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# GATE Mock Test Mechanical Engineering (ME)- 1

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## 65 Questions MCQ Test GATE Mechanical (ME) 2023 Mock Test Series | GATE Mock Test Mechanical Engineering (ME)- 1

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

### A vendor sells his articles at a certain profit percentage. If he sells his articles at 1/4th of his actual selling price then he incurs a loss of 60%. What is his actual profit percentage?

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 1

Let the cost price = 100 Rs.
From the options:
If profit % = 60%
Then SP = 160 Rs.
New SP = 160/4 = 40 Rs.
Then,
Percentage loss= (100-40)/100 = 60%
Hence Verified

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 2

### Direction: Read the following information carefully and answer the questions that follow: The distribution of car sales of 6 companies has been shown in the pie chart below: Note: The total number of cars sold is equal to 36000 If the average cost of a Hyundai car is 2 lakh rupees, then how much money is obtained by selling Hyundai cars?

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 2

Total number of cars sold = 36000
Out of these 15% were Hyundai cars.
∴ Number of Hyundai cars sold = 15/100 × 36000
∴ Number of Hyundai cars sold = 5400
Money earned from Hyundai cars = 5400 × 2 = 10800 lakh rupees
Hence the correct option is option (B).

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 3

### Criteria for selecting candidate for internship programme The candidate: 1) can preferably start the internship between 18th Oct'17 and 17th Nov'17 2) are preferably available for duration of 6 months 3) have computer skills and interest in designing 4) have already graduated or are currently in any year of study 5) knows to deal with customers Nick is a high school student and wants to do an internship as his summer project. He is a very vibrant boy and goes well with people. Is he the right candidate for the internship?

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 3

He does is looking for summer internships and November is not summer time. Hence, option B is the correct option.

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 4

Direction: In the given question, one statement with a blank along with four words is given. Two of the given words can fit into the given blank. Five options with various combinations of these words are given. Choose the combination of the words that best fits into the blank.
Comedian Vasu Primlani takes hilarious ______ at the new trend of renaming Indian cities.
a) Jabs
b) Jokes
c) Satires
d) Gags

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 4

The meaning of the words as follows:
a. Jab as a noun refers to a quick, sharp blow, especially with the fist.
b. A joke is a thing that someone says to cause amusement or laughter, especially a story with a funny punchline.
c. Satire is the use of humour, irony, exaggeration, or ridicule to expose and criticize people's stupidity or vices, particularly in the context of contemporary politics and other topical issues.
d. A gag is a joke or an amusing story, especially one forming part of a comedian's act, or in a film.
‘Hilarious satires’ and ‘hilarious jabs’ seems inappropriate and ambiguous. Among all the options, ‘jokes’ and ‘gags’ fit perfectly in the blank. Therefore, option D is the apt answer.

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 5

Which of the following is MOST OPPOSITE in meaning to Locus?

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 5

Locus (noun) (ठिकाना) - a particular position or place where something occurs or is situated

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 6

The ratio between the speed of a bus and train is 15 : 27, respectively. Also, a car covered a distance of 720 km in 9 h. the speed of the bus is three- fourth of the speed of the car. How much distance will the train cover on 7 h?

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 6

Distance covered by train in 7 h = 108 × 7 = 756 km

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 7

The Union Sports Ministry has approved five lakh rupees from the National Welfare Fund for Sportspersons for Kaur Singh who is suffering from heart disease. Kaur Singh is associated with which of the following sports?

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 7

Kaur Singh, former heavyweight Boxer is struggling with the treatment for heart disease and admitted at private hospital in Mohali. Under such circumstances, the Union Sports Ministry has approved five lakh rupees from the National Welfare Fund for Sportspersons for Kaur Singh.

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 8

Direction: In the following table data is given about a electronic shop. Some data is given and some data is hidden. Study the given data carefully and answer the related questions given below.

Selling price of T.V is what percent of Marked price of laptop ?

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 8

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 9

In below are given three statements followed by two conclusions numbered I and II. You have to take the given two statements to be true even if they seem to be at variance with commonly known facts and then decide which of the given conclusions logically follows from the statements, disregarding commonly known facts. Give answer

Statements: All pencils are papers.
All papers are black.
Conclusions: I. All black things being pencils is a possibility.
II. Some papers are not pencils.

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 9

Correct option is A)

For situation and conclusion questions, there are two following strategies to follow:

I. Possibility

= There exists at least a Venn diagram to justify the conclusion without violating the situations.

II. Definite

= There must not exist any Venn Diagram that is following the conclusion.( without violating the situations)

In the Venn diagrams, Pencils; Papers; Black.

All black things being pencils is a possibility

According to the strategy I, there is a Venn diagram(2) that results in conclusion without violating any of the situations.

So it follows.

Some papers are not pencils.

According to strategy II, there must not exist any Venn diagram but there exist Venn diagrams(1, 2) that are not following the conclusion.

So not follow.

Only conclusion I follow.

Option A

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 10

Direction: In the given question, the 1st part of the sentence is given. The rest of the sentence/passage is split into four parts and named A, B, C and D. These four parts are not given in their proper order. Read the sentence and find out which of the four combinations is correct.
1) According to Indian Express, on Sunday, six men reached South Delhi businessman's house in Malviya Nagar in a Tata Safari car bearing the Haryana government’s sticker fixed on the windscreen.
A) One of the guys first took away all the cell phones of the businessman’s family members alleging that they had come on government duty to investigate a tax evasion charge.
B) The plan could have been successfully executed but one of the family members found their behaviour suspicious.
C) When the family member raised an alarm about the same, about 150 people from the same locality gathered outside the trader's house and the con men were beaten up and interrogated before they were handed over to the police.
D) They “searched” the house, moving from room to room, and collected Rs 20 lakh in cash that they kept in their cars.

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 10

The sentence 1 introduced a situation, and the rest of the sentences should be arranged in the order that they happened. Clearly A is the first in sequence as it uses the word 'first' indicating the first step of these six men. The next step is described in D. Now, the twist comes in sentence C as the suspicions rise. People cannot get suspicious of something unless something actually happened. So, we place A first, followed by D and B. This leaves C for the last, which describes the result of those suspicions. Hence, the correct answer is D.

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 11

For flow of incompressible, viscous flow two configurations are shown. The inlet velocity for the diverging nozzle (Fig (i)) and free-stream velocity for flow past the bluff body (Fig(ii)) is constant and flow is laminar. The relation regarding velocity gradients at point A and B is (. Points A and B are separation points and y is the direction normal to the surface at the point of separation)

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 11

Points A and B are points where flow separation takes place.

*Answer can only contain numeric values
GATE Mock Test Mechanical Engineering (ME)- 1 - Question 12

A pump is running at a speed of 4800 rpm and delivers 2.5 m3/s of water under a head of 20 m. The power input to a pump (in kW) at a shaft speed of 1600 rpm is (assume, pump efficiency = 85 %)

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 12

Given, η0 = 0.85, Q = 2.5 m3/s, H = 20 m, N1 = 4800 rpm, N2 = 1600 rpm
Power at 4800 rpm,

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 13

Figure shows a two composite bars AB and BC of equalcross sectional area are firmly attached at B. The outer end A and C are fixed to rigid supports. The coefficient of expansion of bar AB and BC are α1 and α2 and their modulus of elasticity are E1 and E2 respectively. The lengths are l1 and l2 respectively.

The stresses in both the bars due to a fall in temperature by T0C are

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 13

As the temperature falls both the rods will be subjected to tensile stresses and due to equal cross sectional area, these stresses will be equal. Let σ be the stresses induced in both the rods.
Extension of rod AB due to tensile stresses − Free expansion of rod AB
= Free contraction of rod BC − extension of rod BC due to tensile stresses

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 14

A 3 m diameter riveted boiler sustains an internal pressure of 1 MPa. The allowable safe stress of the material is 80 MPa. Take, diameter of rivet D = 6√t, where, t = plate thickness (in mm). The pitch of the single riveted but joint is (assume efficiency of the riveted joint = 80%)

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 14

Given, d = 3 m, p =1 MPa, η = 0.8
Maximum stress of boiler = hoop stress =
t = 23.4375 mm
Diameter of rivet, D = 6 √23.4375 = 29.047 mm
Efficiency of the riveted joint,

Where, P =pitch of the rivets for longitudinal joint

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 15

A metallic ball in shape of sphere is made up of steel (thermal conductivity of 35W/m-K) of diameter 0.38 m . The outside heat transfer coefficient is 15W/m2. It is to be insulated with film of thermal conductivity 3W/m-K. The thickness of insulation should be

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 15

Thickness=0.4-0.19=0.21m

*Answer can only contain numeric values
GATE Mock Test Mechanical Engineering (ME)- 1 - Question 16

In a heat exchanger water enters at 90℃ and exits at 70℃. Air at entry temperature 25℃ flows at double the mass flow rate of water. The effectiveness of this heat exchanger is______

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 16

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 17

For a fluid with Prandtl number unity flowing over a flat plate, Reynolds Number is 450000, Nusselt Number is 900. The Surface friction coefficient will be

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 17

As per Reynold’s Analogy

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 18

The demand for an item during the re-order period is normally distributed with mean = 500 units and standard deviation = 40 units.
Given data: Area between mean line and Z line corresponding to Z is given in table:

If the reserve stock is 66 units then the probability of stock-out of the units in the firm is

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 18

Given, μ = 500 units, σ = 40 units, RS = 66 units, X =500+40 =540 units
The normal distribution curve is shown in figure.

Probability of stock out = 1−Service level

So the area between mean line μ and Z line = 0.45
So, service level = 0.5 + 0.45 = 0.95
Probability of out of stock = 1−0.95 = 0.05

*Answer can only contain numeric values
GATE Mock Test Mechanical Engineering (ME)- 1 - Question 19

A cylindrical shaft has an ultimate strength (σu) of 900 MPa. The shaft has an endurance strength of of 360 MPa and alternating stress of 500 MPa, a log-log plot is shown in figure below. Calculate the shaft life ____ (In thousand)

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 19

x= 4.78
N = 104.78 = 60256 cycles = 60.2 thousand

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 20

A single shoe block brake is shown in figure, drum diameter is 300 mm and  = 0.3, the breaking torque is 135 N-m, Now which of the following conditions is true?

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 20

Option (C) is correct

Given : T = 135 N-m & T = Fr × 0.15, 135 = Fr × 0.15
Fr = 900 N & Fr = N 900 = 0.3 × N, N = 3000 N
Now, from figure (2)
P × (1) + Fr × 0.4 – 3000 × 0.5 = 0
P = +1140N
Therefore, it is desirable condition of grabbing

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 21

A Roller bearing has a basic dynamic load rating (C10 for 106 revolution) of 50 kN. If the equivalent radial load on the bearing in 70 kN, the expected life in (106 revolutions) is

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 21

Option (A) is correct
Given : C = 50 kN & P = 70 KN

i.e. 0.325 million revolutions

*Answer can only contain numeric values
GATE Mock Test Mechanical Engineering (ME)- 1 - Question 22

In a plane milling operation following data has been taken as,
Length of workpiece = 150 mm
Cutter diameter = 100mm
No. of teeth = 5
Cutter speed = 150 rpm
Feed = 200 mm/min
Depth of cut = 3mm
Determine maximum undeformed chip thickness (in microns) ______.

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 22

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 23

The operation in which liquid is flown into voids by capillary action of a powder metallurgy product is known as

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 23

Infiltration is operation in which liquid is flown into voids by capillary action, thereby decreasing the porosity and improving the strength of component.

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 24

In a hartnell governor with the range of speed is zero, when the radius of rotation of mass of ball is 40mm the downward spring force is 120N and when the radius of rotation is 60mm the downward spring force is (in N)

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 24

It is the case of isochronisms because the range of speed is constant which means the range of speed is zero (ω1= ω 2= ω)
Neglecting mass of sleeve (Not given) (mr2w2) a = (FS2/2)xb (1)
& (mr1w2) a = (FS1/2)xb (2)
(1) Divide (2) = r2/r1 = FS2/FS1
=> FS2/120 = 60/40 = FS2 = 180N

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 25

Match the following:-
Column - I
A) Knife edge follower
B) Roller follower
C) Flat face follower

Column - II
(i) Wear is absent
(ii) Wear is highly reduced
(iii) Excessive wear
(iv) Line of motion passing from center of rotation

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 26

An engine operating at 30% efficiency produces work at a rate of 300 kW. The heat exhausted into the surrounding

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 26

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 27

Air after passing from a heating coil of temperature 45℃ is obtained at 38℃. Calculate inlet air temperature, if the bypass factor of the coil is 0.35.

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 27

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 28

The value of integral

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 28

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 29

There are two containers with one containing 5 red and 4 green ball and other containing 4 blue and 5 green balls. One ball is drawn at random from each container. The probability that one is red and another is blue

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 29

P(one red and other is blue) = P(1st red 2nd blue)
= (5/9)*(4/9)
20/81

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 30

The Fourier cosine series for an even function g(x) is given as

The value for coefficient a2 for g(x)=sin2x in interval [0,π] is

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 30

Hence, a2=-0.5

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 31

The heat is transferred from the hot gases of combustion to the inner surface of chamber by convection and radiation simultaneously and at outer surface by convection to the atmosphere as shown in figure.
Given data: h = 10 W/m2K, K= 20 W/m2K, σ = 5.67×10-8 W/m2K4, T1 = 200 0C, Ts1 = 1800C, Ts2 = 1500C, T2 = 1200C

The thermal resistance per m2 is

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 31

The physical configuration is shown in figure.

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 32

Which of the following is correct for in-line four cylinder four-stroke Engine which has inner cranks (throws) are at 180 degree to the outer throws.
Which of the following option is INCORRECT?

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 32

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 33

A container contains Hg (sp. gr. 13.6) and oil (sp. gr. 0.8) as shown in figure. The oil and Hg are immiscible. The pressure of air in bulb A is 12 cm of Hg vacuum and atmospheric pressure is 100 kN/m2. Assume the fluid in column is Hg only.

The height h of the column is

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 33

The pressure along X-X
PA + ρHg g (h + 0.1) = Patm + ρoil  g × 0.1
13.6×103×9.81×0.12 + 13.6×103×9.81× (h + 0.1) = 105 + 0.8 ×103× 9.81 × 0.1
16009.92 + 133416(h + 0.1) = 105 + 784.8
h = 0.535 m

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 34

A fluid flow is represented by the velocity field, = (x +2y-1)i + (x – y -1)j. The rotational component and rate of shear strain respectively are

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 34

*Answer can only contain numeric values
GATE Mock Test Mechanical Engineering (ME)- 1 - Question 35

An orifice of 20 mm diameter provided in a bottom most side of tank of constant cross sectional area of 0.25 m2. The time taken (in min) to fall of liquid surface in tank from 1.5 m to 0.5 m is (coefficient of discharge = 0.6)

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 35

Volume of liquid leaving the tank = Volume of liquid flowing through orifice in time dt

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 36

A 250 m long and 0.2 m diameter pipe inclined 150 with horizontal through which a lubricating oil (sp. gr. = 0.85, dynamic viscosity = 0.15 N-s/m2) is pumped at the rate of 0.05 m3/s in the upward direction. The pressure drop in the pipe is

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 36

Given, L =250 m, D = 0.2 m, μ = 0.15 Ns/m2, ρ =0.85 × 103 kg/m3, Q = 0.05 m3/s

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 37

A 10 mm × 10 mm rod of a material is subjected to an axial pull of 4000 N. it was found that the lateral dimension of the rod changed to 9.9 mm × 9.9 mm. The Poisson’s ratio is (take modulus of rigidity of the material = 600 MPa)

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 37

Given, A = 100 mm2, C =600 MPa
The axial stress induced in the rod,

*Answer can only contain numeric values
GATE Mock Test Mechanical Engineering (ME)- 1 - Question 38

A hypothetical engineering stress - strain curve has five straight lines PQ, QR, RS and ST with coordinates shown in figure. Q is proportional limit, R is yield point, S is UTS and T is fracture point.

The ratio of the modulus of toughness to the modulus of resilience of the material is

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 38

*Answer can only contain numeric values
GATE Mock Test Mechanical Engineering (ME)- 1 - Question 39

A test is conducted on a brass plate subjected to a principal stresses and obtained the following result:
Principle strain, e1 = 9.81×10-3, e2 = 7.55×10-3
The normal stress (in MPa) on a plane of 300 with the major principal plane is (take E = 100 GPa, and Poisson’s ratio = 0.3)

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 39

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 40

The horizontal deflection of roller end D of the following frame is (take b = 2a and EI is flexural rigidity of the frame)

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 40

At A there will be the horizontal reaction = P Total strain energy stored by the frame (U),
= strain energy stored by the section AB + Strain energy stored by BC + strain energy stored by the section CD

Strain energy stored by the member AB = Strain energy stored by the member CD
U = 2 × Strain energy stored by the section AB + Strain energy stored by section BC
Consider a section Y-Y in AB column at a distance of y from end A,
Bending moment, M = P × y

In section BC, bending moment at any distant x from AB section and it will be constant throughout section BC = = P × b

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 41

A 15 cm long stainless steel pin fin (k = 20 W/mK) having 1.5 cm diameter is fitted to a wall which is exposed to a fluid (h = 4000 W/m2K). Assume the fin is insulated at the end. From this we can conclude that

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 41

Given, L =0.15 m, k = 20 W/mK, d = 1.5 cm = 0.015 m, h = 4000 W/m2K
Effectiveness for the fin insulated at end,

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 42

The outlet header of a steam super heater consists a pipe (ε = 0.9) of diameter 30 cm and it is placed in an enclosure at 270C. The surface temperature of header is 4270C. If the header is enveloped in a 40 cm diameter cylindrical screen (ε = 0.75) then the reduction in heat due to screen provision is (take temperature of screen = 2270C, Stefan- Boltzmann constant = 5.67×10-8 W/m2K4)

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 42

Given, ε1 = 0.9,  ε2 = 0.75, T1 = 4270C = 700 K, T2 = 270C =300 K, Ts = 2270C = 500 K, σ =5.67×10-8 W/m2K4
The heat transfer per unit area by thermal radiation without screen provision,
Q1 =  ε1σ (T14−T24) = 0.9×5.67×10-8 × (7004−3004) = 11.838 kW/m2
The heat transfer per unit area by thermal radiation with screen provision,

After provision of screen the new system reduces to a problem of heat exchange between two concentric cylinders and equivalent emissivity is given as

Q2 = 0.735×5.67×10-8 × (7004−5004) = 7.4 kW/m2
The reduction in heat transfer due to screen provision = 11.838−7.4 = 4.438 kW/m2

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 43

A solid sphere (ε1 = 0.8) of radius, r1 = 15 cm maintained at 700 K and is placed concentrically inside a hollow sphere (ε2  = 0.6) of radius r2 = 25 cm maintained at 500 K as shown in figure.

The net radiative heat transfer from surface 1 to 2 is (Stefan- Boltzmann constant = 5.67×10-8 W/m2K4)

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 43

Given, ε1 = 0.8, ε2 = 0.6, r1 = 0.15 m, r2 = 0.25 m T1 = 700 K, T2 =500 K, σ =5.67×10-8 W/m2K4
A1 = 4πr12 = 4π×0.152 = 0.283 m2,
A2 = 4πr22 = 4π×0.252 = 0.785 m2

Radiative heat transfer from surface 1 to 2,

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 44

Consider the following LPP:
Min Z = −3X1 + 9X2
Subjected to constraint:
−X1 + 3X2≤ 12,
X1 + X2≤ 8,
X1 − X2≤ 4,
X1≥0, X2≥0
From this one can concluded:

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 44

The feasible region obtained is OABCD.

To find the coordinates of B and C these inequalities considered as the equations (i), (ii) and (iii)
−X1 + 3X2 = 12 (i)
X1 + X2 = 8 (ii)
X1 − X2 = 4 (iii)
Coordinate of extreme point B
From eqn (i) and eqn (ii)
X1 = 3, X2 = 5
Coordinate of extreme point C
From eqn (ii) and eqn (iii)
X1 = 6, X2 = 2
Optimal table:

Min Z = -12 (unique optimal solution)

*Answer can only contain numeric values
GATE Mock Test Mechanical Engineering (ME)- 1 - Question 45

The following table shows the grade points in each subject in different semesters. A student has to select one and only one elective in each semester and same elective should not be selected in different semester.

The maximum expected total points is

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 45

As the given problem is of maximization type, so first of all we need to convert it into minimization type problem by subtracting all the elements from maximum one i.e., 10
The minimization table is as follows:

Now using Hungarian method:
→ Row reduction (Subtract the minimum element of each row from all the elements of the respective row)

→  Column reduction (Subtract the minimum element of each column from all the elements of the respective column)

The optimum assignment as follows:
I → Quality control, II→ CAD/CAM, III→ Optimization, IV→ Statistics
The maximum expected total points = 7 + 7 + 7 +10 = 31

*Answer can only contain numeric values
GATE Mock Test Mechanical Engineering (ME)- 1 - Question 46

A small project consists following activities. The relevant data about these activities is given below:

Overhead cost per week is 50 Rs. per week. Total cost of the project (in Rs.) if the project duration is reduced by 2 week is

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 46

The resulting network is shown in figure.
The critical path is 1-3-4-5 and duration = 18 week and the minimum duration = 12 week
Total cost = 18×50 = 900 Rs.

Activities lie on the critical path control the project duration so we can shorten the duration of these critical activities.
The minimum cost of crashing out of (1-3), (3-4), (4-5) activities = 15 Rs per week
Reduced the activities 3-4 by 1 week then the total cost = 17×50 + 15 = 865 Rs
Now, there are two critical path viz. 1-3-4-5 and 1-4-5 and its project duration = 16 week
Now there are two ways of reducing the duration of project further either reduce the activity duration (1-3) and (1-4) combined (crashing cost = 45 Rs. per week) or (1-4) and (3-4) combined (crashing cost = 40 Rs. per week). The minimum cost of crashing is in 2nd case.
Total cost = 16×50 + 15+ 40 = 855 Rs.

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 47

The 4 jobs A, B, C and D are processed on 5 machines and the processing time of jobs on different machines is shown in following table:

According to Johnson’s rule the optimal job sequence is

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 47

First of all we need to convert this problem into 4 jobs and 2 machines problems.
Min time on machine M1 =min {M1} = 5
Min time on machine M5 = min {M5} = 6
Max time on rest of machines = Max {M2, M3, M4} =6
If min {M1} or min {M5} ≥ Max {M2, M3, M4} then this problem can be converted into 4 jobs into 2 machines (say N1 and N2)
As above condition is satisfied so the new table:
N1 = time (M1 + M2 + M3 + M4) on each jobs
N2 = time (M2 + M3 + M4 + M5) on each jobs

According to Johnson’s rule the job sequence is as follows:

*Answer can only contain numeric values
GATE Mock Test Mechanical Engineering (ME)- 1 - Question 48

An electric motor with weight varying from 500N to 800N is mounted on a cantilever beam of 30 mm diameter at a distance of 500 mm from the support. Assume that the yield and endurance strengths of material are 400 MPa and 250 MPa respectively. The factor of safety is?

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 48

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GATE Mock Test Mechanical Engineering (ME)- 1 - Question 49

A cantilever bracket is bolted to a column using four M12 × 1.75 bolts (all identical). The value of maximum shear stress developed in the bolt P (in MPa) is

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 49

 P2 = kλ2  P2 = 405.405 × 60 = 24324.32N
Now forces on bolt ‘P’ are

*Answer can only contain numeric values
GATE Mock Test Mechanical Engineering (ME)- 1 - Question 50

A fit is specified as 30H8/e8, the tolerance value for a nominal diameter of 30 min IT8 is 33 microns and fundamental deviation of shaft is -20 microns. The minimum clearance of the fit (in microns) _________.

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 50

Hole: lower limit = basic size = 30 mm
Higher limit = lower limit + tolerance = 30+.033 = 30.033
Shaft: higher limit = basic size – fundamental deviation = 30 - .02 = 29.98
Lower limit = Higher limit - tolerance = 29.98- 0.033 = 29.947
Therefore min clearance = lower limit of hole – higher limit of shaft
= 30 – 29.98
= 20 microns

*Answer can only contain numeric values
GATE Mock Test Mechanical Engineering (ME)- 1 - Question 51

Block P’ slides outward on link at a uniform velocity of 5 m/sec as shown in figure. Link is rotating at a constant angular velocity of 25 rad/sec clockwise, Angular acceleration of 200 rad/sec2 in counterclockwise direction & outward acceleration of block is 150 m/sec2 the magnitude of total acceleration of point O is ____ m/sec2

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 51

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GATE Mock Test Mechanical Engineering (ME)- 1 - Question 52

In the figure shown below, if the speed of the input shaft of the spur gear train is 2800 rpm and speed of the output shaft is 50 rpm what is the module of gear 4 in mm ___

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 52

Given : N2 = 2800 rpm & N4 = 50 rpm & m = 1 mm

N2T2 = N1T1  2800 × 10 = N1 × 70
N1 = 400 rpm = N3
N3T3 = N4T4 400T3 = 50T4
 1T4 = 8T3 …… (3)
Given T3 = 10, T4 = 80
Put in equation (2) we get
m1(10 + 80) = 80 m1 = 0.88 mm

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 53

A reversible thermodynamic device operates between the temperature limits of 500K, 1100K and 300K and produces 1000kJ of work. If it absorbs 500kJ of heat from Thermal reservoir of 500K, find the heat exchanged with 300K reservoir.

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 53

Let the device absorbs A amount of heat from reservoir at 1100K and B amount of heat from reservoir at 300K.
Using energy balance
A+500+B=1000
A=500-B
Using Clausius equality for a reversible device

This implies 600kJ of heat is rejected from the device.

*Answer can only contain numeric values
GATE Mock Test Mechanical Engineering (ME)- 1 - Question 54

3kg of steam at 120 °C and 1 atm is mixed with 25kg of water at ambient temperature of 25 °C. Calculate the irreversibility (in kJ) produced if the steam condenses at 100 °C with Latent heat of condensation as 2260 kJ/kg. Specific heat of steam is 1.99kJ/kgK.

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 54

Let the final temperature be T

*Answer can only contain numeric values
GATE Mock Test Mechanical Engineering (ME)- 1 - Question 55

In VCR system, the refrigeration capacity is 1800 kJ/min & Heat rejected in condenser is 2400 kJ/min. What will be the heat rejection factor is ____ (up to two decimal)

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 55

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 56

Steam at 40 bar, 500°C flowing at the rate of 1.5 kg/sec expands in an h.p turbine to 2 bar with an is entropic efficiency of 80%. Determine the enthalpy of steam of the exit of high pressure turbine in kW.
At 40 bar, 500°C; V = 0.086 m3/kg, U = 3100 kJ/kg; h = 3445 kJ/kg, s = 7.09 kJ/kg
At 2 bar; vf = 0.001061 m3/kg, vg = 0.886 m3/kg, hf=504.7kJ/kg, hg=2707 kJ/kg,
sf=1.503kJ/kg, sg=7.127kJ/kg

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 56

Option (B) is correct

h1 = 3445 kJ/kg
S1 = 7.09 kJ/kg
S1 = S2s=7.09
7.09 = 1.53 + x2s(7.127 –1.53)
∴ x2s = 0.9933
and h2s = 504.7 + 0.993 (hg –hf)
h25 = 504.7 + 0.993 (2201.9) =2692.04

*Answer can only contain numeric values
GATE Mock Test Mechanical Engineering (ME)- 1 - Question 57

The pressure and temperature at the start of compression of diesel cycle is 1 bar and 15°C. The pressure at the end of expansion is 4bar, the maximum temperature when the compression ratio is 15 and the specific heat at constant pressure is 1.008 kJ/kgK is ____°C

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 57

Option (D) is correct

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 58

A truss shown below

Calculate force in member CD and its nature

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 58

Option (B) is correct

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 59

A stone is dropped from a balloon going up with a uniform velocity of 10 m/s. if the balloon was 40 m high when the stone was dropped, the height of balloon from the ground when the stone hits the ground is (take g = 10 m/s2)

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 59

The stone was going up with 10 m/s velocity and after that it falls freely under gravity.
Considering vertically downward as +ve and upward –ve.

t2 -2t – 8 = 0
t2 – 4t +2t - 8 = 0
t = -2 (no significance in this problem)
t = 4 s
Distance covered by balloon in 4 s in upward direction
= 10 t = 40 m
Total height of balloon = 40 + 40 = 80 m

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 60

If the rank of the matrix  is 2 then the value of λ is

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 60

Option (C) is correct

For rank '2' of matrix A, All element of R3 should be zero

*Answer can only contain numeric values
GATE Mock Test Mechanical Engineering (ME)- 1 - Question 61

By using Simpson's 1/3rd rule find by taking a width of 1

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 61

Divide the internal (0.6) into six parts each of width h = 1
Width h = 1
y = f(x) = sin x

By using Simpson's 1/3rd rule, we have

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 62

A kinematic chain is known as a mechanism when

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 63

Babcock wilcox is a water tube boiler because _________.

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 63

Babcock wilcox is a water tube boiler because water flows inside the tubes and is surrounded by gases.

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 64

In a coupling rod of a locomotive, each of the four pairs is a ________ pair.

GATE Mock Test Mechanical Engineering (ME)- 1 - Question 65

The value of

Detailed Solution for GATE Mock Test Mechanical Engineering (ME)- 1 - Question 65

Option (A) is correct

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