GATE ME 2014: Mechanical Engineering Session 2
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SESSION - 1
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GATE 2014: General Instructions during Examination
1. Total duration of the GATE examination is 180 minutes.
2. The clock will be set at the server. The countdown timer at 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 need not
terminate the examination or submit your paper.
3. Any useful data required for your paper can be viewed by clicking on the Useful
Common Data button that appears on the screen.
4. Use the scribble pad provided to you for any rough work. Submit the scribble pad at
the end of the examination.
5. You are allowed to use a non-programmable type calculator, however, sharing of
calculators is not allowed.
6. The Question Palette displayed on the right side of screen will show the status of
each question using one of the following symbols:
The Marked for Review status for a question simply indicates that you would like to look at
that question again. If a question is answered, but marked for review, then the answer will
be considered for evaluation unless the status is modified by the candidate.
Navigating to a Question :
7. To answer a question, do the following:
a. Click on the question number in the Question Palette to go to that question
directly.
b. Select an answer for a multiple choice type question by clicking on the bubble
placed before the 4 choices, namely A, B, C and D. Use the virtual numeric
keypad to enter a number as answer for a numerical type question.
c. Click on Save & Next to save your answer for the current question and then go
to the next question.
d. Click on Mark for Review & Next to save your answer for the current question
and also mark it for review, and then go to the next question.
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Caution: Note that your answer for the current question will not be saved, if you navigate
to another question directly by clicking on a question number without saving the answer to
the previous question.
You can view all the questions by clicking on the Question Paper button. This feature is
provided, so that if you want you can just see the entire question paper at a glance.
Answering a Question :
8. Procedure for answering a multiple choice (MCQ) type question:
a. Choose one answer from the 4 options (A,B,C,D) given below the question,
click on the bubble placed before the chosen option.
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or click on the Clear Response button.
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d. To save your answer, you MUST click on the Save & Next button.
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a. To enter a number as your answer, use the virtual numerical keypad.
b. A fraction (e.g. -0.3 or -.3) can be entered as an answer with or without '0'
before the decimal point. As many as four decimal points, e.g. 12.5435 or
0.003 or -932.6711 or 12.82 can be entered.
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answer is selected (for MCQ) or entered (for numerical answer type) for a question
that is Marked for Review, that answer will be considered in the evaluation unless
the status is modified by the candidate.
11. 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.
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answering will be considered for evaluation.
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in a Section can be viewed by clicking on the name of that Section. The Section you
are currently viewing will be highlighted.
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select the optional Section for answering, click on the checkbox for that Section.
15. If the checkbox for an optional Section is not selected, the Save & Next button and
the Mark for Review & Next button will NOT be enabled for that Section. You will
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only be able to see questions in this Section, but you will not be able to answer
questions in the Section.
16. After clicking the Save & Next button for the last question in a Section, you will
automatically be taken to the first question of the next Section in sequence.
17. You can move the mouse cursor over the name of a Section to view the answering
status for that Section.
Changing the Optional Section :
18. After answering the chosen optional Section, partially or completely, you can change
the optional Section by selecting the checkbox for a new Section that you want to
attempt. A warning message will appear along with a table showing the number of
questions answered in each of the previously chosen optional Sections and a
checkbox against each of these Sections. Click on a checkbox against a Section that
you want to reset and then click on the RESET button. Note that RESETTING a Section
will DELETE all the answers for questions in that Section. Hence, if you think that you
may want to select this Section again later, you will have to note down your answers
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continue answering the previously chosen optional Section, then click on the BACK
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20. You can shuffle between different Sections or change the optional Sections any
number of times.
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GATE 2014 Examination
ME: Mechanical Engineering
Duration: 180 minutes Maximum Marks: 100
Read the following instructions carefully.
1. To login, enter your Registration Number and password provided to you. Kindly go through the various
symbols used in the test and understand their meaning before you start the examination.
2. Once you login and after the start of the examination, you can view all the questions in the question
paper, by clicking on the View All Questions button in the screen.
3. This question paper consists of 2 sections, General Aptitude (GA) for 15 marks and the subject
specific GATE paper for 85 marks. Both these sections are compulsory.
The GA section consists of 10 questions. Question numbers 1 to 5 are of 1-mark each, while question
numbers 6 to 10 are of 2-mark each.
The subject specific GATE paper section consists of 55 questions, out of which question numbers 1 to
25 are of 1-mark each, while question numbers 26 to 55 are of 2-mark each.
4. Depending upon the GATE paper, there may be useful common data that may be required for
answering the questions. If the paper has such useful data, the same can be viewed by clicking on the
Useful Common Data button that appears at the top, right hand side of the screen.
5. The computer allotted to you at the examination center runs specialized software that permits only one
answer to be selected for multiple-choice questions using a mouse and to enter a suitable number for
the numerical answer type questions using the virtual keyboard and mouse.
6. Your answers shall be updated and saved on a server periodically and also at the end of the
examination. The examination will stop automatically at the end of 180 minutes.
7. In each paper a candidate can answer a total of 65 questions carrying 100 marks.
8. The question paper may consist of questions of multiple choice type (MCQ) and numerical answer
type.
9. Multiple choice type questions will have four choices against A, B, C, D, out of which only ONE is the
correct answer. The candidate has to choose the correct answer by clicking on the bubble (⃝) placed
before the choice.
10. For numerical answer type questions, each question will have a numerical answer and there will not be
any choices. For these questions, the answer should be enteredby using the virtual keyboard that
appears on the monitor and the mouse.
11. All questions that are not attempted will result in zero marks. However, wrong answers for multiple
choice type questions (MCQ) will result in NEGATIVE marks. For all MCQ questions a wrong
answer will result in deduction of⅓ marks for a 1-mark question and ⅔ marks for a 2-mark question.
12. There is NO NEGATIVE MARKING for questions of NUMERICAL ANSWER TYPE.
13. Non-programmable type Calculator is allowed. Charts, graph sheets, and mathematical tables are NOT
allowed in the Examination Hall. You must use the Scribble pad provided to you at the examination
centre for all your rough work. The Scribble Pad has to be returned at the end of the examination.
Declaration by the candidate:
“I have read and understood all the above instructions. I have also read and understood clearly the
instructions given on the admit card and shall follow the same. I also understand that in case I am found to
violate any of these instructions, my candidature is liable to be cancelled. I also confirm that at the start of
the examination all the computer hardware allotted to me are in proper working condition”.
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GATE 2014 SET- 3 General Aptitude -GA
Q. 1 – Q. 5 carry one mark each.
Q.1 Choose the most appropriate phrase from the options given below to complete the following
sentence.
The aircraft take off as soon as its flight plan was filed.
(A) is allowed to (B) will be allowed to
(C) was allowed to (D) has been allowed to
Q.2 Read the statements:
All women are entrepreneurs.
Some women are doctors.
)
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Which of the following conclusions can be logically inferred from the above statements?
(A) All women are doctors (B) All doctors are entrepreneurs
(C) All entrepreneurs are women (D) Some entrepreneurs are doctors
20
Q.3 Choose the most appropriate word from the options given below to complete the following
sentence.
Many ancient cultures attributed disease to supernatural causes. However, modern science has
largely helped _________ such notions.
(A) impel (B) dispel
E (C) propel (D) repel
AT
Q.4 The statistics of runs scored in a series by four batsmen are provided in the following table. Who is
the most consistent batsman of these four?
Batsman Average Standard deviation
(G
K 31.2 5.21
L 46.0 6.35
M 54.4 6.22
N 17.9 5.90
(A) K (B) L (C) M (D) N
3
Q.5 What is the next number in the series?
A0
12 35 81 173 357 ____
G
Q. 6 – Q. 10 carry two marks each.
Q.6 Find the odd one from the following group:
W,E,K,O I,Q,W,A F,N,T,X N,V,B,D
(A) W,E,K,O (B) I,Q,W,A (C) F,N,T,X (D) N,V,B,D
GA 1/2
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GATE 2014 SET- 3 General Aptitude -GA
Q.7 For submitting tax returns, all resident males with annual income below Rs 10 lakh should fill up
Form P and all resident females with income below Rs 8 lakh should fill up Form Q. All people
with incomes above Rs 10 lakh should fill up Form R, except non residents with income above Rs
15 lakhs, who should fill up Form S. All others should fill Form T. An example of a person who
should fill Form T is
(A) a resident male with annual income Rs 9 lakh
(B) a resident female with annual income Rs 9 lakh
(C) a non-resident male with annual income Rs 16 lakh
(D) a non-resident female with annual income Rs 16 lakh
Q.8 A train that is 280 metres long, travelling at a uniform speed, crosses a platform in 60 seconds and
passes a man standing on the platform in 20 seconds. What is the length of the platform in metres?
)
Q.9 The exports and imports (in crores of Rs.) of a country from 2000 to 2007 are given in the
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following bar chart. If the trade deficit is defined as excess of imports over exports, in which year is
the trade deficit 1/5th of the exports?
120
20
110 Exports Imports
100
90
80
70
60
E
50
AT
40
30
20
10
(G
0
2000 2001 2002 2003 2004 2005 2006 2007
(A) 2005 (B) 2004 (C) 2007 (D) 2006
3
Q.10 You are given three coins: one has heads on both faces, the second has tails on both faces, and the
A0
third has a head on one face and a tail on the other. You choose a coin at random and toss it, and it
comes up heads. The probability that the other face is tails is
(A) 1/4 (B) 1/3 (C) 1/2 (D) 2/3
G
END OF THE QUESTION PAPER
GA 2/2
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GATE 2014 SET-1 MECHANICAL – ME
Q. 1 – Q. 25 carry one mark each.
Q.1 1 3 0
Given that the determinant of the matrix 2 6 4 is 12, the determinant of the matrix
1 0 2
2 6 0
4 12 8 is
2 0 4
(A) 96 (B) 24 (C) 24 (D) 96
)
Q.2 x − sin x
Lt is
14
x →0 1 − cos x
(A) 0 (B) 1 (C) 3 (D) not defined
20
Q.3 1+ i
The argument of the complex number , where i = − 1 , is
1− i
π π
(A) − π (B) − (C) (D) π
2
E 2
AT
Q.4 The matrix form of the linear system 3 5 and 4 8 is
d ⎧ x ⎫ ⎡ 3 −5⎤ ⎧ x ⎫ d ⎧ x ⎫ ⎡3 8 ⎤ ⎧ x ⎫
(A) ⎨ ⎬= ⎨ ⎬ (B) ⎨ ⎬= ⎨ ⎬
dt ⎩ y ⎭ ⎣⎢ 4 8 ⎦⎥ ⎩ y ⎭ dt ⎩ y ⎭ ⎣⎢ 4 −5⎦⎥ ⎩ y ⎭
(G
d ⎧ x ⎫ ⎡ 4 −5⎤ ⎧ x ⎫ d ⎧ x ⎫ ⎡4 8 ⎤ ⎧ x ⎫
(C) ⎨ ⎬= ⎨ ⎬ (D) ⎨ ⎬= ⎨ ⎬
dt ⎩ y ⎭ ⎣⎢ 3 8 ⎦⎥ ⎩ y ⎭ dt ⎩ y ⎭ ⎣⎢ 3 −5⎦⎥ ⎩ y ⎭
1
Q.5 Which one of the following describes the relationship among the three vectors, iˆ + ˆj + kˆ ,
2iˆ + 3 ˆj + kˆ and 5iˆ + 6 ˆj + 4 kˆ ?
E0
(A) The vectors are mutually perpendicular (B) The vectors are linearly dependent
(C) The vectors are linearly independent (D) The vectors are unit vectors
M
Q.6 A circular rod of length ‘L’ and area of cross-section ‘A’ has a modulus of elasticity ‘E’ and
coefficient of thermal expansion ‘α’. One end of the rod is fixed and other end is free. If the
temperature of the rod is increased by ∆T, then
(A) stress developed in the rod is E α ∆T and strain developed in the rod is α ∆T
(B) both stress and strain developed in the rod are zero
(C) stress developed in the rod is zero and strain developed in the rod is α ∆T
(D) stress developed in the rod is E α ∆T and strain developed in the rod is zero
ME 1/10
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GATE 20144 SET--1 M
MECHANIC
CAL – ME
Q.7 A metallic
m rod of 500 mm length
l and 500 mm diameeter, when suubjected to a tensile forcee of 100 kN
at the
t ends, exxperiences ann increase inn its length byb 0.5 mm and a reducction in its diameter
d by
0.015 mm. The Poisson’s raatio of the rod material iss _______
Q.8 Criitical dampinng is the
(A)) largest amoount of dampping for whicch no oscillattion occurs inn free vibratiion
(B)) smallest am
mount of dammping for whiich no oscillaation occurs in free vibraation
(C)) largest amoount of damping for which the motion n is simple haarmonic in frree vibration
n
(D)) smallest am
mount of dammping for whiich the motio on is simple harmonic in free vibratioon
)
Q.9 A circular
c objecct of radius r rolls without slipping on
o a horizonttal level floorr with the center having
velocity V. The velocity at the
t point of contact
c between the objecct and the flooor is
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(A)) zero (B)
( V in the direction of motion
(C)) V opposite to
t the directiion of motionn (D)
( V verticaally upward from the floo
or
20
Q.10 Forr the given sttatements:
I. Mating
M spur gear teeth is an example of higher paair
II. A revolute jooint is an exaample of low
wer pair
E
Inddicate the corrrect answer.
(A)) Both I and III are false (B)
( I is true and
a II is falsee
AT
(C)) I is false and II is true (D)
( Both I annd II are true
Q.11 A rigid
r Q is 2 m loong and orieented at 20o to the horizzontal as shoown in the figure. The
link PQ
(G
maggnitude and direction off velocity VQ, and the dirrection of veelocity VP aree given. Thee magnitude
of VP (in m/s) at
a this instantt is
1
E0
M
(A)) 2.14 (B) 1.89 (C) 1.21 (D) 0.96
Q.12 Bioot number siggnifies the raatio of
(A)) convective resistance inn the fluid to conductive resistance
r in the solid
(B)) conductive resistance inn the solid to convective resistance
r in the fluid
(C)) inertia forcee to viscous force
f in the fluid
f
(D)) buoyancy force
fo to viscoous force in thet fluid
ME 2/100
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GATE 2014 SET-1 MECHANICAL – ME
Q.13 The maximum theoretical work obtainable, when a system interacts to equilibrium with a reference
environment, is called
(A) Entropy (B) Enthalpy (C) Exergy (D) Rothalpy
Q.14 Consider a two-dimensional laminar flow over a long cylinder as shown in the figure below.
2
3
U∞ 1
T∞ 4
Ts
)
The free stream velocity is U∞ and the free stream temperature T∞ is lower than the cylinder
surface temperature Ts. The local heat transfer coefficient is minimum at point
14
(A) 1 (B) 2 (C) 3 (D) 4
20
Q.15 For a completely submerged body with centre of gravity ‘G’ and centre of buoyancy ‘B’, the
condition of stability will be
(A) G is located below B (B) G is located above B
(C) G and B are coincident E (D) independent of the locations of G and B
Q.16 In a power plant, water (density = 1000 kg/m3) is pumped from 80 kPa to 3 MPa. The pump has an
AT
isentropic efficiency of 0.85. Assuming that the temperature of the water remains the same, the
specific work (in kJ/kg) supplied to the pump is
(A) 0.34 (B) 2.48 (C) 2.92 (D) 3.43
(G
Q.17 Which one of the following is a CFC refrigerant?
(A) R744 (B) R290 (C) R502 (D) R718
1
Q.18 The jobs arrive at a facility, for service, in a random manner. The probability distribution of number
of arrivals of jobs in a fixed time interval is
E0
(A) Normal (B) Poisson (C) Erlang (D) Beta
Q.19 In exponential smoothening method, which one of the following is true?
M
(A) 0 ≤ α ≤ 1 and high value of α is used for stable demand
(B) 0 ≤ α ≤ 1 and high value of α is used for unstable demand
(C) α ≥ 1 and high value of α is used for stable demand
(D) α ≤ 0 and high value of α is used for unstable demand
ME 3/10
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GATE 2014 SET-1 MECHANICAL – ME
Q.20 For machining a rectangular island represented by coordinates P(0,0), Q(100,0), R(100,50) and
S(0,50) on a casting using CNC milling machine, an end mill with a diameter of 16 mm is used.
The trajectory of the cutter centre to machine the island PQRS is
(A) (−8, −8), (108, −8), (108,58), (−8,58) , (−8, −8)
(B) (8,8), (94,8), (94,44), (8,44), (8,8)
(C) (−8,8), (94,0), (94,44), (8,44), (−8,8)
(D) (0,0), (100,0), (100,50), (50,0), (0,0)
Q.21 Which one of the following instruments is widely used to check and calibrate geometric features of
machine tools during their assembly?
)
(A) Ultrasonic probe (B) Coordinate Measuring Machine (CMM)
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(C) Laser interferometer (D) Vernier calipers
Q.22 The major difficulty during welding of aluminium is due to its
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(A) high tendency of oxidation (B) high thermal conductivity
(C) low melting point (D) low density
Q.23 The main cutting force acting on a tool during the turning (orthogonal cutting) operation of a metal
E
is 400 N. The turning was performed using 2 mm depth of cut and 0.1 mm/rev feed rate. The
specific cutting pressure (in N/mm2) is
AT
(A) 1000 (B) 2000 (C) 3000 (D) 4000
Q.24 The process of reheating the martensitic steel to reduce its brittleness without any significant loss in
its hardness is
(G
(A) normalising (B) annealing (C) quenching (D) tempering
1
Q.25 In solid-state welding, the contamination layers between the surfaces to be welded are removed by
(A) alcohol (B) plastic deformation
E0
(C) water jet (D) sand blasting
M
ME 4/10
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GATE 20144 SET--1 M
MECHANIC
CAL – ME
Q. 26 – Q.. 55 carry two mark
ks each.
Q.26 1
v∫ ( ydx − xdy
d ) is evaluuated along the circle x + y = traversed in counter
2 2
Thee integral
C 4
clockwise direcction. The inttegral is equaal to
π π π
(A)) 0 (B) − (C) − (D)
4 2 4
Q.27 d2 y dy
If y = f(x) is thee solution off 2
= 0 with
w the boun
ndary conditiions y = 5 att x = 0, and = 2 at
dx dx
)
x = 10, f(15) = _______
14
Q.28 In the followinng table, x is a discrete random varriable and p(x)
p is the pprobability density. The
20
stanndard deviatiion of x is
x 1 2 3
p(x)
x) 0.3 0.6 0.1
(A)) 0.18 (B) 0.36 (C) 0.54 (D) 0.6
E
Q.29 Usiing the trapeezoidal rule, and dividingg the intervall of integratioon into threee equal subin
ntervals, the
AT
+1
deffinite integrall ∫ x dx is _______
−1
(G
Q.30 Thee state of sttress at a pooint is givenn by σx = −6 MPa, σy = 4 MPa, annd τxy = −8 MPa. The
maxximum tensiile stress (in MPa)
M at the point
p is ____
____
1
E0
Q.31 A block
b R of mass
m 100 kg is i placed on a block S off mass 150 kgg as shown iin the figure. Block R is
ng PQ. If thee coefficient of static fricction for all
tiedd to the wall by a massleess and inexttensible strin
surfaces is 0.4, the minimumm force F (inn kN) needed d to move thee block S is
M
(A)) 0.69 (B) 0.88 (C) 0.98 (D) 1.37
ME 5/100
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GATE 2014 SET-1 MECHANICAL – ME
Q.32 A pair of spur gears with module 5 mm and a center distance of 450 mm is used for a speed
reduction of 5:1. The number of teeth on pinion is _______
Q.33 Consider a cantilever beam, having negligible mass and uniform flexural rigidity, with length
0.01 m. The frequency of vibration of the beam, with a 0.5 kg mass attached at the free tip, is
100 Hz. The flexural rigidity (in N.m2) of the beam is _______
Q.34 An ideal water jet with volume flow rate of 0.05 m3/s strikes a flat plate placed normal to its path
and exerts a force of 1000 N. Considering the density of water as 1000 kg/m3, the diameter (in mm)
of the water jet is _______
)
14
Q.35 A block weighing 200 N is in contact with a level plane whose coefficients of static and kinetic
friction are 0.4 and 0.2, respectively. The block is acted upon by a horizontal force (in newton)
20
P=10t, where t denotes the time in seconds. The velocity (in m/s) of the block attained after
10 seconds is _______
Q.36
E
A slider crank mechanism has slider mass of 10 kg, stroke of 0.2 m and rotates with a uniform
angular velocity of 10 rad/s. The primary inertia forces of the slider are partially balanced by a
revolving mass of 6 kg at the crank, placed at a distance equal to crank radius. Neglect the mass of
AT
connecting rod and crank. When the crank angle (with respect to slider axis) is 30°, the unbalanced
force (in newton) normal to the slider axis is _______
(G
Q.37 An offset slider-crank mechanism is shown in the figure at an instant. Conventionally, the Quick
Return Ratio (QRR) is considered to be greater than one. The value of QRR is _______
40 mm
20 mm
1
10 mm
E0
M
ME 6/10
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GATE 2014 SET-1 MECHANICAL – ME
Q.38 A rigid uniform rod AB of length L and mass m is hinged at C such that AC = L/3, CB = 2L/3. Ends
A and B are supported by springs of spring constant k. The natural frequency of the system is given
by
k k
C
A B
L/3 2L/3
)
(A) (B) (C) (D)
14
Q.39 A hydrodynamic journal bearing is subject to 2000 N load at a rotational speed of 2000 rpm. Both
bearing bore diameter and length are 40 mm. If radial clearance is 20 µm and bearing is lubricated
20
with an oil having viscosity 0.03 Pa.s, the Sommerfeld number of the bearing is _______
Q.40 A 200 mm long, stress free rod at room temperature is held between two immovable rigid walls.
E
The temperature of the rod is uniformly raised by 250°C. If the Young’s modulus and coefficient of
thermal expansion are 200 GPa and 1×10−5 /°C, respectively, the magnitude of the longitudinal
stress (in MPa) developed in the rod is _______
AT
Q.41 1.5 kg of water is in saturated liquid state at 2 bar (vf = 0.001061 m3/kg, uf = 504.0 kJ/kg,
(G
hf = 505 kJ/kg). Heat is added in a constant pressure process till the temperature of water reaches
400°C (v = 1.5493 m3/kg, u = 2967.0 kJ/kg, h = 3277.0 kJ/kg). The heat added (in kJ) in the process
is _______
1
E0
M
ME 7/10
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GATE 2014 SET-1 MECHANICAL – ME
Q.42 Consider one dimensional steady state heat conduction across a wall (as shown in figure below) of
thickness 30 mm and thermal conductivity 15 W/m.K. At x = 0, a constant heat flux,
q" = 1×105 W/m2 is applied. On the other side of the wall, heat is removed from the wall by
convection with a fluid at 25°C and heat transfer coefficient of 250 W/m2.K. The temperature
(in °C), at x = 0 is _______
T1
q" = 1×105 W/m2
T2
)
T∞ = 25°C
14
x
x=0
20
Q.43 Water flows through a pipe having an inner radius of 10 mm at the rate of 36 kg/hr at 25°C. The
viscosity of water at 25°C is 0.001 kg/m.s. The Reynolds number of the flow is _______
E
AT
Q.44 For a fully developed flow of water in a pipe having diameter 10 cm, velocity 0.1 m/s and
kinematic viscosity 10−5 m2/s, the value of Darcy friction factor is _______
(G
Q.45 In a simple concentric shaft-bearing arrangement, the lubricant flows in the 2 mm gap between the
shaft and the bearing. The flow may be assumed to be a plane Couette flow with zero pressure
gradient. The diameter of the shaft is 100 mm and its tangential speed is 10 m/s. The dynamic
viscosity of the lubricant is 0.1 kg/m.s. The frictional resisting force (in newton) per 100 mm length
of the bearing is _______
1
E0
Q.46 The non-dimensional fluid temperature profile near the surface of a convectively cooled flat plate is
2
TW − T y ⎛ y⎞
given by = a + b + c ⎜ ⎟ , where y is measured perpendicular to the plate, L is the plate
TW − T∞ L ⎝L⎠
M
length, and a, b and c are arbitrary constants. TW and T∞ are wall and ambient temperatures,
respectively. If the thermal conductivity of the fluid is k and the wall heat flux is q" , the Nusselt
q" L
number Nu = is equal to
TW − T∞ k
(A) a (B) b (C) 2c (D) (b+2c)
ME 8/10
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GATE 2014 SET-1 MECHANICAL – ME
Q.47 In an air-standard Otto cycle, air is supplied at 0.1 MPa and 308 K. The ratio of the specific heats
(γ) and the specific gas constant (R) of air are 1.4 and 288.8 J/kg.K, respectively. If the compression
ratio is 8 and the maximum temperature in the cycle is 2660 K, the heat (in kJ/kg) supplied to the
engine is _______
Q.48 A reversible heat engine receives 2 kJ of heat from a reservoir at 1000 K and a certain amount of
heat from a reservoir at 800 K. It rejects 1 kJ of heat to a reservoir at 400 K. The net work output
(in kJ) of the cycle is
(A) 0.8 (B) 1.0 (C) 1.4 (D) 2.0
)
Q.49 An ideal reheat Rankine cycle operates between the pressure limits of 10 kPa and 8 MPa, with
14
reheat being done at 4 MPa. The temperature of steam at the inlets of both turbines is 500°C and
the enthalpy of steam is 3185 kJ/kg at the exit of the high pressure turbine and 2247 kJ/kg at the
exit of low pressure turbine. The enthalpy of water at the exit from the pump is 191 kJ/kg. Use the
following table for relevant data.
20
Superheated steam temperature Pressure ν h s
3
(°C) (MPa) (m /kg) (kJ/kg) (kJ/kg.K)
500 4 0.08644 3446 7.0922
500 8 E 0.04177 3399 6.7266
Disregarding the pump work, the cycle efficiency (in percentage) is _______
AT
Q.50 Jobs arrive at a facility at an average rate of 5 in an 8 hour shift. The arrival of the jobs follows
Poisson distribution. The average service time of a job on the facility is 40 minutes. The service
(G
time follows exponential distribution. Idle time (in hours) at the facility per shift will be
5 14 7 10
(A) (B) (C) (D)
7 3 5 3
1
Q.51 A metal rod of initial length L0 is subjected to a drawing process. The length of the rod at any
E0
instant is given by the expression, L (t ) = L0 (1 + t 2 ) , where t is the time in minutes. The true strain
rate (in min−1) at the end of one minute is _______
M
Q.52 During pure orthogonal turning operation of a hollow cylindrical pipe, it is found that the thickness
of the chip produced is 0.5 mm. The feed given to the zero degree rake angle tool is 0.2 mm/rev.
The shear strain produced during the operation is _______
ME 9/10
Text of page 17
GATE 2014 SET-1 MECHANICAL – ME
Q.53 For the given assembly: 25 H7/g8, match Group A with Group B
Group A Group B
P. H I. Shaft Type
Q. IT8 II. Hole Type
R. IT7 III. Hole Tolerance Grade
S. g IV. Shaft Tolerance Grade
(A) P-I, Q-III, R-IV, S-II (B) P-I, Q-IV, R-III, S-II
(C) P-II, Q-III, R-IV, S-I (D) P-II, Q-IV, R-III, S-I
Q.54 If the Taylor’s tool life exponent n is 0.2, and the tool changing time is 1.5 min, then the tool life
(in min) for maximum production rate is _______
)
14
Q.55 An aluminium alloy (density 2600 kg/m3) casting is to be produced. A cylindrical hole of 100 mm
diameter and 100 mm length is made in the casting using sand core (density 1600 kg/m3). The net
20
buoyancy force (in newton) acting on the core is _______
E
END OF THE QUESTION PAPER
AT
(G
1
E0
M
ME 10/10
Text of page 18
GATE 2014
Answer Keys for ME ‐ Mechanical Engineering
SESSION ‐ ϭ SESSION ‐ ϭ
Section Q. No. Section Q. No.
Key / Range Marks Key / Range Marks
GA 1 C 1 ME 24 A 1
GA 2 D 1 ME 25 B 1
GA 3 B 1 ME 26 C 2
GA 4 A 1 ME 27 34 to 36 2
GA 5 725 to 725 1 ME 28 D 2
GA 6 D 2 ME 29 1.10 to 1.12 2
GA 7 B 2 ME 30 8.4 to 8.5 2
GA 8 560 to 560 2 ME 31 D 2
GA 9 D 2 ME 32 29 to 31 2
GA 10 B 2 ME 33 0.064 to 0.067 2
ME 1 A 1 ME 34 56 to 57 2
ME 2 A 1 ME 35 4.8 to 5.0 2
ME 3 C 1 ME 36 29 to 31 2
ME 4 A 1 ME 37 1.2 to 1.3 2
ME 5 B 1 ME 38 D 2
ME 6 C 1 ME 39 0.75 to 0.85 2
ME 7 0.29 to 0.31 1 ME 40 499 to 501 2
ME 8 B 1 ME 41 4155 to 4160 2
ME 9 A 1 ME 42 620 to 630 2
ME 10 D 1 ME 43 635 to 638 2
ME 11 D 1 ME 44 0.06 to 0.07 2
ME 12 B 1 ME 45 15 to 16 2
ME 13 C 1 ME 46 B 2
ME 14 B 1 ME 47 1400 to 1420 2
ME 15 A 1 ME 48 C 2
ME 16 D 1 ME 49 40 to 42 2
ME 17 C 1 ME 50 B 2
ME 18 B 1 ME 51 0.9 to 1.1 2
ME 19 B 1 ME 52 2.8 to 3.0 2
ME 20 A 1 ME 53 D 2
ME 21 C 1 ME 54 5.9 to 6.1 2
ME 22 A 1 ME 55 7 to 8 2
ME 23 B 1
Text of page 19
SESSION - 2
Text of page 20
GATE 2014: General Instructions during Examination
1. Total duration of the GATE examination is 180 minutes.
2. The clock will be set at the server. The countdown timer at 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 need not
terminate the examination or submit your paper.
3. Any useful data required for your paper can be viewed by clicking on the Useful
Common Data button that appears on the screen.
4. Use the scribble pad provided to you for any rough work. Submit the scribble pad at
the end of the examination.
5. You are allowed to use a non-programmable type calculator, however, sharing of
calculators is not allowed.
6. The Question Palette displayed on the right side of screen will show the status of
each question using one of the following symbols:
The Marked for Review status for a question simply indicates that you would like to look at
that question again. If a question is answered, but marked for review, then the answer will
be considered for evaluation unless the status is modified by the candidate.
Navigating to a Question :
7. To answer a question, do the following:
a. Click on the question number in the Question Palette to go to that question
directly.
b. Select an answer for a multiple choice type question by clicking on the bubble
placed before the 4 choices, namely A, B, C and D. Use the virtual numeric
keypad to enter a number as answer for a numerical type question.
c. Click on Save & Next to save your answer for the current question and then go
to the next question.
d. Click on Mark for Review & Next to save your answer for the current question
and also mark it for review, and then go to the next question.
Text of page 21
Caution: Note that your answer for the current question will not be saved, if you navigate
to another question directly by clicking on a question number without saving the answer to
the previous question.
You can view all the questions by clicking on the Question Paper button. This feature is
provided, so that if you want you can just see the entire question paper at a glance.
Answering a Question :
8. Procedure for answering a multiple choice (MCQ) type question:
a. Choose one answer from the 4 options (A,B,C,D) given below the question,
click on the bubble placed before the chosen option.
b. To deselect your chosen answer, click on the bubble of the chosen option again
or click on the Clear Response button.
c. To change your chosen answer, click on the bubble of another option.
d. To save your answer, you MUST click on the Save & Next button.
9. Procedure for answering a numerical answer type question:
a. To enter a number as your answer, use the virtual numerical keypad.
b. A fraction (e.g. -0.3 or -.3) can be entered as an answer with or without '0'
before the decimal point. As many as four decimal points, e.g. 12.5435 or
0.003 or -932.6711 or 12.82 can be entered.
c. To clear your answer, click on the Clear Response button.
d. To save your answer, you MUST click on the Save & Next button
10. To mark a question for review, click on the Mark for Review & Next button. If an
answer is selected (for MCQ) or entered (for numerical answer type) for a question
that is Marked for Review, that answer will be considered in the evaluation unless
the status is modified by the candidate.
11. 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.
12. Note that ONLY Questions for which answers are saved or marked for review after
answering will be considered for evaluation.
Choosing a Section :
13. Sections in this question paper are displayed on the top bar of the screen. Questions
in a Section can be viewed by clicking on the name of that Section. The Section you
are currently viewing will be highlighted.
14. A checkbox is displayed for every optional Section, if any, in the Question Paper. To
select the optional Section for answering, click on the checkbox for that Section.
15. If the checkbox for an optional Section is not selected, the Save & Next button and
the Mark for Review & Next button will NOT be enabled for that Section. You will
Text of page 22
only be able to see questions in this Section, but you will not be able to answer
questions in the Section.
16. After clicking the Save & Next button for the last question in a Section, you will
automatically be taken to the first question of the next Section in sequence.
17. You can move the mouse cursor over the name of a Section to view the answering
status for that Section.
Changing the Optional Section :
18. After answering the chosen optional Section, partially or completely, you can change
the optional Section by selecting the checkbox for a new Section that you want to
attempt. A warning message will appear along with a table showing the number of
questions answered in each of the previously chosen optional Sections and a
checkbox against each of these Sections. Click on a checkbox against a Section that
you want to reset and then click on the RESET button. Note that RESETTING a Section
will DELETE all the answers for questions in that Section. Hence, if you think that you
may want to select this Section again later, you will have to note down your answers
for questions in that Section. If you do not want to reset the Section and want to
continue answering the previously chosen optional Section, then click on the BACK
button.
19. If you deselect the checkbox for an optional Section in the top bar, the following
warning message will appear: "Deselecting the checkbox will DELETE all the answers
for questions in this Section. Do you want to deselect this Section?” If you want to
deselect, click on the RESET button. If you do not want to deselect, click on the BACK
button.
20. You can shuffle between different Sections or change the optional Sections any
number of times.
Text of page 23
GATE 2014 Examination
ME: Mechanical Engineering
Duration: 180 minutes Maximum Marks: 100
Read the following instructions carefully.
1. To login, enter your Registration Number and password provided to you. Kindly go through the various
symbols used in the test and understand their meaning before you start the examination.
2. Once you login and after the start of the examination, you can view all the questions in the question
paper, by clicking on the View All Questions button in the screen.
3. This question paper consists of 2 sections, General Aptitude (GA) for 15 marks and the subject
specific GATE paper for 85 marks. Both these sections are compulsory.
The GA section consists of 10 questions. Question numbers 1 to 5 are of 1-mark each, while question
numbers 6 to 10 are of 2-mark each.
The subject specific GATE paper section consists of 55 questions, out of which question numbers 1 to
25 are of 1-mark each, while question numbers 26 to 55 are of 2-mark each.
4. Depending upon the GATE paper, there may be useful common data that may be required for
answering the questions. If the paper has such useful data, the same can be viewed by clicking on the
Useful Common Data button that appears at the top, right hand side of the screen.
5. The computer allotted to you at the examination center runs specialized software that permits only one
answer to be selected for multiple-choice questions using a mouse and to enter a suitable number for
the numerical answer type questions using the virtual keyboard and mouse.
6. Your answers shall be updated and saved on a server periodically and also at the end of the
examination. The examination will stop automatically at the end of 180 minutes.
7. In each paper a candidate can answer a total of 65 questions carrying 100 marks.
8. The question paper may consist of questions of multiple choice type (MCQ) and numerical answer
type.
9. Multiple choice type questions will have four choices against A, B, C, D, out of which only ONE is the
correct answer. The candidate has to choose the correct answer by clicking on the bubble (⃝) placed
before the choice.
10. For numerical answer type questions, each question will have a numerical answer and there will not be
any choices. For these questions, the answer should be enteredby using the virtual keyboard that
appears on the monitor and the mouse.
11. All questions that are not attempted will result in zero marks. However, wrong answers for multiple
choice type questions (MCQ) will result in NEGATIVE marks. For all MCQ questions a wrong
answer will result in deduction of⅓ marks for a 1-mark question and ⅔ marks for a 2-mark question.
12. There is NO NEGATIVE MARKING for questions of NUMERICAL ANSWER TYPE.
13. Non-programmable type Calculator is allowed. Charts, graph sheets, and mathematical tables are NOT
allowed in the Examination Hall. You must use the Scribble pad provided to you at the examination
centre for all your rough work. The Scribble Pad has to be returned at the end of the examination.
Declaration by the candidate:
“I have read and understood all the above instructions. I have also read and understood clearly the
instructions given on the admit card and shall follow the same. I also understand that in case I am found to
violate any of these instructions, my candidature is liable to be cancelled. I also confirm that at the start of
the examination all the computer hardware allotted to me are in proper working condition”.
Text of page 24
GATE 2014 SET- 4 General Aptitude -GA
Q. 1 – Q. 5 carry one mark each.
Q.1 Choose the most appropriate word from the options given below to complete the following
sentence.
Communication and interpersonal skills are important in their own ways.
(A) each (B) both (C) all (D) either
Q.2 Which of the options given below best completes the following sentence?
She will feel much better if she ________________.
(A) will get some rest (B) gets some rest
)
(C) will be getting some rest (D) is getting some rest
14
Q.3 Choose the most appropriate pair of words from the options given below to complete the following
sentence.
20
She could not _____ the thought of _________ the election to her bitter rival.
(A) bear, loosing (B) bare, loosing (C) bear, losing (D) bare, losing
Q.4 A regular die has six sides with numbers 1 to 6 marked on its sides. If a very large number of
throws show the following frequencies of occurrence: 1 → 0.167; 2 → 0.167; 3 → 0.152; 4 →
0.166; 5 → 0.168; 6 → 0.180. We call this die
E
(A) irregular (B) biased (C) Gaussian (D) insufficient
AT
Q.5 Fill in the missing number in the series.
2 3 6 15 157.5 630
(G
Q. 6 – Q. 10 carry two marks each.
4
Q.6 Find the odd one in the following group
A0
Q,W,Z,B B,H,K,M W,C,G,J M,S,V,X
(A) Q,W,Z,B (B) B,H,K,M (C) W,C,G,J (D) M,S,V,X
Q.7 Lights of four colors (red, blue, green, yellow) are hung on a ladder. On every step of the ladder
G
there are two lights. If one of the lights is red, the other light on that step will always be blue. If one
of the lights on a step is green, the other light on that step will always be yellow. Which of the
following statements is not necessarily correct?
(A) The number of red lights is equal to the number of blue lights
(B) The number of green lights is equal to the number of yellow lights
(C) The sum of the red and green lights is equal to the sum of the yellow and blue lights
(D) The sum of the red and blue lights is equal to the sum of the green and yellow lights
Q.8 The sum of eight consecutive odd numbers is 656. The average of four consecutive even numbers is
87. What is the sum of the smallest odd number and second largest even number?
GA 1/2
Text of page 25
GATE 2014 SET- 4 General Aptitude -GA
Q.9 The total exports and revenues from the exports of a country are given in the two charts shown
below. The pie chart for exports shows the quantity of each item exported as a percentage of the
total quantity of exports. The pie chart for the revenues shows the percentage of the total revenue
generated through export of each item. The total quantity of exports of all the items is 500 thousand
tonnes and the total revenues are 250 crore rupees. Which item among the following has generated
the maximum revenue per kg?
Exports Revenues
Item 6 Item 1 Item 1
11% Item 6 12%
16%
19%
)
Item 5 Item 2 Item 2
12% 20% Item 5
14
20%
20%
Item 3 Item 3
Item 4 19% Item 4 23%
22% 6%
20
(A) Item 2 (B) Item 3 (C) Item 6 (D) Item 5
Q.10
E
It takes 30 minutes to empty a half-full tank by draining it at a constant rate. It is decided to
simultaneously pump water into the half-full tank while draining it. What is the rate at which water
has to be pumped in so that it gets fully filled in 10 minutes?
AT
(A) 4 times the draining rate (B) 3 times the draining rate
(C) 2.5 times the draining rate (D) 2 times the draining rate
(G
END OF THE QUESTION PAPER
4
A0
G
GA 2/2
Text of page 26
GATE 2014 SET-2 MECHANICAL – ME
Q. 1 – Q. 25 carry one mark each.
Q.1 − 5 2
One of the eigenvectors of the matrix is
− 9 6
− 1 − 2 2 1
(A) (B) (C) (D)
1 9 −1 1
Q.2 e2 x − 1
Lt is equal to
x →0
sin(4 x)
)
(A) 0 (B) 0.5 (C) 1 (D) 2
14
Q.3 Curl of vector F = x 2 z 2iˆ − 2 x y 2 z ˆj + 2 y 2 z 3 kˆ is
20
(A) (4 yz 3 + 2 xy 2 )iˆ + 2 x 2 z ˆj − 2 y 2 z kˆ (B) (4 yz 3 + 2 xy 2 )iˆ − 2 x 2 z ˆj − 2 y 2 z kˆ
(C) 2 xz 2iˆ − 4 x y z ˆj + 6 y 2 z 2 kˆ (D) 2 xz 2iˆ + 4 x y z ˆj + 6 y 2 z 2 kˆ
Q.4
E
A box contains 25 parts of which 10 are defective. Two parts are being drawn simultaneously in a
random manner from the box. The probability of both the parts being good is
AT
7 42 25 5
(A) (B) (C) (D)
20 125 29 9
The best approximation of the minimum value attained by e−xx sin(100xx) for xx ≥ 0 is _______
(G
Q.5
2
Q.6 A steel cube, with all faces free to deform, has Young’s modulus, E, Poisson’s ratio, ν, and
coefficient of thermal expansion, α. The pressure (hydrostatic stress) developed within the cube,
E0
when it is subjected to a uniform increase in temperature, ΔT, is given by
α ( ∆T ) E α ( ∆T ) E α ( ∆T ) E
(A) 0 (B) (C) − (D)
1 − 2ν 1 − 2ν 3 (1 − 2ν )
M
ME 1/11
Text of page 27
GATE 2014 SET-2 MECHANICAL – ME
Q.7 A two member truss ABC is shown in the figure. The force (in kN) transmitted in member AB is
_______
A
1m
B
0.5 m 10 kN
C
)
14
Q.8 A 4-bar mechanism with all revolute pairs has link lengths lf = 20 mm, lin = 40 mm, lco = 50 mm
and lout = 60 mm. The suffixes 'f', 'in', 'co' and 'out' denote the fixed link, the input link, the coupler
and output link respectively. Which one of the following statements is true about the input and
output links?
20
(A) Both links can execute full circular motion
(B) Both links cannot execute full circular motion
(C) Only the output link cannot execute full circular motion
(D) Only the input link cannot execute full circular motion
E
Q.9 In vibration isolation, which one of the following statements is NOT correct regarding
AT
Transmissibility (T)?
(A) T is nearly unity at small excitation frequencies
(B) T can be always reduced by using higher damping at any excitation frequency
(G
(C) T is unity at the frequency ratio of 2
(D) T is infinity at resonance for undamped systems
Q.10 In a structure subjected to fatigue loading, the minimum and maximum stresses developed in a
2
cycle are 200 MPa and 400 MPa respectively. The value of stress amplitude (in MPa) is _______
E0
M
ME 2/11
Text of page 28
GATE 2014 SET-2 MECHANICAL – ME
Q.11 A thin plate of uniform thickness is subject to pressure as shown in the figure below
y y
x z
Under the assumption of plane stress, which one of the following is correct?
(A) Normal stress is zero in the z-direction
(B) Normal stress is tensile in the z-direction
(C) Normal stress is compressive in the z-direction
)
(D) Normal stress varies in the z-direction
14
Q.12 For laminar forced convection over a flat plate, if the free stream velocity increases by a factor of 2,
the average heat transfer coefficient
20
(A) remains same (B) decreases by a factor of 2
(C) rises by a factor of 2 (D) rises by a factor of 4
Q.13
γ (= cp/cv) is given by
E
The thermal efficiency of an air-standard Brayton cycle in terms of pressure ratio rrpp and
AT
1 1 1 1
(A) 1 − γ −1
(B) 1 − (C) 1 − (D) 1 − (γ −1) / γ
rp rpγ 1/ γ
r
p r p
(G
Q.14 �⃗ , which one of the following conditions must be satisfied?
For an incompressible flow field, VV
�⃗
∂∂VV
�⃗ = 0
(A) ∇ ∙ VV �⃗ = 0
(B) ∇× VV �⃗ ∙ ∇�VV
(C) �VV �⃗ = 0 �⃗ ∙ ∇�VV
(D) ∂∂∂∂ + �VV �⃗ = 0
2
Q.15 A pure substance at 8 MPa and 400 °C is having a specific internal energy of 2864 kJ/kg and a
E0
specific volume of 0.03432 m3/kg. Its specific enthalpy (in kJ/kg) is _______
Q.16 In a heat exchanger, it is observed that ∆T1 = ∆T2, where ∆T1 is the temperature difference between
M
the two single phase fluid streams at one end and ∆T2 is the temperature difference at the other end.
This heat exchanger is
(A) a condenser (B) an evaporator
(C) a counter flow heat exchanger (D) a parallel flow heat exchanger
Q.17 The difference in pressure (in N/m2) across an air bubble of diameter 0.001 m immersed in water
(surface tension = 0.072 N/m) is _______
ME 3/11
Text of page 29
GATE 2014 SET-2 MECHANICAL – ME
Q.18 If there are m sources and n destinations in a transportation matrix, the total number of basic
variables in a basic feasible solution is
(A) m + n (B) m + n + 1 (C) m + n − 1 (D) m
Q.19 A component can be produced by any of the four processes I, II, III and IV. The fixed cost and the
variable cost for each of the processes are listed below. The most economical process for producing
a batch of 100 pieces is
Process Fixed cost (in Rs.) Variable cost per piece (in Rs.)
I 20 3
II 50 1
III 40 2
)
IV 10 4
14
(A) I (B) II (C) III (D) IV
Q.20 The flatness of a machine bed can be measured using
20
(A) Vernier calipers (B) Auto collimator
(C) Height gauge (D) Tool maker’s microscope
Q.21
E
A robot arm PQ with end coordinates P(0,0) and Q(2,5) rotates counter clockwise about P in the
XY plane by 90°. The new coordinate pair of the end point Q is
AT
(A) (−2,5) (B) (−5,2) (C) (−5, −2) (D) (2, −5)
Q.22 Match the Machine Tools (Group A) with the probable Operations (Group B):
(G
Group A Group B
P: Centre Lathe 1: Slotting
Q: Milling 2: Counter-boring
R: Grinding 3: Knurling
2
S: Drilling 4: Dressing
(A) P-1, Q-2, R-4, S-3 (B) P-2, Q-1, R-4, S-3
E0
(C) P-3, Q-1, R-4, S-2 (D) P-3, Q-4, R-2, S-1
Q.23 The following four unconventional machining processes are available in a shop floor. The most
appropriate one to drill a hole of square cross section of 6 mm × 6 mm and 25 mm deep is
M
(A) Abrasive Jet Machining (B) Plasma Arc Machining
(C) Laser Beam Machining (D) Electro Discharge Machining
Q.24 The relationship between true strain (εεTT ) and engineering strain (εεEE ) in a uniaxial tension test is
given as
ε E ln (1 + ε T )
(A) = ε E ln (1 − ε T )
(B) =
ε T ln (1 + ε E )
(C) = ε T ln (1 − ε E )
(D) =
ME 4/11
Text of page 30
GATE 2014 SET-2 MECHANICAL – ME
Q.25 With respect to metal working, match Group A with Group B:
Group A Group B
P: Defect in extrusion I: alligatoring
Q: Defect in rolling II: scab
R: Product of skew rolling III: fish tail
S: Product of rolling through cluster mill IV: seamless tube
V: thin sheet with tight tolerance
VI: semi-finished balls of ball bearing
(A) P-II, Q-III, R-VI, S-V (B) P-III, Q-I, R-VI, S-V
(C) P-III, Q-I, R-IV, S-VI (D) P-I, Q-II, R-V, S-VI
)
14
Q. 26 – Q. 55 carry two marks each.
Q.26 An analytic function of a complex variable zz = xx + ii yy is expressed as ff(zz) = uu(xx, yy) + ii vv(xx, yy),
20
where ii = √−1 . If uu(xx, yy) = 2 xx yy, then vv(xx, yy) must be
(A) xx 2 + yy 2 + constant (B) xx 2 − yy 2 + constant
(C) − xx 2 + yy 2 + constant E (D) − xx 2 − yy 2 + constant
AT
Q.27 dy
The general solution of the differential equation= cos( x + y ) , with c as a constant, is
dx
x+ y
(A) y + sin ( x + y ) = x + c (B) tan = y + c
2
(G
x+ y x+ y
(C) cos = x + c (D) tan = x + c
2 2
2
Q.28 Consider an unbiased cubic dice with opposite faces coloured identically and each face coloured
red, blue or green such that each colour appears only two times on the dice. If the dice is thrown
E0
thrice, the probability of obtaining red colour on top face of the dice at least twice is _______
M
Q.29 4
The value of ∫ ln( x) dx calculated using the Trapezoidal rule with five subintervals is _______
2.5
ME 5/11
Text of page 31
GATE 2014 SET-2 MECHANICAL – ME
Q.30 The flexural rigidity (EI) of a cantilever beam is assumed to be constant over the length of the beam
shown in figure. If a load P and bending moment PL/2 are applied at the free end of the beam then
the value of the slope at the free end is
P
PL/2
L
1 PL2 PL2 3 PL2 5 PL2
(A) (B) (C) (D)
2 EI EI 2 EI 2 EI
)
14
Q.31 A cantilever beam of length, L, with uniform cross-section and flexural rigidity, EI, is loaded
uniformly by a vertical load, w per unit length. The maximum vertical deflection of the beam is
given by
wL4 wL4 wL4 wL4
20
(A) (B) (C) (D)
8 EI 16 EI 4 EI 24 EI
Q.32 For the three bolt system shown in the figure, the bolt material has shear yield strength of 200 MPa.
E
For a factor of safety of 2, the minimum metric specification required for the bolt is
AT
(G
(A) M8 (B) M10 (C) M12 (D) M16
Q.33 Consider a flywheel whose mass M is distributed almost equally between a heavy, ring-like rim of
radius R and a concentric disk-like feature of radius R/2. Other parts of the flywheel, such as
2
spokes, etc, have negligible mass. The best approximation for α, if the moment of inertia of the
flywheel about its axis of rotation is expressed as αMR2, is _______
E0
M
ME 6/11
Text of page 32
GATE 2014 SET-2 MECHANICAL – ME
Q.34 What is the natural frequency of the spring mass system shown below? The contact between the
block and the inclined plane is frictionless. The mass of the block is denoted by m and the spring
constants are denoted by k1 and k2 as shown below.
)
14
k1 + k2 k1 + k2 k1 − k2 k1 + k2
(A) (B) (C) (D)
2m 4m m m
20
Q.35 A disc clutch with a single friction surface has coefficient of friction equal to 0.3. The maximum
pressure which can be imposed on the friction material is 1.5 MPa. The outer diameter of the clutch
plate is 200 mm and its internal diameter is 100 mm. Assuming uniform wear theory for the clutch
plate, the maximum torque (in N.m) that can be transmitted is _______
E
AT
Q.36 A truck accelerates up a 10° incline with a crate of 100 kg. Value of static coefficient of friction
between the crate and the truck surface is 0.3. The maximum value of acceleration (in m/s2) of the
truck such that the crate does not slide down is _______
(G
Q.37 Maximum fluctuation of kinetic energy in an engine has been calculated to be 2600 J. Assuming
that the engine runs at an average speed of 200 rpm, the polar mass moment of inertia (in kg.m2) of
a flywheel to keep the speed fluctuation within ±0.5% of the average speed is _______
2
E0
Q.38 Consider the two states of stress as shown in configurations I and II in the figure below. From the
standpoint of distortion energy (von-Mises) criterion, which one of the following statements is true?
M
(A) I yields after II (B) II yields after I
(C) Both yield simultaneously (D) Nothing can be said about their relative yielding
ME 7/11
Text of page 33
GATE 2014 SET-2 MECHANICAL – ME
Q.39 A rigid link PQ of length 2 m rotates about the pinned end Q with a constant angular acceleration of
12 rad/s2. When the angular velocity of the link is 4 rad/s, the magnitude of the resultant
acceleration (in m/s2) of the end P is _______
Q.40 A spur pinion of pitch diameter 50 mm rotates at 200 rad/s and transmits 3 kW power. The pressure
angle of the tooth of the pinion is 20°. Assuming that only one pair of the teeth is in contact, the
total force (in newton) exerted by a tooth of the pinion on the tooth on a mating gear is _______
Q.41 A spherical balloon with a diameter of 10 m, shown in the figure below is used for advertisements.
)
The balloon is filled with helium (RHe = 2.08 kJ/kg.K) at ambient conditions of 15°C and 100 kPa.
14
Assuming no disturbances due to wind, the maximum allowable weight (in newton) of balloon
material and rope required to avoid the fall of the balloon (Rair = 0.289 kJ/kg.K) is _______
20
GATE -2014
E
AT
(G
Q.42 A hemispherical furnace of 1 m radius has the inner surface (emissivity, ε = 1 ) of its roof
maintained at 800 K, while its floor ( ε = 0.5 ) is kept at 600 K. Stefan-Boltzmann constant is
2
5.668 × 10−8 W/m2.K4. The net radiative heat transfer (in kW) from the roof to the floor is _______
E0
Q.43 Water flows through a 10 mm diameter and 250 m long smooth pipe at an average velocity of
0.1 m/s. The density and the viscosity of water are 997 kg/m3 and 855×10−6 N.s/m2, respectively.
M
Assuming fully-developed flow, the pressure drop (in Pa) in the pipe is _______
ME 8/11
Text of page 34
GATE 2014 SET-2 MECHANICAL – ME
Q.44 A material P of thickness 1 mm is sandwiched between two steel slabs, as shown in the figure
below. A heat flux 10 kW/m2 is supplied to one of the steel slabs as shown. The boundary
temperatures of the slabs are indicated in the figure. Assume thermal conductivity of this steel is 10
W/m.K. Considering one-dimensional steady state heat conduction for the configuration, the
thermal conductivity (k, in W/m.K) of material P is _______
)
14
20
Q.45
E
Consider laminar flow of water over a flat plate of length 1 m. If the boundary layer thickness at a
AT
distance of 0.25 m from the leading edge of the plate is 8 mm, the boundary layer thickness
(in mm), at a distance of 0.75 m, is _______
(G
Q.46 In an ideal Brayton cycle, atmospheric air (ratio of specific heats, cp/cv = 1.4, specific heat at
constant pressure = 1.005 kJ/kg.K) at 1 bar and 300 K is compressed to 8 bar. The maximum
temperature in the cycle is limited to 1280 K. If the heat is supplied at the rate of 80 MW, the mass
flow rate (in kg/s) of air required in the cycle is _______
2
Q.47 Steam at a velocity of 10 m/s enters the impulse turbine stage with symmetrical blading having
E0
blade angle 30°. The enthalpy drop in the stage is 100 kJ. The nozzle angle is 20°. The maximum
blade efficiency (in percent) is _______
M
Q.48 In a concentric counter flow heat exchanger, water flows through the inner tube at 25°C and leaves
at 42°C. The engine oil enters at 100°C and flows in the annular flow passage. The exit temperature
of the engine oil is 50°C. Mass flow rate of water and the engine oil are 1.5 kg/s and 1 kg/s,
respectively. The specific heat of water and oil are 4178 J/kg.K and 2130 J/kg.K, respectively. The
effectiveness of this heat exchanger is _______
ME 9/11
Text of page 35
GATE 2014 SET-2 MECHANICAL – ME
Q.49 A heat pump with refrigerant R22 is used for space heating between temperature limits of −20°C
and 25°C. The heat required is 200 MJ/h. Assume specific heat of vapour at the time of discharge
as 0.98 kJ/kg.K. Other relevant properties are given below. The enthalpy (in kJ/kg) of the
refrigerant at isentropic compressor discharge is _______
Saturation Pressure Specific enthalpy Specific entropy
temperature
Tsat (°C) P (MN/m2) hf (kJ/kg) hg (kJ/kg) sf (kJ/kg.K) sg (kJ/kg.K)
−20 0.2448 177.21 397.53 0.9139 1.7841
25 1.048 230.07 413.02 1.1047 1.7183
)
Q.50 A project has four activities P, Q, R and S as shown below.
14
Activity Normal duration (days) Predecessor Cost slope (Rs./day)
P 3 - 500
Q 7 P 100
20
R 4 P 400
S 5 R 200
The normal cost of the project is Rs. 10,000/- and the overhead cost is Rs. 200/- per day.
If the project duration has to be crashed down to 9 days, the total cost (in Rupees) of
the project is _______ E
AT
Q.51 Consider the following data with reference to elementary deterministic economic order quantity
model
Annual demand of an item 100000
Unit price of the item (in Rs.) 10
(G
Inventory carrying cost per unit per year (in Rs.) 1.5
Unit order cost (in Rs.) 30
The total number of economic orders per year to meet the annual demand is _______
2
E0
Q.52 For the CNC part programming, match Group A with Group B:
Group A Group B
P: circular interpolation, counter clock wise I: G02
Q: dwell II: G03
M
R: circular interpolation, clock wise III: G04
S: point to point countering IV: G00
(A) P-II, Q-III, R-I, S-IV (B) P-I, Q-III, R-II, S-IV
(C) P-I, Q-IV, R-II, S-III (D) P-II, Q-I, R-III, S-IV
Q.53 A mild steel plate has to be rolled in one pass such that the final plate thickness is 2/3rd of the initial
thickness, with the entrance speed of 10 m/min and roll diameter of 500 mm. If the plate widens by
2% during rolling, the exit velocity (in m/min) is _______
ME 10/11
Text of page 36
GATE 2014 SET-2 MECHANICAL – ME
Q.54 A hole of 20 mm diameter is to be drilled in a steel block of 40 mm thickness. The drilling is
performed at rotational speed of 400 rpm and feed rate of 0.1 mm/rev. The required approach and
over run of the drill together is equal to the radius of drill. The drilling time (in minute) is
(A) 1.00 (B) 1.25 (C) 1.50 (D) 1.75
Q.55 A rectangular hole of size 100 mm × 50 mm is to be made on a 5 mm thick sheet of steel having
ultimate tensile strength and shear strength of 500 MPa and 300 MPa, respectively. The hole is
made by punching process. Neglecting the effect of clearance, the punching force (in kN) is
(A) 300 (B) 450 (C) 600 (D) 750
)
END OF THE QUESTION PAPER
14
20
E
AT
(G
2
E0
M
ME 11/11
Text of page 37
GATE 2014
Answer Keys for ME ‐ Mechanical Engineering
SESSION ‐ Ϯ SESSION ‐ Ϯ
Section Q. No. Section Q. No.
Key / Range Marks Key / Range Marks
GA 1 B 1 ME 24 C 1
GA 2 B 1 ME 25 B 1
GA 3 C 1 ME 26 C 2
GA 4 B 1 ME 27 D 2
GA 5 45 to 45 1 ME 28 0.25 to 0.27 2
GA 6 C 2 ME 29 1.74 to 1.76 2
GA 7 D 2 ME 30 B 2
GA 8 163 to 163 2 ME 31 A 2
GA 9 D 2 ME 32 B 2
GA 10 A 2 ME 33 0.55 to 0.57 2
ME 1 D 1 ME 34 D 2
ME 2 B 1 ME 35 529 to 532 2
ME 3 A 1 ME 36 1.0 to 1.3 2
ME 4 A 1 ME 37 590 to 595 2
ME 5 ‐1.00 to ‐0.94 1 ME 38 C 2
ME 6 A 1 ME 39 39 to 41 2
ME 7 18 to 22 1 ME 40 638 to 639 2
ME 8 A 1 ME 41 5300 to 5330 2
ME 9 B 1 ME 42 24.0 to 25.2 2
ME 10 99 to 101 1 ME 43 6800 to 6900 2
ME 11 A 1 ME 44 0.09 to 0.11 2
ME 12 C 1 ME 45 13.5 to 14.2 2
ME 13 D 1 ME 46 105 to 112 2
ME 14 A 1 ME 47 85.1 to 89.9 2
ME 15 3135 to 3140 1 ME 48 0.65 to 0.67 2
ME 16 C 1 ME 49 430 to 440 2
ME 17 287 to 289 1 ME 50 12490 to 12510 2
ME 18 C 1 ME 51 49 to 51 2
ME 19 B 1 ME 52 A 2
ME 20 B 1 ME 53 14.6 to 14.8 2
ME 21 B 1 ME 54 B 2
ME 22 C 1 ME 55 B 2
ME 23 D 1
Text of page 38
SESSION - 3
Text of page 39
GATE 2014: General Instructions during Examination
1. Total duration of the GATE examination is 180 minutes.
2. The clock will be set at the server. The countdown timer at 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 need not
terminate the examination or submit your paper.
3. Any useful data required for your paper can be viewed by clicking on the Useful
Common Data button that appears on the screen.
4. Use the scribble pad provided to you for any rough work. Submit the scribble pad at
the end of the examination.
5. You are allowed to use a non-programmable type calculator, however, sharing of
calculators is not allowed.
6. The Question Palette displayed on the right side of screen will show the status of
each question using one of the following symbols:
The Marked for Review status for a question simply indicates that you would like to look at
that question again. If a question is answered, but marked for review, then the answer will
be considered for evaluation unless the status is modified by the candidate.
Navigating to a Question :
7. To answer a question, do the following:
a. Click on the question number in the Question Palette to go to that question
directly.
b. Select an answer for a multiple choice type question by clicking on the bubble
placed before the 4 choices, namely A, B, C and D. Use the virtual numeric
keypad to enter a number as answer for a numerical type question.
c. Click on Save & Next to save your answer for the current question and then go
to the next question.
d. Click on Mark for Review & Next to save your answer for the current question
and also mark it for review, and then go to the next question.
Text of page 40
Caution: Note that your answer for the current question will not be saved, if you navigate
to another question directly by clicking on a question number without saving the answer to
the previous question.
You can view all the questions by clicking on the Question Paper button. This feature is
provided, so that if you want you can just see the entire question paper at a glance.
Answering a Question :
8. Procedure for answering a multiple choice (MCQ) type question:
a. Choose one answer from the 4 options (A,B,C,D) given below the question,
click on the bubble placed before the chosen option.
b. To deselect your chosen answer, click on the bubble of the chosen option again
or click on the Clear Response button.
c. To change your chosen answer, click on the bubble of another option.
d. To save your answer, you MUST click on the Save & Next button.
9. Procedure for answering a numerical answer type question:
a. To enter a number as your answer, use the virtual numerical keypad.
b. A fraction (e.g. -0.3 or -.3) can be entered as an answer with or without '0'
before the decimal point. As many as four decimal points, e.g. 12.5435 or
0.003 or -932.6711 or 12.82 can be entered.
c. To clear your answer, click on the Clear Response button.
d. To save your answer, you MUST click on the Save & Next button
10. To mark a question for review, click on the Mark for Review & Next button. If an
answer is selected (for MCQ) or entered (for numerical answer type) for a question
that is Marked for Review, that answer will be considered in the evaluation unless
the status is modified by the candidate.
11. 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.
12. Note that ONLY Questions for which answers are saved or marked for review after
answering will be considered for evaluation.
Choosing a Section :
13. Sections in this question paper are displayed on the top bar of the screen. Questions
in a Section can be viewed by clicking on the name of that Section. The Section you
are currently viewing will be highlighted.
14. A checkbox is displayed for every optional Section, if any, in the Question Paper. To
select the optional Section for answering, click on the checkbox for that Section.
15. If the checkbox for an optional Section is not selected, the Save & Next button and
the Mark for Review & Next button will NOT be enabled for that Section. You will
Text of page 41
only be able to see questions in this Section, but you will not be able to answer
questions in the Section.
16. After clicking the Save & Next button for the last question in a Section, you will
automatically be taken to the first question of the next Section in sequence.
17. You can move the mouse cursor over the name of a Section to view the answering
status for that Section.
Changing the Optional Section :
18. After answering the chosen optional Section, partially or completely, you can change
the optional Section by selecting the checkbox for a new Section that you want to
attempt. A warning message will appear along with a table showing the number of
questions answered in each of the previously chosen optional Sections and a
checkbox against each of these Sections. Click on a checkbox against a Section that
you want to reset and then click on the RESET button. Note that RESETTING a Section
will DELETE all the answers for questions in that Section. Hence, if you think that you
may want to select this Section again later, you will have to note down your answers
for questions in that Section. If you do not want to reset the Section and want to
continue answering the previously chosen optional Section, then click on the BACK
button.
19. If you deselect the checkbox for an optional Section in the top bar, the following
warning message will appear: "Deselecting the checkbox will DELETE all the answers
for questions in this Section. Do you want to deselect this Section?” If you want to
deselect, click on the RESET button. If you do not want to deselect, click on the BACK
button.
20. You can shuffle between different Sections or change the optional Sections any
number of times.
Text of page 42
GATE 2014 Examination
ME: Mechanical Engineering
Duration: 180 minutes Maximum Marks: 100
Read the following instructions carefully.
1. To login, enter your Registration Number and password provided to you. Kindly go through the various
symbols used in the test and understand their meaning before you start the examination.
2. Once you login and after the start of the examination, you can view all the questions in the question
paper, by clicking on the View All Questions button in the screen.
3. This question paper consists of 2 sections, General Aptitude (GA) for 15 marks and the subject
specific GATE paper for 85 marks. Both these sections are compulsory.
The GA section consists of 10 questions. Question numbers 1 to 5 are of 1-mark each, while question
numbers 6 to 10 are of 2-mark each.
The subject specific GATE paper section consists of 55 questions, out of which question numbers 1 to
25 are of 1-mark each, while question numbers 26 to 55 are of 2-mark each.
4. Depending upon the GATE paper, there may be useful common data that may be required for
answering the questions. If the paper has such useful data, the same can be viewed by clicking on the
Useful Common Data button that appears at the top, right hand side of the screen.
5. The computer allotted to you at the examination center runs specialized software that permits only one
answer to be selected for multiple-choice questions using a mouse and to enter a suitable number for
the numerical answer type questions using the virtual keyboard and mouse.
6. Your answers shall be updated and saved on a server periodically and also at the end of the
examination. The examination will stop automatically at the end of 180 minutes.
7. In each paper a candidate can answer a total of 65 questions carrying 100 marks.
8. The question paper may consist of questions of multiple choice type (MCQ) and numerical answer
type.
9. Multiple choice type questions will have four choices against A, B, C, D, out of which only ONE is the
correct answer. The candidate has to choose the correct answer by clicking on the bubble (⃝) placed
before the choice.
10. For numerical answer type questions, each question will have a numerical answer and there will not be
any choices. For these questions, the answer should be enteredby using the virtual keyboard that
appears on the monitor and the mouse.
11. All questions that are not attempted will result in zero marks. However, wrong answers for multiple
choice type questions (MCQ) will result in NEGATIVE marks. For all MCQ questions a wrong
answer will result in deduction of⅓ marks for a 1-mark question and ⅔ marks for a 2-mark question.
12. There is NO NEGATIVE MARKING for questions of NUMERICAL ANSWER TYPE.
13. Non-programmable type Calculator is allowed. Charts, graph sheets, and mathematical tables are NOT
allowed in the Examination Hall. You must use the Scribble pad provided to you at the examination
centre for all your rough work. The Scribble Pad has to be returned at the end of the examination.
Declaration by the candidate:
“I have read and understood all the above instructions. I have also read and understood clearly the
instructions given on the admit card and shall follow the same. I also understand that in case I am found to
violate any of these instructions, my candidature is liable to be cancelled. I also confirm that at the start of
the examination all the computer hardware allotted to me are in proper working condition”.
Text of page 43
GATE 2014 SET- 5 General Aptitude -GA
Q. 1 – Q. 5 carry one mark each.
Q.1 “India is a country of rich heritage and cultural diversity.”
Which one of the following facts best supports the claim made in the above sentence?
(A) India is a union of 28 states and 7 union territories.
(B) India has a population of over 1.1 billion.
(C) India is home to 22 official languages and thousands of dialects.
(D) The Indian cricket team draws players from over ten states.
Q.2 The value of one U.S. dollar is 65 Indian Rupees today, compared to 60 last year. The Indian Rupee
has ____________.
)
(A) depressed (B) depreciated (C) appreciated (D) stabilized
14
Q.3 'Advice' is ________________.
(A) a verb (B) a noun (C) an adjective (D) both a verb and a noun
20
Q.4 The next term in the series 81, 54, 36, 24, … is ________
Q.5 In which of the following options will the expression P < M be definitely true?
(A) M < R > P > S (B) M > S < P < F
E (C) Q < M < F = P (D) P = A < R < M
AT
Q. 6 – Q. 10 carry two marks each.
Q.6 Find the next term in the sequence: 7G, 11K, 13M, ___
(A) 15Q (B) 17Q (C) 15P (D) 17P
(G
5
A0
G
GA 1/3
Text of page 44
GATE 2014 SET- 5 General Aptitude -GA
Q.7 The multi-level hierarchical pie chart shows the population of animals in a reserve forest. The
correct conclusions from this information are:
)
14
20
E
AT
(i) Butterflies are birds
(ii) There are more tigers in this forest than red ants
(iii) All reptiles in this forest are either snakes or crocodiles
(iv) Elephants are the largest mammals in this forest
(G
(A) (i) and (ii) only (B) (i), (ii), (iii) and (iv)
(C) (i), (iii) and (iv) only (D) (i), (ii) and (iii) only
Q.8 A man can row at 8 km per hour in still water. If it takes him thrice as long to row upstream, as to
5
row downstream, then find the stream velocity in km per hour.
A0
G
GA 2/3
Text of page 45
GATE 2014 SET- 5 General Aptitude -GA
Q.9 A firm producing air purifiers sold 200 units in 2012. The following pie chart presents the share of
raw material, labour, energy, plant & machinery, and transportation costs in the total manufacturing
cost of the firm in 2012. The expenditure on labour in 2012 is Rs. 4,50,000. In 2013, the raw
material expenses increased by 30% and all other expenses increased by 20%. If the company
registered a profit of Rs. 10 lakhs in 2012, at what price (in Rs.) was each air purifier sold?
)
14
20
E
Q.10 A batch of one hundred bulbs is inspected by testing four randomly chosen bulbs. The batch is
AT
rejected if even one of the bulbs is defective. A batch typically has five defective bulbs. The
probability that the current batch is accepted is
(G
END OF THE QUESTION PAPER
5
A0
G
GA 3/3
Text of page 46
GATE 2014 SET-3 MECHANICAL – ME
Q. 1 – Q. 25 carry one mark each.
Q.1 Consider a 3×3 real symmetric matrix S such that two of its eigenvalues are 0, 0 with
respective eigenvectors , . If then equals
(A) a (B) b (C) ab (D) 0
Q.2 If a function is continuous at a point,
(A) the limit of the function may not exist at the point
(B) the function must be derivable at the point
(C) the limit of the function at the point tends to infinity
)
(D) the limit must exist at the point and the value of limit should be same as the value of the
14
function at that point
Q.3 Divergence of the vector field x 2 z iˆ + x y ˆj − y z 2 kˆ at (1, −1, 1) is
20
(A) 0 (B) 3 (C) 5 (D) 6
Q.4 A group consists of equal number of men and women. Of this group 20% of the men and 50% of
E
the women are unemployed. If a person is selected at random from this group, the probability of the
selected person being employed is _______
AT
Q.5 The definite integral d is evaluated using Trapezoidal rule with a step size of 1. The correct
(G
answer is _______
Q.6 A rotating steel shaft is supported at the ends. It is subjected to a point load at the center. The
3
maximum bending stress developed is 100 MPa. If the yield, ultimate and corrected endurance
strength of the shaft material are 300 MPa, 500 MPa and 200 MPa, respectively, then the factor of
E0
safety for the shaft is _______
M
Q.7 Two solid circular shafts of radii R1 and R2 are subjected to same torque. The maximum shear
stresses developed in the two shafts are and . If R1/ R2=2, then / is _______
Q.8 Consider a single degree-of-freedom system with viscous damping excited by a harmonic force. At
resonance, the phase angle (in degree) of the displacement with respect to the exciting force is
(A) 0 (B) 45 (C) 90 (D) 135
ME 1/12
Text of page 47
GATE 2014 SET-3 MECHANICAL – ME
Q.9 A mass m1 of 100 kg travelling with a uniform velocity of 5 m/s along a line collides with a
stationary mass m2 of 1000 kg. After the collision, both the masses travel together with the same
velocity. The coefficient of restitution is
(A) 0.6 (B) 0.1 (C) 0.01 (D) 0
Q.10 Which one of following is NOT correct?
(A) Intermediate principal stress is ignored when applying the maximum principal stress theory
(B) The maximum shear stress theory gives the most accurate results amongst all the failure
theories
(C) As per the maximum strain energy theory, failure occurs when the strain energy per unit
volume exceeds a critical value
(D) As per the maximum distortion energy theory, failure occurs when the distortion energy per
)
unit volume exceeds a critical value
14
Q.11 Gear 2 rotates at 1200 rpm in counter clockwise direction and engages with Gear 3. Gear 3 and
Gear 4 are mounted on the same shaft. Gear 5 engages with Gear 4. The numbers of teeth on Gears
20
2, 3, 4 and 5 are 20, 40, 15 and 30, respectively. The angular speed of Gear 5 is
20T 2
E
3
AT
4 5
40T 15T 30T
(G
(A) 300 rpm counterclockwise (B) 300 rpm clockwise
(C) 4800 rpm counterclockwise (D) 4800 rpm clockwise
3
Q.12 Consider a long cylindrical tube of inner and outer radii, ri and ro , respectively, length, L and
E0
thermal conductivity, k. Its inner and outer surfaces are maintained at Ti and To , respectively
( Ti > To ). Assuming one-dimensional steady state heat conduction in the radial direction, the
thermal resistance in the wall of the tube is
M
1 ⎛r ⎞ (B)
L
(A) ln⎜⎜ i ⎟⎟
2πkL ⎝ ro ⎠ 2πri k
1 ⎛r ⎞ 1 ⎛r ⎞
(C) ln⎜⎜ o ⎟⎟ (D) ln⎜⎜ o ⎟⎟
2πkL ⎝ ri ⎠ 4πkL ⎝ ri ⎠
ME 2/12
Text of page 48
GATE 2014 SET-3 MECHANICAL – ME
Q.13 Which one of the following pairs of equations describes an irreversible heat engine?
δQ δQ
(A) v∫ δ Q > 0 and v∫ T < 0 (B) v∫ δ Q < 0 and v∫ T < 0
δQ δQ
(C) v∫ δ Q > 0 and v∫ T > 0 (D) v∫ δ Q < 0 and v∫ T > 0
Q.14 Consider the turbulent flow of a fluid through a circular pipe of diameter, D. Identify the correct
pair of statements.
I. The fluid is well-mixed
II. The fluid is unmixed
III. ReD < 2300
)
IV. ReD > 2300
14
(A) I, III (B) II, IV (C) II, III (D) I, IV
Q.15 For a gas turbine power plant, identify the correct pair of statements.
20
P. Smaller in size compared to steam power plant for same power output
Q. Starts quickly compared to steam power plant
R. Works on the principle of Rankine cycle
S. Good compatibility with solid fuel
(A) P, Q (B) R, S
E (C) Q, R (D) P, S
AT
Q.16 A source at a temperature of 500 K provides 1000 kJ of heat. The temperature of environment is
27°C. The maximum useful work (in kJ) that can be obtained from the heat source is _______
(G
Q.17 A sample of moist air at a total pressure of 85 kPa has a dry bulb temperature of 30°C (saturation
vapour pressure of water = 4.24 kPa). If the air sample has a relative humidity of 65%, the absolute
humidity (in gram) of water vapour per kg of dry air is _______
3
E0
Q.18 The process utilizing mainly thermal energy for removing material is
(A) Ultrasonic Machining (B) Electrochemical Machining
M
(C) Abrasive Jet Machining (D) Laser Beam Machining
Q.19 The actual sales of a product in different months of a particular year are given below:
September October November December January February
180 280 250 190 240 ?
The forecast of the sales, using the 4-month moving average method, for the month of February
is _______
ME 3/12
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GATE 2014 SET-3 MECHANICAL – ME
Q.20 A straight turning operation is carried out using a single point cutting tool on an AISI 1020 steel
rod. The feed is 0.2 mm/rev and the depth of cut is 0.5 mm. The tool has a side cutting edge angle
of 60°. The uncut chip thickness (in mm) is _______
Q.21 A minimal spanning tree in network flow models involves
(A) all the nodes with cycle/loop allowed (B) all the nodes with cycle/loop not allowed
(C) shortest path between start and end nodes (D) all the nodes with directed arcs
Q.22 Match the casting defects (Group A) with the probable causes (Group B):
)
Group A Group B
14
P: Hot tears 1: Improper fusion of two streams of liquid metal
Q: Shrinkage 2: Low permeability of the sand mould
R: Blow holes 3: Volumetric contraction both in liquid and solid stage
S: Cold Shut 4: Differential cooling rate
20
(A) P-1, Q-3, R-2, S-4 (B) P-4, Q-3, R-2, S-1
(C) P-3, Q-4, R-2, S-1 (D) P-1, Q-2, R-4, S-3
Q.23
interaction, because
E
Cutting tool is much harder than the workpiece. Yet the tool wears out during the tool-work
AT
(A) extra hardness is imparted to the workpiece due to coolant used
(B) oxide layers on the workpiece surface impart extra hardness to it
(C) extra hardness is imparted to the workpiece due to severe rate of strain
(D) vibration is induced in the machine tool
(G
3
E0
M
ME 4/12
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GATE 2014 SET-3 MECHANICAL – ME
Q.24 The stress-strain curve for mild steel is shown in the figure given below. Choose the correct option
referring to both figure and table.
)
14
20
Point on the graph Description of the point
P 1. Upper Yield Point
Q 2. Ultimate Tensile Strength
R 3. Proportionality Limit
S 4. Elastic Limit
T 5. Lower Yield Point
U
E
6. Failure
AT
(A) P-1, Q-2, R-3, S-4, T-5, U-6
(B) P-3, Q-1, R-4, S-2, T-6, U-5
(C) P-3, Q-4, R-1, S-5, T-2, U-6
(D) P-4, Q-1, R-5, S-2, T-3, U-6
(G
Q.25 The hot tearing in a metal casting is due to
(A) high fluidity (B) high melt temperature
(C) wide range of solidification temperature (D) low coefficient of thermal expansion
3
E0
M
ME 5/12
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GATE 2014 SET-3 MECHANICAL – ME
Q. 26 – Q. 55 carry two marks each.
Q.26 An analytic function of a complex variable z = x + i y is expressed as f ( z ) = u ( x , y ) + i v ( x , y ) ,
where i = − 1 . If u ( x, y ) = x 2 − y 2 , then expression for v ( x, y ) in terms of x, y and a general
constant c would be
(A) x y + c
x2 + y2 (C) 2 x y + c
( x − y) 2
(B) +c (D) +c
2 2
Q.27 Consider two solutions and of the differential equation
0, 0, such that 0 1, 0, 0 0, 1.
)
14
The Wronskian at /2 is
20
(A) 1 (B) −1 (C) 0 (D) π/2
Q.28 A machine produces 0, 1 or 2 defective pieces in a day with associated probability of 1/6, 2/3 and
E
1/6, respectively. The mean value and the variance of the number of defective pieces produced by
the machine in a day, respectively, are
AT
(A) 1 and 1/3 (B) 1/3 and 1
(C) 1 and 4/3 (D) 1/3 and 4/3
Q.29 The real root of the equation 5 x − 2 cos x − 1 = 0 (up to two decimal accuracy) is _______
(G
Q.30 A drum brake is shown in the figure. The drum is rotating in anticlockwise direction. The
3
coefficient of friction between drum and shoe is 0.2. The dimensions shown in the figure
are in mm. The braking torque (in N.m) for the brake shoe is _______
E0
1000 N
800
480
M
100
200
Drum
ME 6/12
Text of page 52
GATE 2014 SET-3 MECHANICAL – ME
Q.31 A body of mass (M) 10 kg is initially stationary on a 45° inclined plane as shown in figure. The
coefficient of dynamic friction between the body and the plane is 0.5. The body slides down the
plane and attains a velocity of 20 m/s. The distance travelled (in meter) by the body along the plane
is _______
M
45°
)
Q.32 Consider a simply supported beam of length, 50h, with a rectangular cross-section of depth, h, and
14
width, 2h. The beam carries a vertical point load, P, at its mid-point. The ratio of the maximum
shear stress to the maximum bending stress in the beam is
(A) 0.02 (B) 0.10 (C) 0.05 (D) 0.01
20
Q.33 The damping ratio of a single degree of freedom spring-mass-damper system with mass of 1 kg,
stiffness 100 N/m and viscous damping coefficient of 25 N.s/m is _______
Q.34
E
An annular disc has a mass m, inner radius R and outer radius 2R. The disc rolls on a flat surface
without slipping. If the velocity of the center of mass is v, the kinetic energy of the disc is
AT
9 11 2 13 2 15 2
(A) mv 2 (B) mv (C) mv (D) mv
16 16 16 16
(G
Q.35 A force P is applied at a distance x from the end of the beam as shown in the figure. What would be
the value of x so that the displacement at ‘A’ is equal to zero?
3
E0
M
(A) 0.5L (B) 0.25L (C) 0.33L (D) 0.66L
ME 7/12
Text of page 53
GATE 2014 SET-3 MECHANICAL – ME
Q.36 Consider a rotating disk cam and a translating roller follower with zero offset. Which one of the
following pitch curves, parameterized by t, lying in the interval 0 to 2π, is associated with the
maximum translation of the follower during one full rotation of the cam rotating about the center
at (x, y) = (0, 0) ?
(A) x ( t ) = cos t , y ( t ) = sin t
(B) x ( t ) = cos t , y ( t ) = 2 sin t
1
(C) x ( t ) = + cos t , y ( t ) = 2sin t
2
1
(D) x ( t ) = + cos t , y ( t ) = sin t
2
)
Q.37 A four-wheel vehicle of mass 1000 kg moves uniformly in a straight line with the wheels revolving
14
at 10 rad/s. The wheels are identical, each with a radius of 0.2 m. Then a constant braking torque is
applied to all the wheels and the vehicle experiences a uniform deceleration. For the vehicle to stop
in 10 s, the braking torque (in N.m) on each wheel is _______
20
Q.38 A slider-crank mechanism with crank radius 60 mm and connecting rod length 240 mm is shown in
figure. The crank is rotating with a uniform angular speed of 10 rad/s, counter clockwise. For the
E
given configuration, the speed (in m/s) of the slider is _______
AT
240
60 90°
(G
Q.39 Consider an objective function , 3 9 and the constraints
3
8,
E0
2 4,
0, 0.
The maximum value of the objective function is _______
M
ME 8/12
Text of page 54
GATE 2014 SET-3 MECHANICAL – ME
Q.40 A mass-spring-dashpot system with mass m = 10 kg, spring constant k = 6250 N/m is excited by a
harmonic excitation of 10 cos(25t) N. At the steady state, the vibration amplitude of the mass is
40 mm. The damping coefficient (c, in N.s/m) of the dashpot is _______
F=10 cos(25t)
m
c
k
)
14
Q.41 A certain amount of an ideal gas is initially at a pressure p1 and temperature T1. First, it undergoes a
constant pressure process 1-2 such that T2 = 3T1/4. Then, it undergoes a constant volume process
2-3 such that T3 = T1/2. The ratio of the final volume to the initial volume of the ideal gas is
20
(A) 0.25 (B) 0.75 (C) 1.0 (D) 1.5
Q.42 An amount of 100 kW of heat is transferred through a wall in steady state. One side of the wall is
maintained at 127°C and the other side at 27°C. The entropy generated (in W/K) due to the heat
transfer through the wall is _______
E
AT
Q.43 A siphon is used to drain water from a large tank as shown in the figure below. Assume that the
level of water is maintained constant. Ignore frictional effect due to viscosity and losses at entry
and exit. At the exit of the siphon, the velocity of water is
(G
Q
P
3
E0
O ZQ
ZP
M
ZO
ZR R
Datum
(A) 2 ZQ ZR (B) 2 ZP ZR (C) 2 ZO ZR (D) 2 ZQ
ME 9/12
Text of page 55
GATE 2014 SET-3 MECHANICAL – ME
Q.44 Heat transfer through a composite wall is shown in figure. Both the sections of the wall have equal
thickness (l). The conductivity of one section is k and that of the other is 2k. The left face of the
wall is at 600 K and the right face is at 300 K.
600 K Ti 300 K
Heat flow
k 2k
l l
)
The interface temperature Ti (in K) of the composite wall is _______
14
Q.45 A fluid of dynamic viscosity 2 × 10−5 kg/m.s and density 1 kg/m3 flows with an average velocity of
20
1 m/s through a long duct of rectangular (25 mm × 15 mm) cross-section. Assuming laminar flow,
the pressure drop (in Pa) in the fully developed region per meter length of the duct is _______
Q.46
E
At the inlet of an axial impulse turbine rotor, the blade linear speed is 25 m/s, the magnitude of
absolute velocity is 100 m/s and the angle between them is 25°. The relative velocity and the axial
AT
component of velocity remain the same between the inlet and outlet of the blades. The blade inlet
and outlet velocity triangles are shown in the figure. Assuming no losses, the specific work (in J/kg)
is _______
(G
100 m/s 78 m/s
78 m/s 58.6 m/s
25°
3
25 m/s
E0
Q.47 A solid sphere of radius r1 = 20 mm is placed concentrically inside a hollow sphere of radius
r2 = 30 mm as shown in the figure.
M
1
2
r1
r2
The view factor F21 for radiation heat transfer is
(A) (B) (C) (D)
ME 10/12
Text of page 56
GATE 20144 SET--3 M
MECHANIC
CAL – ME
Q.48 A double-pipe
d counter-flow
w heat exchaanger transfeers heat betw
ween two waater streams.. Tube side
watter at 19 liteer/s is heatedd from 10°C to 38°C. Sh hell side watter at 25 liteer/s is enterin
ng at 46°C.
Asssume constannt propertiess of water; density
d 00 kg/m3 annd specific heeat is 4186 J/kg.K.
is 100 J The
LM
MTD (in °C) is i _______
Q.49 A diesel
d enginne has a com a cut-off takes place at 10% of the stroke.
mpression raatio of 17 and
Asssuming ratio of specific heats
h (γ) as 1.4,
1 the air-sttandard efficiiency (in perrcent) is ____
____
)
Q.50 Connsider the giiven project network, whhere numberrs along variious activitiees represent the normal
14
tim
me. The free float
f on activvity 4-6 and the
t project du
uration, resppectively, aree
2
2 5
3 3
20
1 2 5 5
3 6 7
2 4 E
4
AT
(A)) 2, 13 (B) 0, 13 (C) −2, 13 (D) 2, 12
Q.51 A manufacturer
m r can producce 12000 beaarings per daay. The manuufacturer recceived an ord
der of 8000
beaarings per daay from a cuustomer. Thee cost of hollding a beariing in stock is Rs. 0.20 per month.
(G
Settup cost per production run
r is Rs. 5000. Assuming g 300 working days in a year, the frrequency of
prooduction run should be
(A)) 4.5 days (B) 4.5 months (C) 6.8 days (D) 6.8 months
3
Q.52 A cylindrical
c blind riser wiith diameter d and heightt h, is placedd on the top of the mold cavity of a
closed type sannd mold as shown s he riser is of constant vvolume, then the rate of
in thee figure. If th
E0
soliidification inn the riser is the
t least wheen the ratio h:d
h is
M
(A)) 1:2 (B) 2:1 (C) 1:4 (D) 4:1
ME 11/122
Text of page 57
GATE 2014 SET-3 MECHANICAL – ME
Q.53 The diameter of a recessed ring was measured by using two spherical balls of diameter d2=60 mm
and d1=40 mm as shown in the figure.
)
14
20
The distance H2=35.55 mm and H1=20.55 mm. The diameter (D, in mm) of the ring gauge
is _______
Q.54
E
Which pair of following statements is correct for orthogonal cutting using a single-point cutting
tool?
AT
P. Reduction in friction angle increases cutting force
Q. Reduction in friction angle decreases cutting force
R. Reduction in friction angle increases chip thickness
S. Reduction in friction angle decreases chip thickness
(G
(A) P and R (B) P and S (C) Q and R (D) Q and S
Q.55 For spot welding of two steel sheets (base metal) each of 3 mm thickness, welding current of
3
10000 A is applied for 0.2 s. The heat dissipated to the base metal is 1000 J. Assuming that the heat
required for melting 1 mm3 volume of steel is 20 J and interfacial contact resistance between sheets
is 0.0002 Ω, the volume (in mm3) of weld nugget is _______
E0
M
END OF THE QUESTION PAPER
ME 12/12
Text of page 58
GATE 2014
Answer Keys for ME ‐ Mechanical Engineering
SESSION ‐ ϯ SESSION ‐ ϯ
Section Q. No. Section Q. No.
Key / Range Marks Key / Range Marks
GA 1 C 1 ME 24 C 1
GA 2 B 1 ME 25 C 1
GA 3 B 1 ME 26 C 2
GA 4 16 to 16 1 ME 27 A 2
GA 5 D 1 ME 28 A 2
GA 6 B 2 ME 29 0.53 to 0.56 2
GA 7 D 2 ME 30 63 to 65 2
GA 8 4 to 4 2 ME 31 56 to 59 2
GA 9 20000 to 20000 2 ME 32 D 2
GA 10 0.80 to 0.82 2 ME 33 1.24 to 1.26 2
ME 1 D 1 ME 34 C 2
ME 2 D 1 ME 35 C 2
ME 3 C 1 ME 36 C 2
ME 4 0.64 to 0.66 1 ME 37 9 to 11 2
ME 5 1.1 to 1.2 1 ME 38 0.54 to 0.68 2
ME 6 1.9 to 2.1 1 ME 39 17 to 19 2
ME 7 7.9 to 8.1 1 ME 40 9 to 11 2
ME 8 C 1 ME 41 B 2
ME 9 D 1 ME 42 80 to 85 2
ME 10 B 1 ME 43 B 2
ME 11 A 1 ME 44 399 to 401 2
ME 12 C 1 ME 45 1.7 to 2.0 2
ME 13 A 1 ME 46 3250 to 3300 2
ME 14 D 1 ME 47 B 2
ME 15 A 1 ME 48 10.8 to 11.2 2
ME 16 399 to 401 1 ME 49 58 to 62 2
ME 17 19 to 22 1 ME 50 A 2
ME 18 D 1 ME 51 C 2
ME 19 239 to 241 1 ME 52 A 2
ME 20 0.08 to 0.12 1 ME 53 92 to 94 2
ME 21 B 1 ME 54 D 2
ME 22 B 1 ME 55 140 to 160 2
ME 23 C 1
Text of page 59
SESSION - 4
Text of page 60
GATE 2014: General Instructions during Examination
1. Total duration of the GATE examination is 180 minutes.
2. The clock will be set at the server. The countdown timer at 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 need not
terminate the examination or submit your paper.
3. Any useful data required for your paper can be viewed by clicking on the Useful
Common Data button that appears on the screen.
4. Use the scribble pad provided to you for any rough work. Submit the scribble pad at
the end of the examination.
5. You are allowed to use a non-programmable type calculator, however, sharing of
calculators is not allowed.
6. The Question Palette displayed on the right side of screen will show the status of
each question using one of the following symbols:
The Marked for Review status for a question simply indicates that you would like to look at
that question again. If a question is answered, but marked for review, then the answer will
be considered for evaluation unless the status is modified by the candidate.
Navigating to a Question :
7. To answer a question, do the following:
a. Click on the question number in the Question Palette to go to that question
directly.
b. Select an answer for a multiple choice type question by clicking on the bubble
placed before the 4 choices, namely A, B, C and D. Use the virtual numeric
keypad to enter a number as answer for a numerical type question.
c. Click on Save & Next to save your answer for the current question and then go
to the next question.
d. Click on Mark for Review & Next to save your answer for the current question
and also mark it for review, and then go to the next question.
Text of page 61
Caution: Note that your answer for the current question will not be saved, if you navigate
to another question directly by clicking on a question number without saving the answer to
the previous question.
You can view all the questions by clicking on the Question Paper button. This feature is
provided, so that if you want you can just see the entire question paper at a glance.
Answering a Question :
8. Procedure for answering a multiple choice (MCQ) type question:
a. Choose one answer from the 4 options (A,B,C,D) given below the question,
click on the bubble placed before the chosen option.
b. To deselect your chosen answer, click on the bubble of the chosen option again
or click on the Clear Response button.
c. To change your chosen answer, click on the bubble of another option.
d. To save your answer, you MUST click on the Save & Next button.
9. Procedure for answering a numerical answer type question:
a. To enter a number as your answer, use the virtual numerical keypad.
b. A fraction (e.g. -0.3 or -.3) can be entered as an answer with or without '0'
before the decimal point. As many as four decimal points, e.g. 12.5435 or
0.003 or -932.6711 or 12.82 can be entered.
c. To clear your answer, click on the Clear Response button.
d. To save your answer, you MUST click on the Save & Next button
10. To mark a question for review, click on the Mark for Review & Next button. If an
answer is selected (for MCQ) or entered (for numerical answer type) for a question
that is Marked for Review, that answer will be considered in the evaluation unless
the status is modified by the candidate.
11. 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.
12. Note that ONLY Questions for which answers are saved or marked for review after
answering will be considered for evaluation.
Choosing a Section :
13. Sections in this question paper are displayed on the top bar of the screen. Questions
in a Section can be viewed by clicking on the name of that Section. The Section you
are currently viewing will be highlighted.
14. A checkbox is displayed for every optional Section, if any, in the Question Paper. To
select the optional Section for answering, click on the checkbox for that Section.
15. If the checkbox for an optional Section is not selected, the Save & Next button and
the Mark for Review & Next button will NOT be enabled for that Section. You will
Text of page 62
only be able to see questions in this Section, but you will not be able to answer
questions in the Section.
16. After clicking the Save & Next button for the last question in a Section, you will
automatically be taken to the first question of the next Section in sequence.
17. You can move the mouse cursor over the name of a Section to view the answering
status for that Section.
Changing the Optional Section :
18. After answering the chosen optional Section, partially or completely, you can change
the optional Section by selecting the checkbox for a new Section that you want to
attempt. A warning message will appear along with a table showing the number of
questions answered in each of the previously chosen optional Sections and a
checkbox against each of these Sections. Click on a checkbox against a Section that
you want to reset and then click on the RESET button. Note that RESETTING a Section
will DELETE all the answers for questions in that Section. Hence, if you think that you
may want to select this Section again later, you will have to note down your answers
for questions in that Section. If you do not want to reset the Section and want to
continue answering the previously chosen optional Section, then click on the BACK
button.
19. If you deselect the checkbox for an optional Section in the top bar, the following
warning message will appear: "Deselecting the checkbox will DELETE all the answers
for questions in this Section. Do you want to deselect this Section?” If you want to
deselect, click on the RESET button. If you do not want to deselect, click on the BACK
button.
20. You can shuffle between different Sections or change the optional Sections any
number of times.
Text of page 63
GATE 2014 Examination
ME: Mechanical Engineering
Duration: 180 minutes Maximum Marks: 100
Read the following instructions carefully.
1. To login, enter your Registration Number and password provided to you. Kindly go through the various
symbols used in the test and understand their meaning before you start the examination.
2. Once you login and after the start of the examination, you can view all the questions in the question
paper, by clicking on the View All Questions button in the screen.
3. This question paper consists of 2 sections, General Aptitude (GA) for 15 marks and the subject
specific GATE paper for 85 marks. Both these sections are compulsory.
The GA section consists of 10 questions. Question numbers 1 to 5 are of 1-mark each, while question
numbers 6 to 10 are of 2-mark each.
The subject specific GATE paper section consists of 55 questions, out of which question numbers 1 to
25 are of 1-mark each, while question numbers 26 to 55 are of 2-mark each.
4. Depending upon the GATE paper, there may be useful common data that may be required for
answering the questions. If the paper has such useful data, the same can be viewed by clicking on the
Useful Common Data button that appears at the top, right hand side of the screen.
5. The computer allotted to you at the examination center runs specialized software that permits only one
answer to be selected for multiple-choice questions using a mouse and to enter a suitable number for
the numerical answer type questions using the virtual keyboard and mouse.
6. Your answers shall be updated and saved on a server periodically and also at the end of the
examination. The examination will stop automatically at the end of 180 minutes.
7. In each paper a candidate can answer a total of 65 questions carrying 100 marks.
8. The question paper may consist of questions of multiple choice type (MCQ) and numerical answer
type.
9. Multiple choice type questions will have four choices against A, B, C, D, out of which only ONE is the
correct answer. The candidate has to choose the correct answer by clicking on the bubble (⃝) placed
before the choice.
10. For numerical answer type questions, each question will have a numerical answer and there will not be
any choices. For these questions, the answer should be enteredby using the virtual keyboard that
appears on the monitor and the mouse.
11. All questions that are not attempted will result in zero marks. However, wrong answers for multiple
choice type questions (MCQ) will result in NEGATIVE marks. For all MCQ questions a wrong
answer will result in deduction of⅓ marks for a 1-mark question and ⅔ marks for a 2-mark question.
12. There is NO NEGATIVE MARKING for questions of NUMERICAL ANSWER TYPE.
13. Non-programmable type Calculator is allowed. Charts, graph sheets, and mathematical tables are NOT
allowed in the Examination Hall. You must use the Scribble pad provided to you at the examination
centre for all your rough work. The Scribble Pad has to be returned at the end of the examination.
Declaration by the candidate:
“I have read and understood all the above instructions. I have also read and understood clearly the
instructions given on the admit card and shall follow the same. I also understand that in case I am found to
violate any of these instructions, my candidature is liable to be cancelled. I also confirm that at the start of
the examination all the computer hardware allotted to me are in proper working condition”.
Text of page 64
GATE 2014 SET- 6 General Aptitude -GA
Q. 1 – Q. 5 carry one mark each.
Q.1 Which of the following options is the closest in meaning to the word underlined in the sentence
below?
In a democracy, everybody has the freedom to disagree with the government.
(A) dissent (B) descent (C) decent (D) decadent
Q.2 After the discussion, Tom said to me, 'Please revert!'. He expects me to _________.
(A) retract (B) get back to him (C) move in reverse (D) retreat
Q.3 While receiving the award, the scientist said, "I feel vindicated". Which of the following is closest
)
in meaning to the word ‘vindicated’?
14
(A) punished (B) substantiated (C) appreciated (D) chastened
Q.4 Let ff(xx, yy) = xx nn yy mm = PP. If x is doubled and y is halved, the new value of f is
(A) 2nn−mm PP (B) 2mm −nn PP (C) 2(nn − mm)PP (D) 2(mm − nn)PP
20
Q.5 In a sequence of 12 consecutive odd numbers, the sum of the first 5 numbers is 425. What is the
sum of the last 5 numbers in the sequence?
E
Q. 6 – Q. 10 carry two marks each.
AT
Q.6 Find the next term in the sequence: 13M, 17Q, 19S, ___
(G
(A) 21W (B) 21V (C) 23W (D) 23V
Q.7 If ‘KCLFTSB’ stands for ‘best of luck’ and ‘SHSWDG’ stands for ‘good wishes’, which of the
following indicates ‘ace the exam’?
(A) MCHTX (B) MXHTC (C) XMHCT (D) XMHTC
6
Q.8 Industrial consumption of power doubled from 2000-2001 to 2010-2011. Find the annual rate of
A0
increase in percent assuming it to be uniform over the years.
(A) 5.6 (B) 7.2 (C) 10.0 (D) 12.2
G
GA 1/2
Text of page 65
GATE 2014 SET- 6 General Aptitude -GA
Q.9 A firm producing air purifiers sold 200 units in 2012. The following pie chart presents the share of
raw material, labour, energy, plant & machinery, and transportation costs in the total manufacturing
cost of the firm in 2012. The expenditure on labour in 2012 is Rs. 4,50,000. In 2013, the raw
material expenses increased by 30% and all other expenses increased by 20%. What is the
percentage increase in total cost for the company in 2013?
)
14
20
E
AT
Q.10 A five digit number is formed using the digits 1,3,5,7 and 9 without repeating any of them. What is
the sum of all such possible five digit numbers?
(A) 6666660 (B) 6666600 (C) 6666666 (D) 6666606
(G
END OF THE QUESTION PAPER
6
A0
G
GA 2/2
Text of page 66
GATE 2014 SET-4 MECHANICAL – ME
Q. 1 – Q. 25 carry one mark each.
Q.1 Which one of the following equations is a correct identity for arbitrary 3×3 real matrices P, Q and R?
(A) PP(QQ + RR) = PPPP + RRRR
(B) (PP − QQ)2 = PP2 − 2PPPP + QQ 2
(C) det (PP + QQ) = det PP + det QQ
(D) (PP + QQ)2 = PP2 + PPPP + QQQQ + QQ 2
Q.2 ( x − 1) 2 sin( x − 1)
2
∫0 ( x − 1)2 + cos( x − 1) dx is
)
The value of the integral
14
(A) 3 (B) 0 (C) −1 (D) −2
dyy
20
Q.3 The solution of the initial value problem = −2 xx yy ; yy(0) = 2 is
dxx
2 2 2 2
(A) 1 + e−xx (B) 2 e−xx (C) 1 + exx (D) 2 e xx
Q.4
E
A nationalized bank has found that the daily balance available in its savings accounts follows a
normal distribution with a mean of Rs. 500 and a standard deviation of Rs. 50. The percentage of
AT
savings account holders, who maintain an average daily balance more than Rs. 500 is _______
(G
ss
Q.5 Laplace transform of cos(ωω tt) is . The Laplace transform of e−2 tt cos(4tt) is
ss 2 + ωω 2
ss−2 ss+2
(A) (ss−2)2 + 16
(B) (ss−2)2
+ 16
ss−2 ss+2
4
(C) (ss+2)2 (D) (ss+2)2
+ 16 + 16
E0
Q.6 In a statically determinate plane truss, the number of joints (j) and the number of members (m) are
related by
(A) j = 2m – 3 (B) m = 2j + 1 (C) m = 2j – 3 (D) m = 2j − 1
M
Q.7 If the Poisson's ratio of an elastic material is 0.4, the ratio of modulus of rigidity to Young's
modulus is _______
Q.8 Which one of the following is used to convert a rotational motion into a translational motion?
(A) Bevel gears (B) Double helical gears
(C) Worm gears (D) Rack and pinion gears
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GATE 2014 SET-4 MECHANICAL – ME
Q.9 The number of independent elastic constants required to define the stress-strain relationship for an
isotropic elastic solid is _______
Q.10 A point mass is executing simple harmonic motion with an amplitude of 10 mm and frequency of
4 Hz. The maximum acceleration (m/s2) of the mass is _______
Q.11 Ball bearings are rated by a manufacturer for a life of 106 revolutions. The catalogue rating of a
particular bearing is 16 kN. If the design load is 2 kN, the life of the bearing will be pp × 106
revolutions, where pp is equal to _______
)
14
Q.12 As the temperature increases, the thermal conductivity of a gas
(A) increases (B) decreases
20
(C) remains constant (D) increases up to a certain temperature and then decreases
Q.13 A reversed Carnot cycle refrigerator maintains a temperature of −5° C. The ambient air temperature
is 35°C. The heat gained by the refrigerator at a continuous rate is 2.5 kJ/s. The power (in watt)
E
required to pump this heat out continuously is _______
AT
Q.14 A flow field which has only convective acceleration is
(A) a steady uniform flow (B) an unsteady uniform flow
(C) a steady non-uniform flow (D) an unsteady non-uniform flow
(G
Q.15 Match Group A with Group B:
Group A Group B
4
P: Biot number 1: Ratio of buoyancy to viscous force
Q: Grashof number 2: Ratio of inertia force to viscous force
E0
R: Prandtl number 3: Ratio of momentum to thermal diffusivities
S: Reynolds number 4: Ratio of internal thermal resistance to
boundary layer thermal resistance
(A) P-4, Q-1, R-3, S-2 (B) P-4, Q-3, R-1, S-2
M
(C) P-3, Q-2, R-1, S-4 (D) P-2, Q-1, R-3, S-4
Q.16 Kaplan water turbine is commonly used when the flow through its runner is
(A) axial and the head available is more than 100 m
(B) axial and the head available is less than 10 m
(C) radial and the head available is more than 100 m
(D) mixed and the head available is about 50 m
ME 2/9
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GATE 2014 SET-4 MECHANICAL – ME
Q.17 Moist air at 35°C and 100% relative humidity is entering a psychrometric device and leaving at
25°C and 100% relative humidity. The name of the device is
(A) Humidifier (B) Dehumidifier (C) Sensible heater (D) Sensible cooler
Q.18 The total number of decision variables in the objective function of an assignment problem of size
n × n (n jobs and n machines) is
(A) nn2 (B) 2nn (C) 2nn − 1 (D) nn
Q.19 Demand during lead time with associated probabilities is shown below:
)
Demand 50 70 75 80 85
Probability 0.15 0.14 0.21 0.20 0.30
14
Expected demand during lead time is _______
20
Q.20 Within the Heat Affected Zone (HAZ) in a fusion welding process, the work material undergoes
(A) microstructural changes but does not melt
(B) neither melting nor microstructural changes
E
(C) both melting and microstructural changes after solidification
AT
(D) melting and retains the original microstructure after solidification
Q.21 Two separate slab milling operations, 1 and 2, are performed with identical milling cutters. The
(G
depth of cut in operation 2 is twice that in operation 1. The other cutting parameters are identical.
The ratio of maximum uncut chip thicknesses in operations 1 and 2 is _______
4
Q.22 The principle of material removal in Electrochemical machining is
(A) Fick's law (B) Faraday's laws
E0
(C) Kirchhoff'’s laws (D) Ohm’s law
Q.23 Better surface finish is obtained with a large rake angle because
M
(A) the area of shear plane decreases resulting in the decrease in shear force and cutting force
(B) the tool becomes thinner and the cutting force is reduced
(C) less heat is accumulated in the cutting zone
(D) the friction between the chip and the tool is less
ME 3/9
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GATE 2014 SET-4 MECHANICAL – ME
Q.24 Match the heat treatment processes (Group A) and their associated effects on properties (Group B)
of medium carbon steel
Group A Group B
P: Tempering I: Strengthening and grain refinement
Q: Quenching II: Inducing toughness
R: Annealing III: Hardening
S: Normalizing IV: Softening
(A) P-III, Q-IV, R-II, S-I (B) P-II, Q-III, R-IV, S-I
(C) P-III, Q-II, R-IV, S-I (D) P-II, Q-III, R-I, S-IV
)
Q.25 In a rolling process, the maximum possible draft, defined as the difference between the initial and
14
the final thickness of the metal sheet, mainly depends on which pair of the following parameters?
P: Strain
Q: Strength of the work material
20
R: Roll diameter
S: Roll velocity
T: Coefficient of friction between roll and work
(A) Q, S (B) R, T (C) S, T (D) P, R
E
AT
Q. 26 – Q. 55 carry two marks each.
Q.26 3i
dz
If z is a complex variable, the value of ∫ z is
(G
5
(A) − 0.511−1.57i (B) − 0.511+1.57i
(C) 0.511− 1.57i (D) 0.511+1.57i
4
Q.27 2 x
∫∫e
x+ y
E0
The value of the integral dy dx is
0 0
1 1 2 1 2 1 1
2
(e − 1) (e − 1) 2 (e − e)
e −
(A) (B) (C) (D)
2 2 2 2 e
M
Q.28 The number of accidents occurring in a plant in a month follows Poisson distribution with mean
as 5.2. The probability of occurrence of less than 2 accidents in the plant during a randomly
selected month is
(A) 0.029 (B) 0.034 (C) 0.039 (D) 0.044
ME 4/9
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GATE 2014 SET-4 MECHANICAL – ME
Q.29 dx
Consider an ordinary differential equation = 4t + 4 . If x = x0 at t = 0, the increment in x
dt
calculated using Runge-Kutta fourth order multi-step method with a step size of ∆t = 0.2 is
(A) 0.22 (B) 0.44 (C) 0.66 (D) 0.88
Q.30 A shaft is subjected to pure torsional moment. The maximum shear stress developed in the shaft is
100 MPa. The yield and ultimate strengths of the shaft material in tension are 300 MPa and
450 MPa, respectively. The factor of safety using maximum distortion energy (von-Mises) theory
is _______
)
14
Q.31 A thin gas cylinder with an internal radius of 100 mm is subject to an internal pressure of 10 MPa.
The maximum permissible working stress is restricted to 100 MPa. The minimum cylinder wall
thickness (in mm) for safe design must be _______
20
Q.32 For the truss shown in the figure, the forces F1 and F2 are 9 kN and 3 kN, respectively. The
force (in kN) in the member QS is E
AT
(G
(A) 11.25 tension (B) 11.25 compression (C) 13.5 tension (D) 13.5 compression
4
Q.33 It is desired to avoid interference in a pair of spur gears having a 20° pressure angle. With increase
E0
in pinion to gear speed ratio, the minimum number of teeth on the pinion
(A) increases (B) decreases
(C) first increases and then decreases (D) remains unchanged
M
ME 5/9
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GATE 2014 SET-4 MECHANICAL – ME
Q.34 A uniform slender rod (8 m length and 3 kg mass) rotates in a vertical plane about a horizontal axis
1 m from its end as shown in the figure. The magnitude of the angular acceleration (in rad/s2) of the
rod at the position shown is _______
)
14
Q.35 A bolt of major diameter 12 mm is required to clamp two steel plates. Cross sectional area of the
threaded portion of the bolt is 84.3 mm2. The length of the threaded portion in grip is 30 mm, while
the length of the unthreaded portion in grip is 8 mm. Young's modulus of material is 200 GPa. The
effective stiffness (in MN/m) of the bolt in the clamped zone is _______
20
Q.36 A frame is subjected to a load P as shown in the figure. The frame has a constant flexural rigidity
E
EI. The effect of axial load is neglected. The deflection at point A due to the applied load P is
AT
L
A
(G
L
P
1 PL3 2 PL3 PL3 4 PL3
4
(A) (B) (C) (D)
3 EI 3 EI EI 3 EI
E0
Q.37 A wardrobe (mass 100 kg, height 4 m, width 2 m, depth 1 m), symmetric about the Y-Y axis, stands
on a rough level floor as shown in the figure. A force P is applied at mid-height on the wardrobe so
as to tip it about point Q without slipping. What are the minimum values of the force (in newton)
and the static coefficient of friction µ between the floor and the wardrobe, respectively?
M
Y
2m
P
4m
Q
Y
(A) 490.5 and 0.5 (B) 981 and 0.5
(C) 1000.5 and 0.15 (D) 1000.5 and 0.25
ME 6/9
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GATE 2014 SET-4 MECHANICAL – ME
Q.38 Torque and angular speed data over one cycle for a shaft carrying a flywheel are shown in the
figures. The moment of inertia (in kg.m2) of the flywheel is _______
Torque Angular speed
3000 20 rad/s
N-m
10 rad/s
π 3π /2 2π
π/2 θ
0
π θ
0 π/2 3π /2 2π
-1500
N-m
)
14
20
Q.39 A single degree of freedom system has a mass of 2 kg, stiffness 8 N/m and viscous damping
ratio 0.02. The dynamic magnification factor at an excitation frequency of 1.5 rad/s is _______
Q.40
E
A ladder AB of length 5 m and weight (W) 600 N is resting against a wall. Assuming frictionless
contact at the floor (B) and the wall (A), the magnitude of the force P (in newton) required to
maintain equilibrium of the ladder is _______
AT
A
2.5 m
(G
3m 2.5 m
W
P
B
4m
4
E0
Q.41 A closed system contains 10 kg of saturated liquid ammonia at 10°C. Heat addition required to
convert the entire liquid into saturated vapour at a constant pressure is 16.2 MJ. If the entropy of the
saturated liquid is 0.88 kJ/kg.K, the entropy (in kJ/kg.K) of saturated vapour is _______
M
Q.42 A plane wall has a thermal conductivity of 1.15 W/m.K. If the inner surface is at 1100°C and the
outer surface is at 350°C, then the design thickness (in meter) of the wall to maintain a steady heat
flux of 2500 W/m2 should be _______
ME 7/9
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GATE 2014 SET-4 MECHANICAL – ME
Q.43 Consider the following statements regarding streamline(s):
(i) It is a continuous line such that the tangent at any point on it shows the velocity vector
at that point
(ii) There is no flow across streamlines
dx dy dz
(iii) = = is the differential equation of a streamline, where u, v and w are
u v w
velocities in directions x, y and z, respectively
(iv) In an unsteady flow, the path of a particle is a streamline
Which one of the following combinations of the statements is true?
(A) (i), (ii), (iv) (B) (ii), (iii), (iv)
(C) (i), (iii), (iv) (D) (i), (ii), (iii)
)
14
Q.44 =
Consider a velocity field V K( y iˆ + x kˆ), where K is a constant. The vorticity, ΩZ , is
(A) − K (B) K (C) − K /2 (D) K /2
20
Q.45 Water flows through a tube of diameter 25 mm at an average velocity of 1.0 m/s. The properties of
water are ρρ = 1000 kg/m3 , μμ = 7.25 × 10−4 N.s/m2, kk = 0.625 W/m.K, Pr = 4.85. Using
NNNN = 0.023 RRRR 0.8 PPPP 0.4 , the convective heat transfer coefficient (in W/m2.K) is _______
E
AT
Q.46 Two identical metal blocks L and M (specific heat = 0.4 kJ/kg.K), each having a mass of 5 kg, are
initially at 313 K. A reversible refrigerator extracts heat from block L and rejects heat to block M
until the temperature of block L reaches 293 K. The final temperature (in K) of block M is _______
(G
Q.47 Steam with specific enthalpy (h) 3214 kJ/kg enters an adiabatic turbine operating at steady state
with a flow rate 10 kg/s. As it expands, at a point where h is 2920 kJ/kg, 1.5 kg/s is extracted for
4
heating purposes. The remaining 8.5 kg/s further expands to the turbine exit, where h = 2374 kJ/kg.
Neglecting changes in kinetic and potential energies, the net power output (in kW) of the turbine
E0
is _______
Q.48 Two infinite parallel plates are placed at a certain distance apart. An infinite radiation shield is
M
inserted between the plates without touching any of them to reduce heat exchange between the
plates. Assume that the emissivities of plates and radiation shield are equal. The ratio of the net heat
exchange between the plates with and without the shield is
(A) 1/2 (B) 1/3 (C) 1/4 (D) 1/8
Q.49 In a compression ignition engine, the inlet air pressure is 1 bar and the pressure at the end of
isentropic compression is 32.42 bar. The expansion ratio is 8. Assuming ratio of specific heats (γ)
as 1.4, the air standard efficiency (in percent) is _______
ME 8/9
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GATE 2014 SET-4 MECHANICAL – ME
Q.50 The precedence relations and duration (in days) of activities of a project network are given in the
table. The total float (in days) of activities e and f , respectively, are
Activity Predecessors Duration (days)
a - 2
b - 4
c a 2
d b 3
e c 2
f c 4
g d, e 5
)
(A) 0 and 4 (B) 1 and 4 (C) 2 and 3 (D) 3 and 1
14
Q.51 At a work station, 5 jobs arrive every minute. The mean time spent on each job in the work station
is 1/8 minute. The mean steady state number of jobs in the system is _______
20
Q.52 A GO-No GO plug gauge is to be designed for measuring a hole of nominal diameter 25 mm with a
hole tolerance of ± 0.015 mm. Considering 10% of work tolerance to be the gauge tolerance and no
E
wear condition, the dimension (in mm) of the GO plug gauge as per the unilateral tolerance
system is
AT
+0.003 +0.000 +0.03 +0.003
−0.003 −0.006 −0.03 −0.000
(A) 24.985 (B) 25.015 (C) 24.985 (D) 24.985
(G
Q.53 A cylindrical riser of 6 cm diameter and 6 cm height has to be designed for a sand casting mould
for producing a steel rectangular plate casting of 7 cm × 10 cm × 2 cm dimensions having the total
solidification time of 1.36 minute. The total solidification time (in minute) of the riser is _______
4
E0
Q.54 A cast iron block of 200 mm length is being shaped in a shaping machine with a depth of cut of
4 mm, feed of 0.25 mm/stroke and the tool principal cutting edge angle of 30°. Number of cutting
strokes per minute is 60. Using specific energy for cutting as 1.49 J/mm3, the average power
consumption (in watt) is _______
M
Q.55 A butt weld joint is developed on steel plates having yield and ultimate tensile strength of 500 MPa
and 700 MPa, respectively. The thickness of the plates is 8 mm and width is 20 mm. Improper
selection of welding parameters caused an undercut of 3 mm depth along the weld. The maximum
transverse tensile load (in kN) carrying capacity of the developed weld joint is _______
END OF THE QUESTION PAPER
ME 9/9
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GATE 2014
Answer Keys for ME ‐ Mechanical Engineering
SESSION ‐ 4 SESSION ‐ 4
Section Q. No. Section Q. No.
Key / Range Marks Key / Range Marks
GA 1 A 1 ME 24 B 1
GA 2 B 1 ME 25 B 1
GA 3 B 1 ME 26 B 2
GA 4 A 1 ME 27 B 2
GA 5 495 to 495 1 ME 28 B 2
GA 6 C 2 ME 29 D 2
GA 7 B 2 ME 30 1.7 to 1.8 2
GA 8 B 2 ME 31 9.8 to 10.6 2
GA 9 22 to 22 2 ME 32 A 2
GA 10 B 2 ME 33 A 2
ME 1 D 1 ME 34 1.9 to 2.1 2
ME 2 B 1 ME 35 460 to 470 2
ME 3 B 1 ME 36 D 2
ME 4 49 to 51 1 ME 37 A 2
ME 5 D 1 ME 38 30 to 32 2
ME 6 C 1 ME 39 2.0 to 2.4 2
ME 7 0.35 to 0.36 1 ME 40 399 to 401 2
ME 8 D 1 ME 41 6.4 to 6.7 2
ME 9 1.9 to 2.1 1 ME 42 0.33 to 0.35 2
ME 10 6.3 to 6.4 1 ME 43 D 2
ME 11 500 to 540 1 ME 44 A 2
ME 12 A 1 ME 45 4600 to 4625 2
ME 13 370 to 375 1 ME 46 333 to 335 2
ME 14 C 1 ME 47 7580 to 7582 2
ME 15 A 1 ME 48 A 2
ME 16 B 1 ME 49 59 to 61 2
ME 17 B 1 ME 50 B 2
ME 18 A 1 ME 51 1.62 to 1.70 2
ME 19 74 to 75 1 ME 52 D 2
ME 20 A 1 ME 53 2.5 to 4.5 2
ME 21 0.70 to 0.72 1 ME 54 295 to 305 2
ME 22 B 1 ME 55 68 to 72 2
ME 23 A 1
Official key not published for this paper.
Page 1 of 75
Source: GATE. Question paper published by GATE.