

The probability of completion of the project in 24 days is:

Select one:

A. 8 cm

B. 4 cm

C. 16 cm

D. 2 cm

Select one:

A. 10 m-Kgf

B. 100 m-Kgf

C. 124 m-Kgf

D. 710 m-Kgf

Select one:

A. 1.20 min

B. 1.31 min

C. 2.05 min

D. 2.25 min

Select one:

A. 68.2%

B. 84.1%

C. 95.4%

D. 97.7%

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9 of 20 1/16/2013 9:00 PM

Q 33

If the rod fitted snugly between the supports as shown in figure, is heated, the stress induced in it due to20o C rise in temperature will be

Q 34Compare the strength of a solid shaft and a hollow shaft, both having outside diameter D. Hollow shafthas inside diameter D/2 The strength of hollow shaft in comparison to solid shaft is:

Q 35

Select one:

A. 0.07945 Mpa

B. -0.07945 Mpa

C. -0.03972 Mpa

D. 0.03972 MPa

Select one:

A. 1/2 times

B. 1/4 times

C. 3/4 times

D. 15/16 times

Select one:

A. A, B, C

B. C, D, E

C. B, C, D

D. D, E, F

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10 of 20 1/16/2013 9:00 PM

Q 36 Match List I with List II and select correct answer.

Q 37If a material had a modulus of elasticity of and a modulus of rigidity of

Kgf/cm2 then the approximate value of the Poissons ratio of the material would be:

Q 38Two long parallel plates of same emissivity 0.5 are maintained at different temperatures and haveradiation heat exchanger between them. The radiation shield of emissivity 0.25 placed in the middle willreduce radiation heat exchange to

Q 39One end of a cantilever beam shown in figure rests against a linear spring. Before the distributed load is applied, the deflection in the spring is zero. Calculate the spring reaction.

Select one:

A. (A)-3 (B)-2 (C)-1 (D)-4

B. (A)-4 (B)-2 (C)-1 (D)-3

C. (A)-3 (B)-1 (C)-2 (D)-4

D. (A)-4 (B)-1 (C)-2 (D)-3

Select one:

A. 0.26

B. 0.31

C. 0.47

D. 0.5

Select one:

A. 1/2

B. 1/4

C. 3/10

D. 3/5

Select one:

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Q 40A weight W is supported by two cables as shown in figure. The tension in the cable making angle will bethe minimum when the value of is:

Q 41 Match List I and List II and select the correct answer.

Q 42A machine of 100 Kg mass has a 20 Kg rotor with 0.5 mm eccentricity. The mounting springs havestiffness 85 KN/m, and damping is negligible. If the operation speed is rad/s and the unit isconstrained to move vertically, the dynamic amplitude of the machine will be

A.

B.

C.

D. None of these.

Select one:

A. 0

B. 30

C. 45

D. 60

Select one:

A. (A)-3 (B)-2 (C)-1 (D)-4

B. (A)-3 (B)-1 (C)-2 (D)-4

C. (A)-1 (B)-2 (C)-4 (D)-3

D. (A)-1 (B)-3 (C)-4 (D)-2

Select one:

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Q 43At a particular section of reaction turbine, the diameter of blade is 1.8 m, the velocity of flow of steam is49 m/s and the quantity of steam flow is 5.4 m3 / s The blade height at this section will be approximately

Q 44An impulse turbine produces 50 kw f power when the blade mean speed is 400m/s. What is the rate ofthe change of momentum tangential to the rotor?

Q 45 In the network shown in figure, the critical path is along

Q 46A cube at high temperature is immersed in a constant temperature bath. If loses heat form its top, bottomand side surfaces with heat transfer co-efficient of h

1, h

2 and h

3 respectively. The average heat transfer

co-efficient for the cube is:

A.

B.

C.

D.

Select one:

A. 4 cm

B. 2 cm

C. 1 cm

D. 0.5 cm

Select one:

A. 200N

B. 175N

C. 150N

D. 125N

Select one:

A. 1 2 3 4 8 9

B. 1 2 3 5 6 7 8 9

C. 1 2 4 7 8 9

D. 1 2 5 6 7 8 9

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Q 47A trapezoidal open channel has cross-section as in figure. In order to have maximum hydraulic efficiency,the hydraulic radius, R and the length of the side, d should be

Q 48Common data:

A thrust shaft of a ship has 6 collars of 600 mm external diameter and 300 mm internal diameter. The totalthrust from the propeller is 100 KN. If the co-efficient of friction is 0.12 and speed of the engine 90 rpm,then

Power absorbed in friction at the thrust block assuming uniform pressure is:

Q 49Common data:

A thrust shaft of a ship has 6 collars of 600 mm external diameter and 300 mm internal diameter. The totalthrust from the propeller is 100 KN. If the co-efficient of friction is 0.12 and speed of the engine 90 rpm,

Select one:

A.

B.

C.

D. None of these

Select one:

A. respectively

B. respectively

C. respectively

D. respectively

Select one:

A. 22.6 KW

B. 20.8 KW

C. 28.2 KW

D. 26.4 KW

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14 of 20 1/16/2013 9:00 PM

then

Power absorbed in friction assuming uniform wear is:

Q 50Common Data

A 50 mm diameter shaft is loaded statically in pure torque at a shear stress of 70 N/mm2. The yield pointstress is 435 N/mm2.

The factor of safety according to maximum shear stress theory

Q 51Common Data:

A 50 mm diameter shaft is loaded statically in pure torque at a shear stress of 70 N/mm2. The yield pointstress is 435 N/mm2.

The factor of safety according to distortion energy theory

Q 52Linked Answer Questions:

Statement for Linked Answer Questions:

A gas engine working on the Otto cycle has a cylinder of diameter 200 mm and stroke 250 mm. Theclearance volume is 1570 cc.

The value of is:

Select one:

A. 25.45 KW

B. 40.35 KW

C. 20.18 KW

D. 29.40 KW

Select one:

A. 2.52

B. 3.10

C. 3.86

D. 4.12

Select one:

A. 2.94

B. 3.62

C. 2.66

D. 3.58

Select one:

A. 2.4

B. 1.7

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15 of 20 1/16/2013 9:00 PM



A gas engine working on the Otto cycle has a cylinder of diameter 200 mm and stroke 250 mm. Theclearance volume is 1570 cc.

Air standard efficiency is:



A mass m1 hanging at the end of a string moves a mass m2 along the surface of a smooth table. If mass

m2 on table is doubled, tension in the string is increased by one-half

Tension in the string before doubling the mass



A mass m1 hanging at the end of a string moves a mass m2 along the surface of a smooth table. If mass

m2 on table is doubled, tension in the string is increased by one-half

The ratio of is :

C. 1.4

D. 2.8

Select one:

A. 52.9%

B. 48.7%

C. 60%

D. 51.2%

Select one:

A.

B.

C.

D. None of these

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16 of 20 1/16/2013 9:00 PM

Q 56 The word recuperate means

Q 57 Choose the sentence that represents the best English usage

Q 58 The antonym for Flagitious is

Q 59Anupam said to a lady sitting in a car, The only daughter of the brother of my wife is the sister in law ofthe brother of your sister. How the husband of the lady is related to Anupam?

Select one:

A.

B.

C. 1

D. 2

Select one:

A. to respond in a positive manner

B. to become well again after illness

C. to extend help to a co-worker

D. to deny co-operation

Select one:

A. of the two runners, Tom is the worst

B. Tom is the best of the two runners

C. of the two runners, Tom is better

D. Tom is the worst of the two runners

Select one:

A. Clever

B. Dampen

C. Innocent

D. Rigid

Select one:

A. Maternal uncle

B. Uncle

C. Father

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Q 60A person has 14 red socks and 14 white socks in a drawer. What is the minimum number of socks that heshould take to get a correct pair?

Q 61After the completion of the first famous dance competition, the organizers thought of organizing the showfor the second time. To make the competition more entertaining this time, they decided that the teamsmust consist of cricketers and TV actresses. They selected five cricketers A, B, C, D and E and four TVactresses L, M, N and O. But before the starting of the show, the participants had a verbal spat with eachother. Due to this some of them refused to participate with some of the other participants. Now every timea team of five participants is chosen, they must perform under following constraints:

A team must consist of 3 actresses and 2 cricketers1.A and D cannot participate together2.D and C cannot participate together3.B cannot participate with either E or N4.E and M cannot participate together5.A and O cannot participate together6.

Among the below given teams which one is not possible?



A girl, a boy, and a dog start walking down a road. They start at the same time, from the same point, in

D. Son-in-law

Select one:

A. 2

B. 3

C. 4

D. 5

Select one:

A. DELNO

B. AELMN

C. BCLMO

D. BDLMO

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18 of 20 1/16/2013 9:00 PM

the same direction. The boy walks at 5 km/h the girl at 6 km/h. The dog runs from boy to girl and backagain with a constant speed of 10 km/h. The dog does not slow down on the turn. How far does the dogtravel in 1 hour?



The average age of a class is 15.8 years. The average age of boys in the class is 16.4 years, while that ofgirls is 15.4. What is the ratio of boys to girls in the class?



Six bells commence tolling together and toll at intervals 2, 4, 6, 8, 10 and 12 seconds respectively. At theend of 30th Minutes, how many times they have tolled together?

Select one:

A. 5 km

B. 10 km

C. 12 km

D. 15 km

Select one:

A. 2 : 3

B. 3 : 2

C. 3 : 4

D. 1 : 3

Select one:

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19 of 20 1/16/2013 9:00 PM

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David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. Atthe same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rateof 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross?

A. 4

B. 10

C. 15

D. 16

Select one:

A. 19

B. 28

C. 30

D. 37

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Full Length Practice Test - 01