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This mock test of Mechanical Engineering (ME) : Mock Test 3 For GATE for GATE helps you for every GATE entrance exam.
This contains 65 Multiple Choice Questions for GATE Mechanical Engineering (ME) : Mock Test 3 For GATE (mcq) to study with solutions a complete question bank.
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QUESTION: 1

Solution:

QUESTION: 2

Break : Piece

Solution:

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.

Solution:

QUESTION: 4

Which one of the following represents open thermodynamic system?

Solution:

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?

Solution:

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 Chiragâ€™s salary?

Solution:
Let x be Chiragâ€™s salary:

x = 17500 Rs

x = 17500 Rs

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?

Solution:

t = 6 min

t = 6 min

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.

Solution:
Probability that atleast one of them solves the problem = P

QUESTION: 9

What is the probability that a leap year has 53 Sundays and 52 Mondays?

Solution:
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

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

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 ?

Solution:

r = 12% per annum

r = 12% per annum

QUESTION: 11

The value of is

Solution:

QUESTION: 12

Suppose f(x) = If f(x) = f(1), the possible values of a and b are

Solution:

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

Solution:

QUESTION: 14

The inverse Laplace transform of

Solution:
Using partial fractions, we can write

Taking Inverse Laplace

Taking Inverse Laplace

QUESTION: 15

The equation has

Solution:

QUESTION: 16

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

Solution:

Feed per minute = 0.3 × 10 = 3 mm

Time taken = 400/3 = 133.33 min

QUESTION: 17

Which one of the following is the correct relationship between the boundary layer thickness d, displacement thickness and the momentum thickness q?

Solution:

QUESTION: 18

Using Johnsons' rule, find the optimal sequence

Solution:

4 - 1 - 3 - 2 â€“ 5

4 - 1 - 3 - 2 â€“ 5

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

Solution:

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

1. Efficiency of cycle increases

2. Work ratio increases

3. Compressor work decreases

Which of the above statements are true

Solution:

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 1.4 W/mK.)

Solution:
The heat flow by conduction = Heat flow by convection

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

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

QUESTION: 22

Flow separation is caused by

Solution:
Positive pressure gradient is adverse pressure gradient which causes flow separation

QUESTION: 23

A hole of 30 mm diameter is pierced in a steel sheet of 5 mm thickness without shear on the tool. Shear strength of steel is 450 and penetration is 20%. What is the expected percentage load reduction, if a shear of 1.5 mm. is provided on punch?

Solution:

QUESTION: 24

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

Solution:

= 0.9075 Nm

= 0.9075 Nm

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

Final pressure of gas

Final pressure of gas

Solution:

QUESTION: 26

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

Work done during process

Solution:

QUESTION: 27

Equation of motion for single degree of freedom system is Where x is displacement from mean position. Which of following is true

Solution:

QUESTION: 28

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

Solution:

QUESTION: 29

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:-

Solution:
Components of velocity along rod:-

QUESTION: 30

Given

Max Subject to

It will give

Max Subject to

It will give

Solution:

So, it is unbounded solution

So, it is unbounded solution

QUESTION: 31

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

Solution:

QUESTION: 32

Which of the following statement is incorrect

Solution:

QUESTION: 33

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.

Solution:

QUESTION: 34

A beam carrying a uniformly distribute load rests on two supports â€˜bâ€™ apart with equal overhangs â€˜aâ€™ at each end. The ratio b/a for zero bending moment at midspan is.

Solution:

(a + b / 2)= b

a = b/2

b/a = 2

Correct option = D

(a + b / 2)= b

a = b/2

b/a = 2

Correct option = D

QUESTION: 35

Which of the following is true

Solution:

QUESTION: 36

X is a continuous random variable with probability density function given by

The value of K is

The value of K is

Solution:

QUESTION: 37

The coefficient of in the Taylor series expansion of sinx

Solution:

QUESTION: 38

A random variable X has the following probability distribution

The expected value of (x â€“ 1) is

The expected value of (x â€“ 1) is

Solution:

= (1â€“1) (0.12) + (2-1) (0.18) + (3-1) (0.20) + (4-1) (0.15) + (5-1)

(0.35)

= 2.43

= (1â€“1) (0.12) + (2-1) (0.18) + (3-1) (0.20) + (4-1) (0.15) + (5-1)

(0.35)

= 2.43

QUESTION: 39

The divergence of the field at (1, 2, 1) is

Solution:

QUESTION: 40

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.

Solution:

QUESTION: 41

Consider a PERT network for a project involving six tasks (a to f)

The standard deviation of the critical path of the project is

The standard deviation of the critical path of the project is

Solution:

QUESTION: 42

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]

Solution:
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

= 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

QUESTION: 43

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

Solution:

QUESTION: 44

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

Solution:
The energy balance yields:

(Heat received by radiation â€“ Heat convected + Heat generated ) = Heat stored

But Heat stored = Heat capacity Ã— change in temperature

(Heat received by radiation â€“ Heat convected + Heat generated ) = Heat stored

But Heat stored = Heat capacity Ã— change in temperature

QUESTION: 45

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 Assuming ambient to be and neglect latent heat of melting, further consider that of the total electrical power is available for melting. The melting efficiency of wire electrode [%] is:

Solution:

= 39.58 %

= 39.58 %

QUESTION: 46

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?

What is the maximum shear stress in the bar?

Solution:

QUESTION: 47

By application of tensile force, the cross-sectional area of bar â€˜Pâ€™ is first reduced by 30% and then by additional 25%. Another bar â€˜Qâ€™ 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 â€˜Pâ€™ to bar â€˜Qâ€™ will be

Solution:

QUESTION: 48

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

-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

Solution:
During return stroke,

[Note: similarly of it is asked to calculate for outstroke, then

[Note: similarly of it is asked to calculate for outstroke, then

QUESTION: 49

For a riser ,it is used to feed a casting 20 c.m. Ã— 20 c.m. Ã— 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:

Solution:

Solving:- 15c.m.

Solving:- 15c.m.

QUESTION: 50

The bending moment at the mid span location X-X in the beam with overhangs shown below is equal to

Solution:

BM at X â€“ X = 25 Ã— 1 â€“ 20 Ã— 2 = -15 kNm

BM at X â€“ X = 25 Ã— 1 â€“ 20 Ã— 2 = -15 kNm

QUESTION: 51

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

Solution:

The mass entrainment between the two sections i.e. at x = 250 mm and x = 500 mm

The mass entrainment between the two sections i.e. at x = 250 mm and x = 500 mm

QUESTION: 52

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)

Solution:

25- 80+ s = 0

s = 55MPa

QUESTION: 53

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.

Solution:

Ãž m= tan b= 0.76

Ãž m= tan b= 0.76

QUESTION: 54

For the loading of truss as shown, the force in the member CD is

Solution:

Consider Joint A in equilibrium

For Joint C:-

Consider Joint A in equilibrium

For Joint C:-

QUESTION: 55

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)

Solution:

Q= 0

W = w = 173.2 watt

Q= 0

W = w = 173.2 watt

QUESTION: 56

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):

Solution:

QUESTION: 57

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.

Solution:
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.

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 helix angle of the worm

The helix angle of the worm

Solution:
The lead angle of worm

QUESTION: 59

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

The efficiency of the drive

Solution:

QUESTION: 60

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

Solution:

QUESTION: 61

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)

Solution:
= 15 c.m.

i.e. two deductions

i.e. two deductions

QUESTION: 62

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.

Solution:

QUESTION: 63

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]

Solution:

QUESTION: 64

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.

Solution:
Consider a unit depth of the duct. For irrotational flow the velocity variation is.

Difference in velocity = 2.466 â€“ 1.644 = 0.822 m/s

Difference in velocity = 2.466 â€“ 1.644 = 0.822 m/s

QUESTION: 65

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

Solution:

SFEE

Q = 27337.5 kJ/h = 27.34 mJ/h

SFEE

Q = 27337.5 kJ/h = 27.34 mJ/h

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