Be Paitent While your exam is being loaded

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 Main 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

View Solution

Participate to compete with other aspirants at an all India level.

Attempt Mock Test

Participate to compete with other aspirants at an all India level.

General Instructions

Choose Your Default Language

Please read the instructions carefully

General Instructions:

- Total duration of is 160 min.
The clock will be set at the server. The countdown timer in the top right corner of screen will display the remaining time available for you to complete the examination. When the timer reaches zero, the examination will end by itself. You will not be required to end or submit your examination.
The Questions Palette displayed on the right side of screen will show the status of each question using one of the following symbols:
1. You have not visited the question yet.
2. You have not answered the question.
3. You have answered the question.
4. You have NOT answered the question, but have marked the question for review.
5. The question(s) "Answered and Marked for Review" will be considered for evalution.
You can click on the ">" arrow which apperes to the left of question palette to collapse the question palette thereby maximizing the question window. To view the question palette again, you can click on "<" which appears on the right side of question window.
You can click on your "Profile" image on top right corner of your screen to change the language during the exam for entire question paper. On clicking of Profile image you will get a drop-down to change the question content to the desired language.
You can click on to navigate to the bottom and to navigate to top of the question are, without scrolling.

Navigating to a Question:

To answer a question, do the following:
1. Click on the question number in the Question Palette at the right of your screen to go to that numbered question directly. Note that using this option does NOT save your answer to the current question.
2. Click on Save & Next to save your answer for the current question and then go to the next question.
3. Click on Mark for Review & Next to save your answer for the current question, mark it for review, and then go to the next question.

Answering a Question:

Procedure for answering a multiple choice type question:
1. To select you answer, click on the button of one of the options.
2. To deselect your chosen answer, click on the button of the chosen option again or click on the Clear Response button
3. To change your chosen answer, click on the button of another option
4. To save your answer, you MUST click on the Save & Next button.
5. To mark the question for review, click on the Mark for Review & Next button.
To change your answer to a question that has already been answered, first select that question for answering and then follow the procedure for answering that type of question.

Navigating through sections:

Sections in this question paper are displayed on the top bar of the screen. Questions in a section can be viewed by click on the section name. The section you are currently viewing is highlighted.
After click the Save & Next button on the last question for a section, you will automatically be taken to the first question of the next section.
You can shuffle between sections and questions anything during the examination as per your convenience only during the time stipulated.
Candidate can view the corresponding section summery as part of the legend that appears in every section above the question palette.

Please note all questions will appear in your default language. This language can be changed for a particular question later on.

I have read and understood the instructions. All computer hardware allotted to me are in proper working condition. I declare that I am not in possession of / not wearing / not carrying any prohibited gadget like mobile phone, bluetooth devices etc. /any prohibited material with me into the Examination Hall.I agree that in case of not adhering to the instructions, I shall be liable to be debarred from this Test and/or to disciplinary action, which may include ban from future Tests / Examinations

Proceed

Category: GATE Mechanical Engineering 2020 set 1

Question 1:

Multiplication of real valued square matrices of same dimension is

associative

commutative

always positive definite

not always possible to computer

Category: GATE Mechanical Engineering 2020 set 1

Question 2:

The value of

\lim_{x \to 1} (\frac{1 - e^{- c (1 - x)}}{1 - x e^{- c (1 - x)}}) i s

A	c	B	c+1
C	$\frac{c}{c + 1}$	D	$\frac{c + 1}{c}$

Category: GATE Mechanical Engineering 2020 set 1

Question 3:

The Laplace transform of a function

f (t) i s ℒ (f) = \frac{1}{(s^{2} + ω^{2})} .

Then, f (t) is

A	$f (t) = \frac{1}{ω^{2}} (1 - \cos ω t)$	B	$f (t) = \frac{1}{ω} \cos ω t$
C	$f (t) = \frac{1}{ω} \sin ω t$	D	$f (t) = \frac{1}{ω^{2}} (1 - \sin ω t)$

Category: GATE Mechanical Engineering 2020 set 1

Question 4:

Which of the following function f(z) , of the complex variable z, is NOT analytic at all the points of the complex plane?

A	$f (z) = z^{2}$	B	$f (z) = e^{z}$
C	$f (z) = \sin z$	D	$f (z) = \log z$

Category: GATE Mechanical Engineering 2020 set 1

Question 5:

The members carrying zero force ( i.e. zero-force members )in the truss shown in the figure, for any load P > 0 with no appreciable deformation of the truss ( i. e. with no appreciable change in angles between the members ), are

BF and DH only

BF, DH and GC only

BF, DH, GC, CD and DE only

BF, DH, GC, FG and GH only

Category: GATE Mechanical Engineering 2020 set 1

Question 6:

A single-degree-of-freedom oscillator is subject to harmonic excitation F(t) =

F_{0}

cos( ωt ) as shown in the figure.

The non-zero value of ω, for which the amplitude of the force transmitted to the ground will be

F_{0}

, is

A	$\sqrt{\frac{k}{2 m}}$	B	$\sqrt{\frac{k}{m}}$
C	$\sqrt{\frac{2 k}{m}}$	D	$2 \sqrt{\frac{k}{m}}$

Category: GATE Mechanical Engineering 2020 set 1

Question 7:

The stress state at point in a material under plane stress condition is equi-biaxial tension with a magnitude of 10 MPa. If one unit on the σ-τ plane is 1 MPa, the Mohr's circle representation of the state-of-stress is given by

A	a circle with a radius equal to principal stress and its center at the origin of the σ-τ plane
B	a point on the σ axis at a distance of 10 units from the origin
C	a circle with a radius of 10 units on the σ - τ plane
D	a point on the τ axis at a distance of 10 units from the origin

Category: GATE Mechanical Engineering 2020 set 1

Question 8:

A four bar mechanism is shown below.

For the mechanism to be a crank-rocker mechanism, the length of the link PQ can be

80 mm

200 mm

300 mm

350 mm

Category: GATE Mechanical Engineering 2020 set 1

Question 9:

A helical gear with 20° pressure angle and 30° helix angle mounted at the mid-span of a shaft that is supported between two bearing at the ends. The nature of the stresses induced in the shaft is

a	normal stresses due to bending only	b	normal stress due to bending in one plane and axial loading; shear stress due to torsion
c	normal stress due to bending in two planes and axial loading; shear stress due to torsion	d	normal stress due to bending in two planes; shear stress due to torsion

A and B

A and C

A and D

Category: GATE Mechanical Engineering 2020 set 1

Question 10:

The crystal structure of γ iron (austenite phase) is

BCC

FCC

HCP

BCT

Category: GATE Mechanical Engineering 2020 set 1

Question 11:

Match the following

Heat treatment process	Effect
P: Tempering	1. Strengthening
Q: Quenching	2. Toughening
R: Annealing	3. Hardening
S: Normalizing	4. Softening

P-2, Q-3, R-4, S-1

P-1, Q-1, R-3, S-2

P-3, Q-3, R-1, S-3

P-4, Q-3, R-2, S-1

Category: GATE Mechanical Engineering 2020 set 1

Question 12:

The base of a brass bracket needs rough grinding. for this purpose, the most suitable grinding wheel grade specification is

C30Q12V

A50G8V

C90J4B

A30D12V

Category: GATE Mechanical Engineering 2020 set 1

Question 13:

In the Critical Path Method (CPM), the cost-time slope of an activity is given by

A	$\frac{crash Cost - Normal Cost}{Crash Time}$
B	$\frac{Normal cost}{Crash Time - Normal time}$
C	$\frac{Crash Cost}{Crash Time - Normal Time}$
D	$\frac{Crash Time - Normal Cost}{Normal Cost - Crash Time}$

Category: GATE Mechanical Engineering 2020 set 1

Question 14:

Froude number is the ratio of

Buoyancy Forces to viscous Forces

inertia forces to viscous forces

Buoyancy forces to inertia forces

inertia forces to gravity forces

Category: GATE Mechanical Engineering 2020 set 1

Question 15:

Match the following non-dimensional numbers with the corresponding definitions:

Non-dimensional number			Definitions
P	Reynolds number	1	$\frac{Buoyancy force}{Viscous force}$
Q	Grashof number	2	$\frac{Momentum diffusivity}{Thermal diffusivity}$
R	Nusselt number	3	$\frac{Inertia force}{Viscous force}$
S	Prandtl number	4	$\frac{Convective heat transfer}{Conduction heat transfer}$

P-1, Q-3, R-2, S-4

P-3, Q-1, R-2, S-4

P-4, Q-3, R-1, S-2

P-3, Q-1, R-4, S-2

Category: GATE Mechanical Engineering 2020 set 1

Question 16:

The velocity field of an incompressible flow in a Cartesian system is represented by

\vec{V} = 2 (x^{2} - y^{2}) \hat{i} + v \hat{j} + 3 \hat{k}

which on of the following expressions for v is valid?

-4xz+6xy

-4xy-4xz

4xz-6xy

4xy+4xz

Category: GATE Mechanical Engineering 2020 set 1

Question 17:

For an ideal gas, the value of the joule-Thomson coefficient is

positive

negative

zero

indeterminate

Category: GATE Mechanical Engineering 2020 set 1

Question 18:

For an ideal gas, a constant pressure line and a constant volume line intersect at a point, in the Temperature (T) versus specific entropy (s) diagram.

C_{P}

is the specific heat at constant pressure and

C_{v}

is the specific heat at constant volume. The ratio of the slopes of the constant pressure and constant volume lines at the point of intersection is

A	$\frac{C_{p} - C_{v}}{C_{p}}$	B	$\frac{C_{p}}{C_{p}}$
C	$\frac{C_{p} - C_{v}}{C_{v}}$	D	$\frac{C_{v}}{C_{p}}$

Category: GATE Mechanical Engineering 2020 set 1

Question 19:

For three

\vec{A} = 2 \hat{j} - 3 \hat{k}, \vec{B} = - 2 \hat{i} + \hat{K} a n d \vec{C} = 3 \hat{i} - \hat{j}, w h e r e \hat{i}, \hat{j} a n d \hat{k}

are unit vectors along the axes of a right-handed rectangular/Cartesian coordinate system, the value of

(\vec{A \cdot} (\vec{B} \times \vec{C}) + 6)

is ________________.

2 to 2

4 to 4

6 to 6

8 to 8

Category: GATE Mechanical Engineering 2020 set 1

Question 20:

A flywheel is attached to an engine to keep its rotational speed between 100 rad/s and 110 rad/s. Of the energy fluctuation in the flywheel these two speeds is 1.50 kl then the moment of inertia of the flywheel is __________________

k g . m^{2}

( round off to 2 decimal places ) .

0.98 to 1.01

0.98 to 1.02

0.98 to 1.03

0.98 to 1.04

Category: GATE Mechanical Engineering 2020 set 1

Question 21:

A balanced rigid disc mounted on a rigid rotor has four identical point masses, each of 10 grams, attached to four points on the 100 mm radius circle shown in the figure.

The sheet metal with a motor at uniform angular speed 10 rad/s. If one of the masses gets detached then the magnitude of the resultant unbalance force on the rotor is _____________________ N (round off to 2 decimal places).

0.03 to 0.05

0.05 to 0.07

0.07 to 0.09

0.09 to 0.11

Category: GATE Mechanical Engineering 2020 set 1

Question 22:

A sheet metal with a stock hardness of 250 HRC has to be sheared using a punch and a die having a clearance of 1 mm between them. If the stock hardness of the sheet metal increases to 400 HRC, the clearance between the punch and the die should be ______________mm.

1.0 to 1.0

1.0 to 1.1

1.0 to 1.2

1.0 to 1.3

Category: GATE Mechanical Engineering 2020 set 1

Question 23:

A company is hiring to fill four managerial vacancies. The candidates are five men and three women. If every candidate is equally likely to be chosen then the probability that at least one women will be selected is ____________(round off to 2 decimal places)

0.98 to 0.95

0.98 to 0.96

0.98 to 0.97

0.98 to 0.98

Category: GATE Mechanical Engineering 2020 set 1

Question 24:

The compressor of a gas turbine plant, operating on an ideal intercooled Brayton cycle, accomplishes an overall compression ratio of 6 in a two-stage compression process, Intercooling is used to cool the air coming out from the stage to the inlet temperature of the first stage, before its entry to the second stage. Air enters the compressor at 300 K and Kpa. If the properties of gas are constant, the intercooling pressure for minimum compressor work is __________________kPa (round off to 2 decimal places).

12 to 13

13 to 14

14 to 15

None of these

Category: GATE Mechanical Engineering 2020 set 1

Question 25:

In a concentric tube counter-flow heat exchanger, hot oil enters at 102°C and leaves at 65°C. Cold water enters at 25°C and leaves at 42°C. The log mean temperature difference (LMTD) is _____________°C (round off to one decimal place).

46.8 to 47.8

47.8 to 48.8

48.8 to 49.8

49.8 to 50.8

Category: GATE Mechanical Engineering 2020 set 1

Question 26:

The evaluation of the definite integral

\int_{- 1}^{1.4} x x dx by using Simpson' s 1 / 3^{rd}

(one-third) rule with step size h = 0.6 yields

0.914

1.248

0.581

0.592

Category: GATE Mechanical Engineering 2020 set 1

Question 27:

A vector field is defined as

\vec{f} (x, y, z) = \frac{x}{{[x^{2} + y^{2} + z^{2}]}^{\frac{3}{2}}} \hat{i} + \frac{y}{{[x^{2} + y^{2} + z^{2}]}^{\frac{3}{2}}} \hat{j} + \frac{z}{{[x^{2} + y^{2} + z^{2}]}^{\frac{3}{2}}} \hat{k}

Where,

\hat{i}, \hat{j}, \hat{k}

are unit vectors along the axes of a right-handed rectangular /Cartesian coordinate system. The surface integral

\iint \vec{f} . d \vec{S}

(where

d \vec{S}

is an elemental surface area vector) evaluated over the inner and outer surfaces of a spherical shell formed by two concentric spheres with origin as the center, and internal and external radii of 1 and 2, respectively, is

A	0	B	$2 π$
C	$4 π$	D	$8 π$

Category: GATE Mechanical Engineering 2020 set 1

Question 28:

Bars of square and circular cross-section with 0.5 m length are made of a material with shear strength of 20 MPa. The square bar cross-section dimension is 4 cm x 4 cm and the cylindrical bar cross-section diameter is 4 cm. The specimens are loaded as shown in the figure.

Which specimen(s) will fail due to the applied load as per maximum shear stress theory?

Tensile and compressive load specimens

Torsional load specimens

Bending load specimens

None of the specimens

Category: GATE Mechanical Engineering 2020 set 1

Question 29:

The 2 kg block shown in figure (top view) rests on a smooth horizontal surface and is attached to a massless elastic cord that has a stiffness 5 N/m.

The cord hinged at O is initially unstretched and always remains elastic. The block is given a velocity v of 1.5 m/s perpendicular to the cord. The magnitude of velocity in m/s of the block at the instant the cord is stretched by 0.4 m is

0.83

1.07

1.36

1.50

Category: GATE Mechanical Engineering 2020 set 1

Question 30:

The truss shown in the figure has four members of length l and flexural rigidity El, and one member of length l

\sqrt{2}

and flexural rigidity 4El. The truss is loaded by a pair of forces of magnitude P, as shown in the figure

The smallest value of P, at which any of the truss members will buck is

A	undefined	B	undefined
C	undefined	D	undefined

Category: GATE Mechanical Engineering 2020 set 1

Question 31:

A rigid mass-less rod of length L is connected to a disc (pulley) of mass m and radius r = L/4 through a friction-less revolute joint. The other end of that rod is attached to the wall through a friction-less hinge. A spring of stiffness 2k is attached to the rod at its mid-span. An inextensible rope passes over half the disc periphery and is securely tied to a spring of stiffness k at point C as shown in the figure. There is no slip between the rope and the pulley. The system is in static equilibrium in the configuration shown in the figure and the rope is always taut.

Neglecting the influence of gravity, the natural frequency of the system for small amplitude vibration is

A	undefined	B	undefined
C	undefined	D	$\sqrt{\frac{k}{m}}$

Category: GATE Mechanical Engineering 2020 set 1

Question 32:

A strip of thickness 40 mm is to be rolled to a thickness of 20 mm using a two-high mill having rolls of diameter 200 mm. Coefficient of friction and are length in mm, respectively are

0.45 and 38.84

0.39 and 38.84

0.39 and 44.72

0.45 and 44.72

Category: GATE Mechanical Engineering 2020 set 1

Question 33:

For an assembly line, the production rate was 4 pieces per hour and the average processing time was 60 minutes. The WIP inventory was calculated. Now, the production rate is kept the same, and the average processing time is brought down by 30 percent. As a result of this change in the processing time, the WIP inventory

decreases by 25%

increases by 25%

decreases by 30%

increases by 30%

Category: GATE Mechanical Engineering 2020 set 1

Question 34:

A small metal bead (radius 0.5 mm), initially at 100°C, when placed in a stream of fluid at 20°C, attains a temperature of 28°C in 4.35 seconds. The density and specific heat of the metal are 8500 kg/

m^{3}

and 400 J/kg.K, respectively. If the bead is considered as lumped system, the convective heat transfer coefficient (in

W / m^{2} . K

) between the metal bead and the fluid stream is

283.3

299.8

149.9

449.7

Category: GATE Mechanical Engineering 2020 set 1

Question 35:

An analytic function of a complex variable undefined is defined as undefined where ψ( x, y ) is a real function. The value of the imaginary part of f (z) at z=(1+i) is ______________ (round off to 2 decimal places).

1.96 to 1.98

1.97 to 1.99

1.98 to 2.00

1.99 to 2.01

Category: GATE Mechanical Engineering 2020 set 1

Question 36:

Consider two exponentially distributed random variables X and Y, both having a Y. If the variance of Z equals 0, then the value of e is ___________________(round off to 2 decimal places)

-1.00 to -0.98

-1.00 to -0.96

-1.00 to -0.94

-1.00 to -0.92

Category: GATE Mechanical Engineering 2020 set 1

Question 37:

In a disc-type axial clutch, the frictional contact takes place within an annular region with outer and inner diameters 250 mm and 50 mm, respectively. An axial force

F_{1}

is needed to transmit a torque by a new clutch. However, to transmit the same torque. one needs an axial force

F_{2}

when the clutch wears out. If contact pressure remains uniform during operation of a new clutch while the wear is assumed to be uniform for an old clutch , and the coefficient of friction does not change, then ratio

F_{1} / F_{2}

is _____________________( round off to 2 decimal places ).

0.85 to 0.86

0.85 to 0.87

0.85 to 0.88

0.85 to 0.89

Category: GATE Mechanical Engineering 2020 set 1

Question 38:

A cam with a translating flat-face follower is desired to have the following motion

$y (θ) = 4 [2 π θ - θ^{2}], 0 \leq θ \leq 2 π .$

Contact stress considerations dictate that the radius of curvature of the cam profile should not be less than 40 mm anywhere. The minimum permissible base circle radius is _______________mm (round off to one decimal place)

47.9 to 48.0

47.9 to 48.1

47.9 to 48.2

47.9 to 48.3

Category: GATE Mechanical Engineering 2020 set 1

Question 39:

A rectangular steel bar of length 500 mm, width 100 mm, and thickness 15 mm is cantilevered to a 200 mm steel channel using 4 bolts, as shown

For an external load of 10 kN applied at the tip of the sheet bar, the resultant shear load on the bolt at B is ___________________kN ( round off to one decimal place ).

15.9 to 16.0

15.9 to 16.1

15.9 to 16.2

15.9 to 16.3

Category: GATE Mechanical Engineering 2020 set 1

Question 40:

The barrier shown between two water tanks of unit width ( 1 m ) into the plane of the screen is modeled as a cantilever.

Taking the density of water as 1000 kg/

m^{3}

, and the acceleration due to gravity as undefined , the maximum absolute bending moment developed in the cantilever is _____________ kN.m (round of to the nearest integer).

100 to 102

102 to 104

104 to 106

106 to 108

Category: GATE Mechanical Engineering 2020 set 1

Question 41:

The magnitude of reaction force at joint C of the hinge-beam shown in the figure is ____________kN (round off to 2 decimal places )

16.95 to 17.05

17.95 to 18.05

18.95 to 19.05

19.95 to 20.05

Category: GATE Mechanical Engineering 2020 set 1

Question 42:

A slot of 25 mm x 25 mm is to be milled in a workpiece of 300 mm length using a side and face milling cutter of diameter 100 mm, width 25 mm, width 25 mm and having 20 teeth For a depth of cut 5 mm, feed per tooth 0.1 mm, cutting speed 25 m/min and approach and over travel distance of 5 mm each, the time required for milling the slot is ___________minutes ( round of to one decimal place ).

1 to 3

3 to 5

5 to 7

7 to 9

Category: GATE Mechanical Engineering 2020 set 1

Question 43:

The following data applies to basic shaft system: tolerance for hole = 0.002 mm, tolerance for shaft = 0.001 mm, allowance = 0.003 mm, basic size = 50 mm. The maximum hole size is ___________mm ( round off to 3 decimal places ).

50.005 to 50.005

50.006 to 50.006

50.007 to 50.007

50.008 to 50.008

Category: GATE Mechanical Engineering 2020 set 1

Question 44:

A steel part with surface area of 125

{cm}^{2}

is to be chrome coated through an electroplating process using chromium acid sulphate as an electrolyte. An increasing current is applied to the part according to the following current time relation:

l =12 + 0.2t

where, l = current (A) and t = time (minutes). The part is submerged in the plating solution for a duration of 20 minutes for plating purpose. Assuming the cathode efficiency of chromium to be 15% and the plating constant of chromium acid sulphate to be 2.50 x

10^{2} {mm}^{3} / A . s,

the resulting coating thickness on the part surface is _________________μm (round off to one decimal place).

0 to 0

0 to 1

1 to 1

1 to 2

Category: GATE Mechanical Engineering 2020 set 1

Question 45:

In a turning using orthogonal tool geometry . a chip length of 100 mm is obtained for an uncut chip length of 250 mm. The cutting conditions are: cutting speed = 30 m/min, rake angle = 20°. The shear plane angle is ______________degrees ( round off to one decimal place ).

21 to 25

22 to 25

23 to 25

24 to 25

Category: GATE Mechanical Engineering 2020 set 1

Question 46:

The thickness of a steel plate with material strength coefficient of 210 MPa, has to be reduced from 20 mm to 15 mm in a single pass in a two-high rolling mill with a roll radius of 450 mm and rolling velocity of 28 m/min. If the plate has a width of 200 mm and its strain hardening exponent, n is 0.25, the rolling force required for the operation is ________________kN (round off to 2 decimal places) Note Average Flow Stress = Material Strength Coefficient x

\frac{{(True Strain)}^{n}}{(1 + n)}

1161 to 1168

1162 to 1168

1163 to 1168

1164 to 1168

Category: GATE Mechanical Engineering 2020 set 1

Question 47:

Two business owners Shveta and Ashok run their businesses in two different state. Each of them , independent of the other, produces two products A and B, sells them at Rs. 2,000 per kg and Rs. 3,000 per kg, respectively, and uses Linear programming to determine the optimal quantity of A and B to maximize their respective daily revenue. their constraints are as follows: i) for each business owner, the production process is such that daily production of A has to be at least as much as b, and the upper limit for production of B is 10 kg per day, and ii)the respective sate regulations restrict Shvet's production of A to less than 20 kg per day / and Ashok's production of A to les than 15 kg per day . The demand of both A and B in both the states is very high and everything produced is sold. The absolute value of the difference in daily (optimal revenue of Shveta and Ashok is _______________thousand Rupees (round off to 2 decimal places ).

9.70 to 10.10

9.80 to 10.10

9.90 to 10.10

10.00 to 10.10

Category: GATE Mechanical Engineering 2020 set 1

Question 48:

Consider two cases as below. Case 1: A company buys 100 pieces per year of a certain part from vendor 'X' . The changeover time is 2 hours and the price is Rs. 10 per piece. The holding cost rate per part is10% per year. Case 2: For the same part, another vendor 'Y' offers a design where the changeover time is 6 minutes, with a price of Rs. 5 per piece, and a holding cost rate per part of 100% per year. The order size is 800 pieces per year from 'X' and 200 pieces per year from 'Y' Assume the cost of downtime as Rs. 200 per hour. The percentage reduction in the annual cost for case 2 , as compared to case 1 is __________(round off to 2 decimal places)

8.19 to 8.21

8.19 to 8.23

8.19 to 8.25

8.19 to 8.27

Category: GATE Mechanical Engineering 2020 set 1

Question 49:

Consider steady, viscous, fully developed flow of a fluid through a circular pipe of internal diameter D. We know that the velocity profile forms a paraboloid about the pipe centre line, given by: V = -C undefined m/s, where C is a constant. The rate of kinetic energy (in J/s) at the control surface A-B, as shown in the figure, is proportional to undefined . The value of n is ____________.

2 to 2

4 to 4

6 to 6

8 to 8

Category: GATE Mechanical Engineering 2020 set 1

Question 50:

Air discharges steadily through a horizontal nozzle and impinges on a stationary vertical plate as shown in figure.

The inlet and outlet areas of the nozzle are

m^{2}

and 0.02

m^{2}

, respectively. Take air density as constant and equal to 1.2 kg/

m^{3}

. If the inlet gauge pressure of air is 0.36 kPa, the gauge pressure at point O on the plate is ___________kPa (round off to two decimal places).

0.37 to 0.45

0.39 to 0.47

0.41 to 0.49

0.43 to 0.51

Category: GATE Mechanical Engineering 2020 set 1

Question 51:

Air (ideal gas) enters a perfectly insulated compressor at a temperature of 310 K. The pressure ratio of the compressor is 6. Specific heat at constant pressure and for air is 1005. J/kg.K and ratio of specific heats at constant pressure and constant volume is is 1.4 Assume that specific heats of air are constant. If the isentropic efficiency of the compressor is 85 percent, the difference in enthalpies of air between the exit and the inlet of the compressor is kJ/kg (round off to nearest integer).

242 to 246

244 to 246

246 to 246

248 to 246

Category: GATE Mechanical Engineering 2020 set 1

Question 52:

One kg of air, initially at a temperature of 127°C, expands reversibly at a constant pressure until the volume is doubled. if the gas constant of air is 287 J/kg.K, the magnitude of work transfer is ______________ kJ (round off to 2 decimal places).

114.6 to 115.0

114.6 to 115.1

114.6 to 115.2

114.6 to 115.3

Category: GATE Mechanical Engineering 2020 set 1

Question 53:

For an ideal Rankine cycle operating between pressures of 30 bar and 0.04 bar, the work output from the turbine is 903 kJ/kg and the work input to the feed pump is 3 kJ/kg. The specific steam consumption is ______________kg/kW.h (round off to 2 decimal places).

3.98 to 4.01

3.98 to 4.02

3.98 to 4.03

3.98 to 4.04

Category: GATE Mechanical Engineering 2020 set 1

Question 54:

For a Kaplan (axial flow) turbine, the outlet blade velocity diagram at a section is shown in figure.

The diameter at this section is 3 m. The hub and tip diameters of the blade are 2 m and 4 m, respectively. The water volume flow rate is 100 undefined . The rotational speed of the turbine is 300 rpm. The blade β is ______________degrees (round off to one decimal place).

10.0 to 13.0

11.0 to 14.0

12.0 to 15.0

13.0 to 16.0

Category: GATE Mechanical Engineering 2020 set 1

Question 55:

The indicated power developed by an engine with compression ratio of 8, is calculate using an air-standard Otto cycle (constant properties). The rate of heat addition is 10 kW. The ratio of specific heats at constant pressure and constant volume is 1.4. The mechanical efficiency of the engine is 80 percent The brake power output of the engine is __________kW (round off to one decimal place).

4.0 to 4.2

4.2 to 4.4

4.4 to 4.6

4.6 to 4.8

⮜ Back Next ⮞

Not Visited	0	Not Answered
Answered	0	Marked for Review
Answered & Marked for Review (will be considered for evaluation)

Question 1:

Multiplication of real valued square matrices of same dimension is

Correct Answer : associative

Question 2:

The value of

\lim_{x \to 1} (\frac{1 - e^{- c (1 - x)}}{1 - x e^{- c (1 - x)}}) i s

A	c	B	c+1
C	$\frac{c}{c + 1}$	D	$\frac{c + 1}{c}$

Correct Answer : C

Question 3:

The Laplace transform of a function

f (t) i s ℒ (f) = \frac{1}{(s^{2} + ω^{2})} .

Then, f (t) is

A	$f (t) = \frac{1}{ω^{2}} (1 - \cos ω t)$	B	$f (t) = \frac{1}{ω} \cos ω t$
C	$f (t) = \frac{1}{ω} \sin ω t$	D	$f (t) = \frac{1}{ω^{2}} (1 - \sin ω t)$

Correct Answer : C

Question 4:

Which of the following function f(z) , of the complex variable z, is NOT analytic at all the points of the complex plane?

A	$f (z) = z^{2}$	B	$f (z) = e^{z}$
C	$f (z) = \sin z$	D	$f (z) = \log z$

Correct Answer : D

Question 5:

Correct Answer : BF, DH, GC, CD and DE only

Question 6:

A single-degree-of-freedom oscillator is subject to harmonic excitation F(t) =

F_{0}

cos( ωt ) as shown in the figure.

The non-zero value of ω, for which the amplitude of the force transmitted to the ground will be

F_{0}

, is

A	$\sqrt{\frac{k}{2 m}}$	B	$\sqrt{\frac{k}{m}}$
C	$\sqrt{\frac{2 k}{m}}$	D	$2 \sqrt{\frac{k}{m}}$

Correct Answer : C

Question 7:

A	a circle with a radius equal to principal stress and its center at the origin of the σ-τ plane
B	a point on the σ axis at a distance of 10 units from the origin
C	a circle with a radius of 10 units on the σ - τ plane
D	a point on the τ axis at a distance of 10 units from the origin

Correct Answer : B

Question 8:

A four bar mechanism is shown below.

For the mechanism to be a crank-rocker mechanism, the length of the link PQ can be

Correct Answer : 80 mm

Question 9:

A helical gear with 20° pressure angle and 30° helix angle mounted at the mid-span of a shaft that is supported between two bearing at the ends. The nature of the stresses induced in the shaft is

a	normal stresses due to bending only	b	normal stress due to bending in one plane and axial loading; shear stress due to torsion
c	normal stress due to bending in two planes and axial loading; shear stress due to torsion	d	normal stress due to bending in two planes; shear stress due to torsion

Correct Answer : A and C

Question 10:

The crystal structure of γ iron (austenite phase) is

Correct Answer : FCC

Question 11:

Match the following

Heat treatment process	Effect
P: Tempering	1. Strengthening
Q: Quenching	2. Toughening
R: Annealing	3. Hardening
S: Normalizing	4. Softening

Correct Answer : P-2, Q-3, R-4, S-1

Question 12:

The base of a brass bracket needs rough grinding. for this purpose, the most suitable grinding wheel grade specification is

Correct Answer : C30Q12V

Question 13:

In the Critical Path Method (CPM), the cost-time slope of an activity is given by

A	$\frac{crash Cost - Normal Cost}{Crash Time}$
B	$\frac{Normal cost}{Crash Time - Normal time}$
C	$\frac{Crash Cost}{Crash Time - Normal Time}$
D	$\frac{Crash Time - Normal Cost}{Normal Cost - Crash Time}$

Correct Answer : D

Question 14:

Froude number is the ratio of

Correct Answer : inertia forces to gravity forces

Question 15:

Match the following non-dimensional numbers with the corresponding definitions:

Non-dimensional number			Definitions
P	Reynolds number	1	$\frac{Buoyancy force}{Viscous force}$
Q	Grashof number	2	$\frac{Momentum diffusivity}{Thermal diffusivity}$
R	Nusselt number	3	$\frac{Inertia force}{Viscous force}$
S	Prandtl number	4	$\frac{Convective heat transfer}{Conduction heat transfer}$

Correct Answer : P-3, Q-1, R-4, S-2

Question 16:

The velocity field of an incompressible flow in a Cartesian system is represented by

\vec{V} = 2 (x^{2} - y^{2}) \hat{i} + v \hat{j} + 3 \hat{k}

which on of the following expressions for v is valid?

Correct Answer : -4xy-4xz

Question 17:

For an ideal gas, the value of the joule-Thomson coefficient is

Correct Answer : zero

Question 18:

For an ideal gas, a constant pressure line and a constant volume line intersect at a point, in the Temperature (T) versus specific entropy (s) diagram.

C_{P}

is the specific heat at constant pressure and

C_{v}

is the specific heat at constant volume. The ratio of the slopes of the constant pressure and constant volume lines at the point of intersection is

A	$\frac{C_{p} - C_{v}}{C_{p}}$	B	$\frac{C_{p}}{C_{p}}$
C	$\frac{C_{p} - C_{v}}{C_{v}}$	D	$\frac{C_{v}}{C_{p}}$

Correct Answer : D

Question 19:

For three

\vec{A} = 2 \hat{j} - 3 \hat{k}, \vec{B} = - 2 \hat{i} + \hat{K} a n d \vec{C} = 3 \hat{i} - \hat{j}, w h e r e \hat{i}, \hat{j} a n d \hat{k}

are unit vectors along the axes of a right-handed rectangular/Cartesian coordinate system, the value of

(\vec{A \cdot} (\vec{B} \times \vec{C}) + 6)

is ________________.

Correct Answer : 6 to 6

Question 20:

k g . m^{2}

( round off to 2 decimal places ) .

Correct Answer : 0.98 to 1.02

Question 21:

A balanced rigid disc mounted on a rigid rotor has four identical point masses, each of 10 grams, attached to four points on the 100 mm radius circle shown in the figure.

Correct Answer : 0.09 to 0.11

Question 22:

Correct Answer : 1.0 to 1.3

Question 23:

Correct Answer : 0.98 to 0.95

Question 24:

Correct Answer : None of these

Question 25:

Correct Answer : 48.8 to 49.8

Question 26:

The evaluation of the definite integral

\int_{- 1}^{1.4} x x dx by using Simpson' s 1 / 3^{rd}

(one-third) rule with step size h = 0.6 yields

Correct Answer : 0.592

Question 27:

A vector field is defined as

\vec{f} (x, y, z) = \frac{x}{{[x^{2} + y^{2} + z^{2}]}^{\frac{3}{2}}} \hat{i} + \frac{y}{{[x^{2} + y^{2} + z^{2}]}^{\frac{3}{2}}} \hat{j} + \frac{z}{{[x^{2} + y^{2} + z^{2}]}^{\frac{3}{2}}} \hat{k}

Where,

\hat{i}, \hat{j}, \hat{k}

are unit vectors along the axes of a right-handed rectangular /Cartesian coordinate system. The surface integral

\iint \vec{f} . d \vec{S}

(where

d \vec{S}

A	0	B	$2 π$
C	$4 π$	D	$8 π$

Correct Answer : A

Question 28:

Which specimen(s) will fail due to the applied load as per maximum shear stress theory?

Correct Answer : Tensile and compressive load specimens

Question 29:

The 2 kg block shown in figure (top view) rests on a smooth horizontal surface and is attached to a massless elastic cord that has a stiffness 5 N/m.

Correct Answer : 1.36

Question 30:

The truss shown in the figure has four members of length l and flexural rigidity El, and one member of length l

\sqrt{2}

and flexural rigidity 4El. The truss is loaded by a pair of forces of magnitude P, as shown in the figure

The smallest value of P, at which any of the truss members will buck is

A	undefined	B	undefined
C	undefined	D	undefined

Correct Answer : C

Question 31:

Neglecting the influence of gravity, the natural frequency of the system for small amplitude vibration is

A	undefined	B	undefined
C	undefined	D	$\sqrt{\frac{k}{m}}$

Correct Answer : C

Question 32:

A strip of thickness 40 mm is to be rolled to a thickness of 20 mm using a two-high mill having rolls of diameter 200 mm. Coefficient of friction and are length in mm, respectively are

Correct Answer : 0.45 and 44.72

Question 33:

Correct Answer : decreases by 30%

Question 34:

m^{3}

and 400 J/kg.K, respectively. If the bead is considered as lumped system, the convective heat transfer coefficient (in

W / m^{2} . K

) between the metal bead and the fluid stream is

Correct Answer : 299.8

Question 35:

Correct Answer : 1.99 to 2.01

Question 36:

Consider two exponentially distributed random variables X and Y, both having a Y. If the variance of Z equals 0, then the value of e is ___________________(round off to 2 decimal places)

Correct Answer : -1.00 to -0.98

Question 37:

In a disc-type axial clutch, the frictional contact takes place within an annular region with outer and inner diameters 250 mm and 50 mm, respectively. An axial force

F_{1}

is needed to transmit a torque by a new clutch. However, to transmit the same torque. one needs an axial force

F_{2}

F_{1} / F_{2}

is _____________________( round off to 2 decimal places ).

Correct Answer : 0.85 to 0.89

Question 38:

A cam with a translating flat-face follower is desired to have the following motion

$y (θ) = 4 [2 π θ - θ^{2}], 0 \leq θ \leq 2 π .$

Correct Answer : 47.9 to 48.1

Question 39:

A rectangular steel bar of length 500 mm, width 100 mm, and thickness 15 mm is cantilevered to a 200 mm steel channel using 4 bolts, as shown

For an external load of 10 kN applied at the tip of the sheet bar, the resultant shear load on the bolt at B is ___________________kN ( round off to one decimal place ).

Correct Answer : 15.9 to 16.1

Question 40:

The barrier shown between two water tanks of unit width ( 1 m ) into the plane of the screen is modeled as a cantilever.

Taking the density of water as 1000 kg/

m^{3}

, and the acceleration due to gravity as undefined , the maximum absolute bending moment developed in the cantilever is _____________ kN.m (round of to the nearest integer).

Correct Answer : 104 to 106

Question 41:

The magnitude of reaction force at joint C of the hinge-beam shown in the figure is ____________kN (round off to 2 decimal places )

Correct Answer : 19.95 to 20.05

Question 42:

Correct Answer : 7 to 9

Question 43:

Correct Answer : 50.005 to 50.005

Question 44:

A steel part with surface area of 125

{cm}^{2}

is to be chrome coated through an electroplating process using chromium acid sulphate as an electrolyte. An increasing current is applied to the part according to the following current time relation:

l =12 + 0.2t

10^{2} {mm}^{3} / A . s,

the resulting coating thickness on the part surface is _________________μm (round off to one decimal place).

Correct Answer : 0 to 0

Question 45:

Correct Answer : 22 to 25

Question 46:

\frac{{(True Strain)}^{n}}{(1 + n)}

Correct Answer : 1164 to 1168

Question 47:

Correct Answer : 9.90 to 10.10

Question 48:

Correct Answer : 8.19 to 8.23

Question 49:

Correct Answer : 8 to 8

Question 50:

Air discharges steadily through a horizontal nozzle and impinges on a stationary vertical plate as shown in figure.

The inlet and outlet areas of the nozzle are

m^{2}

and 0.02

m^{2}

, respectively. Take air density as constant and equal to 1.2 kg/

m^{3}

. If the inlet gauge pressure of air is 0.36 kPa, the gauge pressure at point O on the plate is ___________kPa (round off to two decimal places).

Correct Answer : 0.37 to 0.45

Question 51:

Correct Answer : 244 to 246

Question 52:

Correct Answer : 114.6 to 115.0

Question 53:

Correct Answer : 3.98 to 4.02

Question 54:

For a Kaplan (axial flow) turbine, the outlet blade velocity diagram at a section is shown in figure.

Correct Answer : 11.0 to 14.0

Question 55:

Correct Answer : 4.4 to 4.6

Back
Scrore Card
Total Question		Total Attempted
Correct Answers		Incorrect Answers
Score

GATE 2020 Mechanical Engineering Main exam set 1 Practice Online with solution

View Solution

Attempt Mock Test

General Instructions

Please read the instructions carefully

General Instructions:

Navigating to a Question:

Answering a Question:

Navigating through sections:

Question 1:

Question 2:

Question 3:

Question 4:

Question 5:

Question 6:

Question 7:

Question 8:

Question 9:

Question 10:

Question 11:

Question 12:

Question 13:

Question 14:

Question 15:

Question 16:

Question 17:

Question 18:

Question 19:

Question 20:

Question 21:

Question 22:

Question 23:

Question 24:

Question 25:

Question 26:

Question 27:

Question 28:

Question 29:

Question 30:

Question 31:

Question 32:

Question 33:

Question 34:

Question 35:

Question 36:

Question 37:

Question 38:

Question 39:

Question 40:

Question 41:

Question 42:

Question 43:

Question 44:

Question 45:

Question 46:

Question 47:

Question 48:

Question 49:

Question 50:

Question 51:

Question 52:

Question 53:

Question 54:

Question 55:

Exam Summary

Are you sure you want to submit for final marking? No changes will be allowed after submission.

Thank you, Submitted Successfully.

Question 1:

Question 2:

Question 3:

Question 4:

Question 5:

Question 6:

Question 7:

Question 8:

Question 9:

Question 10:

Question 11:

Question 12:

Question 13:

Are you sure you want to submit for final marking?
No changes will be allowed after submission.