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GATE Mock Test Mechanical Engineering (ME) - 3


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65 Questions MCQ Test GATE Mechanical (ME) 2023 Mock Test Series | GATE Mock Test Mechanical Engineering (ME) - 3

GATE Mock Test Mechanical Engineering (ME) - 3 for GATE 2022 is part of GATE Mechanical (ME) 2023 Mock Test Series preparation. The GATE Mock Test Mechanical Engineering (ME) - 3 questions and answers have been prepared according to the GATE exam syllabus.The GATE Mock Test Mechanical Engineering (ME) - 3 MCQs are made for GATE 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for GATE Mock Test Mechanical Engineering (ME) - 3 below.
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GATE Mock Test Mechanical Engineering (ME) - 3 - Question 1

Choose the word or phrase which is nearest in meaning to the key word Lethargy

GATE Mock Test Mechanical Engineering (ME) - 3 - Question 2

The following question comprise two words that have a certain relationship between them followed by four pairs of words. Select the pair that has same relationship as the original pair of words.
Break : Piece

GATE Mock Test Mechanical Engineering (ME) - 3 - Question 3

Replace the phrase printed in bold to make it grammatically correct ?
"Even though many companies" are now penetrating rural India, it would help to give India a real chance of witnessing a double digit GDP growth.

GATE Mock Test Mechanical Engineering (ME) - 3 - Question 4

Which one of the following represents open thermodynamic system?

GATE Mock Test Mechanical Engineering (ME) - 3 - Question 5

What is the deformation or dynamic factor if sum of errors on meshing teeth of steel pinion and gear is 32 x 10-3 mm?

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 5

For steel and pinion gears tooth form factor (K) is 0.111 and modulus of elasticity for pinion and gear is 207 x 103 N/mm2.

Substituting these values in formula for deformation factor

 

C = K.e [(Ep x Eg ) / (Ep + Eg )]

C = 11500e

 

Therefore substituting value of e = 32 x 10-3, we get

C = 368 N/mm

GATE Mock Test Mechanical Engineering (ME) - 3 - Question 6
Chirag decided to give 12% of his salary to his younger brother as a pocket money. But he gave 1260 Rs which was 60% of what he had decided earlier. How much is Chirag’s salary?
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 6 Let x be Chirag’s salary:

x = 17500 Rs
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 7
Two pipes can fill a tank in 15 minutes and 25 minutes respectively. Both the pipes are opened together and after some time, the first pipe is closed and the tank is completely full in 15 minutes. For how many minutes is the first pipe opened?
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 7
t = 6 min
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 8
A and B are required to solve a problem independently. If 1/2 and 1/3 are their respectively probabilities of solving the problem, then the probability that atleast one of them solves the problem.
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 8 Probability that atleast one of them solves the problem = P
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 9
What is the probability that a leap year has 53 Sundays and 52 Mondays?
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 9 In leap year there are 366 days.
There are 52 weeks + 2 days
1. - Mon. + Tue.
2. - Tue. + Wed.
3. - Wed. + Thu.
4. - Thu. + Fri.
5. - Fri. + Sat.
6. - Sat. + Sun. = 53 Sundays + 52 Mondays
7. - Sun. + Mon.
Probability =1/7
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 10
A certain sum of money is invested for one year at a certain rate of simple interest. If the rate of interest is 3% higher, then the interest earned will be 25% more than the interest earned earlier. What is the earlier rate of interest ?
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 10
r = 12% per annum
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 11
The value of is
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 12
Suppose  f(x) = If  f(x) = f(1), the possible values of a and b are
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 13
On her vacations, Katrina visits four cities (A, B, C and D) in a random order. The probability that she visits A either first or second place is
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 14
The inverse Laplace transform of   
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 14 Using partial fractions, we can write

Taking Inverse Laplace
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 15
The equation has
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 16

A work piece of 150 cm length and 40 cm width is machined by planning operation with a feed of 0.3 mm/stroke. The machine tool executes 10 double strokes/min. The planning time (in min) for a single pass is

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 16

Feed per minute = 0.3 × 10 = 3 mm
Time taken = 400/3 = 133.33 min

GATE Mock Test Mechanical Engineering (ME) - 3 - Question 17
Which one of the following is the correct relationship between the boundary layer thickness d, displacement thickness and the momentum thickness q?
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 17
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 18
Using Johnsons' rule, find the optimal sequence
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 18
4 - 1 - 3 - 2 – 5
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 19

The maximum interference in mm after assembly between a bush of size 30+0.06+0.03 and a shaft of size 30+0.04+0.02 is

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 19


 

GATE Mock Test Mechanical Engineering (ME) - 3 - Question 20
In a gas turbine operating on Brayton cycle with intercooling
1. Efficiency of cycle increases
2. Work ratio increases
3. Compressor work decreases
Which of the above statements are true
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 21

A glass plate at  is heated by passing hot air over it with a convection co-efficient of 18 K. If the temperature change over the thickness is not to exceed to avoid damage, the maximum allowable temperature of the air will be. (Thermal conductivity of the plate matrial is 1.9 W/mK.). Thickness of plate is 1 mm.

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 21

The heat flow by conduction = Heat flow by convection
The conduction heat flow is found using the allowable temperature drop over 1 mm thickness.

GATE Mock Test Mechanical Engineering (ME) - 3 - Question 22
Flow separation is caused by
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 22 Positive pressure gradient is adverse pressure gradient which causes flow separation
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 23
A single radial ball bearing of base diameter of 55 mm and subject to a radial load of 22 kN. The shaft rotates at 600 rpm. assume f = 0.0015 The frictional torque in N.m. is
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 23
= 0.9075 Nm
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 24
During a non-flow isothermal reversible expansion, 1 kmol of at 350 k expands from 0.06 to 0.15 Use Vander waals equation to determine 
Final pressure of gas
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 25
During a non-flow isothermal reversible expansion, 1 kmol of at 350 k expands from 0.06 to 0.15 .Use Vander waals equation to determine
Work done during process
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 25
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 26
Equation of motion for single degree of freedom system is Where x is displacement from mean position. Which of following is true
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 26
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 27
In a pure rolling the draft is increased by 100% and diameter of the roll is also increased by 100%. The bite will increase by
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 27
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 28
Rod of length l slides down along the inclined wall as shown. At the instant shown, the speed of end A is v, then the speed of B will be:-
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 28 Components of velocity along rod:-
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 29
Given
Max Subject to

It will give
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 29
So, it is unbounded solution
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 30
The mechanical efficiency of a single cylinder four stroke engine is 80%. If the break power is estimated to 100 KW, the frictional power will be
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 30
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 31
Which of the following statement is incorrect
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 32
Two masses of 10 kg and 20 kg respectively are connected by massless spring as shown. A force of 200 N acts on the 20 kg mass. At the instant when 10 kg mass has an acceleration of 12 ,the acceleration of 20 kg mass is.
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 32
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 33
A beam carrying a uniformly distribute load rests on two supports ‘b’ apart with equal overhangs ‘a’ at each end. The ratio b/a for zero bending moment at midspan is.
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 33

(a + b / 2)= b
a = b/2
b/a = 2
Correct option = D
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 34
Which of the following is true
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 35
X is a continuous random variable with probability density function given by

The value of K is
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 35
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 36
The coefficient of in the Taylor series expansion of sinx
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 36
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 37
A random variable X has the following probability distribution

The expected value of (x – 1) is
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 37
= (1–1) (0.12) + (2-1) (0.18) + (3-1) (0.20) + (4-1) (0.15) + (5-1)
(0.35)
= 2.43
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 38
The divergence of the field at (1, 2, 1) is
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 38
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 39
Sub-cooling heat exchanger is used in a refrigeration cycle, enthalpy at the condenser outlet and evaporator outlet are 90 kJ/kg and 200 kJ/kg. Enthalpy at outlet of isentropic compression is 250 kJ/kg and enthalpy of sub-cooled liquid is 80 kJ/kg COP of cycle is.
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 39
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 40
Consider a PERT network for a project involving six tasks (a to f)

The standard deviation of the critical path of the project is
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 40
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 41
A cylinder of diameter 100 mm and height 50 mm is melted and cast into a sphere of uniform density. If the melting time takes 1 min., diameter of sprue base is 5 mm and height of pouring basin is 20 mm, solidification factor is the total time for conversion of solid cylinder to solid sphere will be [Neglect any time losses]
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 41 Total time of conversion = Time for melting cylinder + Mould filing time + Time for solidification volume of casting


= 31.919 seconds
Let R be the radius of sphere
Equating volume of sphere and cylinder

T = 222. 3845 seconds
Total time, T = 60 + 31. 927 + 222. 384
= 314.318 seconds
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 42

Ice kept in a wall insulated thermo-flask is an example of which system?

GATE Mock Test Mechanical Engineering (ME) - 3 - Question 43
A solid receives heat by radiation over its surface at 4kW and the heat convection rate over the surface of the solid to the surrounding is 5.2 kW, and heat is generated at a rate of 1.7 kW over the volume of the solid. The heat capacity of the solid if the time rate of change of the average temperature of the solid at Will be
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 43 The energy balance yields:
(Heat received by radiation – Heat convected + Heat generated ) = Heat stored
But Heat stored = Heat capacity × change in temperature
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 44

During a steady state gas metal are welding with direct current electrode positive,the welding current voltage and welding speed are 150 A, 30 V, 6 m/min. A metallic wire electrode of diameter 1.2 mm is being fed at a constant rate of 12m/min. The density , specific heat and melting temperature of the wire electrode are 7000 kg/m3 , 500 J/kg, 1530ºC. Assuming ambient to be 30º and neglect latent heat of melting, further consider that 2/3 of the total electrical power is available for melting. The melting efficiency of wire electrode [%] is:

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 44



= 39.58 %
 

GATE Mock Test Mechanical Engineering (ME) - 3 - Question 45
A prismatic bar AB of solid circular cross-section (diameter-d) is loaded by a distributed torque. The intensity of the torque, that is, the torque per unit distance, is denoted by t(x) and varies linearly from maximum value at end A to zero at end B. Also the length of bar is L and shear modulus of elasticity of material is G.

What is the maximum shear stress in the bar?
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 45
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 46
By application of tensile force, the cross-sectional area of bar ‘P’ is first reduced by 30% and then by additional 25%. Another bar ‘Q’ of the same material is reduced in cross sectional area by 50% in single step by applying tensile force. After deformation, the ratio of true strain in the bar ‘P’ to bar ‘Q’ will be
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 46
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 47
A roller follower moves with cycloidal motion during out stroke and return stroke with the following details:
-Outstroke with maximum displacement of 44 mm during of cam rotation
-Return stroke for next of cam rotation, and
-Dwell for the remaining of cam rotation
The maximum velocity and maximum acceleration during return stroke, if the cam rotates uniformly at 500 rpm is
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 47 During return stroke,

[Note: similarly of it is asked to calculate for outstroke, then
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 48
For a riser ,it is used to feed a casting 20 c.m. × 20 c.m. × 10 c.m. Volume shrinkage on solidification is 3% for steel and that the volume of riser is 3 times that directed by shrinkage considerations alone is:
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 48

Solving:- 15c.m.
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 49
The bending moment at the mid span location X-X in the beam with overhangs shown below is equal to
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 49
BM at X – X = 25 × 1 – 20 × 2 = -15 kNm
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 50
Air at 1 bar and at temperature of u = 0.06717 kg/ms flows at a speed of 1.2m/s over a flat plate. Assume the parabolic velocity distribution as : .The mass flow rate (kg/hr) between the distance of 250 mm and 500 mm from the leading edge of the plate is
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 50
The mass entrainment between the two sections i.e. at x = 250 mm and x = 500 mm
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 51

For a steel cube shown in the figure, the net volume change after loading is found to be zero. The magnitude of s will be? (Given 0.5)

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 51



25- 80+ s = 0
s = 55MPa

GATE Mock Test Mechanical Engineering (ME) - 3 - Question 52
In an orthogonal metal cutting operation, rake angle is uncut chip thickness is 0.127 mm, chip thickness is 0.228 mm. The value of friction coefficient is.
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 52

Þ m= tan b= 0.76
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 53
For the loading of truss as shown, the force in the member CD is
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 53
Consider Joint A in equilibrium

For Joint C:-
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 54
An air compressor takes in air at 1 atm & & discharges into a line having inside diameter of 10 mm. Average air velocity in the line of a point close to discharge is 7.5 m/s & discharge pressure is 3 atm. Assuming that compression quasistatic & adiabatic, calculate compression work. Assume that inlet air velocity is very small.(r = 1.4, R = 287 J/kgk = 1004 J/kgk)
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 54

Q= 0
W = w = 173.2 watt
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 55
Rotor has mass 10 kg and is mounted on a 10 mm diameter shaft with short leaving at ends 1 m apart. Shaft rotates at 1500 rpm with rotor having eccentricity of 0.1 mm. Find the deflection produced due to centrifugal force (E = 200 GPa):
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 55

GATE Mock Test Mechanical Engineering (ME) - 3 - Question 56
A Flat smooth rectangular plate is placed edgewise in a stream of fluid. At what fraction of the length from the leading edge would the drag force on the front portion be equal to the half of the total drag force? Assume the boundary layer to be laminar.
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 56 Let x be the distance from the leading edge such that the drag force in the distance x is half of the total drag force.

GATE Mock Test Mechanical Engineering (ME) - 3 - Question 57
A doubled thread worm, drives a worm wheel of 30 teeth. The worm has a pressure angle of a pitch of 19 mm and a pitch circle diameter of 50 mm. If the worm rotates at 1000 rpm, for m= 0.05.
The helix angle of the worm
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 57 The lead angle of worm

GATE Mock Test Mechanical Engineering (ME) - 3 - Question 58
A doubled thread worm, drives a worm wheel of 30 teeth. The worm has a pressure angle of  a pitch of 19 mm and a pitch circle diameter of 50 mm. If the worm rotates at 1000 rpm, for m= 0.05
The efficiency of the drive
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 58
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 59

In an assembly line for assembling toys, five workers are assigned tasks which take times of 10, 9, 7, 9 and 8 minutes. The balance delay (%) for the line is

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 59

GATE Mock Test Mechanical Engineering (ME) - 3 - Question 60
Cup of 10 c.m. height and 5 c.m. diameter is to be made from a sheet metal of 2 mm thickness. The number of deductions necessary will be (Limiting Draw Ratio = 1.9)
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 60 = 15 c.m.

i.e. two deductions
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 61
A counter flow double pipe heat exchanger using super heated steam is used to heat water at the rate of 10500 kg/h. The steam enters the heat exchanger at and leaves at .The inlet and exit temperature of water are and respectively. If overall heat transfer coefficient from steam to water is 814 and the fluid flow changes to parallel. The increase in area is.
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 61
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 62
A gas turbine plant operates on Brayton cycle between and  .Pressure ratio of the cycle is 5. The work ratio of the cycle will be [use  = 1.4]
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 62
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 63
An irrotational two-dimensional flow leaves a straight duct and enters a bend of the same width, in the horizontal plane. Find the velocity difference at the inner and outer wall of the bend.
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 63 Consider a unit depth of the duct. For irrotational flow the velocity variation is.


Difference in velocity = 2.466 – 1.644 = 0.822 m/s
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 64
An air & water mixture having an enthalpy of 125 kJ/kg enters a dehumidifier at rate of 350 kg/h. Water with enthalpy of 42 kJ/kg drains out of dehumidifier at rate of 7.5 kg/h. Air and water vapour mixture leaves the dehumidifier with enthalpy of 47 kJ/kg. Calculate the heat removed in MJ/kg
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 64
SFEE

Q = 27337.5 kJ/h = 27.34 mJ/h
GATE Mock Test Mechanical Engineering (ME) - 3 - Question 65

Find the blanking force required to punch 10 mm diameter holes in a steel sheet of 3 mm thickness. Given shear strength of material = 400 MPa, penetration = 40% and shear provided on the punch = 2 mm.

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 3 - Question 65

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