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GATE Mock Test Mechanical Engineering (ME) - 10


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65 Questions MCQ Test GATE Mechanical (ME) 2023 Mock Test Series | GATE Mock Test Mechanical Engineering (ME) - 10

GATE Mock Test Mechanical Engineering (ME) - 10 for GATE 2022 is part of GATE Mechanical (ME) 2023 Mock Test Series preparation. The GATE Mock Test Mechanical Engineering (ME) - 10 questions and answers have been prepared according to the GATE exam syllabus.The GATE Mock Test Mechanical Engineering (ME) - 10 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) - 10 below.
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GATE Mock Test Mechanical Engineering (ME) - 10 - Question 1

“Wanted a two bedroom flat in the court area for immediate possession” - An Advertisement.
Assumptions:
I. Flats are available in the court area
II. Some people will respond to the advertisement
III. It is a practice to give such an advertisement

GATE Mock Test Mechanical Engineering (ME) - 10 - Question 2

Which of the following is most similar in meaning to the given word
DIRE

GATE Mock Test Mechanical Engineering (ME) - 10 - Question 3

In the question given below, the sentence has a part printed in bold. That part may contain a grammatical error. Replace that part with four choices given below:
The famous playwright has been in the sick bed from the last one week

GATE Mock Test Mechanical Engineering (ME) - 10 - Question 4
He always _________ you in his letters
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 5
His health ____________ under the pressure of work.
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 6
A, B and C shoots to hit a target. If A hits the target 4 times in 5 trials, B hits in 3 times in 4 trials and C hits it 2 times in 3 trials. What is the probability that the target is hit by at least 2 persons?
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 6 Probability that A hits the target = 4/5
Probability that B hits the target = 3/4
Probability that C hits the target = 2/3
P (at least 2) = P(2) + P(3)
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 7
Two liquids are mixed in the ratio 4:3 and the mixture is sold at Rs 20 with a profit of %. If the first liquid is costlier than the second by Rs 7. Find the sum of costs of both the liquids.
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 7 Profit= %
CP= =15 Rs
Cost of 1 unit of liquid 1 = x+7
Cost of 1 unit of liquid 2 = x
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 8
Henry and Ford worked together to complete a task in 10 days. Had Henry worked with half of his efficiency and Ford at 5 times of his efficiency it would have taken them to finish the job in 50% of the scheduled time. In how many days can Ford complete the job working alone?
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 8 Let henry’s one day work be x
Let ford’s one day work be y

Hence, Ford can complete the job working alone in 30 days
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 9
A new flag is to be designed with six vertical stripes using some or all of the colours- yellow, green, blue and red. Then the number of ways this can be done such that no two adjacent stripes have the same colour out is:
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 9 There are 6 stripes. The stripe can be coloured in 4ways, in 3, in 3 and so on.Thus, total number of ways = 4×3×3×3×3×3=12×81
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 10
Find the value of
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 10
=y
=3y
y(y-3) = 0
y = 3
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 11
Identify the incorrect statement
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 12
The divergence of the field at (1, 2, 1) is
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 12
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 13
The argument of the complex number is
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 13
Complex number is lying in second quadrant hence argument is
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 14

The velocity ratio in case of an inclined plane inclined at angle θ to the horizontal and weight being pulled up the inclined plane by vertical effort is

GATE Mock Test Mechanical Engineering (ME) - 10 - Question 15
During non-flow reversible process, a gas enclosed in piston cylinder assembly expands from 3 to 6 P = -3v+15 where, P is in bar, V is volume in Determine the work interaction.
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 15
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 16
 
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 17
Surface is at and is exposed to surroundings at and convicts and radiates heat to the surroundings. The convection co-efficient is 80 K.The radiation factor is one. If the heat is conducted to the surface through a solid of conductivity 12 W then the temperature gradient at the surface of the solid is
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 17 Heat conducted + heat radiated = heat conducted considering 1,
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 18
Air at 1100 K & 101.32 kPa is passing through a converging nozzle and leaves it at 300K. Determine velocity of air at nozzle exit. Nozzle is horizontal. Inlet velocity of air can be ignored. = 1 kJ/kg K
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 18 S.F.E.E.
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 19
In an NC machine, the tool is programmed to move along a circular arc from to taking the center of the arc O[15, 20]. The tool path command followed by the tool is
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 19
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 20
During a certain reversible process, for a closed system, the entropy of system increases by 4 kJ/K. If the process occurs at a constant temperature of 500 K, the heat input to the system will be
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 20 500(4)=2000 kJ
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 21

The polar modulus for a hollow shaft of outer diameter (D) and inner diameter (d) is

GATE Mock Test Mechanical Engineering (ME) - 10 - Question 22
The men's department of a large store employs one tailor for customer fittings. The number of customers requiring fitting appears to follow a Poisson distribution with a mean arrival rate is 24 per hour. Customers fitting time follows an exponential distribution with a mean of 2 minute. The time (minute) a customer is expected to spend in the fitting row is………….
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 22
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 23

A boat sails across a river with a velocity of 10 km/hr. If resultant boat velocity is 14 km/hr, then what is the velocity of river water? 

GATE Mock Test Mechanical Engineering (ME) - 10 - Question 24

Which of the following is incorrectly matched?

GATE Mock Test Mechanical Engineering (ME) - 10 - Question 25
When an ideal gas expands, its temperature
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 26
A steel rod 12 mm is diameter and 60 mm long, with an insulated end,is to be used as a spine. It is exposed to surroundings with a temperature of 60°C and a heat transfer coefficient of 55 W/m2°C. The temperature at the base of fin is 95°C. The fin efficiency is
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 26 For insulated end
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 27
In a certain cooling dehumidification operation, 360 kg/h of air (DBT 35°C & RH 50%) is blown over a cooling coil having apparatus dew point of 5°C, assuming a bypass factor 15% determine outlet conditions of air
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 27
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 28
If amplitude of vibration reduces to 0.25 of its initial value after five oscillations. The longitudinal decrement will be:
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 28
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 29
In ECM, the material removal rate will be higher for metal with:
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 30
Which of the following statement is correct? In case of clutches, the uniform pressure theory
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 31
Consider the I-section of a beam shown below:

If the shear stress at the level of junction in flange is 5 what will be shear stress in web at the level of junction?
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 31
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 32
In fusion welding process, which of the following holds good within the heat affected zone.
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 33
For the internal expanding shoe brake shown in the figure. Which shoe is self energizing?

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 33
In the leading shoe friction forces are helping the applied force F i.e. the moment produced by the friction forces about the hingeare in the same direction as produced by force F about Therefore leading shoe is self energizing. However in case of trailing shoe moments produced by friction forces about are opposing the moment produced by F about and therefore trailing shoe is not self energizing.However, if the direction of rotation is changed then leading shoe will
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 34
A simple pendulum of length 5m with a bob of mass 1 kg, is in simple harmonicmotion. As it passes through its mean position, the bob has a speed of 5m/s. The net force on the bob at the mean position is:-
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 35

A helical gear made of plain carbon steel has face width 10 times the normal module. If number of teeth on pinion and gear are 20 and 60 respectively, then what will be the wear strength of helical gear? (Assume mn = 5, BHN = 200 & Ψ = 24o)

GATE Mock Test Mechanical Engineering (ME) - 10 - Question 36

The particular solution of the differential equation is

GATE Mock Test Mechanical Engineering (ME) - 10 - Question 37

There are 200 individuals with a skin disorder, 120 had been exposed to the chemical c1, 50 to chemical c2, and 30 to both chemicals c1 and c2. find the number of individuals exposed to chemical c2​ but not chemical c1​

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 37

Let U= set of individuals suffering from the skin disorder

A= set of individuals exposed to the chemical c1

B= set of individual exposed to the chemical c2

Then n(u)=200, n(A)=120, n(B)=50 and n(A∩B)=30

Similarly, B=(B−A)∪(A∩B)

∴n(B)=n(B−A)+n(A∩B)

∵n(B−A)∩(A∩B)=φ

∴n(B−A)=n(B)−n(A∩B)

=50−30=20

Hence, 20 individuals exposed to chemical c2​ but not to chemical c1

GATE Mock Test Mechanical Engineering (ME) - 10 - Question 38
Which of the following is not a solution of the differential equation
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 38
Thus differential equation is
D (D - 1)y – 2Dy +2y = 0

Therefore, D = 1, 2
Roots are real and distinct

From this general solution we cannot get 1/x
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 39
Suppose that the reliability of a HIV test is specified as follows: Of people having HIV, 90% of the test detect the disease but 10% go undetected of
people free of HIV, 99% of the test are judged HIV –ve but 1% are diagnosed as showing HIV +ve. From a large population of which only 0.1% have HIV, one person is selected at random, given the HIV test, and the pathologist reports him/her as HIV +ve. What is the probability that the person actually has HIV?
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 39
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 40
In the given figure below, the slope at point P will be:
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 40
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 41
In a laminar boundary layer, the velocity distribution can be assumed to be given, in usual notation asWhich of the following is the correct expression for the displacement thickness for this boundary layer?
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 41
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 42
In a reduction gear shown in the figure, the input S has 24 teeth. P & C constitute a compound planet having 30 and 18 teeth respectively. Considering same pitch for all the gears and A to be fixed, the ratio of speeds of gear S to gear D is:

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 42


GATE Mock Test Mechanical Engineering (ME) - 10 - Question 43
The dimension of null space of the matrix
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 43 No. of columns = 3

determinant of matrix is zero = rank = 2
Dimension of null space
= No. of columns - rank
= 3 – 2 = 1
Hint ? Refer Rank Nullity theorem
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 44
The equation is to be solved using Newton – Raphson method with intial guess 1.8500 the value obtained after one iteration step
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 44

= 1.8556
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 45
In spot pulsed laser welding of aluminum plates (density = 2700 specific heat =896J/kg, melting temperature = 933K, latent heat of melting is 380 kJ/kg) at a temperature of Pulse with energy of 0.5 J is focused on to area of 0.05 mm2. If the entire energy is coupled into the material. What will be depth of weld assuming crosssection area of weld as circular and uniform throughout depth and only heat conduction in direction of penetration?
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 45 Let depth = d
Volume of weld = Ad

d = 3.84 mm
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 46
A block slides down an inclined plane of with an acceleration The kinetic friction coefficient is:-
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 46
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 47
A pelton wheel is required to develop 6 MW when working under a head of 300m. It rotates with a speed of 550rpm. Assuming jet ratio as 10 and overall efficiency as 85%. The diameter of wheel and number of jets respectively are:[ (coefficient of velocity of jet)= 0.98 and (coefficient of peripheral velocity)= 0.46]
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 47 Velocity of jet,

Tangential [Peripheral] velocity of wheel,

GATE Mock Test Mechanical Engineering (ME) - 10 - Question 48
Historical data on the sales of cars of company for the year 2000 to 2006 is given below

Projection of the forecast for the year 2007 is
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 48
For 2007, x = 4
y = 10416.7
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 49
A hole of 60mm diameter is pierced in a steel sheet of 4mm thickness without shear on the tool. Shear strength of steel is 600 and penetration is 25%. The expected percentage load reduction if a shear of 1mm is provided on the punch is:
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 49
50% load reduction
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 50

Two masses are placed on the opposite side of the shaft axis in the same axial plane as shown in the figure. The masses to be added at locations. A and D respectively at radius 40mm which will produce complete static and dynamic balance

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 50

Since the given configuration is already in static balance, therefore for dynamic balancing,

GATE Mock Test Mechanical Engineering (ME) - 10 - Question 51
A balloon of 20 cm diameter is filled with air at 1.2 bar and 35°C. It is heated to 500°C,as a result its diameter increases to 25 cm. During heating process, pressure varies linearly with diameter rising to maximum value of 1.5 bar. Estimate heat transfer to balloon, if energy change in air where is change in temperature in Kelvin.
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 51

= 1860 + 543.4
= 2403.4 J
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 52
A cube shaped solid 20 cm side having a density of 2500 kg/m3 and specific heat of 0.52 kJ/kg K has a uniform heat generation rate of 100 kJ/m3s If heat is received over it’s surfaces at 240 W, the time rate of temperature change of the solid (in °C/sec) is ----
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 52 The energy equation yields,
Heat transfer + heat generated = heat stored
Heat stored = volume × density × specific heat × temperature rise
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 53
A thin cylindrical pressure vessel 5.5m in diameter is made of 16mm steel plates. The longitudinal joint is a double riveted lap joint with no staggering between the rows. The rivets are 20mm nominal diameter with a pitch of 75mm. Allowable stress are 140 MPa in tension, 110 MPa in shear and 240 MPa in bearing. The efficiency of joint and safe pressure inside the vessel will be
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 53 Strength of the rivets pitch in shear,
= 6.91 kN
(n = 2, because rivets in single shear and rows of rivets are two)
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 54
An ideal sprue basin system has been modeled in the laboratories as shown. Consider the sprue design as parabolic when the vertex of this parabola passes through A. The mould cavity is of dimension For how many values of   the above condition will be satisfied.
 
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 54
d = 0.0252 m
r = 0.0126 m
Equation of parabola

This will give a cubic equation in x on solving, we get 3 real values of x
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 55
A gear box of machine is operating under steady state. Input shaft receives 46 kW from prime mover and transmits 30 kW to output shaft, the rest being lost to friction etc. Gear box surface is at an average temperature of 47°C and losses heat to surrounding at 27°C. Find the irreversibility involved.
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 55 Heat loss due to friction = 46-30 = 16 kW
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 56
Consider the PERT network shown below


The desired completion date for the project if probability of finishing the project is 19% (Z(0.87) = 0.19) is
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 56 Critical path A - B - D - F - G
Project time = 38
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 57

A square plate hangs in water from one of its corners and its centroid lies at 8m from the free water surface. Find the total pressure force on the top half of the plate

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 57

GATE Mock Test Mechanical Engineering (ME) - 10 - Question 58
Degree of freedom of the given linkage is

Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 58
F = 3[8-1]-2[10]
F = 21-20
F = 1
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 59
A round plate of diameter 500 mm has to be faced on both sides to reduce its thickness from 30mm to 20mm. Maximum depth of cut allowed is 3mm. If the crossfeed is 0.05 cm/rev and cutting velocity is 785 m/min, the machining time will be:
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 59
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 60
An engine working on OTTO cycle have compression ratio of 5. The maximum and minimum pressure during the cycle are 40 bar and 1 bar respectively. The mean effective pressure of the cycle will be:
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 60
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 61
A hollow shaft having outer diameter equal to 3 times the inner diameter. It transmits 40 kW power at 2500 RPM. If the maximum permissible shear stress is 32 MPa, then outer diameter is
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 61
P = 40 kW
N = 2500 rpm
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 62
In a certain machining operation with cutting speed of 50m/min, tool life of 45 min was observed; when the cutting speed was increased to 100m/min, tool life decreased to 10 min. The cutting speed for maximum productivity if tool change time is 2 minutes is:
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 62
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 63
An air refrigerator of 10 ton capacity operates in Bell Coleman cycle between pressure limits of 1 bar and 4 bar. Air at inlet of compressor is at 1 bar and 253 K. Air at exit of cooler is at 313 K. After air is cooled to 290 K at constant pressure in cooler, it is allowed to expand isentropically to 1 bar in expansion cylinder where temperature limit of cycle. Cold air is then sent to cold chamber to extract heat (Refrigerating effect) determine COP of refrigerator.
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 63
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 64
A power plant cycle with entropy at various points is shown in figure below. All other processes in the steady flow cycle are adiabatic.


Power plant cycle is
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 64 Heat transferred in the boiler/kg of fluid

Heat transferred from the condenser per kg of fluid

Hence the cycle will be irreversible
GATE Mock Test Mechanical Engineering (ME) - 10 - Question 65
A rigid beam ABCD is hinged at D and supported by 2 springs at A and B as shown in the given figure. The beam carries a vertical load P at C. The stiffness of spring at A is 2k and that at B is 3k. The ratio of forces of spring B to that of spring A is:
Detailed Solution for GATE Mock Test Mechanical Engineering (ME) - 10 - Question 65

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