GATE XE 2014: Engineering Sciences
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GATE 2014: General Instructions during Examination
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GATE 2014 Examination
XE: Engineering Sciences
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 paper consists of 8sections: GA (General Aptitude), A (Engineering Mathematics), B (Fluid
Mechanics), C (Materials Science), D (Solid Mechanics), E (Thermodynamics), F (Polymer Science &
Engineering) and G (Food Technology).
Section GA (General Aptitude) and Section A (Engineering Mathematics) are compulsory.
Attempt any 2 sections out of the 6 optional Sections B through G.
There are 10 questions carrying 15 marks in the compulsory General Aptitude (GA) section.
Question numbers 1 to 5 of this section carry 1 mark each, and question numbers 6 to 10 carry 2 marks
each.
There are 11 questions carrying 15 marks in Section A(Engineering Mathematics).
Question numbers 1 to 7 of this section carry 1 mark each, and question numbers 8 to 11 carry 2 marks
each.
Each of the other sections (Sections B through G) contains 22 questions carrying 35 marks.
In each of these sections, question numbers 1 to 9 carry 1 mark each and question numbers 10 to 22
carry 2 marks each.
4. Depending upon the GATE paper, there may be useful common data that may be required for
answering the questions. If this 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.
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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.
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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
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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 is in proper working condition”.
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GATE 2014 SET- 1 General Aptitude -GA
Q. 1 – Q. 5 carry one mark each.
Q.1 A student is required to demonstrate a high level of comprehension of the subject, especially in the
social sciences.
The word closest in meaning to comprehension is
(A) understanding (B) meaning (C) concentration (D) stability
Q.2 Choose the most appropriate word from the options given below to complete the following
sentence.
One of his biggest ______ was his ability to forgive.
(A) vice (B) virtues (C) choices (D) strength
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Q.3 Rajan was not happy that Sajan decided to do the project on his own. On observing his
unhappiness, Sajan explained to Rajan that he preferred to work independently.
Which one of the statements below is logically valid and can be inferred from the above sentences?
(A) Rajan has decided to work only in a group.
(B) Rajan and Sajan were formed into a group against their wishes.
Q.4
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(C) Sajan had decided to give in to Rajan’s request to work with him.
(D) Rajan had believed that Sajan and he would be working together.
If y = 5x2 + 3, then the tangent at x = 0, y = 3
(A) passes through x = 0, y = 0 (B) has a slope of +1
(C) is parallel to the x-axis (D) has a slope of −1
Q.5 A foundry has a fixed daily cost of Rs 50,000 whenever it operates and a variable cost of Rs 800Q,
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where Q is the daily production in tonnes. What is the cost of production in Rs per tonne for a daily
production of 100 tonnes?
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Q. 6 – Q. 10 carry two marks each.
Q.6 Find the odd one in the following group: ALRVX, EPVZB, ITZDF, OYEIK
(A) ALRVX (B) EPVZB (C) ITZDF (D) OYEIK
G
Q.7 Anuj, Bhola, Chandan, Dilip, Eswar and Faisal live on different floors in a six-storeyed building
(the ground floor is numbered 1, the floor above it 2, and so on). Anuj lives on an even-numbered
floor. Bhola does not live on an odd numbered floor. Chandan does not live on any of the floors
below Faisal’s floor. Dilip does not live on floor number 2. Eswar does not live on a floor
immediately above or immediately below Bhola. Faisal lives three floors above Dilip. Which of the
following floor-person combinations is correct?
Anuj Bhola Chandan Dilip Eswar Faisal
(A) 6 2 5 1 3 4
(B) 2 6 5 1 3 4
(C) 4 2 6 3 1 5
(D) 2 4 6 1 3 5
GA 1/2
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GATE 2014 SET- 1 General Aptitude -GA
Q.8 The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral. The
ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle is twice its
smallest angle. What is the sum, in degrees, of the second largest angle of the triangle and the
largest angle of the quadrilateral?
Q.9 One percent of the people of country X are taller than 6 ft. Two percent of the people of country Y
are taller than 6 ft. There are thrice as many people in country X as in country Y. Taking both
countries together, what is the percentage of people taller than 6 ft?
(A) 3.0 (B) 2.5 (C) 1.5 (D) 1.25
Q.10 The monthly rainfall chart based on 50 years of rainfall in Agra is shown in the following figure.
Which of the following are true? (k percentile is the value such that k percent of the data fall below
that value)
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20
E
(i) On average, it rains more in July than in December
(ii) Every year, the amount of rainfall in August is more than that in January
(iii) July rainfall can be estimated with better confidence than February rainfall
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(iv) In August, there is at least 500 mm of rainfall
(A) (i) and (ii) (B) (i) and (iii)
(C) (ii) and (iii) (D) (iii) and (iv)
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END OF THE QUESTION PAPER
GA 2/2
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GATE 2014 ENGINEERING MATHEMATICS (COMPULSORY) – XE-A
A : ENGINEERING MATHEMATICS ( COMPULSORY)
Q. 1 – Q. 7 carry one mark each.
Q.1 If 1, 0, and -1 are the eigenvalues of a 3 3 matrix A, then the trace of A 2 5 A is equal to
______________.
Q.2 Which of the following is a solution of the differential equation
x 2 y ' ' xy ' y 4 sin(ln x), x 0 ?
)
(A) y 2 x sin(ln x )
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(B) y 2 x sin(ln x )
(C) y 2 ln x cos(ln x )
(D) y 2 ln x cos(ln x )
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At z 0 , the complex function f ( z ) z | z | 2
Q.3
(A) satisfies the Cauchy-Riemann equations and is differentiable
(B) satisfies the Cauchy-Riemann equations but is not differentiable.
(C) does not satisfy the Cauchy-Riemann equations but is differentiable.
E
(D) does not satisfy the Cauchy-Riemann equations and is not differentiable.
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Q.4 Ten chocolates are distributed randomly among three children standing in a row. The probability
that the first child receives exactly three chocolates is
5 211
(A)
39
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5 210
(B)
39
1
(C) 9
3
1
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(D)
3
Q.5 Let the function f : [0, 5] R be defined by
2 x 5, 0 x 1
f (x ) 2 x 2 5, 1 x 2
2 3 23
3 x 3 , 2 x 5.
The number of points where f is not differentiable in (0, 5) , is ___________.
XE-A 1/3
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GATE 2014 ENGINEERING MATHEMATICS (COMPULSORY) – XE-A
Q.6 An integrating factor of the differential equation (3 x 2 y 3e y y 3 y 2 ) dx ( x 3 y 3e y xy ) dy 0 is
1
(A)
y
1
(B) 2
y
1
(C) 3
y
(D) ln y
Q.7 If a cubic polynomial passes through the points (0, 1), (1, 0), (2, 1) and (3, 10), then it also passes
through the point
)
(A) ( 2, 11)
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(B) ( 1, 2)
(C) ( 1, 4)
(D) ( 2, 23)
Q. 8 – Q. 11 carry two marks each.
Q.8 20
Let the function f : [0, ) R be such that f ( x)
8
for x 0 and f (0) 1. Then
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x 3x 4
2
f (1) lies in the interval
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(A) [0, 1]
(B) [2, 3]
(C) [4, 5]
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(D) [6, 7]
Q.9 The perimeter of a rectangle having the largest area that can be inscribed in the ellipse
x2 y2
1 , is ________.
8 32
XE
Q.10 If the work done in moving a particle once around a circle x 2 y 2 4 under the force field
F ( x, y) (2 x ay) i (2 y ax) j is 16 , then a is equal to _________.
XE-A 2/3
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GATE 2014 ENGINEERING MATHEMATICS (COMPULSORY) – XE-A
Q.11 1 2 0 1
Let r and s be real numbers. If A 2 0 3 and b 1 , then the system of linear
r s 0 s 1
equations AX b has
(A) no solutions for s 2r .
(B) infinitely many solutions for s 2 r 2 .
(C) a unique solution for s 2r 2 .
(D) infinitely many solutions for s 2r 2 .
)
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END OF THE QUESTION PAPER
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E
AT
(G
XE
XE-A 3/3
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GATE 2014 FLUID MECHANICS – XE-B
B : FLUID MECHANICS
Q. 1 – Q. 9 carry one mark each.
Q.1 A dam with a curved shape is shown in the figure. The cross sectional area of the dam (shaded
portion) is 100 m2 and its centroid is at x = 10 m. The vertical component of the hydrostatic force,
Fz , is acting at a distance x p . The value of x p is ____ m.
z
)
Fz
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xp
40 m
20
G
O x
x
E
15 m
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Q.2 ( )
For an unsteady incompressible fluid flow, the velocity field is V = 3 x 2 + 3 t iˆ − 6 xyt ˆj , where
x , y are in meters and t is in seconds. Acceleration in m/s2 at the point x = 10 m and y = 0 , as
measured by a stationary observer is
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(A) 303 (B) 162 (C) 43 (D) 13
Q.3 For an incompressible flow, the existence of components of acceleration for different types of flow
is described in the table below.
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Type of Flow Components of Acceleration
P: Steady and uniform 1: Local exists, convective does not exist
Q: Steady and non-uniform 2: Both exist
R: Unsteady and uniform 3: Both do not exist
S: Unsteady and non-uniform 4: Local does not exist, convective exists
Which one of the following options connecting the left column with the right column is correct?
(A) P – 1; Q – 4; R – 3; S – 2
(B) P – 4; Q – 1; R – 2; S – 3
(C) P – 3; Q – 2; R – 1; S – 4
(D) P – 3; Q – 4; R – 1; S – 2
XE-B 1/8
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GATE 2014 FLUID MECHANICS – XE-B
Q.4 Velocity in a two-dimensional flow field is specified as: u = x 2 y ; v = − y 2 x . The magnitude of
the rate of angular deformation at a location ( x = 2 m and y = 1 m) is ____ s-1.
Q.5 For a plane irrotational flow, equi-potential lines and streamlines are
(A) parallel to each other. (B) at an angle of 90o to each other.
(C) at an angle of 45o to each other. (D) at an angle of 60o to each other.
)
Q.6 Flow around a Rankine half-body is represented by the superposition of
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(A) source and vortex flows. (B) source and uniform flows.
(C) vortex and uniform flows. (D) source, vortex and uniform flows.
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Q.7 It is required to carry out model studies on a boat having a characteristic length of 3.6 m and
travelling at a speed of 3 m/s. Assume the acceleration due to gravity as 10 m/s2 and neglect the
effects due to viscous and surface tension forces. The value of appropriate non-dimensional number
is ____.
E
AT
Q.8 Which one of the following velocity profiles typically represents a fully developed incompressible,
turbulent flow in a pipe?
(G
XE
(A) (B) (C) (D)
XE-B 2/8
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GATE 2014 FLUID MECHANICS – XE-B
Q.9 Consider an incompressible, laminar flow past a circular cylinder of diameter d . The flow is
uniform at the far upstream. Which one of the following figures typically represents the wake
velocity profile just downstream of the cylinder?
d d
(A) (B)
)
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d d
20
(C) (D)
E
AT
(G
XE
XE-B 3/8
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GATE 2014 FLUID MECHANICS – XE-B
Q. 10 – Q. 22 carry two marks each.
Q.10 A container of square cross-section is partially filled with a liquid of density ρ1 . The cylinder is
intended to float in another liquid of density ρ 2 as shown in the figure. The distance between
I
metacentre and centre of buoyancy is , where I and Vsub are area moment of inertia of the
Vsub
cross-section and submerged volume, respectively. Neglect the weight of the container.
)
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h
20b
Which one of the following is the correct condition for stability?
E
ρ2 b h ρ ρ2 b h ρ
(A) − 1 − 1 > 0 (B) − 1 + 1 > 0
AT
6 ρ1 h b ρ2 6 ρ1 h b ρ2
ρ2 b h ρ ρ2 b h ρ
(C) + 1 − 1 > 0 (D) + 1 + 1 > 0
6 ρ1 h b ρ2 6 ρ1 h b ρ2
(G
Q.11 In a steady state two-dimensional potential flow field due to a point source, the acceleration of a
particle at a distance r from the point source is
XE
(A) proportional to r −1 . (B) proportional to r .
(C) a constant. (D) proportional to r −3 .
Q.12 Velocity in a two-dimensional flow at time t and location ( x, y ) is described as:
V= 3t 2 iˆ + ( x − 1) ˆj . The equation for the path line of a particle passing through the point (1,0) at
t = 0 is
(A) x 4 − 4 y 3 = (B) ( x − 1) − 2 y 4 =
3
0 0
(C) ( x − 1) − 64 y 3 = (D) ( x + 1) − 16 y 3 =
4 4
0 0
XE-B 4/8
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GATE 2014 FLUID MECHANICS – XE-B
Q.13 The gravity driven flow over a hump of height h in a canal is shown in the figure. The height of
the free surface from the canal bed at upstream of the hump is H . The free surface height reduces
to H1 above the hump.
H1
H
h
Assuming the canal bed to be horizontal, the discharge per unit width is given by
)
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(A) (B)
2gg(HH − HH1 − ℎ) 2ggℎ
� 1 1 � 1 1
− −
HH12 HH 2 (HH1 + ℎ)2 HH 2
(C)
�
2gg(HH − HH1 )
1 1
20
(D)
2gg(HH − HH1 )
� 1 1
E
− −
(HH1 + ℎ)2 HH 2 HH12 HH 2
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Q.14 Steady state incompressible flow through a pipe network is shown in the figure. Inlets marked as
(1), (2) and (3) and exit marked as (4), are shown with their respective diameters. The exit flow rate
at (4) is 0.1 m3/s. A 20% increase in flow rate through (3) results in a 10% increase in flow rate
through (4). The original velocity through inlet (3) is _____ m/s.
(G
(3)
XE
(2) (4)
5 cm 10 cm
(1)
XE-B 5/8
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GATE 2014 FLUID MECHANICS – XE-B
Q.15 A reducing elbow is used to deflect water upward by 30o as shown in the figure. The mass flow rate
at the inlet is 14 kg/s. Water is entering at a gauge pressure of 200 kPa and exits to the atmosphere.
The cross-sectional area is 113 cm2 at the inlet and 7 cm2 at the exit. Density of water and
acceleration due to gravity are 1000 kg/m3 and 10 m/s2, respectively. Magnitude of x - component
of the water force on the elbow is ____ N.
)
14
Q.16 A source with a strength of k1 and a vortex with a strength of k2 are located at the origin. The
resultant velocity at a radial distance r from the origin due to the superposition of the source and
vortex is expressed as
(A)
k1 + k2
r (B)
k12 + k22
r
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(C)
k12 − k22
r
(D)
k1 − k2
r
E
Q.17 ( )
Velocity potential for an incompressible fluid flow is given as: φ= 2 x 2 + 2 y − y 2 . Assume the
value of stream function at the origin to be zero. The value of stream function at [ ( x, y ) ≡ ( 2, 2 ) ]
AT
is ____.
Q.18 The model of a conduit is scaled to 1/100 of the actual size. Seawater is used in the prototype and
(G
fresh water is used in the model. Velocity in the prototype is 0.5 m/s. Density and dynamic
viscosity of the seawater are 1025 kg/m3 and 1.07 × 10-3 kg/m-s, respectively. Density and
dynamic viscosity of fresh water are 1000 kg/m3 and 1 × 10-3 kg/m-s, respectively. Assume the
viscous forces to be dominant. The velocity to be maintained in the model to ensure dynamic
similarity is____ m/s.
XE
Q.19 A fluid is flowing through a pipe of circular cross-section. Reynolds number of the flow is 1600.
The head loss over a 45 m length of the pipe is 0.6 m. The average flow velocity of the fluid is
1 m/s and the acceleration due to gravity is 10 m/s2. The diameter of the pipe is ____ m.
XE-B 6/8
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GATE 2014 FLUID MECHANICS – XE-B
Q.20 Consider a laminar flow over a flat plate of width w . At Section 1-1, the velocity profile is uniform
as shown in the figure. The x -direction velocity profile at Section 2-2 is given by
2
u y y
= 2 − , where δ is the boundary layer thickness.
U δ δ
1 U 2 U
y u ( y) δ
1 2
x
)
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The volume flow rate through Section 2-2 is given by
1 1 2
(A) U wδ (B) U wδ (C) U w δ (D) U wδ
2 3 3
Q.21
20
A cube of weight W and side a falls at a constant speed in a medium as shown in the figure. If the
medium is air (mass density =ρρair ) let U air be the velocity of the cube. If the medium is water
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(mass density =ρρwater ) let U water be the velocity of the cube.
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a
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W
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Neglecting the buoyancy force and assuming drag coefficient to be same for both cases, the ratio of
U air
velocities, is given by
U water
ρair ρair ρ water
(A) (B) (C) (D) 1
ρ water ρ water ρair
XE-B 7/8
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GATE 2014 FLUID MECHANICS – XE-B
Q.22 Water is flowing through a venturimeter having a diameter of 0.25 m at the entrance (Station 1) and
0.125 m at the throat (Station 2) as shown in the figure. A mercury manometer measures the
piezometric head difference between Stations 1 and 2 as 1.3505 m. The loss of head between these
two stations, is 1/7 times the velocity head at the Station 2. Assume the acceleration due to gravity
to be 10 m/s2. The velocity of water at the throat is ____ m/s.
diameter 0.25 m
diameter 0.125 m
1• 2•
)
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Mercury
Manometer
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END OF THE QUESTION PAPER
(G
XE
XE-B 8/8
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GATE 2014 MATERIAL SCIENCE- XE-C
C : MATERIALS SCIENCE
Useful constants
Avogadro’s Number : 6.023 x 1023 mol-1
Boltzmann’s constant, k : 1.38 x 10-23 J.K-1
Electron Charge, e : 1.6 x 10-19 C
Electron rest mass, mo : 9.1 x 10-31 kg
Universal gas constant, R : 8.314 J.mol-1.K-1
Speed of light, c : 3 x 108 m.s-1
Planck’s constant, h : 6.63 x 10-34 J.s
1 eV = 1.6 x 10-19 J
Q. 1 – Q. 9 carry one mark each.
)
Q.1 Neoprene is rendered non-inflammable because
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(A) it has a highly cross-linked structure
(B) it has a highly linear chain structure
(C) of the presence of chlorine atom in the structure
(D) of the absence of chlorine atom in the structure
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Q.2 Nylon-6 is manufactured from
(A) caprolactum
(B) adipic acid and hexamethylene diamine
(C) maleic anhydride and hexamethylene diamine
(D) sebasic acid and hexamethylene diamine
E
Q.3 At room temperature, the typical barrier potential for silicon p-n junction in Volt (V) is
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(A) 0.7x10-23 (B) 0.07 (C) 0.70 (D) 7.0
Q.4 Quantitative measurement of the roughness of a polysilicon wafer can be performed with
(A) scanning tunneling microscopy (B) scanning electron microscopy
(C) transmission electron microscopy (D) atomic force microscopy
(G
Q.5 The temperature of the antiferromagnetic-to-paramagnetic transition is called
(A) Curie temperature (B) Curie-Weiss temperature
(C) Neel temperature (D) Debye temperature
XE
Q.6 At low injection level, a forward biased p-n junction would have
(A) no charge carriers
(B) minority carrier concentration much more than majority carrier concentration
(C) minority carrier concentration equal to majority carrier concentration
(D) minority carrier concentration much less than majority carrier concentration
Q.7 Which of the following mechanical properties of a material depend on the mobile dislocation
density in it.
(P) Young’s modulus (Q) yield strength (R) ductility (S) fracture toughness
(A) P, Q, R (B) Q, R, S (C) P, R, S (D) S, P, Q
Q.8 The equilibrium concentration of vacancies in a pure metal
(A) increases exponentially with temperature (B) decreases exponentially with temperature
(C) varies linearly with temperature (D) is independent of temperature
XE-C 1/4
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GATE 2014 MATERIAL SCIENCE- XE-C
Q.9 The materials belonging to which one of the following crystal classes would be both piezoelectric
and ferroelectric
(A) 222 (B) 4mm (C) 1� (D) 2/m
Q. 10 – Q. 22 carry two marks each.
Q.10 Polymerized isotactic polybutadiene has a molecular weight of 3 x 105 g/mol. The degree of
polymerization is _______________.
)
Q.11 A bar of Ti with Young’s modulus of 110 GPa and yield strength of 880 MPa is tested in tension. It
14
is noticed that the alloy does not exhibit any strain hardening and fails at a total strain of 0.108. The
mechanical energy that is necessary to break the material in MJ/m3 is ____________.
Q.12 A copper cup weighing 140 g contains 80 g of water at 4 °C. Specific heats of water and copper are
20
4.18 and 0.385 J/g °C, respectively. If 100 g of water that is at 90 °C is added to the cup, the final
temperature of water in °C is ______________.
Q.13 Match the reaction in Column I with its name in Column II.
L – liquid, α, β, γ – different solid solution phases
E
Column I Column II
cccccccccccccc (1) peritectic
(P) L �⎯⎯⎯⎯� α + β
AT
cccccccccccccc (2) eutectic
(Q) L + β �⎯⎯⎯⎯� γ (3) monotectic
cccccccccccccc
(R) α �⎯⎯⎯⎯� β + γ (4) eutectoid
(A) P-1, Q-4, R-3 (B) P-2, Q-1, R-4
(G
(C) P-2, Q-3, R-1 (D) P-4, Q-2, R-3
Q.14 The Young’s modulus of a unidirectional SiC fiber reinforced Ti matrix composite is 185 GPa. If
the Young’s moduli of Ti and SiC are 110 and 360 GPa respectively, the volume fraction of fibers
in the composite is _________.
XE
Q.15 Match the composite in Column I with the most suitable application in Column II.
Column I Column II
(P) Glass fibre reinforced plastic (1) Missile cone heads
(Q) SiC particle reinforced Al alloy (2) Commercial automobile chasis
(R) Carbon-carbon composite (3) Airplane wheel tyres
(S) Metal fibre reinforced rubber (4) Car piston rings
(5) High performance skate boards
(A) P-4, Q-5, R-1, S-2 (B) P-3, Q-5, R-2, S-4
(C) P-5, Q-4, R-1, S-3 (D) P-4, Q-2, R-3, S-1
XE-C 2/4
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GATE 2014 MATERIAL SCIENCE- XE-C
Q.16 Which among the following rules need to be satisfied for obtaining an isomorphous phase diagram
in a binary alloy system?
(P) The atomic size difference should be less than 15%.
(Q) Both the end components should have the same crystal structure
(R) The valency of the end components should be the same.
(S) The end components should have dissimilar electronegativities
(A) P, Q, R (B) Q, R, S (C) R, S, P (D) S, P, Q
Q.17 The energy in eV and the wavelength in µm, respectively, of the photon emitted when an electron
in a hydrogen atom falls from n = 4 to n = 2 state is
(A) 3.0, 0.413 (B) 2.55, 0.365 (C) 2.75, 0.451 (D) 2.55, 0.487
)
Q.18 The weight in kg of gallium (Ga) to be mixed with arsenic (As) for obtaining 1.0 kg of gallium
arsenide (GaAs) is ______________. (MGa = 69.72 g/mol; MAs = 74.92 g/mol)
14
Q.19 Match the material in Column I with the property in Column II
Column I Column II
20
(P) Pb(Zr,Ti)O3 (1) Shape memory alloy
(Q) Ni50Ti50 (2) Piezoelectric ceramic
(R) GaAs (3) High temperature superconductor
(S) YBa2Cu3O7 (4) Optoelectronic semiconductor
(A) P-1, Q-2, R-3, S-4 (B) P-2, Q-3, R-4, S-1
E
(C) P-4, Q-1, R-2, S-3 (D) P-2, Q-1, R-4, S-3
Q.20 Relevant portion of a binary phase diagram of elements A and B is shown below. The mass fraction
AT
of liquid phase at 1000 °C for an alloy with 15 wt.% B is ___________.
(G
XE
Q.21 The expected diffraction angle (in degrees) for the first order reflection from the (113) set of planes
for face centered cubic Pt (lattice parameter = 0.392 nm) using monochromatic radiation of
wavelength 0.1542 nm is ___________.
XE-C 3/4
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GATE 2014 MATERIAL SCIENCE- XE-C
Q.22 The diffusion coefficients of Mg in Al at 500 and 550 °C are 1.9x10-13 and 5.8x10-13 m2/s
respectively. The activation energy for diffusion of Mg in Al in kJ/mol is ___________.
END OF THE QUESTION PAPER
)
14
20
E
AT
(G
XE
XE-C 4/4
Text of page 22
GATE 2014 SOLID MECHANICS – XE-D
D: SOLID MECHANICS
Q. 1 – Q. 9 carry one mark each.
Q.1 A steel wire of diameter 5 mm is bent around a cylindrical drum of radius 0.5 m. The steel wire has
modulus of elasticity of 200 GPa. Find the bending moment in the wire in N-m.
R = 0.5 m d = 5 mm
)
14
Q.2 A compressed air tank having an inner diameter of 480 mm and a wall thickness of 8 mm is formed
20
by welding two steel hemispheres. If the allowable shear stress in the steel is 40 MPa, find the
maximum permissible pressure (in MPa) inside the tank.
Q.3 The Euler’s buckling load of a column fixed at both the ends is P. If one of the ends is made free,
E
the buckling load shall change to
(A) P/16 (B) P/8
AT
(C) P/4 (D) P/2
Q.4 A point in a body is subjected to a bi-axial state of stress, equal in magnitude but opposite in nature.
On a plane inclined at an angle 45° with respect to x-axis (passing through the point), the
(G
(A) shear and normal stresses are zero
(B) normal stress is maximum and shear stress is zero
(C) shear stress is maximum and normal stress is zero
(D) shear stress is maximum and normal stress is non-zero
XE
XE-D 1/9
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GATE 2014 SOLID MECHANICS – XE-D
Q.7 The supporting structure of a water tank is made of reinforced concrete (RC) with a tubular cross
section of inner diameter di, outer diameter do, height l, and Young’s modulus E. The mass of the
tank is m. If mass of the supporting structure is neglected, then the natural frequency of the water
tank in transverse direction is
3ππππ �dd oo4 − dd ii4 � ππππ �dd oo4 − dd ii4 �
(A) � (B) �
64ll 3 mm 8ll 3 mm
384ππππ �dd oo4 − dd ii4 � ππππ �dd oo4 − dd ii4 �
(C) ) � (D) �
360ll 3 mm 64ll 3 mm
Q.8 A mass is attached to a spring and placed horizontally in a frictionless surface. A simple pendulum
)
has been pivoted to the mass. The degree of freedom of this system is
14
X
20
l y
E
x
AT
(A) 1 (B) 2 (C) 3 (D) 4
(G
XE
XE-D 3/9
Text of page 25
GATE 2014 SOLID MECHANICS – XE-D
Q.9 Consider the following two statements
Statement 1: A body of weight W falls from a height h and strikes the ground. If the body starts
from rest, the velocity with which it strikes the ground is �2ggℎ , where g is the acceleration due to
gravity.
W
h
)
14
Statement 2: If the same body (initially at rest) slides without friction along an inclined plane PQ
(angle of inclination α) starting from an elevation h above point Q, then its velocity at point Q is
�2ggℎ
20
P
h W
E
α
AT
Q
The correct option is
(A) Both statements 1 and 2 are true
(G
(B) Statement 1 is true and 2 is false
(C) Statement 1 is false and 2 is true
(D) Both statements 1 and 2 are false
XE
XE-D 4/9
Text of page 26
GATE 2014 SOLID MECHANICS – XE-D
Q. 10 – Q. 22 carry two marks each.
Q.10 A composite bar of length ‘L’ is made of a centrally placed steel plate (50 mm wide x 10 mm thick)
with two copper plates (each 30 mm wide x 5 mm thick) connected rigidly on each side. If the
temperature of the composite bar is raised by 50°C, find the stress developed in each copper plate in
MPa.
(For Steel: Es = 2x105 MPa and αs= 12x10-6 /°C; For Copper: Ec = 1x105 MPa and αc= 17x10-6 /°C)
Copper plate 5 mm
Steel plate 10 mm
Copper plate 5 mm
)
14
L
20
Q.11 The vertical deflection at the free end of the cantilever beam as shown in figure is
100 kN
EI = flexural rigidity
2m 1m
E
(A) 1400/EI (B) 1400/3EI (C) 200/EI (D) 100/EI
AT
Q.12 A hollow shaft and a solid shaft have the same length and the same outer radius R. The inner radius
of the hollow shaft is 0.6 R. Assuming that both the shafts are made of same material and are
subjected to the same torque, find the ratio of shear stress in hollow shaft to that in solid shaft.
(G
Q.13 A beam with overhangs carries one point load acting downwards and the other upward. The
clockwise moment Pb is applied at each support. The bending moment at the midpoint of the beam
is
XE
P Pb Pb P
b L b
(A) 0 (B) PL/2 (C) PL (D) PbL
XE-D 5/9
Text of page 27
GATE 2014 SOLID MECHANICS – XE-D
Q.14 A cantilever beam of length L supports a concentrated load P at the free end. The cross section of
the beam is rectangular with constant width b and varying depth h. The depth h of this idealized
cantilever beam varies in such a way that the maximum normal stress at every cross section remains
equal to the allowable bending stress. Considering only the bending stresses, the depth hx of the
fully stressed beam at any distance x from the free end shall vary
P
L
(A) with square of x (B) with square root of x
(C) linearly with x (D) with cube of x
)
14
Q.15 A cantilever beam is subjected to following three different loading conditions:
(a) a concentrated load P at its free end,
(b) a couple Mo at its free end and
(c) both loads acting simultaneously
20
P
L
(a)
E
Mo
AT
L
(b)
P
Mo
L
(G
(c)
The flexural rigidity of the beam may be assumed as EI. The strain energy due to bending when
both loads act simultaneously
XE
(A) can be determined by applying the principle of superposition and the strain energy is
PP 2 LL3 MM 2 LL
oo
+ 2EEEE
6EEEE
(B) can be determined by applying the principle of superposition and the strain energy is
PP 2 LL2 MM LL3
oo
+ 2EEEE
6EEEE
(C) cannot be determined by applying the principle of superposition and the strain energy is
PP 2 LL3 ooMM 2 LL PPMMoo LL2
+ 2EEEE +
6EEEE 2EEEE
(D) cannot be determined by applying the principle of superposition and the strain energy is
PP 2 LL2 ooMM LL3 PPMMoo LL2
+ 2EEEE +
6EEEE 2EEEE
XE-D 6/9
Text of page 28
GATE 2014 SOLID MECHANICS – XE-D
Q.16 A tapered rod has diameter d1 at one end which reduces uniformly to a diameter d2 over the length
(L). If the modulus of elasticity of the material is E, the change in the length of the rod due to the
application of axial force (P) is
4PPPP 4PPPP PPPP 2PPPP
(A) (B) (C) (D)
ππππ dd 1 dd 2 ππππ �dd 12 −dd 22 � ππππ dd 1 dd 2 ππππ �dd 12 −dd 22 �
Q.17 For a point in a body subjected to a plane stress condition (σx= 100 MPa, σy= 50 MPa and
τxy = τyx = 25 MPa), the maximum principal stress in MPa is_____________
An isotropic body is subjected to a state of stress given by: σx= 10 MPa and τxy = τyx = −20 MPa.
)
Q.18
Assuming G = 0.4E, the volumetric strain is
14
(A) 5/E (B) 7.5/E (C) 10/E (D) 15/E
20
Q.19 A block of weight Q rests on an inclined plane and it is attached to a string which runs over a
frictionless pulley to carry a block of weight P at its other end. The coefficient of friction between
the block of weight Q and the inclined plane is µ. Consider the following cases:
Case I: weight Q starts moving down the inclined plane
Case II: weight P starts falling down
E
AT
(G
The limiting values of ratio P/Q for Case I and Case II respectively are
(A) (sin αα − μμ cos αα) and (sin αα + μμ cos αα)
(B) (μμsin αα − cos αα) and (μμsin αα + cos αα)
XE
(C) (sin αα + μμ cos αα) and (sin αα − μμ cos αα)
(D) (μμsin αα + cos αα) and μμ(sin αα − cos αα)
XE-D 7/9
Text of page 29
GATE 2014 SOLID MECHANICS – XE-D
Q.20 To unload an item from a truck a crane boom is raised with a constant angular velocity of 1 rad/s
relative to the cab and then the cab is rotated about a vertical axis with constant angular velocity of
0.5 rad/s.
Z
Boom
P
Cab 45°
O Y
)
14
X
If the length of the boom (OP) is 10 m, the velocity of the tip (P) of the boom in m/s is
20
√2 √2
(A) 5 �−2ii� − jĵ + 2kk� � (B) 5 �−ii� − 2jĵ + kk� �
5 5
(C) �−2ii� − jĵ + 2kk� � (D) �−ii� − 2 jĵ + 2kk� �
√2 √2
E
Q.21 A block of mass 5 kg moves up on a smooth inclined plane with a velocity of 10 m/s in the
AT
direction shown. A bullet of mass 60 g travelling at 500 m/s strikes the block centrally and gets
embedded in it. The velocity of the block and embedded bullet in m/s immediately after the impact
is
(G
y 10 m/s
30°
x
XE
500 m/s
(A) 12.54 at 30° (B) 13.84 at 51.78° (C) 13.84 at 30° (D) 15.62 at 51.78°
XE-D 8/9
Text of page 30
GATE 2014 SOLID MECHANICS – XE-D
Q.22 A balloon with ballast (weight) inside it has a gross weight of 500 N. It is falling vertically with a
constant acceleration of 2 m/s2. If air resistance is negligible, find the weight of ballast (in N) that
must be thrown out in order to give the balloon an upward acceleration of 2 m/s2. (Acceleration due
to gravity, g = 9.81 m/s2)
)
14
500 N
20
E
END OF THE QUESTION PAPER
AT
(G
XE
XE-D 9/9
Text of page 31
GATE 2014 THERMODYNAMICS – XE-E
E : THERMODYNAMICS
Notations used:
P-pressure, V-volume, T-temperature, S-entropy, H-enthalpy, U-internal energy, cp-specific heat at constant
pressure, cv-specific heat at constant volume; specific properties are designated by lower case symbols.
Subscripts: R-reduced, C-critical, f-saturated liquid, g-saturated vapor,
Properties of air: cp = 1.005 kJ/(kg.K), specific heat ratio γ = 1.4, Gas constant = 0.287 kJ/(kg.K), Molecular
weight = 29 gm/mol.
Universal gas constant = 8.314 kJ/(kmol.K).
)
Q. 1 – Q. 9 carry one mark each.
14
Q.1 Entropy is a
(A) Path function (B) Point function
(C) Property independent function (D) Neither path nor point function
20
Q.2 A small container has gas at high pressure. It is placed in an evacuated space. If the container is
punctured, work done by the gas is
(A) Positive (B) Negative (C) Zero (D) ∞
Q.3 The molecular weight of a mixture is 38.4 gm/mol. The mixture is composed of methane and
E
carbon-dioxide gases. The atomic weights of the elements C, H, and O are 12, 1, and 16 gm/mol,
respectively. The mole fraction of methane (Xmethane) is ____________ and that of carbon-dioxide
(X carbon-dioxide) is _______.
AT
(A) Xmethane = 0.2; X carbon-dioxide = 0.8
(B) Xmethane = 0.8; X carbon-dioxide = 0.2
(C) Xmethane = 0.3; X carbon-dioxide = 0.7
(D) Xmethane= 0.7; X carbon-dioxide = 0.3
(G
Q.4 A system undergoes a change from state 1 to state 2. During this process, the change in the internal
energy is ∆U. The change in internal energy of the system when executing the cycle 1-2-1 is equal
to
(A) ∆U (B) 2∆U (C) Zero (D) −2∆U
XE
XE-E 1/5
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GATE 2014 THERMODYNAMICS – XE-E
Q.5 Which among the following plots represents a line joining two states with the same dew point
temperature on a standard psychrometric chart, with the dry bulb temperature on the X-axis and the
humidity ratio on the Y-axis?
(A) (B)
(C) (D)
)
14
Q.6 The efficiency of a reversible engine operating between two temperatures is 40 % . The COP of a
reversible refrigerator operating between the same temperatures is
20
(A) 1.5 (B) 2.5 (C) 0.4 (D) 3.5
Q.7 For a superheated vapor that cannot be approximated as an ideal gas, the expression determining a
small change in the specific internal energy is
∂u
(A) du = c p dT +
E
dv
∂v T
∂u
(B) du = c p dT +
AT
dP
∂P T
∂u
(C) du = cv dT + dv
∂v T
(D) du = cv dT
(G
Q.8 The minimum and maximum volumes in an air standard Otto cycle are 100 and 800 cm3. Its
thermal efficiency (%) is
(A) 56.47 (B) 94.55 (C) 54.08 (D) 87.50
XE
Q.9 At a saturation temperature Tsat, the difference between the entropy of saturated vapor and entropy
of saturated liquid can be expressed as
( )
(A) h f − hg Tsat ( )T
(B) hg − h f sat
(C) (u − u ) T
g f sat (D) (u − u ) T
f g sat
Q. 10 – Q. 22 carry two marks each.
Q.10 A gas in a closed system is compressed reversibly from an initial volume of 0.2 m3 to 0.1 m3 at a
constant pressure of 3 bar. During this process, there was a heat transfer of 50 kJ from the gas. The
change in internal energy of the gas during this process in kJ is
(A) 20 (B) −80 (C) 80 (D) −20
XE-E 2/5
Text of page 33
GATE 2014 THERMODYNAMICS – XE-E
Q.11 In a closed rigid vessel, air is initially at a pressure of 0.3 MPa and volume of 0.1 m3 at 300 K. A
stirrer supplies 100 kJ of work to the air, while 20 kJ of heat is lost to the atmosphere across the
container walls. After these processes, the temperature of air changes to _________K.
(A) 321.9 (B) 702.4 (C) 782.4 (D) 620.2
Q.12 A reversible heat engine (E) operates using three thermal reservoirs with temperatures as shown in
the following figure. If Q1=Q2, the efficiency of the engine is ___________.
Reservoir 1 Reservoir 2
)
T1 = 1200K T2 = 600 K
14
W
Q1 Q2
20
E
Q3
Reservoir 3
E
T3 = 300 K
(A) 0.25 (B) 0.125 (C) 0.625 (D) 0.75
AT
Q.13 A metal block of mass 25 kg at 300 K is immersed in an infinitely large liquid nitrogen bath
maintained at 77 K. The system comprising of the block and liquid nitrogen attains thermal
equilibrium. The average specific heat of the metal is 0.45 kJ/(kg.K). The entropy generated during
the process is ___________kJ/K.
(G
(A) 17.28 (B) 32.5 (C) 47.8 (D) −47.8
Q.14 a
For a gas obeying the equation of state given by P + v = RT , the values of the critical
v2
volume and the critical temperature are 0.004 m3/kg and 100 °C, respectively. If the value of the
XE
gas constant is 250 J/(kg.K), then the value of the constant ‘a’ is _____________ (N.m4/kg2). Note
that the critical point is the point of inflection on the critical isotherm.
(A) 124.3 (B) 0.75 (C) 186.58 (D) 248.67
XE-E 3/5
Text of page 34
GATE 2014 THERMODYNAMICS – XE-E
Q.15 A rigid closed vessel is initially filled with 2 kg of water which is a mixture of saturated liquid and
saturated vapor states at 2 bar. The vessel is placed in an oven which heats the mixture to the
critical state. Using the saturated and critical property values from the table given below, the heat
transferred from the oven to the vessel is __________kJ.
Pressure = 2 bar
3
vf (m /kg) vg (m3/kg) uf (kJ/kg) ug (kJ/kg)
0.0010605 0.8857 504.49 2529.5
Critical pressure
vc (m3/kg) uc (kJ/kg)
0.003155 2029.6
(A) 3035.8 (B) 3040.6 (C) 3036.2 (D) 3044.9
Q.16 The equation of state for a certain gas is given by v = RT / P − C1 / T + C2 , where C1 is 50,000
)
2
∂h ∂v
14
(K2.m3)/kg and C2 is 0.8 m3/kg. The relation = v −T is known for the gas. The inversion
∂P T ∂T P
∂h
temperature, given by the condition, = 0 is _________K.
∂P T
20
(A) 500.0 (B) 433.0 (C) 353.6 (D) 250.0
Q.17 The maximum pressure and temperature in an air standard diesel cycle are 44 bar and 1600 K,
respectively. If the minimum pressure and temperature are 1 bar and 300 K, respectively, then the
cut-off ratio (the ratio of the volume at the end of the heat addition process to that at the beginning
E
of the heat addition process) is
(A) 1.000 (B) 14.920 (C) 2.809 (D) 1.809
AT
Q.18 The thermal efficiency of an air standard Brayton cycle 0.35. The pressure ratio across the turbine
is
(A) 4.516 (B) 5.232 (C) 7.535 (D) 8.234
Q.19 Steam is isentropically expanded in a turbine from 80 bar to 7 bar. At the inlet of the turbine (state
(G
1) h1 is 3246 kJ/kg and s1 is 6.52 kJ/(kg.K).
Pressure = 7 bar
hf (kJ/kg) hg (kJ/kg) sf [kJ/(kg.K)] sg [kJ/(kg.K)]
697 2763 2.0 6.7
XE
The enthalpy of the steam exiting the turbine (state 2) in kJ/kg is
(A) 2683.87 (B) 2657.17 (C) 1986.87 (D) 3354.17
XE-E 4/5
Text of page 35
GATE 2014 THERMODYNAMICS – XE-E
Q.20 A thin insulating membrane separates two tanks initially filled with nitrogen [mean cv = 21.6
J/(mol.K)] and carbon-dioxide [mean cv = 11.6 J/(mol.K)] as shown below.
Perfect
insulation
0.8 moles of N2 at 0.2 moles of CO2 at
2 bar and 350 K 1 bar and 300 K
The membrane is ruptured and the gases are allowed to mix to form a homogeneous mixture at
equilibrium. During this process there are no heat or work interactions between the tank contents
and the surroundings. The final temperature at the equilibrium state in Kelvin is
)
14
(A) 344.1 (B) 306.3 (C) 325.0 (D) 346.1
Q.21 Two moist air streams MAS1 and MAS2 are mixed adiabatically. The details of MAS1 and MAS2
are given below in the table.
20
MAS1 MAS2
h (kJ/kg of dry air) 42 80
v (m3/kg of dry air) 0.85 0.9
Flow rate (m3/min) 85 90
With pressure remaining same and with no work interactions during the mixing process, the
E
enthalpy of the mixed stream is ________________ kJ/kg of dry air.
(A) 122 (B) 61 (C) 81 (D) 108
AT
Q.22 Consider the steady flow of air through an insulated nozzle. The pressure and temperature at the
inlet are 120 kPa and 320 K, respectively. The outlet pressure is 1 bar. The inlet velocity is very
small and the air undergoes a reversible adiabatic process. The outlet velocity, in m/s, is
(A) 303.7 (B) 180.7 (C) 5.7 (D) 127.3
(G
END OF THE QUESTION PAPER
XE
XE-E 5/5
Text of page 36
GATE 2014 POLYMER SCIENCE AND ENGINEERING – XE-F
F : POLYMER SCIENCE AND ENGINEERING
Q. 1 – Q. 9 carry one mark each.
Q.1 The estimation of the molecular weight of a polymer by gel permeation chromatography (GPC) is
based on its
(A) polarity (B) size
(C) adsorption to stationary phase (D) crystallinity
Q.2 Elastomers are characterized by
(A) high modulus and high elongation at break
)
(B) high modulus and low elongation at break
14
(C) low modulus and high elongation at break
(D) low modulus and low elongation at break
Q.3 Thermodynamically, two polymers with enthalpy of mixing (∆H) and entropy of mixing (∆S) form
a miscible blend at temperature T when
20
∆H ∆H ∆H ∆H
(A) = 0.5T (B) =T (C) = 1.5T (D) = 2T
∆S ∆S ∆S ∆S
Q.4 The tensile strain of a uniformly extending plastic specimen of initial length L0 and extended length
L is
E
L L L0 L−L0
(A) 0 (B) (C) (D)
L L0 L−L0 L0
AT
Q.5 In natural rubber compounding, a peptizer is added
(A) at the beginning of the compounding cycle
(B) after the addition of filler
(C) at the end of the compounding cycle
(G
(D) after the addition of antioxidant
Q.6 A continuous annular product is produced by
(A) compression molding (B) extrusion
(C) blow molding (D) injection molding
XE
Q.7 Relate the three varieties of polyethylene in the left column with their chain structures given in the
right column.
P. HDPE 1. long as well as short branches
Q. LDPE 2. only short branches
R. LLDPE 3. no branches
(A) P-1, Q-3, R-2 (B) P-3, Q-2, R-1 (C) P-2, Q-3, R-1 (D) P-3, Q-1, R-2
Q.8 Match the following changes observed in the calorimetric analysis of a polymer sample when heat
flow (y-axis) is plotted against temperature (x-axis):
P. step increase in heat flow 1. crystallization
Q. exothermic peak 2. melting
R. endothermic peak 3. glass transition
(A) P-1, Q-2, R-3 (B) P-2, Q-1, R-3 (C) P-3, Q-1, R-2 (D) P-3, Q-2, R-1
XE-F
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GATE 2014 POLYMER SCIENCE AND ENGINEERING – XE-F
Q.9 A Bingham plastic fluid is flowing under gravity, down a vertical plate, as a film. Find the
appropriate match for the fully developed velocity profile of the fluid in the film, from among those
shown below.
(A) (B)
x x
y film air y film air
vvyy =0 vvyy =0
vvyy vvyy
)
14
(C) (D)
x x
air air
y film y film
vvyy =0 vvyy =0
vvyy vvyy
20
E
AT
Q. 10 – Q. 22 carry two marks each.
(G
Q.10 Calculate the mass percent of the crystalline phase in a polymer sample of density 975 kg/m3. The
density of amorphous phase is 866 kg/m3 and that of the crystalline phase is 996 kg/m3.
Q.11 Find the rate of initiation (molL-1s-1) of a polymerization reaction using a peroxide initiator with a
half life of 0.1 s and efficiency of 70%, if the concentration of the initiator is 0.05 molL-1.
XE
Q.12 The constitutive equation of a shear thinning polymeric fluid is given by
μ0 γ̇
σ=
1 + (γ̇ ⁄γ̇ 0 )
where σ represents shear stress (Pa), and γ̇ , the corresponding shear rate (s-1). The quantities μ0 =
20 Pas and γ̇ 0 = 10 s −1 are constants. Find the apparent viscosity of the sample (Pas) when the
applied shear rate is 40 s-1.
XE-F
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GATE 2014 POLYMER SCIENCE AND ENGINEERING – XE-F
Q.13 Identify the monomer for the polymer shown below prepared by ring opening metathesis
polymerization.
n
)
14
(A) (B)
(C)
20
(D)
E
Q.14 The most appropriate order of toughness of nylon based materials is
(A) talc filled nylon < dry nylon < wet nylon
(B) dry nylon < wet nylon < talc filled nylon
AT
(C) wet nylon < dry nylon < talc filled nylon
(D) wet nylon < talc filled nylon < dry nylon
Q.15 The shear rates involved in calendering (γ̇ cal), compression molding (γ̇ comp), extrusion (γ̇ ext), and
injection molding (γ̇ inj) processes follow the order
(G
(A) γ̇ inj < γ̇ cal < γ̇ ext < γ̇ comp (B) γ̇ comp < γ̇ ext < γ̇ cal < γ̇ inj
(C) γ̇ comp < γ̇ inj < γ̇ ext < γ̇ cal (D) γ̇ comp < γ̇ cal < γ̇ ext < γ̇ inj
XE
Q.16 The dynamic mechanical response of a thermoplastic automotive component has shown a loss
angle of 45° and storage modulus of 3500 MPa. Calculate the loss modulus (MPa) of the
component.
Q.17 Match the terms in Column A with the appropriate terms in Column B:
Column A Column B
P. processability 1. Rockwell scale
Q. moisture permeation 2. rubber modification
R. hardness 3. melt flow index
S. fracture toughening 4. Fick's law
(A) P-3; Q-4; R-2; S-1 (B) P-3; Q-4; R-1; S-2
(C) P-4; Q-3; R-1; S-2 (D) P-4; Q-3; R-2; S-1
XE-F
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GATE 2014 POLYMER SCIENCE AND ENGINEERING – XE-F
Q.18 Match the following additives for plastics with their respective functions:
Additive Function 3/4
P. dilaurylthiodipropionate 1. solid layer lubricant
Q. graphite 2. flame retardant
R. antimony trioxide 3. reinforcement
S. carbon fibre 4. antioxidant
(A) P-4; Q-1; R-2; S-3 (B) P-1; Q-4; R-2; S-3
(C) P-4; Q-1; R-3; S-2 (D) P-1; Q-4; R-3; S-2
Q.19 Match the following catalyst/initiator with the type of polymerization reaction:
)
14
Catalyst/initiator Polymerization reaction
P. butyl lithium 1. Ziegler-Natta
Q. TiCl4 + Et3Al 2. cationic
R. CuBr 3. anionic
S. H2SO4 4. atom transfer radical polymerization
20
(A) P-2; Q-1; R-4; S-3 (B) P-2; Q-4; R-1; S-3
(C) P-3; Q-1; R-4; S-2 (D) P-3; Q-4; R-1; S-2
Q.20 For AIBN (mol. wt. = 164 gmol-1) initiated free radical polymerization of methyl methacrylate
����
E
(mol. wt. = 100 gmol-1), where the termination is only by radical coupling, the M n of PMMA is
-1
found to be 4636 gmol . Calculate the degree of polymerization.
AT
Q.21 A polymer solution is made by dissolving 5 g of polymer in 1000 ml of solvent. The flow time of
the solvent and that of the polymer solution between two appropriate marks in a viscometer are 40 s
and 60 s, respectively. The reduced viscosity (in dLg-1) of the polymer solution is:
(A) 0.25 (B) 0.50 (C) 1.0 (D) 1.5
(G
Q.22 The volume resistivity of a polymeric material is 107 Ωm. Find the resistance (in MΩ) of a cube of
the material of side 1 cm. The direction of current flow is as shown in the figure below.
XE
I
END OF THE QUESTION PAPER
XE-F
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GATE 2014 POLYMER SCIENCE AND ENGINEERING – XE-F
4/4
)
14
20
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XE-F
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GATE 2014 FOOD TECHNOLOGY – XE-G
G: FOOD TECHNOLOGY
Q. 1 – Q. 9 carry one mark each.
Q.1 The systematic name of sucrose is
(A) α-D-Fructofuranosyl (1 2) β -D-Glucopyranoside
(B) α-D-Glucopyranosyl (1 2) β-D-Fructofuranoside
(C) α-D-Glucopyranosyl (2 1) β-D-Fructofuranoside
(D) α-D-Fructofuranosyl ((2 1) β-D-Glucopyranoside
)
14
Q.2 A non-hydrolyzable lipid is
(A) Lecithin (B) Arachidic acid (C) Tocopherol (D) Tristearin
20
Q.3 The respiratory quotient (RQ) for the reaction 2 C57H110O6 + 163 O2 114 CO2 + 110 H2O is
(A) 0.70 (B) 1.14 (C) 1.43 (D) 0.14
Q.4 Liver necrosis may be caused by the deficiency of
E
(A) Vitamin A (B) Vitamin D (C) Vitamin K (D) Vitamin E
AT
Q.5 Which of the following non-nutritive sweeteners contains similar calories per gram as that of
sucrose?
(A) Saccharin (B) Aspartame (C) Sucralose (D) Cyclamate
(G
Q.6 The objective of heating milk to about 65°C before homogenization is to inactivate
(A) Glucose oxidase (B) Lipases (C) Lactases (D) Invertases
Q.7 Make the correct match of the processes in Column I with the suitable materials/products in
XE
Column II
Column I Column II
1) Rendering P) Lecithin
2) Hydrogenation Q) Fullers’ earth
3) Degumming R) Lard
4) Bleaching S) Margarine
(A) 1-R, 2-P, 3-Q, 4-S (B) 1-P, 2-Q, 3-S, 4-R
(C) 1-R, 2-P, 3-S, 4-Q (D) 1-R, 2-S, 3-P, 4-Q
XE-G 1/5
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GATE 2014 FOOD TECHNOLOGY – XE-G
Q.8 A fruit juice of viscosity µ and density ρ is agitated using an impeller of diameter D at a speed of N
P D2 N ρ NN 2 DD
revolutions per minute. The terms XX = ρ N 3 D 5 , Y = µ
, Z = gg
represent three process related
numbers, where P is power imparted by impeller and g is acceleration due to gravity. Which of the
following is correct representation of these numbers?
(A) X = Power, Y= Froude, Z = Reynolds (B) X = Power, Y = Reynolds, Z = Froude
(C) X = Froude, Y= Reynolds, Z = Power (D) X = Reynolds, Y = Power, Z = Froude
Q.9 The energy required to reduce the size of a food material from a mean diameter of 12 mm to 4 mm
is 10 kJ kg-1. From Rittingers’ law, the energy needed to reduce the same material from a diameter
of 1.2 mm to 0.4 mm in kJ kg-1 is __________
)
Q. 10 – Q. 22 carry two marks each.
14
Q.10 Saccharomyces cerevisiae (mean doubling time 3.2 h) is grown in a batch fermenter with an
operating volume of 12 m3. A 2% (v/v) inoculum, which contains 5 kg cells per 100 m3 is
mixed with the substrate. The residence time in the fermenter is 24 h and the density of broth is
1010 kg m-3. The mass of S. cerevisiae obtained from the fermenter, in kg, is ________
20
Q.11 Make the correct combination of operations in Column I with the machines in Column II
Column I Column II
1) Rice milling P) Pin mill
2) Wheat milling Q) Rubber rolls
E
3) Mustard oil expelling R) Break rolls
4) Pepper grinding S) Screw press
AT
(A) 1-Q, 2-R, 3-S, 4-P (B) 1-R, 2- Q, 3-S, 4-P
(C) 1-Q, 2-P, 3-S, 4-R (D) 1-Q, 2-R, 3- P, 4- S
Q.12 The correct order for D121 values of the spores of food spoilage bacteria in aqueous medium is
(G
(A) B. stearothermophilus > C. sporogenes > C. botulinum type A > B. coagulans
(B) C. sporogenes > B. stearothermophilus > C. botulinum type A > B .coagulans
(C) C. botulinum type A > B. stearothermophilus > C. sporogenes > B. coagulans
XE
(D) B. stearothermophilus > C. botulinum type A > C. sporogenes > B. coagulans
Q.13 Make the correct combination of pigments/microorganisms in Column I with the process/ products
in Column II
Column I Column II
1) Anthocyanin P) Ropiness
2) Chlorophyll Q) Koji
3) Bacillus subtilis R) Glycosides
4) Aspergillus oryzae S) Porphyrins
(A) 1-S, 2- R, 3-P, 4-Q (B) 1-R, 2-S, 3-Q, 4- P
(C) 1-Q, 2-S, 3-P, 4-R (D) 1-R, 2-S, 3-P, 4-Q
XE-G 2/5
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GATE 2014 FOOD TECHNOLOGY – XE-G
Q.14 Make the correct combination of underlying principles in Column I with the processes in
Column II
Column I Column II
1) Carbonyl derivatives react with free amino P) Gelatinization
acids to yield aldehydes
2) Starch aggregates and forms micro-crystals Q) Strecker degradation
3) Starch granules swell and leach amylose R) Caramelization
4) Pyranose or furanose rings open up by S) Retrogradation
pyrolytic reactions to form furfural
derivatives
(A) 1-Q, 2-R, 3-P, 4- S (B) 1-Q, 2-S, 3-P, 4-R
(C) 1-R, 2-S, 3-P, 4- Q (D) 1-Q, 2-P, 3- S, 4-R
)
14
Q.15 Which one of the following statements is FASLE?
(A) The peptide bond is planar offering restricted rotation around its axis.
(B) Full range of water activity is 0 ≤ aw ≤ 1 and it has well defined unit.
20
(C) The autooxidation of lipids proceeds via free radical mechanism.
(D) The carbonyl group of sugar reacts with nucleophilic amino group of amino acids in
Amadori rearrangement.
E
Q.16 Which one of the following statements is TRUE?
(A) Pectate lyase hydrolyzes methyl ester bond of pectin.
AT
(B) α-Solanine is a non-toxic compound found in solanaceae plants.
(C) Egg proteins have lower digestibility than pea proteins.
(D) Lipoxygenase catalyses the conversion of cis, cis-1,4-pentadiene to hydroperoxides.
(G
Q.17 Fish fillet having 84% moisture (wet basis) is frozen from top using an air blast freezer maintained
at −32°C. The initial temperature of the fillet (density 1050 kg m-3) is −2°C (freezing point).
Convective heat transfer coefficient of air is 25 Wm-2 K-1, thermal conductivity of frozen fish is 1.0
Wm-1K-1 and latent heat of crystallization is 340 kJ kg-1. The freezing time, in min, for a 20 mm
thick block of fish fillet weighing 1 kg is __________
XE
Q.18 Make the correct combination of properties in Column I with their dimensions in Column II
Column I Column II
1) Dynamic viscosity P) m2 s-2 K-1
2) Thermal conductivity Q) kg m s-2
3) Specific heat R) kg m-1 s-1
4) Force S) kg m s-3 K-1
(A) 1-R, 2-S, 3-Q, 4- P (B) 1- Q, 2-S, 3-P, 4- R
(C) 1-R, 2-S, 3-P, 4-Q (D) 1- S, 2-R, 3-P, 4-Q
XE-G 3/5
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GATE 2014 FOOD TECHNOLOGY – XE-G
Q.19 The viscosity and density of a fruit juice at 21°C are 6.3 x 10-3 Pa s and 1029 kg m-3, respectively.
The juice flows at the rate of 0.12 m3 min-1 in a 2.54 cm inner diameter steel pipe. Correct
combination of the Reynolds number (NRe) and the nature of flow of juice is
(A) NRe = 1048, Laminar (B) NRe = 2056, Laminar
(C) NRe = 16375, Turbulent (D) NRe = 28656, Turbulent
Q.20 For a typical food sorption isotherm curve (Figure 1), which one of the following statements is
CORRECT ?
30
)
Equilibrium moisture content (%)
14
25 C
20
15
20
10
B
5 A
0
E
0.0 0.2 0.4 0.6 0.8 1.0
Water activity
AT
Figure 1: Food sorption isotherm curve
(A) Y-coordinate of A represents monolayer water content of food, A-B represents water
absorbed in the multilayer within the food and B-C represents free water within the
capillary network of the food.
(G
(B) Y-coordinate of B represents monolayer water content of food, A-B represents water
absorbed in the multilayer within the food and B-C represents free water within the
capillary network of the food.
(C) Y-coordinate of A represents monolayer water content of food, Y-coordinate of B
XE
represents water absorbed in the multilayer within the food and B-C represents free water
within the capillary network of the food.
(D) Y-coordinate of A represents monolayer water content of food, A-C represents water
absorbed in the multilayer within the food and Y-coordinate of C represents free water
within the capillary network of the food.
XE-G 4/5
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GATE 2014 FOOD TECHNOLOGY – XE-G
Q.21 10,000 kg milk (7% fat) is passed through a cream separator to obtain cream (40% fat) and skim
milk (0.1 % fat). The cream, thus obtained, is churned to make butter of 80.5% fat. If a loss of 0.5%
of initial milk fat occurs during the manufacturing process, the % overrun is _________________
Q.22 A 50 mm thick pack of farm fresh berries is cooled at one side from 24°C to 7°C. The relevant
properties of berries are: density 1025 kg m-3, specific heat 3.78 kJ kg-1K-1, convective heat transfer
coefficient 30 Wm-2K-1, and thermal conductivity 0.3 Wm-1 K-1. The Fourier number for a cooling
span of 30 min is ________________
)
14
END OF THE QUESTION PAPER
20
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XE
XE-G 5/5
Text of page 46
GATE 2014
Answer Keys for XE ‐ Engineering Sciences
Section Q. No. Key / Range Marks Section Q. No. Key / Range Marks
XE‐GA 1 A 1 XE‐B 17 8 to 8 2
XE‐GA 2 B 1 XE‐B 18 47.52 to 48.50 2
XE‐GA 3 D 1 XE‐B 19 0.145 to 0.155 2
XE‐GA 4 C 1 XE‐B 20 D 2
XE‐GA 5 1300 to 1300 1 XE‐B 21 C 2
XE‐GA 6 D 2 XE‐B 22 4.8 to 5.2 2
XE‐GA 7 B 2 XE‐C 1 C 1
XE‐GA 8 180 to 180 2 XE‐C 2 A 1
XE‐GA 9 D 2 XE‐C 3 C 1
XE‐GA 10 B 2 XE‐C 4 D 1
XE‐A 1 2 to 2 1 XE‐C 5 C 1
XE‐A 2 C 1 XE‐C 6 D 1
XE‐A 3 A 1 XE‐C 7 B 1
XE‐A 4 B 1 XE‐C 8 A 1
XE‐A 5 1 to 1 1 XE‐C 9 B 1
XE‐A 6 C 1 XE‐C 10 5555 to 5556 2
XE‐A 7 B 1 XE‐C 11 91 to 92 2
XE‐A 8 B 2 XE‐C 12 48 to 49 2
XE‐A 9 24 to 24 2 XE‐C 13 B 2
XE‐A 10 2 to 2 2 XE‐C 14 0.29 to 0.31 2
XE‐A 11 D 2 XE‐C 15 C 2
XE‐B 1 7 to 7 1 XE‐C 16 A 2
XE‐B 2 A 1 XE‐C 17 D 2
XE‐B 3 D 1 XE‐C 18 0.47 to 0.49 2
XE‐B 4 3 to 3 1 XE‐C 19 D 2
XE‐B 5 B 1 XE‐C 20 0.24 to 0.26 2
XE‐B 6 B 1 XE‐C 21 40 to 41 2
XE‐B 7 0.48 to 0.52 1 XE‐C 22 115 to 120 2
XE‐B 8 C 1 XE‐D 1 12.20 to 12.22 1
XE‐B 9 C 1 XE‐D 2 5.3 to 5.4 1
XE‐B 10 A 2 XE‐D 3 A 1
XE‐B 11 D 2 XE‐D 4 C 1
XE‐B 12 C 2 XE‐D 5 C 1
XE‐B 13 A 2 XE‐D 6 0 to 0 1
XE‐B 14 17.55 to 17.75 2 XE‐D 7 A 1
XE‐B 15 2033 to 2036 2 XE‐D 8 B 1
XE‐B 16 B 2 XE‐D 9 A 1
Page 1 of 2
Text of page 47
GATE 2014
Answer Keys for XE ‐ Engineering Sciences
Section Q. No. Key / Range Marks Section Q. No. Key / Range Marks
XE‐D 10 19.1 to 19.3 2 XE‐F 6 B 1
XE‐D 11 B 2 XE‐F 7 D 1
XE‐D 12 1.14 to 1.16 2 XE‐F 8 C 1
XE‐D 13 A 2 XE‐F 9 C 1
XE‐D 14 B 2 XE‐F 10 85.15 to 86.15 2
XE‐D 15 C 2 XE‐F 11 0.48 to 0.50 2
XE‐D 16 A 2 XE‐F 12 4 to 4 2
XE‐D 17 110.3 to 110.5 2 XE‐F 13 B 2
XE‐D 18 A 2 XE‐F 14 A 2
XE‐D 19 A 2 XE‐F 15 D 2
XE‐D 20 D 2 XE‐F 16 3500 to 3500 2
XE‐D 21 B 2 XE‐F 17 B 2
XE‐D 22 169.3 to 169.4 2 XE‐F 18 A 2
XE‐E 1 B 1 XE‐F 19 C 2
XE‐E 2 C 1 XE‐F 20 45 to 45 2
XE‐E 3 A 1 XE‐F 21 C 2
XE‐E 4 C 1 XE‐F 22 1000 to 1000 2
XE‐E 5 D 1 XE‐G 1 B 1
XE‐E 6 A 1 XE‐G 2 C 1
XE‐E 7 C 1 XE‐G 3 A 1
XE‐E 8 A 1 XE‐G 4 D 1
XE‐E 9 B 1 XE‐G 5 B 1
XE‐E 10 D 2 XE‐G 6 B 1
XE‐E 11 D 2 XE‐G 7 D 1
XE‐E 12 C 2 XE‐G 8 B 1
XE‐E 13 A 2 XE‐G 9 100 to 100 1
XE‐E 14 C 2 XE‐G 10 2.1 to 2.2 2
XE‐E 15 B 2 XE‐G 11 A 2
XE‐E 16 B 2 XE‐G 12 A 2
XE‐E 17 D 2 XE‐G 13 D 2
XE‐E 18 A 2 XE‐G 14 B 2
XE‐E 19 A 2 XE‐G 15 B 2
XE‐E 20 A 2 XE‐G 16 D 2
XE‐E 21 B 2 XE‐G 17 74 to 76 2
XE‐E 22 B 2 XE‐G 18 C 2
XE‐F 1 B 1 XE‐G 19 C 2
XE‐F 2 C 1 XE‐G 20 A 2
XE‐F 3 A 1 XE‐G 21 22.0 to 22.2 2
XE‐F 4 D 1 XE‐G 22 0.055 to 0.057 2
XE‐F 5 A 1
Page 2 of 2
Official key not published for this paper.
Page 1 of 47
Source: GATE. Question paper published by GATE.