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GATE (Graduate Aptitude Test in Engineering) Mechanical Engineering is an online examination conducted to get admission in M-Tech (Masters in Technology), ME (Master of Engineering ) and PhD at IITs (Indian Institutes of Technology), NITs (National Institutes of Technology), IIITs (Indian Institutes of Information Technology) and other universities in India. GATE exam is jointly conducted by IIT Bombay, IIT Delhi, IIT Guwahati, IIT Kanpur, IIT Kharagpur, IIT Madras, IIT Roorkee and Indian Institute for Science, Bangalore (IISC Bangalore). The exam is divided into two different parts General Aptitude (GA) and Candidate’s Selected Subject (Core Subjects). GATE Mechanical Engineering online mock tests help candidates in preparing for the GATE exam. By attempting GATE online mock tests candidates get familiar with the pattern of actual question paper. BrPaper provides all GATE question papers completely free. Here you can practice free online mock tests of complete exam of GATE Mechanical Engineering. We advise candidates to solve the online GATE Mechanical Engineering mock tests to get good marks in the exam. Start practicing MechanicalGATE 2020 Mock tests here online for free

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Category: GATE Mechanical Engineering 2020 set 2 General Aptitude

Question 1:

While I agree _________ his proposal this time, I do not often agree _________him

to, with

with, to

with, with

to, to

Category: GATE Mechanical Engineering 2020 set 2 General Aptitude

Question 2:

The recent measures to improve the output would ___________the level of production to our satisfaction.

increase

decrease

speed

equalise

Category: GATE Mechanical Engineering 2020 set 2 General Aptitude

Question 3:

Select the word that fits the analogy: White: Whitening : : Light_______

Lightning

Lightening

Lighting

Enlightening

Category: GATE Mechanical Engineering 2020 set 2 General Aptitude

Question 4:

In one of the greatest innings ever seen in 142 years of Test history, ben Stokes upped the tempo in a five-and-a-half hour long stay of 219 balls including 11 fours and 8 sixes that saw him finish on a 135 not cut as England squared the five-match series. Based on their connotations in the given passage, which one of the following meanings DOES NOT match?

upped=increased

squared=lost

tempo=enthusiasm

saw=resulted in

Category: GATE Mechanical Engineering 2020 set 2 General Aptitude

Question 5:

There are five levels {P,Q,R,S,T} in a linear supply chain before a product reaches customers, as shown in the figure.

At each pf the five levels, The price of the product is increased by 25%. If the product is produced at level P at the cost of Rs. 120 per unit, what is the price paid 9in rupees) by the customers?

187.50

234.38

292.96

366.21

Category: GATE Mechanical Engineering 2020 set 2 General Aptitude

Question 6:

Climate change and resilience deal with two aspects - reduction of sources of non-renewable energy resources and reducing vulnerability of climate change aspects. The terms 'mitigation' and 'adaptation' are used to refer to these aspects, respectively Which of the following assertions is best supported by the the above information?

Mitigation deals with consequences of climate change.

Adaptation deals with causes of climate change.

Mitigation deals with actions taken to reduce the use of fossil fuels

Adaptation deals with actions taken to combat green-house gas emissions.

Category: GATE Mechanical Engineering 2020 set 2 General Aptitude

Question 7:

Find the missing element in the following figure.

Category: GATE Mechanical Engineering 2020 set 2 General Aptitude

Question 8:

It was estimated that 52 men can complete a strip in a newly constructed highway connecting cities P and Q in 10 days. Due to an emergency, 12 men were sent to another project. How many number of days, more than the original estimate, will be required to complete the strip?

3 days

5 days

10 days

13 days

Category: GATE Mechanical Engineering 2020 set 2 General Aptitude

Question 9:

An engineer measures THREE quantities X, Y and Z in an experiment. She finds that they follow a relationship that is represented in the figure below: (the product of X and Y linearly varies with Z)

Then, which of the following statements is FALSE?

For fixed Z; X is proportional to Y

For fixed Y; X is proportional to Z

For fixed X; Z is proportional to Y

XY/Z is constant

Category: GATE Mechanical Engineering 2020 set 2 General Aptitude

Question 10:

The two pie-charts given below show the data of total students and only girls registered in different steams in a university. If the total number of students registered in the university is 5000, and the total number of the registered girls is 1500; then, the ratio of boys enrolled in Art to the girls enrolled in Management is ________________

2:1

9:22

11:9

22:9

Category: GATE Mechanical Engineering 2020 set 2

Question 11:

The sum of two normally distributed random variables X and Y is

A	always normally distributed
B	normally distributed, only if X and Y are independent
C	normally distributed, only if X and Y are independent
D	normally distributed, only if X and Y have the same standard deviation

A and B

B and C

C and D

None of these

Category: GATE Mechanical Engineering 2020 set 2

Question 12:

A matrix P is decomposed into its symmetric part S and skew symmetric part V. If

S = (\begin{matrix} - 4 & 4 & 2 \\ 4 & 3 & 7 / 2 \\ 2 & 7 / 2 & 2 \end{matrix}), V = (\begin{matrix} 0 & - 2 & 3 \\ 2 & 0 & 7 / 2 \\ - 3 & - 7 / 2 & 0 \end{matrix}) .

then matrix P is

A	$(\begin{matrix} - 4 & 6 & - 1 \\ 2 & 3 & 0 \\ 5 & 7 & 2 \end{matrix})$	B	$(\begin{matrix} - 4 & 2 & 5 \\ 6 & 3 & 7 \\ - 1 & 0 & 2 \end{matrix})$
C	$(\begin{matrix} 4 & - 6 & 1 \\ - 2 & - 3 & 0 \\ - 5 & - 7 & - 2 \end{matrix})$	D	$(\begin{matrix} - 2 & 9 / 2 & - 1 \\ - 1 & 81 / 4 & 11 \\ - 2 & 45 / 2 & 73 / 4 \end{matrix})$

Category: GATE Mechanical Engineering 2020 set 2

Question 13:

Let I = \int_{x = 0}^{1} \int_{y = 0}^{x^{2}} {xy}^{2} dy dx .

Then, l may also be expressed as

A	$\int_{y = 0}^{1} \int_{x = 0}^{\sqrt{y}} x y^{2} d x d y$	B	$\int_{y = 0}^{1} \int_{x = 0}^{1} y x^{2} d x d y$
C	$\int_{y = 0}^{1} \int_{x = \sqrt{y}}^{1} x y^{2} d x d y$	D	$\int_{y = 0}^{1} \int_{x = 0}^{\sqrt{y}} y x^{2} d x d y$

Category: GATE Mechanical Engineering 2020 set 2

Question 14:

The solution of

\frac{d^{2} y}{d t^{2}} - y = 1,

Which additionally satisfies

y_{t = 0} = {\frac{dy}{dt}}_{t = 0} = 0 in the Laplace s - domain is

A	$\frac{1}{s (s + 1) (s - 1)}$	B	$\frac{1}{s (s + 1)}$
C	$\frac{1}{s (s - 1)}$	D	$\frac{1}{s - 1}$

Category: GATE Mechanical Engineering 2020 set 2

Question 15:

An attempt is made to pull a roller of weight W over a curb (step) by applying a horizontal force F as shown in the figure.

The coefficient of static friction between the roller and the ground (including the edge of the step) is μ. Identify the correct free body diagram (FBD) of the roller when the roller is just about to climb over the step.

A		B
C		D

Category: GATE Mechanical Engineering 2020 set 2

Question 16:

A circular disk of radius r is confined to roll without slipping at P and Q as shown in the figure.

If the plates have velocities as shown, the magnitude of the angular velocity of the disk is

A	$\frac{v}{r}$	B	$\frac{v}{2 r}$
C	$\frac{2 v}{3 r}$	D	$\frac{3 v}{2 r}$

Category: GATE Mechanical Engineering 2020 set 2

Question 17:

The equation of motion of a spring-mass-damper system is given by

\frac{d^{2} x}{{dt}^{2}} + 3 \frac{dx}{dt} + 9 x = 10 \sin (5 t)

The damping factor for the system is

0.25

0.5

Category: GATE Mechanical Engineering 2020 set 2

Question 18:

The number of qualitatively distinct kinematic inversions possible for a Grashof chain with four revolute pairs is

Category: GATE Mechanical Engineering 2020 set 2

Question 19:

The process, that uses a tapered horn to amplify and focus the mechanical energy for machining of glass, is

electrochemical machining

electrical discharge machining

ultrasonic machining

abrasive jet machining

Category: GATE Mechanical Engineering 2020 set 2

Question 20:

Two plates, each of 6 mm thickness, are to be butt-welded. Consider the following processes and select the correct sequence in increasing order of size of the heat affected zone. 1. Are welding 2. MIG welding 3. Laser beam welding 4. Submerged are welding

1-4-2-3

3-4-2-1

4-3-2-1

3-2-4-1

Category: GATE Mechanical Engineering 2020 set 2

Question 21:

Which one of the following statements about a phase diagram is INCORRECT?

It indicates the temperature at which different phases start to melt

Relative amount of different phases can be found under given equillibrium conditions

It gives information on transformation rates

Solid solubility limits are depicted by it

Category: GATE Mechanical Engineering 2020 set 2

Question 22:

The figure below shows a symbolic representation of the surface texture in a perpendicular lay orientation with indicative values (I through VI) marking the various specifications whose definitions are listed below. P: Maximum Waviness Height (mm); Q: Maximum Roughness Height (mm); R: Minimum Roughness Height (mm); S: Maximum Waviness Width (mm); T: Maximum Roughness Width (mm); U: Roughness Width Cutoff (mm).

The correct match between the specifications and the symbols (I to VI) is

I-R, II-Q, III-P, IV-S, V-U, VI-T

I-R, II-P, III-U, IV-S, V-T, VI-Q

I-U, II-S, III-Q, IV-T, V-R, VI-P

I-Q, II-U, III-R, IV-T, V-S, VI-P

Category: GATE Mechanical Engineering 2020 set 2

Question 23:

In Materials Requirement Planning, if the inventory holding cost is very high and the setup cost is zero, which one of the following lot sizing approaches should be used?

Economic Order Quantity

Lot-for-Lot

Base Stock Level

Fixed Period Quantity, for 2 periods

Category: GATE Mechanical Engineering 2020 set 2

Question 24:

Which of the following conditions is used to determine the stable equilibrium of all partially submerged floating bodies?

Centre of buoyancy must be above the centre of gravity

Centre of buoyancy must be below the centre of gravity

Metacentre must be at a higher level than the centre of gravity

Metacentre must be at a lower level than the centre of gravity

Category: GATE Mechanical Engineering 2020 set 2

Question 25:

In the space above the mercury column in a barometer tube, the gauge pressure of the vapour is

positive, but more than one atmosphere

negative

zero

positive, but less than one atmosphere

Category: GATE Mechanical Engineering 2020 set 2

Question 26:

A closed vessel contains pure water, in thermal equilibrium with its vapour at 25°C (Stage #1), as shown.

The vessel in this stage is then kept inside an isothermal oven which is having an atmosphere of hot air maintained at 80°C. The vessel exchanges heat with the oven atmosphere and attains a new thermal equilibrium (Stage #2). If the Valve A is now opened inside the oven, what will happen immediately after opening the valve?

Water vapor inside the vessel will come out of the Valve A

Hot air will go inside the vessel through Valve A

Nothing will happen-the vessel will continue to remain in equilibrium

All the vapor inside the vessel will immediately condense

Category: GATE Mechanical Engineering 2020 set 2

Question 27:

For an air-standard Diesel cycle,

heat addition is at constant volume and heat rejection is at constant pressure

heat addition is at constant pressure and heat rejection is at constant pressure

heat addition is at constant pressure and heat rejection is at constant volume

heat addition is at constant volume and heat rejection is at constant volume

Category: GATE Mechanical Engineering 2020 set 2

Question 28:

The values of enthalpies at the stator inlet and rotor outlet of a hydraulic turbomachine stage are

h_{1} and h_{3}

respectively. The enthalpy at the stator outlet (or, rotor inlet) is

h_{2}

. The condition

(h_{2} - h_{1}) = (h_{3} - h_{2})

indicates that the degree of reaction of this stage is

zero

50%

75%

100%

Category: GATE Mechanical Engineering 2020 set 2

Question 29:

Let I be a 100 dimensional identity matrix and E be the set of its distinct ( no value appears more than once in E) real eigenvalues. The number of elements in E is __________________

0 to 0

1 to 1

2 to 2

3 to 3

Category: GATE Mechanical Engineering 2020 set 2

Question 30:

A beam of negligible mass is hinged at support P and has a roller support Q shown in the figure.

A point load of 1200 N is applied at point R. The magnitude of the reaction force at support Q is ____________N.

1100 to 1100

1300 to 1300

1500 to 1500

1700 to 1700

Category: GATE Mechanical Engineering 2020 set 2

Question 31:

A machine member is subjected to fluctuating stress . The endurance limit of the material is 350 MPa. If the factor of safety used in the design is 3.5 then the maximum allowable value of

σ_{0}

is ______________MPa (round off to 2 decimal places).

99.98 to 100.1

99.98 to 100.2

99.98 to 100.3

99.98 to 100.4

Category: GATE Mechanical Engineering 2020 set 2

Question 32:

Consider the following network of activities, with each activity named A-I, illustrated in the nodes of the network.

The number of hours required for each activity is shown alongside the nodes. The slack on the activity L, is ________ hours.

0 to 0

1 to 1

2 to 2

3 to 3

Category: GATE Mechanical Engineering 2020 set 2

Question 33:

In a furnace, the inner and outer sides of the brick wall undefined are maintained at 1100°C and 700°C, respectively as shown in figure.

The brick wall is covered by an insulating material of thermal conductivity

k_{2}

. The thickness of the insulation is

1 / 4^{t h}

of the thickness of the brick wall. The outer surface of the insulation is at 200°C. The heat flux through the composite walls is 2500 undefined. The value of

k_{2}

is __________ W/m.K (round off to one decimal place).

0.5 to 0.52

0.3 to 0.5

0.4 to 0.5

0.5 to 0.5

Category: GATE Mechanical Engineering 2020 set 2

Question 34:

If a reversed Carnot cycle operates between the temperature limits of 27°C and -3°C, then the ratio of the COP of a refrigerator to that of a heat pump (COP of refrigerator / COP of heat pump ) based on the cycle is _____________(round off to 2 decimal places).

0.87 to 0.89

0.89 to 0.91

0.91 to 0.93

0.93 to 0.95

Category: GATE Mechanical Engineering 2020 set 2

Question 35:

The directional derivative of

f (x, y, z) = x y z

at point (-1,1,3) in the direction of vector

\hat{i} - 2 \hat{j} + 2 \hat{k} i s

A	$3 \hat{i} - 3 \hat{j} - \hat{k}$	B	$- \frac{7}{3}$
C	$\frac{7}{3}$	D	7

Category: GATE Mechanical Engineering 2020 set 2

Question 36:

The function

f (z)

of complex variable z = x + i y, where

i = \sqrt{- 1},

is given as

f (z) = (x^{3} - 3 x y^{2}) + i v (x, y) .

For this function to be analytic,

v (x, y)

should be

A	$(3 {xy}^{2} - y^{3}) + constant$	B	$(3 {xy}^{2} y^{2} - y^{3}) + constant$
C	$(x^{3} - 3 x^{2} y) + constant$	D	$(3 x^{2} y - y^{3}) + constant$

Category: GATE Mechanical Engineering 2020 set 2

Question 37:

A cantilever of length l, and flexural rigidity El, stiffened by a spring of stiffness k, is loaded by a transverse force P, as shown.

The transverse deflection under the load is

A	undefined	B	undefined
C	undefined	D	undefined

Category: GATE Mechanical Engineering 2020 set 2

Question 38:

The sun (S) and the planet (P) of an epicyclic gear train shown in the figure have identical number of teeth.

If the sun (S) and the outer ring (R) gears are rotated in the same direction with angular speed undefined respectively, then the angular speed of the arm AB is

A	undefined	B	undefined
C	undefined	D	undefined

Category: GATE Mechanical Engineering 2020 set 2

Question 39:

A helical spring has spring constant k. If the wire diameter, spring diameter and the number of coils are all doubled then the spring constant of the new spring becomes

k/2

16k

Category: GATE Mechanical Engineering 2020 set 2

Question 40:

Two rollers of diameters

D_{1}

(in mm) and

D_{2}

(in mm) are used to measure the internal taper angle in the V-groove of a machined component. The heights

H_{1}

(in mm) and

H_{2}

(in mm) are measured by using a height gauge after inserting the roller into the same V-groove as shown in the figure.

Which one of the following is the correct relationship to evaluate the angle α as shown in the figure?

A	undefined
B	undefined
C	undefined
D	undefined

Category: GATE Mechanical Engineering 2020 set 2

Question 41:

The forecast for the monthly demand of a product is given in the table-below.

Month	Forecast	Actual Sales
1	33.00	30.00
2	31.80	32.00
3	31.82	30.00

The forecast is made by using the exponential smoothing method. The exponential smoothing coefficient used in forecasting the demand is

0.10

0.40

0.50

1.00

Category: GATE Mechanical Engineering 2020 set 2

Question 42:

One kg of air in a closed system undergoes an irreversible process from an initial sate of

p_{1} = 1

bar (absolute) and

T_{1} = 27 ° C

, to a final state of

p_{2} = 3

bar (absolute) and

T_{2} = 127 ° C .

If the gas constant of air is 287 J/kg.K and the ratio of the air in the process is

-26.3

28.4

172.0

indeterminate, as the process is irreversible

Category: GATE Mechanical Engineering 2020 set 2

Question 43:

For the integral

\int_{0}^{π / 2} (8 + 4 \cos x) d x,

the absolute percentage error in numerical evaluation with the Trapezoidal rule, using only the end points, is_____________(round off to one decimal place).

5.0 to 5.4

5.1 to 5.5

5.2 to 5.6

5.3 to 5.7

Category: GATE Mechanical Engineering 2020 set 2

Question 44:

A fair coin is tossed 20 times. The probability that 'head' will appear exactly 4 times in the first ten tosses, and 'tail' will appear exactly 4 times in the next ten tosses is _______________(round off to 3 decimal places).

0.041 to 0.043

Category: GATE Mechanical Engineering 2020 set 2

Question 45:

A hollow spherical ball of radius 20 cm floats in still water, with half of its volume submerged. Taking the density of water as

1000 kg / m^{3}

, and the acceleration due to gravity as

10 m / s^{2}

, the natural frequency of small oscillations of the ball, normal to the water surface is ______________ radians/s (round off to 2 decimal places).

8.30 to 8.40

8.40 to 8.50

8.50 to 8.60

8.60 to 8.70

Category: GATE Mechanical Engineering 2020 set 2

Question 46:

Uniaxial compression test date for a solid metal bar of length 1 m is shown in the figure.

The bar material has a linear elastic response from O to P followed by a nonlinear response. The point P represents the yield point of the material. The rod is pinned at both the ends. The minimum diameter of the bar so that it does not buckle under axial loading before reaching the yield point is __________mm (round off to one decimal place).

55.0 to 58.0

Category: GATE Mechanical Engineering 2020 set 2

Question 47:

The turning moment diagram of a flywheel fitted to a fictitious engine is shown in the figure.

The mean turning moment is 2000 Nm. The average engine speed is 1000 rpm. For fluctuation in the speed to be within

\pm 2 %

of the average speed, the mass moment of inertia of the flywheel is __________ kg.

m^{2}

3.55 to 3.65

Category: GATE Mechanical Engineering 2020 set 2

Question 48:

A rigid block of mass undefined =10 kg having velocity

v_{0}

=2 m/s strikes a stationary block of mass undefined =30 kg after traveling 1 m along a frictionless horizontal surface as shown in the figure.

The two masses stick together and jointly move by a distance of 0.25 m further along the same frictionless surface, before, they touch the mass-less buffer that is connected to the rigid vertical wall by means of a linear spring having a spring constant undefined The maximum deflection of the spring is _____________cm (round off to 2 decimal places).

0.98 to 1.02

Category: GATE Mechanical Engineering 2020 set 2

Question 49:

A bolt head has to be made a the end of a rod of diameter d=12 mm by localized forging (upsetting) operation. The length of the unsupported portion of the rod is 40 mm. To avoid buckling of the rod, a closed forging operation has to be performed with a maximum die diameter of ________________mm.

15 to 19.5

16 to 19.5

17 to 19.5

18 to 19.5

Category: GATE Mechanical Engineering 2020 set 2

Question 50:

A thin-walled cylinder of radius r and thickness t is open at both ends, and fits snugly between two rigid walls under ambient conditions, as shown in the figure.

The material of the cylinder has Young's modulus E, Poisson's ratio v, and coefficient of thermal expansion α. What is the minimum rise in temperature ΔT of the cylinder (assume uniform cylinder temperature with no buckling of the cylinder) required to prevent gas leakage if the cylinder has to store the gas at an internal pressure of p above the atmosphere?

A	undefined	B	undefined
C	undefined	D	undefined

Category: GATE Mechanical Engineering 2020 set 2

Question 51:

A mould cavity of 1200

{cm}^{2}

volume has to be filled through a sprue of 10 cm length feeding a horizontal runner. Cross-sectional area at the base of the sprue is 2

{cm}^{2}

. Consider acceleration due to gravity as 9.81

m / s^{2}

. Neglecting frictional losses due to molten metal flow, the time taken to fill the mould cavity is __________ seconds (round off to 2 decimal places).

4 to 9

5 to 10

6 to 11

7 to 12

Category: GATE Mechanical Engineering 2020 set 2

Question 52:

There are two identical shaping machines

S_{1} and S_{2}

. In machine

S_{2}

, the width of the workpiece is increased by 10% and the feed is decreased by 10% with respect to the of

S_{1}

If all other condition remain the same then ratio of ratio of total time per pass in

S_{1}

and

S_{2}

will be __________( round off to one decimal place).

0.3 to 0.9

0.5 to 0.9

0.7 to 0.9

0.9 to 0.9

Category: GATE Mechanical Engineering 2020 set 2

Question 53:

A cylindrical bar with 200 mm diameter is being turned with a tool having geometry

0 ° - 9 ° - 7 ° - 8 ° - 15 ° - 30 ° - 0.05

inch (Coordinate system, ASA) resulting in a cutting force

F_{c 1}

. I the tool geometry is changed to

0 ° - 9 ° - 7 ° - 8 ° - 15 ° - 0 ° - 0.05

inch (Coordinate system, ASA) and all other parameters remain unchanged, the cutting force changes to

F_{c 2}

. Specific cutting energy (in/

J / m m^{3}

) is

U_{c} = U_{0} {(t_{1})}^{- 0.4}

, where

U_{0}

is the specific energy coefficient, and

t_{1}

is the uncut thickness in mm. The value of percentage change in cutting force

F_{c 2}, i . e .

(\frac{F_{C 2} - F_{C 1}}{F_{C 1}}) x 100,

is __________________(round off to one decimal place).

5.8 to 5.5

5.8 to 5.6

5.8 to 5.7

5.8 to 5.8

Category: GATE Mechanical Engineering 2020 set 2

Question 54:

Bars of 250 mm length and 25 mm diameter are to be turned on a lathe with a feed of 0.2 mm/rev. Each regrinding of the tool costs Rs.20. The time required for each tool change is given as undefined (where cutting speed V is in m/min and tool life T is in min). The optimum tool cost piece for maximum production rate is Rs. __________ (round off to 2 decimal places).

26.00 to 28.00

Category: GATE Mechanical Engineering 2020 set 2

Question 55:

A point 'P' on a CNC controlled XY- stage is moved to another point 'Q' using the coordinate system shown in the figure below and rapid positioning command (G00).

A pair of stepping motors with maximum speed of 800 rpm, controlling both the X and Y motion of the stage, are directly coupled to a pair of lead screws, each with a uniform pitch of 0.5 mm. The time needed to position the point 'P' to the point 'Q' is __________minutes (round off to 2 decimal places)

1.40 to 1.60

Category: GATE Mechanical Engineering 2020 set 2

Question 56:

For a single item inventory system, the demand is continuous, which is 10000 per year. The replenishment is instantaneous and backorders (S units) per cycle are allowed as shown in the figure.

As soon as the quantity (Q units) from the supplier is received, the backordered quantity is issued to the customers. The ordering cost is Rs. 300 per order. The carrying cost is Rs. 4 per unit per year. The cost of backordering is Rs. 25 per unit per year. Based on the total cost minimization criteria, the maximum inventory reached in the system is __________(round off to nearest integer).

1130 to 1140

Category: GATE Mechanical Engineering 2020 set 2

Question 57:

Consider a flow through a nozzle, as shown in the figure below.

The air flow is steady, incompressible and inviscid. The density of air is 1.23 undefined The pressure difference, undefined is _____________kPa (round off to decimal places).

1.50 to 1.55

Category: GATE Mechanical Engineering 2020 set 2

Question 58:

Water (density 1000 kg

m^{2}

) flows through an inclined pipe of uniform diameter. The velocity, pressure and elevation at section A are

V_{A} = 3.2 m / s, p_{A} = 186 kPa

and

z_{A} = 24.5 m,

respectively, and those at section B are

V_{B} = 3.2 m / s, p_{B} = 260

kPa and

z_{B} = 9.1 m,

respectively. If acceleration due to gravity is 10

m / s, p_{B} = 260 kPa and z_{B} = 9.1 m,

respectively. If acceleration due to gravity is 10

m / s^{2}

then the head lost due to friction is ___________m (round off to one decimal place)

7.9 to 8.0

7.9 to 8.1

7.9 to 8.2

7.9 to 8.3

Category: GATE Mechanical Engineering 2020 set 2

Question 59:

The spectral distribution of radiation from a black body

T_{1} = 3000 K

has a maximum at wavelength

λ_{\max}

. The body cools down to a temperature

T_{2}

. If the wavelength corresponding to the maximum of the spectral distribution at

T_{2}

is 1.2 times of the original wavelength

λ_{m a x}

, Then the temperature

T_{2}

is ___________ K (round off to the nearest integer).

2499 to 2501

2499 to 2502

2499 to 2503

2499 to 2504

Category: GATE Mechanical Engineering 2020 set 2

Question 60:

Water flower through a tube of 3 cm internal diameter and length 20 m. The outside surface of the tube is heated electrically so that it is subjected to uniform heat flux circumferentially and axially. The mean inlet and exit temperatures of the water are 10°C and 70°C, respectively. The mass flow rate of the water is 720 kg/h. Disregard the thermal resistance of the tube wall. The internal heat transfer coefficient is 1697

W / m^{2} . K .

Take specific heat

C_{p}

of water as 4.179 kJ/kg.K. The inner surface temperature at the exit section of the tube is _______________°C (round off to one decimal place).

83.1 to 84.1

85.1 to 86.1

86.1 to 87.1

88.1 to 89.1

Category: GATE Mechanical Engineering 2020 set 2

Question 61:

Air is contained in a frictionless piston-cylinder arrangement as shown in the figure.

The atmospheric pressure is 100 kPa and the initial pressure of air in the cylinder is 105 kPa. The area of piston is 300

{cm}^{2}

. Heat is added and the piston moves slowly from its initial position until it reaches the stops. The spring constant of the linear spring is 12.5 N/mm. Considering the air inside the cylinder as the system, the work interaction is ___________J (round off to the nearest integer).

543 to 545

Category: GATE Mechanical Engineering 2020 set 2

Question 62:

Moist air at 105 kPa, 30°C and 80% relative humidity flows over a cooling coil in an insulated air-conditioning duct. Saturated air exits the duct at 100 kPa and 15°C. The saturation pressures of water at 30°C and 15°C are 4.24 kPa and 1.7 kPa respectively. Molecular weight of water is 18 g/mol and that of air is 28.94 g/mol. The mass of water condensing out from the duct is _____________g/kg of dry air (round off to the nearest integer).

5 to 5

10 to 10

15 to 15

20 to 20

Category: GATE Mechanical Engineering 2020 set 2

Question 63:

In a steam power plant, superheated steam at 10 MPa and 500°C, is expanded isentropically in a turbine until it becomes a saturated vapour. It is then reheated at constant pressure to 500°C. The stream is next expanded isentropically in another turbine until it reaches the condenser pressure of 20 kPa. Relevant properties of steam are given in the following two tables. The work done by both the turbines together is __________KJ/Kg (round off to the nearest integer). Superheated Steam Table:

Pressure, P (MPa)	Temperature, T (°C)	Enthalpy, h (kJ/kg)	Entropy, s (kJ/kg.K)
10	500	3373.6	6.5965
1	500	3478.4	7.7621

Saturated Steam Table:

Pressure, p	Sat. Temp. $T_{s a t} (° C)$	Enthalpy, h (kJ/kg)		Entropy, s (kJ/kg)
		Enthalpy, h (kJ/kg)		Entropy, s (kJ/kg)		$h_{f}$	$h_{g}$	$s f$	$s g$
		1 MPa	179.91	762.9	2778.1	2.1386	6.5965
20 kPa	60.06	251.38	2609.7	0.8319	7.9085

1500 to 1525

1500 to 1526

1500 to 1527

1500 to 1528

Category: GATE Mechanical Engineering 2020 set 2

Question 64:

Keeping all other parameters identical, the Compression Ratio (CR) of an air standard diesel cycle is increased from 15 to 21. Take ratio of specific heats =1.3 and cut-off ratio of the cycle

r_{c} = 2 .

The difference between the new and the old efficiency values, in percentage,

(η_{n e w C R = 21}) - (η_{o l d R = 15}) =___________%

(round off to decimal place).

4.3 to 4.6

4.4 to 4.7

4.5 to 4.8

4.6 to 4.9

Category: GATE Mechanical Engineering 2020 set 2

Question 65:

A steel spur pinion has a module (m) of 1.25 mm, 20 teeth and 20° pressure angle. The pinion rotates at 1200 rpm and transmits power to a 60 teeth gear. The face width (f) is 50 mm, Lewis from factor Y=0.322 and a dynamic factor undefined =1.26. The bending stress (σ) induced in a tooth can be calculated by using the Lewis formula given below. If the maximum bending stress experienced by the pinion is 400 MPa, the power transmitted is __________kW (round off to one decimal places). Lewis formula undefined where undefined is the tangential load acting on the pinion.

9.8 to 10.8

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Answered & Marked for Review (will be considered for evaluation)

Question 1:

While I agree _________ his proposal this time, I do not often agree _________him

Correct Answer : to, with

Question 2:

The recent measures to improve the output would ___________the level of production to our satisfaction.

Correct Answer : increase

Question 3:

Select the word that fits the analogy: White: Whitening : : Light_______

Correct Answer : Lightening

Question 4:

Correct Answer : squared=lost

Question 5:

There are five levels {P,Q,R,S,T} in a linear supply chain before a product reaches customers, as shown in the figure.

At each pf the five levels, The price of the product is increased by 25%. If the product is produced at level P at the cost of Rs. 120 per unit, what is the price paid 9in rupees) by the customers?

Correct Answer : 366.21

Question 6:

Correct Answer : Mitigation deals with actions taken to reduce the use of fossil fuels

Question 7:

Find the missing element in the following figure.

Correct Answer : d

Question 8:

Correct Answer : 3 days

Question 9:

An engineer measures THREE quantities X, Y and Z in an experiment. She finds that they follow a relationship that is represented in the figure below: (the product of X and Y linearly varies with Z)

Then, which of the following statements is FALSE?

Correct Answer : For fixed Z; X is proportional to Y

Question 10:

Correct Answer : 22:9

Question 11:

The sum of two normally distributed random variables X and Y is

A	always normally distributed
B	normally distributed, only if X and Y are independent
C	normally distributed, only if X and Y are independent
D	normally distributed, only if X and Y have the same standard deviation

Correct Answer : None of these

Question 12:

A matrix P is decomposed into its symmetric part S and skew symmetric part V. If

S = (\begin{matrix} - 4 & 4 & 2 \\ 4 & 3 & 7 / 2 \\ 2 & 7 / 2 & 2 \end{matrix}), V = (\begin{matrix} 0 & - 2 & 3 \\ 2 & 0 & 7 / 2 \\ - 3 & - 7 / 2 & 0 \end{matrix}) .

then matrix P is

A	$(\begin{matrix} - 4 & 6 & - 1 \\ 2 & 3 & 0 \\ 5 & 7 & 2 \end{matrix})$	B	$(\begin{matrix} - 4 & 2 & 5 \\ 6 & 3 & 7 \\ - 1 & 0 & 2 \end{matrix})$
C	$(\begin{matrix} 4 & - 6 & 1 \\ - 2 & - 3 & 0 \\ - 5 & - 7 & - 2 \end{matrix})$	D	$(\begin{matrix} - 2 & 9 / 2 & - 1 \\ - 1 & 81 / 4 & 11 \\ - 2 & 45 / 2 & 73 / 4 \end{matrix})$

Correct Answer : B

Question 13:

Let I = \int_{x = 0}^{1} \int_{y = 0}^{x^{2}} {xy}^{2} dy dx .

Then, l may also be expressed as

A	$\int_{y = 0}^{1} \int_{x = 0}^{\sqrt{y}} x y^{2} d x d y$	B	$\int_{y = 0}^{1} \int_{x = 0}^{1} y x^{2} d x d y$
C	$\int_{y = 0}^{1} \int_{x = \sqrt{y}}^{1} x y^{2} d x d y$	D	$\int_{y = 0}^{1} \int_{x = 0}^{\sqrt{y}} y x^{2} d x d y$

Correct Answer : C

Question 14:

The solution of

\frac{d^{2} y}{d t^{2}} - y = 1,

Which additionally satisfies

y_{t = 0} = {\frac{dy}{dt}}_{t = 0} = 0 in the Laplace s - domain is

A	$\frac{1}{s (s + 1) (s - 1)}$	B	$\frac{1}{s (s + 1)}$
C	$\frac{1}{s (s - 1)}$	D	$\frac{1}{s - 1}$

Correct Answer : A

Question 15:

An attempt is made to pull a roller of weight W over a curb (step) by applying a horizontal force F as shown in the figure.

A		B
C		D

Correct Answer : B

Question 16:

A circular disk of radius r is confined to roll without slipping at P and Q as shown in the figure.

If the plates have velocities as shown, the magnitude of the angular velocity of the disk is

A	$\frac{v}{r}$	B	$\frac{v}{2 r}$
C	$\frac{2 v}{3 r}$	D	$\frac{3 v}{2 r}$

Correct Answer : D

Question 17:

The equation of motion of a spring-mass-damper system is given by

\frac{d^{2} x}{{dt}^{2}} + 3 \frac{dx}{dt} + 9 x = 10 \sin (5 t)

The damping factor for the system is

Correct Answer : 0.5

Question 18:

The number of qualitatively distinct kinematic inversions possible for a Grashof chain with four revolute pairs is

Correct Answer : 3

Question 19:

The process, that uses a tapered horn to amplify and focus the mechanical energy for machining of glass, is

Correct Answer : ultrasonic machining

Question 20:

Correct Answer : 3-2-4-1

Question 21:

Which one of the following statements about a phase diagram is INCORRECT?

Correct Answer : It gives information on transformation rates

Question 22:

The correct match between the specifications and the symbols (I to VI) is

Correct Answer : I-R, II-Q, III-P, IV-S, V-U, VI-T

Question 23:

In Materials Requirement Planning, if the inventory holding cost is very high and the setup cost is zero, which one of the following lot sizing approaches should be used?

Correct Answer : Lot-for-Lot

Question 24:

Which of the following conditions is used to determine the stable equilibrium of all partially submerged floating bodies?

Correct Answer : Metacentre must be at a higher level than the centre of gravity

Question 25:

In the space above the mercury column in a barometer tube, the gauge pressure of the vapour is

Correct Answer : negative

Question 26:

A closed vessel contains pure water, in thermal equilibrium with its vapour at 25°C (Stage #1), as shown.

Correct Answer : Hot air will go inside the vessel through Valve A

Question 27:

For an air-standard Diesel cycle,

Correct Answer : heat addition is at constant pressure and heat rejection is at constant volume

Question 28:

The values of enthalpies at the stator inlet and rotor outlet of a hydraulic turbomachine stage are

h_{1} and h_{3}

respectively. The enthalpy at the stator outlet (or, rotor inlet) is

h_{2}

. The condition

(h_{2} - h_{1}) = (h_{3} - h_{2})

indicates that the degree of reaction of this stage is

Correct Answer : 50%

Question 29:

Let I be a 100 dimensional identity matrix and E be the set of its distinct ( no value appears more than once in E) real eigenvalues. The number of elements in E is __________________

Correct Answer : 1 to 1

Question 30:

A beam of negligible mass is hinged at support P and has a roller support Q shown in the figure.

A point load of 1200 N is applied at point R. The magnitude of the reaction force at support Q is ____________N.

Correct Answer : 1500 to 1500

Question 31:

A machine member is subjected to fluctuating stress . The endurance limit of the material is 350 MPa. If the factor of safety used in the design is 3.5 then the maximum allowable value of

σ_{0}

is ______________MPa (round off to 2 decimal places).

Correct Answer : 99.98 to 100.2

Question 32:

Consider the following network of activities, with each activity named A-I, illustrated in the nodes of the network.

The number of hours required for each activity is shown alongside the nodes. The slack on the activity L, is ________ hours.

Correct Answer : 2 to 2

Question 33:

In a furnace, the inner and outer sides of the brick wall undefined are maintained at 1100°C and 700°C, respectively as shown in figure.

The brick wall is covered by an insulating material of thermal conductivity

k_{2}

. The thickness of the insulation is

1 / 4^{t h}

of the thickness of the brick wall. The outer surface of the insulation is at 200°C. The heat flux through the composite walls is 2500 undefined. The value of

k_{2}

is __________ W/m.K (round off to one decimal place).

Correct Answer : 0.5 to 0.5

Question 34:

Correct Answer : 0.89 to 0.91

Question 35:

The directional derivative of

f (x, y, z) = x y z

at point (-1,1,3) in the direction of vector

\hat{i} - 2 \hat{j} + 2 \hat{k} i s

A	$3 \hat{i} - 3 \hat{j} - \hat{k}$	B	$- \frac{7}{3}$
C	$\frac{7}{3}$	D	7

Correct Answer : C

Question 36:

The function

f (z)

of complex variable z = x + i y, where

i = \sqrt{- 1},

is given as

f (z) = (x^{3} - 3 x y^{2}) + i v (x, y) .

For this function to be analytic,

v (x, y)

should be

A	$(3 {xy}^{2} - y^{3}) + constant$	B	$(3 {xy}^{2} y^{2} - y^{3}) + constant$
C	$(x^{3} - 3 x^{2} y) + constant$	D	$(3 x^{2} y - y^{3}) + constant$

Correct Answer : D

Question 37:

A cantilever of length l, and flexural rigidity El, stiffened by a spring of stiffness k, is loaded by a transverse force P, as shown.

The transverse deflection under the load is

A	undefined	B	undefined
C	undefined	D	undefined

Correct Answer : D

Question 38:

The sun (S) and the planet (P) of an epicyclic gear train shown in the figure have identical number of teeth.

If the sun (S) and the outer ring (R) gears are rotated in the same direction with angular speed undefined respectively, then the angular speed of the arm AB is

A	undefined	B	undefined
C	undefined	D	undefined

Correct Answer : A

Question 39:

A helical spring has spring constant k. If the wire diameter, spring diameter and the number of coils are all doubled then the spring constant of the new spring becomes

Correct Answer : k

Question 40:

Two rollers of diameters

D_{1}

(in mm) and

D_{2}

(in mm) are used to measure the internal taper angle in the V-groove of a machined component. The heights

H_{1}

(in mm) and

H_{2}

(in mm) are measured by using a height gauge after inserting the roller into the same V-groove as shown in the figure.

Which one of the following is the correct relationship to evaluate the angle α as shown in the figure?

A	undefined
B	undefined
C	undefined
D	undefined

Correct Answer : A

Question 41:

The forecast for the monthly demand of a product is given in the table-below.

Month	Forecast	Actual Sales
1	33.00	30.00
2	31.80	32.00
3	31.82	30.00

The forecast is made by using the exponential smoothing method. The exponential smoothing coefficient used in forecasting the demand is

Correct Answer : 0.10

Question 42:

One kg of air in a closed system undergoes an irreversible process from an initial sate of

p_{1} = 1

bar (absolute) and

T_{1} = 27 ° C

, to a final state of

p_{2} = 3

bar (absolute) and

T_{2} = 127 ° C .

If the gas constant of air is 287 J/kg.K and the ratio of the air in the process is

Correct Answer : -26.3

Question 43:

For the integral

\int_{0}^{π / 2} (8 + 4 \cos x) d x,

the absolute percentage error in numerical evaluation with the Trapezoidal rule, using only the end points, is_____________(round off to one decimal place).

Correct Answer : 5.1 to 5.5

Question 44:

Correct Answer : 0.041 to 0.043

Question 45:

A hollow spherical ball of radius 20 cm floats in still water, with half of its volume submerged. Taking the density of water as

1000 kg / m^{3}

, and the acceleration due to gravity as

10 m / s^{2}

, the natural frequency of small oscillations of the ball, normal to the water surface is ______________ radians/s (round off to 2 decimal places).

Correct Answer : 8.60 to 8.70

Question 46:

Uniaxial compression test date for a solid metal bar of length 1 m is shown in the figure.

Correct Answer : 55.0 to 58.0

Question 47:

The turning moment diagram of a flywheel fitted to a fictitious engine is shown in the figure.

The mean turning moment is 2000 Nm. The average engine speed is 1000 rpm. For fluctuation in the speed to be within

\pm 2 %

of the average speed, the mass moment of inertia of the flywheel is __________ kg.

m^{2}

Correct Answer : 3.55 to 3.65

Question 48:

A rigid block of mass undefined =10 kg having velocity

v_{0}

=2 m/s strikes a stationary block of mass undefined =30 kg after traveling 1 m along a frictionless horizontal surface as shown in the figure.

Correct Answer : 0.98 to 1.02

Question 49:

Correct Answer : 18 to 19.5

Question 50:

A thin-walled cylinder of radius r and thickness t is open at both ends, and fits snugly between two rigid walls under ambient conditions, as shown in the figure.

A	undefined	B	undefined
C	undefined	D	undefined

Correct Answer : C

Question 51:

A mould cavity of 1200

{cm}^{2}

volume has to be filled through a sprue of 10 cm length feeding a horizontal runner. Cross-sectional area at the base of the sprue is 2

{cm}^{2}

. Consider acceleration due to gravity as 9.81

m / s^{2}

. Neglecting frictional losses due to molten metal flow, the time taken to fill the mould cavity is __________ seconds (round off to 2 decimal places).

Correct Answer : 4 to 9

Question 52:

There are two identical shaping machines

S_{1} and S_{2}

. In machine

S_{2}

, the width of the workpiece is increased by 10% and the feed is decreased by 10% with respect to the of

S_{1}

If all other condition remain the same then ratio of ratio of total time per pass in

S_{1}

and

S_{2}

will be __________( round off to one decimal place).

Correct Answer : 0.7 to 0.9

Question 53:

A cylindrical bar with 200 mm diameter is being turned with a tool having geometry

0 ° - 9 ° - 7 ° - 8 ° - 15 ° - 30 ° - 0.05

inch (Coordinate system, ASA) resulting in a cutting force

F_{c 1}

. I the tool geometry is changed to

0 ° - 9 ° - 7 ° - 8 ° - 15 ° - 0 ° - 0.05

inch (Coordinate system, ASA) and all other parameters remain unchanged, the cutting force changes to

F_{c 2}

. Specific cutting energy (in/

J / m m^{3}

) is

U_{c} = U_{0} {(t_{1})}^{- 0.4}

, where

U_{0}

is the specific energy coefficient, and

t_{1}

is the uncut thickness in mm. The value of percentage change in cutting force

F_{c 2}, i . e .

(\frac{F_{C 2} - F_{C 1}}{F_{C 1}}) x 100,

is __________________(round off to one decimal place).

Correct Answer : 5.8 to 5.5

Question 54:

Correct Answer : 26.00 to 28.00

Question 55:

A point 'P' on a CNC controlled XY- stage is moved to another point 'Q' using the coordinate system shown in the figure below and rapid positioning command (G00).

Correct Answer : 1.40 to 1.60

Question 56:

For a single item inventory system, the demand is continuous, which is 10000 per year. The replenishment is instantaneous and backorders (S units) per cycle are allowed as shown in the figure.

Correct Answer : 1130 to 1140

Question 57:

Consider a flow through a nozzle, as shown in the figure below.

The air flow is steady, incompressible and inviscid. The density of air is 1.23 undefined The pressure difference, undefined is _____________kPa (round off to decimal places).

Correct Answer : 1.50 to 1.55

Question 58:

Water (density 1000 kg

m^{2}

) flows through an inclined pipe of uniform diameter. The velocity, pressure and elevation at section A are

V_{A} = 3.2 m / s, p_{A} = 186 kPa

and

z_{A} = 24.5 m,

respectively, and those at section B are

V_{B} = 3.2 m / s, p_{B} = 260

kPa and

z_{B} = 9.1 m,

respectively. If acceleration due to gravity is 10

m / s, p_{B} = 260 kPa and z_{B} = 9.1 m,

respectively. If acceleration due to gravity is 10

m / s^{2}

then the head lost due to friction is ___________m (round off to one decimal place)

Correct Answer : 7.9 to 8.1

Question 59:

The spectral distribution of radiation from a black body

T_{1} = 3000 K

has a maximum at wavelength

λ_{\max}

. The body cools down to a temperature

T_{2}

. If the wavelength corresponding to the maximum of the spectral distribution at

T_{2}

is 1.2 times of the original wavelength

λ_{m a x}

, Then the temperature

T_{2}

is ___________ K (round off to the nearest integer).

Correct Answer : 2499 to 2501

Question 60:

W / m^{2} . K .

Take specific heat

C_{p}

of water as 4.179 kJ/kg.K. The inner surface temperature at the exit section of the tube is _______________°C (round off to one decimal place).

Correct Answer : 85.1 to 86.1

Question 61:

Air is contained in a frictionless piston-cylinder arrangement as shown in the figure.

The atmospheric pressure is 100 kPa and the initial pressure of air in the cylinder is 105 kPa. The area of piston is 300

{cm}^{2}

Correct Answer : 543 to 545

Question 62:

Correct Answer : 10 to 10

Question 63:

Pressure, P (MPa)	Temperature, T (°C)	Enthalpy, h (kJ/kg)	Entropy, s (kJ/kg.K)
10	500	3373.6	6.5965
1	500	3478.4	7.7621

Saturated Steam Table:

Pressure, p	Sat. Temp. $T_{s a t} (° C)$	Enthalpy, h (kJ/kg)		Entropy, s (kJ/kg)
		Enthalpy, h (kJ/kg)		Entropy, s (kJ/kg)		$h_{f}$	$h_{g}$	$s f$	$s g$
		1 MPa	179.91	762.9	2778.1	2.1386	6.5965
20 kPa	60.06	251.38	2609.7	0.8319	7.9085

Correct Answer : 1500 to 1525

Question 64:

Keeping all other parameters identical, the Compression Ratio (CR) of an air standard diesel cycle is increased from 15 to 21. Take ratio of specific heats =1.3 and cut-off ratio of the cycle

r_{c} = 2 .

The difference between the new and the old efficiency values, in percentage,

(η_{n e w C R = 21}) - (η_{o l d R = 15}) =___________%

(round off to decimal place).

Correct Answer : 4.6 to 4.9

Question 65:

Correct Answer : 9.8 to 10.8

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