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This mock test of Mechanical Engineering (ME) : Mock Test For GATE for GATE helps you for every GATE entrance exam.
This contains 65 Multiple Choice Questions for GATE Mechanical Engineering (ME) : Mock Test For GATE (mcq) to study with solutions a complete question bank.
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QUESTION: 1

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

Solution:

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

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?

Solution:

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).

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?

Solution:

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

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

Solution:

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.

QUESTION: 5

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

Solution:

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

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?

Solution:

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

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?

Solution:

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.

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 ?

Solution:

QUESTION: 9

**Direction:** In given question below there are three statements followed by two conclusions numbered I and II. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusion logically follows from the given statements disregarding commonly known facts.

**Statements:**

All oils are sands

Some clays are oils

All clays are rocks

Solution:

Statements

All oils are sands

Some clays are oils

All clays are rocks

Combining all three statements, we get

Conclusions

I. At least some clays are sands ü

II. Some oil is not rock û

Conclusion I

Some clays are oils + All oils are sands = Some clays are sands

Hence, Thus, conclusion I follows.

Conclusion II

Some clays are oils → conversion → some oils are clays + All clays are rocks = Some oils are rock. Hence, conclusion II does not follows.

QUESTION: 10

**Direction:** In the given question, the 1^{st} 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.

Solution:

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.

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)

Solution:

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

*Answer can only contain numeric values

QUESTION: 12

A pump is running at a speed of 4800 rpm and delivers 2.5 m^{3}/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 %)

Solution:

Given, η_{0} = 0.85, Q = 2.5 m^{3}/s, H = 20 m, N_{1} = 4800 rpm, N_{2} = 1600 rpm

Power at 4800 rpm,

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 α_{1} and α_{2} and their modulus of elasticity are E_{1} and E_{2} respectively. The lengths are l_{1} and l_{2} respectively.

The stresses in both the bars due to a fall in temperature by T^{0}C are

Solution:

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

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%)

Solution:

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

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/m^{2}. It is to be insulated with film of thermal conductivity 3W/m-K. The thickness of insulation should be

Solution:

Thickness=0.4-0.19=0.21m

*Answer can only contain numeric values

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______

Solution:

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

Solution:

As per Reynold’s Analogy

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

Solution:

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

QUESTION: 19

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

Solution:

x= 4.78

N = 10^{4.78} = 60256 cycles = 60.2 thousand

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?

Solution:

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 undesirable condition of grabbing

QUESTION: 21

A Roller bearing has a basic dynamic load rating (C_{10} for 10^{6} revolution) of 50 kN. If the equivalent radial load on the bearing in 70 kN, the expected life in (10^{6} revolutions) is

Solution:

Option (A) is correct

Given : C = 50 kN & P = 70 KN

i.e. 0.325 million revolutions

*Answer can only contain numeric values

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) ______.

Solution:

QUESTION: 23

Which of the following approaches normally applied for the economic analysis of machining

1) Minimum cost criterion

2) Maximum production rate

3) Maximum profit criterion

Solution:

*Answer can only contain numeric values

QUESTION: 24

A gray cast iron block of size 200mm x 60mm x 20mm with a central cylindrical cavity of diameter 5mm are sand cast. The shrinkage allowance for the pattern is 5%, the ratio of the volume of the pattern to volume of the cavity is________.

Solution:

For gray cast iron = No (liquid + solidification shrinkage), only solid shrinkage occurs.

Ratio of the volume of the pattern to volume of the cavity

= 1.11 x 10^{-3}

=0.001

QUESTION: 25

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

Solution:

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

QUESTION: 26

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)

Solution:

It is the case of isochronisms because the range of speed is constant which means the range of speed is zero (ω_{1}= ω _{2}= ω)

Neglecting mass of sleeve (Not given) (mr_{2}w^{2}) a = (F_{S2}/2)xb (1)

& (mr_{1}w^{2}) a = (F_{S1}/2)xb (2)

(1) Divide (2) = r_{2}/r_{1} = F_{S2}/F_{S1}

=> F_{S2}/120 = 60/40 = F_{S2} = 180N

QUESTION: 27

Match the following:-

Column - I

A) Knife edge follower

B) Roller follower

C) Flat face follower

D) Radial follower

Column - II

(i) Wear is absent

(ii) Wear is highly reduced

(iii) Excessive wear

(iv) Line of motion passing from center of rotation

Solution:

QUESTION: 28

Given polytropic index, n = 1.3 & r = 1.4 for ideal gas, δQ = 100kW then δW is

Solution:

Option (D) is correct

QUESTION: 29

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

Solution:

QUESTION: 30

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.

Solution:

QUESTION: 31

The value of integral

Solution:

QUESTION: 32

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

Solution:

P(one red and other is blue) = P(1^{st} red 2^{nd} blue)

= (5/9)*(4/9)

= **20/81**

QUESTION: 33

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

The value for coefficient a_{2} for g(x)=sin^{2}x in interval [0,π] is

Solution:

Hence, a_{2}=-0.5

QUESTION: 34

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/m^{2}K, K= 20 W/m^{2}K, σ = 5.67×10^{-8} W/m^{2}K^{4}, T_{1} = 200 ^{0}C, T_{s1} = 180^{0}C, T_{s2} = 150^{0}C, T_{2} = 120^{0}C

The thermal resistance per m^{2} is

Solution:

The physical configuration is shown in figure.

QUESTION: 35

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?

Solution:

QUESTION: 36

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/m^{2}. Assume the fluid in column is Hg only.

The height h of the column is

Solution:

The pressure along X-X

P_{A} + ρHg g (h + 0.1) = P_{atm} + ρoil g × 0.1

13.6×10^{3}×9.81×0.12 + 13.6×10^{3}×9.81× (h + 0.1) = 10^{5} + 0.8 ×10^{3}× 9.81 × 0.1

16009.92 + 133416(h + 0.1) = 10^{5} + 784.8

h = 0.535 m

QUESTION: 37

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

Solution:

*Answer can only contain numeric values

QUESTION: 38

An orifice of 20 mm diameter provided in a bottom most side of tank of constant cross sectional area of 0.25 m^{2}. 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)

Solution:

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

QUESTION: 39

A 250 m long and 0.2 m diameter pipe inclined 15^{0} with horizontal through which a lubricating oil (sp. gr. = 0.85, dynamic viscosity = 0.15 N-s/m^{2}) is pumped at the rate of 0.05 m^{3}/s in the upward direction. The pressure drop in the pipe is

Solution:

Given, L =250 m, D = 0.2 m, μ = 0.15 Ns/m^{2}, ρ =0.85 × 10^{3} kg/m^{3}, Q = 0.05 m^{3}/s

Pressure gradient in pipe,

QUESTION: 40

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)

Solution:

Given, A = 100 mm^{2}, C =600 MPa

The axial stress induced in the rod,

*Answer can only contain numeric values

QUESTION: 41

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

Solution:

*Answer can only contain numeric values

QUESTION: 42

A test is conducted on a brass plate subjected to a principal stresses and obtained the following result:

Principle strain, e_{1} = 9.81×10^{-3}, e_{2} = 7.55×10^{-3}

The normal stress (in MPa) on a plane of 30^{0} with the major principal plane is (take E = 100 GPa, and Poisson’s ratio = 0.3)

Solution:

QUESTION: 43

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

Solution:

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

QUESTION: 44

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

Solution:

Given, L =0.15 m, k = 20 W/mK, d = 1.5 cm = 0.015 m, h = 4000 W/m^{2}K

Effectiveness for the fin insulated at end,

QUESTION: 45

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 27^{0}C. The surface temperature of header is 427^{0}C. 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 = 227^{0}C, Stefan- Boltzmann constant = 5.67×10^{-8} W/m^{2}K^{4})

Solution:

Given, ε_{1} = 0.9, ε_{2} = 0.75, T_{1} = 427^{0}C = 700 K, T_{2} = 27^{0}C =300 K, T_{s} = 227^{0}C = 500 K, σ =5.67×10^{-8} W/m^{2}K^{4}

The heat transfer per unit area by thermal radiation without screen provision,

Q_{1} = ε_{1}σ (T_{1}^{4}−T_{2}^{4}) = 0.9×5.67×10^{-8} × (700^{4}−300^{4}) = 11.838 kW/m^{2}

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

Q_{2} = 0.735×5.67×10^{-8} × (700^{4}−500^{4}) = 7.4 kW/m^{2}

The reduction in heat transfer due to screen provision = 11.838−7.4 = 4.438 kW/m^{2}

QUESTION: 46

A solid sphere (ε_{1} = 0.8) of radius, r_{1} = 15 cm maintained at 700 K and is placed concentrically inside a hollow sphere (ε_{2} = 0.6) of radius r_{2} = 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/m^{2}K^{4})

Solution:

Given, ε_{1} = 0.8, ε_{2} = 0.6, r_{1} = 0.15 m, r_{2} = 0.25 m T_{1} = 700 K, T_{2} =500 K, σ =5.67×10^{-8} W/m^{2}K^{4}

A_{1} = 4πr_{1}^{2} = 4π×0.15^{2} = 0.283 m^{2},

A_{2} = 4πr_{2}^{2} = 4π×0.25^{2} = 0.785 m^{2}

Radiative heat transfer from surface 1 to 2,

QUESTION: 47

Consider the following LPP:

Min Z = −3X_{1} + 9X_{2}

Subjected to constraint:

−X_{1} + 3X_{2}≤ 12,

X_{1} + X_{2}≤ 8,

X_{1} − X_{2}≤ 4,

X_{1}≥0, X_{2}≥0

From this one can concluded:

Solution:

The feasible region obtained is OABCD.

To find the coordinates of B and C these inequalities considered as the equations (i), (ii) and (iii)

−X_{1} + 3X_{2} = 12 (i)

X_{1} + X_{2} = 8 (ii)

X_{1} − X_{2} = 4 (iii)

Coordinate of extreme point B

From eq^{n} (i) and eq^{n} (ii)

X_{1} = 3, X_{2} = 5

Coordinate of extreme point C

From eq^{n} (ii) and eq^{n} (iii)

X_{1} = 6, X_{2} = 2

Optimal table:

Min Z = -12 (unique optimal solution)

*Answer can only contain numeric values

QUESTION: 48

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

Solution:

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

QUESTION: 49

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

Solution:

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 2^{nd} case.

Total cost = 16×50 + 15+ 40 = 855 Rs.

QUESTION: 50

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

Solution:

First of all we need to convert this problem into 4 jobs and 2 machines problems.

Min time on machine M_{1} =min {M_{1}} = 5

Min time on machine M_{5} = min {M_{5}} = 6

Max time on rest of machines = Max {M_{2}, M_{3}, M_{4}} =6

If min {M_{1}} or min {M_{5}} ≥ Max {M_{2}, M_{3}, M_{4}} then this problem can be converted into 4 jobs into 2 machines (say N_{1} and N_{2})

As above condition is satisfied so the new table:

N_{1} = time (M_{1} + M_{2} + M_{3} + M_{4}) on each jobs

N_{2} = time (M_{2} + M_{3} + M_{4} + M_{5}) on each jobs

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

*Answer can only contain numeric values

QUESTION: 51

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?

Solution:

*Answer can only contain numeric values

QUESTION: 52

A cantilever bracket is bolted to a column using four M^{12} × 1.75 bolts (all identical). The value of maximum shear stress developed in the bolt P (in MPa) is

Solution:

P_{2} = kλ_{2} P_{2} = 405.405 × 60 = 24324.32N

Now forces on bolt ‘P’ are

*Answer can only contain numeric values

QUESTION: 53

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) _________.

Solution:

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

QUESTION: 54

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/sec^{2} in counterclockwise direction & outward acceleration of block is 150 m/sec^{2} the magnitude of total acceleration of point O is ____ m/sec^{2
}

Solution:

*Answer can only contain numeric values

QUESTION: 55

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 ___

Solution:

Given : N_{2} = 2800 rpm & N_{4} = 50 rpm & m = 1 mm

N_{2}T_{2} = N_{1}T_{1} 2800 × 10 = N_{1} × 70

N_{1} = 400 rpm = N_{3}

N_{3}T_{3} = N_{4}T_{4} 400T_{3} = 50T_{4}

^{1}T_{4} = 8T_{3} …… (3)

Given T_{3} = 10, T_{4} = 80

Put in equation (2) we get

m_{1}(10 + 80) = 80 m_{1} = 0.88 mm

QUESTION: 56

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.

Solution:

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

QUESTION: 57

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.

Solution:

Let the final temperature be T

*Answer can only contain numeric values

QUESTION: 58

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)

Solution:

QUESTION: 59

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 m^{3}/kg, U = 3100 kJ/kg; h = 3445 kJ/kg, s = 7.09 kJ/kg

At 2 bar; v_{f} = 0.001061 m^{3}/kg, v_{g} = 0.886 m^{3}/kg, h_{f}=504.7kJ/kg, h_{g}=2707 kJ/kg,

s_{f}=1.503kJ/kg, s_{g}=7.127kJ/kg

Solution:

Option (B) is correct

h_{1} = 3445 kJ/kg

S_{1} = 7.09 kJ/kg

S_{1} = S_{2s}=7.09

7.09 = 1.53 + x_{2s}(7.127 –1.53)

∴ x_{2s} = 0.9933

and h_{2s} = 504.7 + 0.993 (h_{g} –h_{f})

h_{25} = 504.7 + 0.993 (2201.9) =2692.04

*Answer can only contain numeric values

QUESTION: 60

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

Solution:

Option (D) is correct

QUESTION: 61

A truss shown below

Calculate force in member CD and its nature

Solution:

Option (B) is correct

QUESTION: 62

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)

Solution:

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.

t^{2} -2t – 8 = 0

t^{2} – 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**

QUESTION: 63

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

Solution:

Option (C) is correct

For rank '2' of matrix A, All element of R_{3} should be zero

*Answer can only contain numeric values

QUESTION: 64

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

Solution:

Divide the internal (0.6) into six parts each of width h = 1

Width h = 1

y = f(x) = sin x

Put calculator in radian mode

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

QUESTION: 65

The value of

Solution:

Option (A) is correct

### Syllabus - Mechanical Engineering : ME, GATE

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