Download GATE (Graduate Aptitude Test in Engineering) Last 10 Years 2020, 2019, 2018, 2017, 2016, 2015, 2014, 2013, 2012, 2011 and 2010 MT Metallurgical Engineering Question Papers With Solutions And Answer Keys
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 If I were you, I __________ that laptop. It?s much too expensive.
(A) won?t buy (B) shan?t buy
(C) wouldn?t buy (D) would buy
Q.2 He turned a deaf ear to my request.
What does the underlined phrasal verb mean?
(A) ignored (B) appreciated (C) twisted (D) returned
Q.3 Choose the most appropriate set of words from the options given below to complete the following
sentence.
_________ ___________ is a will, _________ is a way.
(A) Wear, there, their (B) Were, their, there
(C) Where, there, there (D) Where, their, their
Q.4 (x % of y) + (y % of x) is equivalent to .
(A) 2 % of xy (B) 2 % of (xy/100) (C) xy % of 100 (D) 100 % of xy
Q.5 The sum of the digits of a two digit number is 12. If the new number formed by reversing the digits
is greater than the original number by 54, find the original number.
(A) 39 (B) 57 (C) 66 (D) 93
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GATE 2016 General Aptitude ? GA Set-7
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 If I were you, I __________ that laptop. It?s much too expensive.
(A) won?t buy (B) shan?t buy
(C) wouldn?t buy (D) would buy
Q.2 He turned a deaf ear to my request.
What does the underlined phrasal verb mean?
(A) ignored (B) appreciated (C) twisted (D) returned
Q.3 Choose the most appropriate set of words from the options given below to complete the following
sentence.
_________ ___________ is a will, _________ is a way.
(A) Wear, there, their (B) Were, their, there
(C) Where, there, there (D) Where, their, their
Q.4 (x % of y) + (y % of x) is equivalent to .
(A) 2 % of xy (B) 2 % of (xy/100) (C) xy % of 100 (D) 100 % of xy
Q.5 The sum of the digits of a two digit number is 12. If the new number formed by reversing the digits
is greater than the original number by 54, find the original number.
(A) 39 (B) 57 (C) 66 (D) 93
GATE 2016 General Aptitude ? GA Set-7
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 Two finance companies, P and Q, declared fixed annual rates of interest on the amounts invested
with them. The rates of interest offered by these companies may differ from year to year. Year-wise
annual rates of interest offered by these companies are shown by the line graph provided below.
If the amounts invested in the companies, P and Q, in 2006 are in the ratio 8:9, then the amounts
received after one year as interests from companies P and Q would be in the ratio:
(A) 2:3
(B) 3:4
(C) 6:7
(D) 4:3
Q.7 Today, we consider Ashoka as a great ruler because of the copious evidence he left behind in the
form of stone carved edicts. Historians tend to correlate greatness of a king at his time with the
availability of evidence today.
Which of the following can be logically inferred from the above sentences?
(A) Emperors who do not leave significant sculpted evidence are completely forgotten.
(B) Ashoka produced stone carved edicts to ensure that later historians will respect him.
(C) Statues of kings are a reminder of their greatness.
(D) A king?s greatness, as we know him today, is interpreted by historians.
7
9
8
10
7.5
6.5
6
6.5
8
9.5
8
9
8
4
2000 2001 2002 2003 2004 2005 2006
P Q
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude ? GA Set-7
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 If I were you, I __________ that laptop. It?s much too expensive.
(A) won?t buy (B) shan?t buy
(C) wouldn?t buy (D) would buy
Q.2 He turned a deaf ear to my request.
What does the underlined phrasal verb mean?
(A) ignored (B) appreciated (C) twisted (D) returned
Q.3 Choose the most appropriate set of words from the options given below to complete the following
sentence.
_________ ___________ is a will, _________ is a way.
(A) Wear, there, their (B) Were, their, there
(C) Where, there, there (D) Where, their, their
Q.4 (x % of y) + (y % of x) is equivalent to .
(A) 2 % of xy (B) 2 % of (xy/100) (C) xy % of 100 (D) 100 % of xy
Q.5 The sum of the digits of a two digit number is 12. If the new number formed by reversing the digits
is greater than the original number by 54, find the original number.
(A) 39 (B) 57 (C) 66 (D) 93
GATE 2016 General Aptitude ? GA Set-7
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 Two finance companies, P and Q, declared fixed annual rates of interest on the amounts invested
with them. The rates of interest offered by these companies may differ from year to year. Year-wise
annual rates of interest offered by these companies are shown by the line graph provided below.
If the amounts invested in the companies, P and Q, in 2006 are in the ratio 8:9, then the amounts
received after one year as interests from companies P and Q would be in the ratio:
(A) 2:3
(B) 3:4
(C) 6:7
(D) 4:3
Q.7 Today, we consider Ashoka as a great ruler because of the copious evidence he left behind in the
form of stone carved edicts. Historians tend to correlate greatness of a king at his time with the
availability of evidence today.
Which of the following can be logically inferred from the above sentences?
(A) Emperors who do not leave significant sculpted evidence are completely forgotten.
(B) Ashoka produced stone carved edicts to ensure that later historians will respect him.
(C) Statues of kings are a reminder of their greatness.
(D) A king?s greatness, as we know him today, is interpreted by historians.
7
9
8
10
7.5
6.5
6
6.5
8
9.5
8
9
8
4
2000 2001 2002 2003 2004 2005 2006
P Q
GATE 2016 General Aptitude ? GA Set-7
3/3
Q.8 Fact 1: Humans are mammals.
Fact 2: Some humans are engineers.
Fact 3: Engineers build houses.
If the above statements are facts, which of the following can be logically inferred?
I. All mammals build houses.
II. Engineers are mammals.
III. Some humans are not engineers.
(A) II only. (B) III only.
(C) I, II and III. (D) I only.
Q.9 A square pyramid has a base perimeter x, and the slant height is half of the perimeter. What is the
lateral surface area of the pyramid?
(A) x
2
(B) 0.75 x
2
(C) 0.50 x
2
(D) 0.25 x
2
END OF THE QUESTION PAPER
Q.10 Ananth takes 6 hours and Bharath takes 4 hours to read a book. Both started reading copies of the
book at the same time. After how many hours is the number of pages to be read by Ananth, twice
that to be read by Bharath? Assume Ananth and Bharath read all the pages with constant pace.
(A) 1 (B) 2 (C) 3 (D) 4
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GATE 2016 General Aptitude ? GA Set-7
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 If I were you, I __________ that laptop. It?s much too expensive.
(A) won?t buy (B) shan?t buy
(C) wouldn?t buy (D) would buy
Q.2 He turned a deaf ear to my request.
What does the underlined phrasal verb mean?
(A) ignored (B) appreciated (C) twisted (D) returned
Q.3 Choose the most appropriate set of words from the options given below to complete the following
sentence.
_________ ___________ is a will, _________ is a way.
(A) Wear, there, their (B) Were, their, there
(C) Where, there, there (D) Where, their, their
Q.4 (x % of y) + (y % of x) is equivalent to .
(A) 2 % of xy (B) 2 % of (xy/100) (C) xy % of 100 (D) 100 % of xy
Q.5 The sum of the digits of a two digit number is 12. If the new number formed by reversing the digits
is greater than the original number by 54, find the original number.
(A) 39 (B) 57 (C) 66 (D) 93
GATE 2016 General Aptitude ? GA Set-7
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 Two finance companies, P and Q, declared fixed annual rates of interest on the amounts invested
with them. The rates of interest offered by these companies may differ from year to year. Year-wise
annual rates of interest offered by these companies are shown by the line graph provided below.
If the amounts invested in the companies, P and Q, in 2006 are in the ratio 8:9, then the amounts
received after one year as interests from companies P and Q would be in the ratio:
(A) 2:3
(B) 3:4
(C) 6:7
(D) 4:3
Q.7 Today, we consider Ashoka as a great ruler because of the copious evidence he left behind in the
form of stone carved edicts. Historians tend to correlate greatness of a king at his time with the
availability of evidence today.
Which of the following can be logically inferred from the above sentences?
(A) Emperors who do not leave significant sculpted evidence are completely forgotten.
(B) Ashoka produced stone carved edicts to ensure that later historians will respect him.
(C) Statues of kings are a reminder of their greatness.
(D) A king?s greatness, as we know him today, is interpreted by historians.
7
9
8
10
7.5
6.5
6
6.5
8
9.5
8
9
8
4
2000 2001 2002 2003 2004 2005 2006
P Q
GATE 2016 General Aptitude ? GA Set-7
3/3
Q.8 Fact 1: Humans are mammals.
Fact 2: Some humans are engineers.
Fact 3: Engineers build houses.
If the above statements are facts, which of the following can be logically inferred?
I. All mammals build houses.
II. Engineers are mammals.
III. Some humans are not engineers.
(A) II only. (B) III only.
(C) I, II and III. (D) I only.
Q.9 A square pyramid has a base perimeter x, and the slant height is half of the perimeter. What is the
lateral surface area of the pyramid?
(A) x
2
(B) 0.75 x
2
(C) 0.50 x
2
(D) 0.25 x
2
END OF THE QUESTION PAPER
Q.10 Ananth takes 6 hours and Bharath takes 4 hours to read a book. Both started reading copies of the
book at the same time. After how many hours is the number of pages to be read by Ananth, twice
that to be read by Bharath? Assume Ananth and Bharath read all the pages with constant pace.
(A) 1 (B) 2 (C) 3 (D) 4
GATE 2016 MT
MT 1/12
Useful Data:
Gas constant (R) 8.314 J.mol
-1
K
-1
Acceleration due to gravity (g) 9.81 m
2
.s
-1
Atomic weight of oxygen 16 g.mol
-1
Atomic weight of silicon 28 g.mol
-1
Atomic weight of iron 56 g.mol
-1
Q. 1 ? Q. 25 carry one mark each.
Q.1 For the transformation shown below, if one of the eigenvalues is 6, the other eigenvalue of
the matrix is ______
52
2 2
Q.2 The solution of the differential equation
is
(A) C (B)
C
(C)
(D)
[where, C, C
1
and C
2
are constants]
Q.3
If
, the divergence of is
(A)
(B)
(C) 5
(D) 0
Q.4 The first law of thermodynamics can be stated as
(A) dE = ?Q ? ?W
(B) dQ = dE ? ?W
(C) ?W = dQ + dE
(D) dW = ?Q ? ?E
[where, E, Q and W denote internal energy, heat and work, respectively]
Q.5 In a typical Ellingham diagram for the oxides, the C + O
2
= CO
2
line is nearly horizontal
because
(A) The slope of the line is equal to the enthalpy change at standard state, which is
approximately zero in this case
(B) The slope of the line is equal to the entropy change at standard state, which is
approximately zero in this case
(C) CO
2
shows non-ideal behaviour
(D) CO
2
is a gaseous oxide
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GATE 2016 General Aptitude ? GA Set-7
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 If I were you, I __________ that laptop. It?s much too expensive.
(A) won?t buy (B) shan?t buy
(C) wouldn?t buy (D) would buy
Q.2 He turned a deaf ear to my request.
What does the underlined phrasal verb mean?
(A) ignored (B) appreciated (C) twisted (D) returned
Q.3 Choose the most appropriate set of words from the options given below to complete the following
sentence.
_________ ___________ is a will, _________ is a way.
(A) Wear, there, their (B) Were, their, there
(C) Where, there, there (D) Where, their, their
Q.4 (x % of y) + (y % of x) is equivalent to .
(A) 2 % of xy (B) 2 % of (xy/100) (C) xy % of 100 (D) 100 % of xy
Q.5 The sum of the digits of a two digit number is 12. If the new number formed by reversing the digits
is greater than the original number by 54, find the original number.
(A) 39 (B) 57 (C) 66 (D) 93
GATE 2016 General Aptitude ? GA Set-7
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 Two finance companies, P and Q, declared fixed annual rates of interest on the amounts invested
with them. The rates of interest offered by these companies may differ from year to year. Year-wise
annual rates of interest offered by these companies are shown by the line graph provided below.
If the amounts invested in the companies, P and Q, in 2006 are in the ratio 8:9, then the amounts
received after one year as interests from companies P and Q would be in the ratio:
(A) 2:3
(B) 3:4
(C) 6:7
(D) 4:3
Q.7 Today, we consider Ashoka as a great ruler because of the copious evidence he left behind in the
form of stone carved edicts. Historians tend to correlate greatness of a king at his time with the
availability of evidence today.
Which of the following can be logically inferred from the above sentences?
(A) Emperors who do not leave significant sculpted evidence are completely forgotten.
(B) Ashoka produced stone carved edicts to ensure that later historians will respect him.
(C) Statues of kings are a reminder of their greatness.
(D) A king?s greatness, as we know him today, is interpreted by historians.
7
9
8
10
7.5
6.5
6
6.5
8
9.5
8
9
8
4
2000 2001 2002 2003 2004 2005 2006
P Q
GATE 2016 General Aptitude ? GA Set-7
3/3
Q.8 Fact 1: Humans are mammals.
Fact 2: Some humans are engineers.
Fact 3: Engineers build houses.
If the above statements are facts, which of the following can be logically inferred?
I. All mammals build houses.
II. Engineers are mammals.
III. Some humans are not engineers.
(A) II only. (B) III only.
(C) I, II and III. (D) I only.
Q.9 A square pyramid has a base perimeter x, and the slant height is half of the perimeter. What is the
lateral surface area of the pyramid?
(A) x
2
(B) 0.75 x
2
(C) 0.50 x
2
(D) 0.25 x
2
END OF THE QUESTION PAPER
Q.10 Ananth takes 6 hours and Bharath takes 4 hours to read a book. Both started reading copies of the
book at the same time. After how many hours is the number of pages to be read by Ananth, twice
that to be read by Bharath? Assume Ananth and Bharath read all the pages with constant pace.
(A) 1 (B) 2 (C) 3 (D) 4
GATE 2016 MT
MT 1/12
Useful Data:
Gas constant (R) 8.314 J.mol
-1
K
-1
Acceleration due to gravity (g) 9.81 m
2
.s
-1
Atomic weight of oxygen 16 g.mol
-1
Atomic weight of silicon 28 g.mol
-1
Atomic weight of iron 56 g.mol
-1
Q. 1 ? Q. 25 carry one mark each.
Q.1 For the transformation shown below, if one of the eigenvalues is 6, the other eigenvalue of
the matrix is ______
52
2 2
Q.2 The solution of the differential equation
is
(A) C (B)
C
(C)
(D)
[where, C, C
1
and C
2
are constants]
Q.3
If
, the divergence of is
(A)
(B)
(C) 5
(D) 0
Q.4 The first law of thermodynamics can be stated as
(A) dE = ?Q ? ?W
(B) dQ = dE ? ?W
(C) ?W = dQ + dE
(D) dW = ?Q ? ?E
[where, E, Q and W denote internal energy, heat and work, respectively]
Q.5 In a typical Ellingham diagram for the oxides, the C + O
2
= CO
2
line is nearly horizontal
because
(A) The slope of the line is equal to the enthalpy change at standard state, which is
approximately zero in this case
(B) The slope of the line is equal to the entropy change at standard state, which is
approximately zero in this case
(C) CO
2
shows non-ideal behaviour
(D) CO
2
is a gaseous oxide
GATE 2016 MT
MT 2/12
Q.6 Activation energy of a chemical reaction, homogeneous or heterogeneous, is graphically
estimated from a plot between
(A) k versus T (B) 1/k versus T
(C) 1/k versus ln T (D) ln k versus 1/T
[where, k is the rate constant and T is the absolute temperature]
Q.7 The passive film in stainless steel forms above the
(A) Primary passive potential
(B) Breakdown potential
(C) Trans-passive potential
(D) Pitting potential
Q.8 During the roasting of a sulfide ore of a metal M, the possible solid phases are M, MS, MO
and MSO
4
. Assuming that both SO
2
and O
2
are always present in the roaster, the solid
phases that can co-exist at thermodynamic equilibrium are
(A) M, MS, MO, MSO
4
(B) M, MO, MSO
4
(C) MS, MO, MSO
4
(D) M, MSO
4
Q.9 Match the entities in Column I with the corresponding processes in Column II.
Column I Column II
[P] Xanthate salts [1] Extraction of Al
[Q] Thiobacillus Ferrooxidans [2] Flotation
[R] Hydrocyclone [3] Classification
[S] Anode effect [4] Bacterial Leaching
(A) P-4, Q-2, R-3, S-1
(B) P-2, Q-4, R-3, S-1
(C) P-3, Q-4, R-1, S-2
(D) P-4, Q-1, R-2, S-3
Q.10 A sub-lance is used to monitor composition and temperature in
(A) BOF (B) Ladle refining furnace
(C) Continuous casting mould (D) Blast furnace
Q.11 The chemical formula of w?stite is
(A) FeS
2
(B) Fe
2
O
3
(C) Fe
3
O
4
(D) Fe
1-x
O
Q.12 The lattice parameter of face-centered cubic iron ( ?-Fe) is 0.3571 nm. The radius (in nm) of
the octahedral void in ?-Fe is ___________
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GATE 2016 General Aptitude ? GA Set-7
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 If I were you, I __________ that laptop. It?s much too expensive.
(A) won?t buy (B) shan?t buy
(C) wouldn?t buy (D) would buy
Q.2 He turned a deaf ear to my request.
What does the underlined phrasal verb mean?
(A) ignored (B) appreciated (C) twisted (D) returned
Q.3 Choose the most appropriate set of words from the options given below to complete the following
sentence.
_________ ___________ is a will, _________ is a way.
(A) Wear, there, their (B) Were, their, there
(C) Where, there, there (D) Where, their, their
Q.4 (x % of y) + (y % of x) is equivalent to .
(A) 2 % of xy (B) 2 % of (xy/100) (C) xy % of 100 (D) 100 % of xy
Q.5 The sum of the digits of a two digit number is 12. If the new number formed by reversing the digits
is greater than the original number by 54, find the original number.
(A) 39 (B) 57 (C) 66 (D) 93
GATE 2016 General Aptitude ? GA Set-7
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 Two finance companies, P and Q, declared fixed annual rates of interest on the amounts invested
with them. The rates of interest offered by these companies may differ from year to year. Year-wise
annual rates of interest offered by these companies are shown by the line graph provided below.
If the amounts invested in the companies, P and Q, in 2006 are in the ratio 8:9, then the amounts
received after one year as interests from companies P and Q would be in the ratio:
(A) 2:3
(B) 3:4
(C) 6:7
(D) 4:3
Q.7 Today, we consider Ashoka as a great ruler because of the copious evidence he left behind in the
form of stone carved edicts. Historians tend to correlate greatness of a king at his time with the
availability of evidence today.
Which of the following can be logically inferred from the above sentences?
(A) Emperors who do not leave significant sculpted evidence are completely forgotten.
(B) Ashoka produced stone carved edicts to ensure that later historians will respect him.
(C) Statues of kings are a reminder of their greatness.
(D) A king?s greatness, as we know him today, is interpreted by historians.
7
9
8
10
7.5
6.5
6
6.5
8
9.5
8
9
8
4
2000 2001 2002 2003 2004 2005 2006
P Q
GATE 2016 General Aptitude ? GA Set-7
3/3
Q.8 Fact 1: Humans are mammals.
Fact 2: Some humans are engineers.
Fact 3: Engineers build houses.
If the above statements are facts, which of the following can be logically inferred?
I. All mammals build houses.
II. Engineers are mammals.
III. Some humans are not engineers.
(A) II only. (B) III only.
(C) I, II and III. (D) I only.
Q.9 A square pyramid has a base perimeter x, and the slant height is half of the perimeter. What is the
lateral surface area of the pyramid?
(A) x
2
(B) 0.75 x
2
(C) 0.50 x
2
(D) 0.25 x
2
END OF THE QUESTION PAPER
Q.10 Ananth takes 6 hours and Bharath takes 4 hours to read a book. Both started reading copies of the
book at the same time. After how many hours is the number of pages to be read by Ananth, twice
that to be read by Bharath? Assume Ananth and Bharath read all the pages with constant pace.
(A) 1 (B) 2 (C) 3 (D) 4
GATE 2016 MT
MT 1/12
Useful Data:
Gas constant (R) 8.314 J.mol
-1
K
-1
Acceleration due to gravity (g) 9.81 m
2
.s
-1
Atomic weight of oxygen 16 g.mol
-1
Atomic weight of silicon 28 g.mol
-1
Atomic weight of iron 56 g.mol
-1
Q. 1 ? Q. 25 carry one mark each.
Q.1 For the transformation shown below, if one of the eigenvalues is 6, the other eigenvalue of
the matrix is ______
52
2 2
Q.2 The solution of the differential equation
is
(A) C (B)
C
(C)
(D)
[where, C, C
1
and C
2
are constants]
Q.3
If
, the divergence of is
(A)
(B)
(C) 5
(D) 0
Q.4 The first law of thermodynamics can be stated as
(A) dE = ?Q ? ?W
(B) dQ = dE ? ?W
(C) ?W = dQ + dE
(D) dW = ?Q ? ?E
[where, E, Q and W denote internal energy, heat and work, respectively]
Q.5 In a typical Ellingham diagram for the oxides, the C + O
2
= CO
2
line is nearly horizontal
because
(A) The slope of the line is equal to the enthalpy change at standard state, which is
approximately zero in this case
(B) The slope of the line is equal to the entropy change at standard state, which is
approximately zero in this case
(C) CO
2
shows non-ideal behaviour
(D) CO
2
is a gaseous oxide
GATE 2016 MT
MT 2/12
Q.6 Activation energy of a chemical reaction, homogeneous or heterogeneous, is graphically
estimated from a plot between
(A) k versus T (B) 1/k versus T
(C) 1/k versus ln T (D) ln k versus 1/T
[where, k is the rate constant and T is the absolute temperature]
Q.7 The passive film in stainless steel forms above the
(A) Primary passive potential
(B) Breakdown potential
(C) Trans-passive potential
(D) Pitting potential
Q.8 During the roasting of a sulfide ore of a metal M, the possible solid phases are M, MS, MO
and MSO
4
. Assuming that both SO
2
and O
2
are always present in the roaster, the solid
phases that can co-exist at thermodynamic equilibrium are
(A) M, MS, MO, MSO
4
(B) M, MO, MSO
4
(C) MS, MO, MSO
4
(D) M, MSO
4
Q.9 Match the entities in Column I with the corresponding processes in Column II.
Column I Column II
[P] Xanthate salts [1] Extraction of Al
[Q] Thiobacillus Ferrooxidans [2] Flotation
[R] Hydrocyclone [3] Classification
[S] Anode effect [4] Bacterial Leaching
(A) P-4, Q-2, R-3, S-1
(B) P-2, Q-4, R-3, S-1
(C) P-3, Q-4, R-1, S-2
(D) P-4, Q-1, R-2, S-3
Q.10 A sub-lance is used to monitor composition and temperature in
(A) BOF (B) Ladle refining furnace
(C) Continuous casting mould (D) Blast furnace
Q.11 The chemical formula of w?stite is
(A) FeS
2
(B) Fe
2
O
3
(C) Fe
3
O
4
(D) Fe
1-x
O
Q.12 The lattice parameter of face-centered cubic iron ( ?-Fe) is 0.3571 nm. The radius (in nm) of
the octahedral void in ?-Fe is ___________
GATE 2016 MT
MT 3/12
Q.13 For an ideal hexagonal-closed packed structure, the c/a ratio and packing efficiency
respectively are
(A) 1.633 and 52% (B) 1.633 and 74%
(C) 1.733 and 68% (D) 1.733 and 74%
Q.14 A schematic of X-ray diffraction pattern of a single phase cubic polycrystal is given below.
The miller indices of peak A is
(A) 210 (B) 220
(C) 222 (D) 310
Q.15 Which of the following cooling curves (shown in schematic) in an eutectoid steel will
produce 50% bainitic structure?
(A) P (B) Q (C) R (D) S
2 ?
Intensity?(a.u.)
110
200
211
A
Ms
Ac
1
time?
Temperature
Pearlite
Bainite
Martensite
Austenite
Q
S
R
P
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GATE 2016 General Aptitude ? GA Set-7
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 If I were you, I __________ that laptop. It?s much too expensive.
(A) won?t buy (B) shan?t buy
(C) wouldn?t buy (D) would buy
Q.2 He turned a deaf ear to my request.
What does the underlined phrasal verb mean?
(A) ignored (B) appreciated (C) twisted (D) returned
Q.3 Choose the most appropriate set of words from the options given below to complete the following
sentence.
_________ ___________ is a will, _________ is a way.
(A) Wear, there, their (B) Were, their, there
(C) Where, there, there (D) Where, their, their
Q.4 (x % of y) + (y % of x) is equivalent to .
(A) 2 % of xy (B) 2 % of (xy/100) (C) xy % of 100 (D) 100 % of xy
Q.5 The sum of the digits of a two digit number is 12. If the new number formed by reversing the digits
is greater than the original number by 54, find the original number.
(A) 39 (B) 57 (C) 66 (D) 93
GATE 2016 General Aptitude ? GA Set-7
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 Two finance companies, P and Q, declared fixed annual rates of interest on the amounts invested
with them. The rates of interest offered by these companies may differ from year to year. Year-wise
annual rates of interest offered by these companies are shown by the line graph provided below.
If the amounts invested in the companies, P and Q, in 2006 are in the ratio 8:9, then the amounts
received after one year as interests from companies P and Q would be in the ratio:
(A) 2:3
(B) 3:4
(C) 6:7
(D) 4:3
Q.7 Today, we consider Ashoka as a great ruler because of the copious evidence he left behind in the
form of stone carved edicts. Historians tend to correlate greatness of a king at his time with the
availability of evidence today.
Which of the following can be logically inferred from the above sentences?
(A) Emperors who do not leave significant sculpted evidence are completely forgotten.
(B) Ashoka produced stone carved edicts to ensure that later historians will respect him.
(C) Statues of kings are a reminder of their greatness.
(D) A king?s greatness, as we know him today, is interpreted by historians.
7
9
8
10
7.5
6.5
6
6.5
8
9.5
8
9
8
4
2000 2001 2002 2003 2004 2005 2006
P Q
GATE 2016 General Aptitude ? GA Set-7
3/3
Q.8 Fact 1: Humans are mammals.
Fact 2: Some humans are engineers.
Fact 3: Engineers build houses.
If the above statements are facts, which of the following can be logically inferred?
I. All mammals build houses.
II. Engineers are mammals.
III. Some humans are not engineers.
(A) II only. (B) III only.
(C) I, II and III. (D) I only.
Q.9 A square pyramid has a base perimeter x, and the slant height is half of the perimeter. What is the
lateral surface area of the pyramid?
(A) x
2
(B) 0.75 x
2
(C) 0.50 x
2
(D) 0.25 x
2
END OF THE QUESTION PAPER
Q.10 Ananth takes 6 hours and Bharath takes 4 hours to read a book. Both started reading copies of the
book at the same time. After how many hours is the number of pages to be read by Ananth, twice
that to be read by Bharath? Assume Ananth and Bharath read all the pages with constant pace.
(A) 1 (B) 2 (C) 3 (D) 4
GATE 2016 MT
MT 1/12
Useful Data:
Gas constant (R) 8.314 J.mol
-1
K
-1
Acceleration due to gravity (g) 9.81 m
2
.s
-1
Atomic weight of oxygen 16 g.mol
-1
Atomic weight of silicon 28 g.mol
-1
Atomic weight of iron 56 g.mol
-1
Q. 1 ? Q. 25 carry one mark each.
Q.1 For the transformation shown below, if one of the eigenvalues is 6, the other eigenvalue of
the matrix is ______
52
2 2
Q.2 The solution of the differential equation
is
(A) C (B)
C
(C)
(D)
[where, C, C
1
and C
2
are constants]
Q.3
If
, the divergence of is
(A)
(B)
(C) 5
(D) 0
Q.4 The first law of thermodynamics can be stated as
(A) dE = ?Q ? ?W
(B) dQ = dE ? ?W
(C) ?W = dQ + dE
(D) dW = ?Q ? ?E
[where, E, Q and W denote internal energy, heat and work, respectively]
Q.5 In a typical Ellingham diagram for the oxides, the C + O
2
= CO
2
line is nearly horizontal
because
(A) The slope of the line is equal to the enthalpy change at standard state, which is
approximately zero in this case
(B) The slope of the line is equal to the entropy change at standard state, which is
approximately zero in this case
(C) CO
2
shows non-ideal behaviour
(D) CO
2
is a gaseous oxide
GATE 2016 MT
MT 2/12
Q.6 Activation energy of a chemical reaction, homogeneous or heterogeneous, is graphically
estimated from a plot between
(A) k versus T (B) 1/k versus T
(C) 1/k versus ln T (D) ln k versus 1/T
[where, k is the rate constant and T is the absolute temperature]
Q.7 The passive film in stainless steel forms above the
(A) Primary passive potential
(B) Breakdown potential
(C) Trans-passive potential
(D) Pitting potential
Q.8 During the roasting of a sulfide ore of a metal M, the possible solid phases are M, MS, MO
and MSO
4
. Assuming that both SO
2
and O
2
are always present in the roaster, the solid
phases that can co-exist at thermodynamic equilibrium are
(A) M, MS, MO, MSO
4
(B) M, MO, MSO
4
(C) MS, MO, MSO
4
(D) M, MSO
4
Q.9 Match the entities in Column I with the corresponding processes in Column II.
Column I Column II
[P] Xanthate salts [1] Extraction of Al
[Q] Thiobacillus Ferrooxidans [2] Flotation
[R] Hydrocyclone [3] Classification
[S] Anode effect [4] Bacterial Leaching
(A) P-4, Q-2, R-3, S-1
(B) P-2, Q-4, R-3, S-1
(C) P-3, Q-4, R-1, S-2
(D) P-4, Q-1, R-2, S-3
Q.10 A sub-lance is used to monitor composition and temperature in
(A) BOF (B) Ladle refining furnace
(C) Continuous casting mould (D) Blast furnace
Q.11 The chemical formula of w?stite is
(A) FeS
2
(B) Fe
2
O
3
(C) Fe
3
O
4
(D) Fe
1-x
O
Q.12 The lattice parameter of face-centered cubic iron ( ?-Fe) is 0.3571 nm. The radius (in nm) of
the octahedral void in ?-Fe is ___________
GATE 2016 MT
MT 3/12
Q.13 For an ideal hexagonal-closed packed structure, the c/a ratio and packing efficiency
respectively are
(A) 1.633 and 52% (B) 1.633 and 74%
(C) 1.733 and 68% (D) 1.733 and 74%
Q.14 A schematic of X-ray diffraction pattern of a single phase cubic polycrystal is given below.
The miller indices of peak A is
(A) 210 (B) 220
(C) 222 (D) 310
Q.15 Which of the following cooling curves (shown in schematic) in an eutectoid steel will
produce 50% bainitic structure?
(A) P (B) Q (C) R (D) S
2 ?
Intensity?(a.u.)
110
200
211
A
Ms
Ac
1
time?
Temperature
Pearlite
Bainite
Martensite
Austenite
Q
S
R
P
GATE 2016 MT
MT 4/12
Q.16
The Burger?s vector of a dislocation in a cubic crystal (with lattice parameter a) is
11 0
and dislocation line is along [112] direction. The angle (in degrees) between the dislocation
line and its Burger?s vector is_______
Q.17 For the tensile stress-strain curve of a material shown in the schematic, the resilience (in
MPa) is _________
Q.18 A plastically deformed metal crystal at low temperature exhibits wavy slip line pattern due
to
(A) Dislocation pile-up
(B) Large number of slip systems
(C) Low stacking fault energy
(D) Dislocation climb
Q.19 Creep resistance decreases due to
(A) Small grain size
(B) Fine dispersoid size
(C) Low stacking fault energy
(D) High melting point
Q.20 The operation NOT associated with casting is
(A) Gating (B) Fettling
(C) Stack Moulding (D) Calendaring
0
20
40
60
80
100
120
140
160
180
200
0.00 0.01 0.02 0.03 0.04 0.05 0.06
Stress,?MPa
Strain
0.01
0.1
360
510
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude ? GA Set-7
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 If I were you, I __________ that laptop. It?s much too expensive.
(A) won?t buy (B) shan?t buy
(C) wouldn?t buy (D) would buy
Q.2 He turned a deaf ear to my request.
What does the underlined phrasal verb mean?
(A) ignored (B) appreciated (C) twisted (D) returned
Q.3 Choose the most appropriate set of words from the options given below to complete the following
sentence.
_________ ___________ is a will, _________ is a way.
(A) Wear, there, their (B) Were, their, there
(C) Where, there, there (D) Where, their, their
Q.4 (x % of y) + (y % of x) is equivalent to .
(A) 2 % of xy (B) 2 % of (xy/100) (C) xy % of 100 (D) 100 % of xy
Q.5 The sum of the digits of a two digit number is 12. If the new number formed by reversing the digits
is greater than the original number by 54, find the original number.
(A) 39 (B) 57 (C) 66 (D) 93
GATE 2016 General Aptitude ? GA Set-7
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 Two finance companies, P and Q, declared fixed annual rates of interest on the amounts invested
with them. The rates of interest offered by these companies may differ from year to year. Year-wise
annual rates of interest offered by these companies are shown by the line graph provided below.
If the amounts invested in the companies, P and Q, in 2006 are in the ratio 8:9, then the amounts
received after one year as interests from companies P and Q would be in the ratio:
(A) 2:3
(B) 3:4
(C) 6:7
(D) 4:3
Q.7 Today, we consider Ashoka as a great ruler because of the copious evidence he left behind in the
form of stone carved edicts. Historians tend to correlate greatness of a king at his time with the
availability of evidence today.
Which of the following can be logically inferred from the above sentences?
(A) Emperors who do not leave significant sculpted evidence are completely forgotten.
(B) Ashoka produced stone carved edicts to ensure that later historians will respect him.
(C) Statues of kings are a reminder of their greatness.
(D) A king?s greatness, as we know him today, is interpreted by historians.
7
9
8
10
7.5
6.5
6
6.5
8
9.5
8
9
8
4
2000 2001 2002 2003 2004 2005 2006
P Q
GATE 2016 General Aptitude ? GA Set-7
3/3
Q.8 Fact 1: Humans are mammals.
Fact 2: Some humans are engineers.
Fact 3: Engineers build houses.
If the above statements are facts, which of the following can be logically inferred?
I. All mammals build houses.
II. Engineers are mammals.
III. Some humans are not engineers.
(A) II only. (B) III only.
(C) I, II and III. (D) I only.
Q.9 A square pyramid has a base perimeter x, and the slant height is half of the perimeter. What is the
lateral surface area of the pyramid?
(A) x
2
(B) 0.75 x
2
(C) 0.50 x
2
(D) 0.25 x
2
END OF THE QUESTION PAPER
Q.10 Ananth takes 6 hours and Bharath takes 4 hours to read a book. Both started reading copies of the
book at the same time. After how many hours is the number of pages to be read by Ananth, twice
that to be read by Bharath? Assume Ananth and Bharath read all the pages with constant pace.
(A) 1 (B) 2 (C) 3 (D) 4
GATE 2016 MT
MT 1/12
Useful Data:
Gas constant (R) 8.314 J.mol
-1
K
-1
Acceleration due to gravity (g) 9.81 m
2
.s
-1
Atomic weight of oxygen 16 g.mol
-1
Atomic weight of silicon 28 g.mol
-1
Atomic weight of iron 56 g.mol
-1
Q. 1 ? Q. 25 carry one mark each.
Q.1 For the transformation shown below, if one of the eigenvalues is 6, the other eigenvalue of
the matrix is ______
52
2 2
Q.2 The solution of the differential equation
is
(A) C (B)
C
(C)
(D)
[where, C, C
1
and C
2
are constants]
Q.3
If
, the divergence of is
(A)
(B)
(C) 5
(D) 0
Q.4 The first law of thermodynamics can be stated as
(A) dE = ?Q ? ?W
(B) dQ = dE ? ?W
(C) ?W = dQ + dE
(D) dW = ?Q ? ?E
[where, E, Q and W denote internal energy, heat and work, respectively]
Q.5 In a typical Ellingham diagram for the oxides, the C + O
2
= CO
2
line is nearly horizontal
because
(A) The slope of the line is equal to the enthalpy change at standard state, which is
approximately zero in this case
(B) The slope of the line is equal to the entropy change at standard state, which is
approximately zero in this case
(C) CO
2
shows non-ideal behaviour
(D) CO
2
is a gaseous oxide
GATE 2016 MT
MT 2/12
Q.6 Activation energy of a chemical reaction, homogeneous or heterogeneous, is graphically
estimated from a plot between
(A) k versus T (B) 1/k versus T
(C) 1/k versus ln T (D) ln k versus 1/T
[where, k is the rate constant and T is the absolute temperature]
Q.7 The passive film in stainless steel forms above the
(A) Primary passive potential
(B) Breakdown potential
(C) Trans-passive potential
(D) Pitting potential
Q.8 During the roasting of a sulfide ore of a metal M, the possible solid phases are M, MS, MO
and MSO
4
. Assuming that both SO
2
and O
2
are always present in the roaster, the solid
phases that can co-exist at thermodynamic equilibrium are
(A) M, MS, MO, MSO
4
(B) M, MO, MSO
4
(C) MS, MO, MSO
4
(D) M, MSO
4
Q.9 Match the entities in Column I with the corresponding processes in Column II.
Column I Column II
[P] Xanthate salts [1] Extraction of Al
[Q] Thiobacillus Ferrooxidans [2] Flotation
[R] Hydrocyclone [3] Classification
[S] Anode effect [4] Bacterial Leaching
(A) P-4, Q-2, R-3, S-1
(B) P-2, Q-4, R-3, S-1
(C) P-3, Q-4, R-1, S-2
(D) P-4, Q-1, R-2, S-3
Q.10 A sub-lance is used to monitor composition and temperature in
(A) BOF (B) Ladle refining furnace
(C) Continuous casting mould (D) Blast furnace
Q.11 The chemical formula of w?stite is
(A) FeS
2
(B) Fe
2
O
3
(C) Fe
3
O
4
(D) Fe
1-x
O
Q.12 The lattice parameter of face-centered cubic iron ( ?-Fe) is 0.3571 nm. The radius (in nm) of
the octahedral void in ?-Fe is ___________
GATE 2016 MT
MT 3/12
Q.13 For an ideal hexagonal-closed packed structure, the c/a ratio and packing efficiency
respectively are
(A) 1.633 and 52% (B) 1.633 and 74%
(C) 1.733 and 68% (D) 1.733 and 74%
Q.14 A schematic of X-ray diffraction pattern of a single phase cubic polycrystal is given below.
The miller indices of peak A is
(A) 210 (B) 220
(C) 222 (D) 310
Q.15 Which of the following cooling curves (shown in schematic) in an eutectoid steel will
produce 50% bainitic structure?
(A) P (B) Q (C) R (D) S
2 ?
Intensity?(a.u.)
110
200
211
A
Ms
Ac
1
time?
Temperature
Pearlite
Bainite
Martensite
Austenite
Q
S
R
P
GATE 2016 MT
MT 4/12
Q.16
The Burger?s vector of a dislocation in a cubic crystal (with lattice parameter a) is
11 0
and dislocation line is along [112] direction. The angle (in degrees) between the dislocation
line and its Burger?s vector is_______
Q.17 For the tensile stress-strain curve of a material shown in the schematic, the resilience (in
MPa) is _________
Q.18 A plastically deformed metal crystal at low temperature exhibits wavy slip line pattern due
to
(A) Dislocation pile-up
(B) Large number of slip systems
(C) Low stacking fault energy
(D) Dislocation climb
Q.19 Creep resistance decreases due to
(A) Small grain size
(B) Fine dispersoid size
(C) Low stacking fault energy
(D) High melting point
Q.20 The operation NOT associated with casting is
(A) Gating (B) Fettling
(C) Stack Moulding (D) Calendaring
0
20
40
60
80
100
120
140
160
180
200
0.00 0.01 0.02 0.03 0.04 0.05 0.06
Stress,?MPa
Strain
0.01
0.1
360
510
GATE 2016 MT
MT 5/12
Q.21 Of the following welding processes
[P] Laser Beam Welding
[Q] Submerged Arc Welding
[R] Metal Inert Gas Welding
the width of the heat-affected zone in decreasing order is
(A) P > Q > R (B) Q > R > P
(C) R > P > Q (D) P > R > Q
Q.22 Railway tracks are typically manufactured using
(A) Forging (B) Extrusion
(C) Deep Drawing (D) Rolling
Q.23 For dye-penetrant test, identify the CORRECT statement
(A) Pre- and post-cleaning of parts are not required
(B) Internal defects can be detected
(C) Surface oxides helps in crack identification
(D) Dye with low contact angle is required
Q.24 Aluminium powder having an apparent density of 810 kg.m
-3
is compacted in a cylindrical
die at 600 MPa. The density of the as-pressed aluminium compact is 1755 kg.m
-3
. If the
height of the as-pressed compact is 12 mm, the fill height (in mm) required is
___________
Q.25 A rolling mill has a roll diameter of 200 mm. If coefficient of friction is 0.1, then the
maximum possible reduction (in mm) during rolling of a 250 mm thick plate is
___________
Q. 26 ? Q. 55 carry two marks each.
Q.26 A hot body cools according to the following equation
where, T is the instantaneous temperature at time t, and the constant c = 0.05 s
-1
. Reduce
the differential equation into its finite difference form using forward difference.
For
maintaining numerical stability, the maximum value of the time step ?t (in seconds) is
________
Q.27 Solve the equation e
using Newton-Raphson method. Starting with an initial guess
value x
0
= 0, the value of x after the first iteration is ____________
Q.28 A coin is tossed three times. It is known that out of the three tosses, one is a HEAD. The
probability of the other two tosses also being HEADs is _____________
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GATE 2016 General Aptitude ? GA Set-7
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 If I were you, I __________ that laptop. It?s much too expensive.
(A) won?t buy (B) shan?t buy
(C) wouldn?t buy (D) would buy
Q.2 He turned a deaf ear to my request.
What does the underlined phrasal verb mean?
(A) ignored (B) appreciated (C) twisted (D) returned
Q.3 Choose the most appropriate set of words from the options given below to complete the following
sentence.
_________ ___________ is a will, _________ is a way.
(A) Wear, there, their (B) Were, their, there
(C) Where, there, there (D) Where, their, their
Q.4 (x % of y) + (y % of x) is equivalent to .
(A) 2 % of xy (B) 2 % of (xy/100) (C) xy % of 100 (D) 100 % of xy
Q.5 The sum of the digits of a two digit number is 12. If the new number formed by reversing the digits
is greater than the original number by 54, find the original number.
(A) 39 (B) 57 (C) 66 (D) 93
GATE 2016 General Aptitude ? GA Set-7
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 Two finance companies, P and Q, declared fixed annual rates of interest on the amounts invested
with them. The rates of interest offered by these companies may differ from year to year. Year-wise
annual rates of interest offered by these companies are shown by the line graph provided below.
If the amounts invested in the companies, P and Q, in 2006 are in the ratio 8:9, then the amounts
received after one year as interests from companies P and Q would be in the ratio:
(A) 2:3
(B) 3:4
(C) 6:7
(D) 4:3
Q.7 Today, we consider Ashoka as a great ruler because of the copious evidence he left behind in the
form of stone carved edicts. Historians tend to correlate greatness of a king at his time with the
availability of evidence today.
Which of the following can be logically inferred from the above sentences?
(A) Emperors who do not leave significant sculpted evidence are completely forgotten.
(B) Ashoka produced stone carved edicts to ensure that later historians will respect him.
(C) Statues of kings are a reminder of their greatness.
(D) A king?s greatness, as we know him today, is interpreted by historians.
7
9
8
10
7.5
6.5
6
6.5
8
9.5
8
9
8
4
2000 2001 2002 2003 2004 2005 2006
P Q
GATE 2016 General Aptitude ? GA Set-7
3/3
Q.8 Fact 1: Humans are mammals.
Fact 2: Some humans are engineers.
Fact 3: Engineers build houses.
If the above statements are facts, which of the following can be logically inferred?
I. All mammals build houses.
II. Engineers are mammals.
III. Some humans are not engineers.
(A) II only. (B) III only.
(C) I, II and III. (D) I only.
Q.9 A square pyramid has a base perimeter x, and the slant height is half of the perimeter. What is the
lateral surface area of the pyramid?
(A) x
2
(B) 0.75 x
2
(C) 0.50 x
2
(D) 0.25 x
2
END OF THE QUESTION PAPER
Q.10 Ananth takes 6 hours and Bharath takes 4 hours to read a book. Both started reading copies of the
book at the same time. After how many hours is the number of pages to be read by Ananth, twice
that to be read by Bharath? Assume Ananth and Bharath read all the pages with constant pace.
(A) 1 (B) 2 (C) 3 (D) 4
GATE 2016 MT
MT 1/12
Useful Data:
Gas constant (R) 8.314 J.mol
-1
K
-1
Acceleration due to gravity (g) 9.81 m
2
.s
-1
Atomic weight of oxygen 16 g.mol
-1
Atomic weight of silicon 28 g.mol
-1
Atomic weight of iron 56 g.mol
-1
Q. 1 ? Q. 25 carry one mark each.
Q.1 For the transformation shown below, if one of the eigenvalues is 6, the other eigenvalue of
the matrix is ______
52
2 2
Q.2 The solution of the differential equation
is
(A) C (B)
C
(C)
(D)
[where, C, C
1
and C
2
are constants]
Q.3
If
, the divergence of is
(A)
(B)
(C) 5
(D) 0
Q.4 The first law of thermodynamics can be stated as
(A) dE = ?Q ? ?W
(B) dQ = dE ? ?W
(C) ?W = dQ + dE
(D) dW = ?Q ? ?E
[where, E, Q and W denote internal energy, heat and work, respectively]
Q.5 In a typical Ellingham diagram for the oxides, the C + O
2
= CO
2
line is nearly horizontal
because
(A) The slope of the line is equal to the enthalpy change at standard state, which is
approximately zero in this case
(B) The slope of the line is equal to the entropy change at standard state, which is
approximately zero in this case
(C) CO
2
shows non-ideal behaviour
(D) CO
2
is a gaseous oxide
GATE 2016 MT
MT 2/12
Q.6 Activation energy of a chemical reaction, homogeneous or heterogeneous, is graphically
estimated from a plot between
(A) k versus T (B) 1/k versus T
(C) 1/k versus ln T (D) ln k versus 1/T
[where, k is the rate constant and T is the absolute temperature]
Q.7 The passive film in stainless steel forms above the
(A) Primary passive potential
(B) Breakdown potential
(C) Trans-passive potential
(D) Pitting potential
Q.8 During the roasting of a sulfide ore of a metal M, the possible solid phases are M, MS, MO
and MSO
4
. Assuming that both SO
2
and O
2
are always present in the roaster, the solid
phases that can co-exist at thermodynamic equilibrium are
(A) M, MS, MO, MSO
4
(B) M, MO, MSO
4
(C) MS, MO, MSO
4
(D) M, MSO
4
Q.9 Match the entities in Column I with the corresponding processes in Column II.
Column I Column II
[P] Xanthate salts [1] Extraction of Al
[Q] Thiobacillus Ferrooxidans [2] Flotation
[R] Hydrocyclone [3] Classification
[S] Anode effect [4] Bacterial Leaching
(A) P-4, Q-2, R-3, S-1
(B) P-2, Q-4, R-3, S-1
(C) P-3, Q-4, R-1, S-2
(D) P-4, Q-1, R-2, S-3
Q.10 A sub-lance is used to monitor composition and temperature in
(A) BOF (B) Ladle refining furnace
(C) Continuous casting mould (D) Blast furnace
Q.11 The chemical formula of w?stite is
(A) FeS
2
(B) Fe
2
O
3
(C) Fe
3
O
4
(D) Fe
1-x
O
Q.12 The lattice parameter of face-centered cubic iron ( ?-Fe) is 0.3571 nm. The radius (in nm) of
the octahedral void in ?-Fe is ___________
GATE 2016 MT
MT 3/12
Q.13 For an ideal hexagonal-closed packed structure, the c/a ratio and packing efficiency
respectively are
(A) 1.633 and 52% (B) 1.633 and 74%
(C) 1.733 and 68% (D) 1.733 and 74%
Q.14 A schematic of X-ray diffraction pattern of a single phase cubic polycrystal is given below.
The miller indices of peak A is
(A) 210 (B) 220
(C) 222 (D) 310
Q.15 Which of the following cooling curves (shown in schematic) in an eutectoid steel will
produce 50% bainitic structure?
(A) P (B) Q (C) R (D) S
2 ?
Intensity?(a.u.)
110
200
211
A
Ms
Ac
1
time?
Temperature
Pearlite
Bainite
Martensite
Austenite
Q
S
R
P
GATE 2016 MT
MT 4/12
Q.16
The Burger?s vector of a dislocation in a cubic crystal (with lattice parameter a) is
11 0
and dislocation line is along [112] direction. The angle (in degrees) between the dislocation
line and its Burger?s vector is_______
Q.17 For the tensile stress-strain curve of a material shown in the schematic, the resilience (in
MPa) is _________
Q.18 A plastically deformed metal crystal at low temperature exhibits wavy slip line pattern due
to
(A) Dislocation pile-up
(B) Large number of slip systems
(C) Low stacking fault energy
(D) Dislocation climb
Q.19 Creep resistance decreases due to
(A) Small grain size
(B) Fine dispersoid size
(C) Low stacking fault energy
(D) High melting point
Q.20 The operation NOT associated with casting is
(A) Gating (B) Fettling
(C) Stack Moulding (D) Calendaring
0
20
40
60
80
100
120
140
160
180
200
0.00 0.01 0.02 0.03 0.04 0.05 0.06
Stress,?MPa
Strain
0.01
0.1
360
510
GATE 2016 MT
MT 5/12
Q.21 Of the following welding processes
[P] Laser Beam Welding
[Q] Submerged Arc Welding
[R] Metal Inert Gas Welding
the width of the heat-affected zone in decreasing order is
(A) P > Q > R (B) Q > R > P
(C) R > P > Q (D) P > R > Q
Q.22 Railway tracks are typically manufactured using
(A) Forging (B) Extrusion
(C) Deep Drawing (D) Rolling
Q.23 For dye-penetrant test, identify the CORRECT statement
(A) Pre- and post-cleaning of parts are not required
(B) Internal defects can be detected
(C) Surface oxides helps in crack identification
(D) Dye with low contact angle is required
Q.24 Aluminium powder having an apparent density of 810 kg.m
-3
is compacted in a cylindrical
die at 600 MPa. The density of the as-pressed aluminium compact is 1755 kg.m
-3
. If the
height of the as-pressed compact is 12 mm, the fill height (in mm) required is
___________
Q.25 A rolling mill has a roll diameter of 200 mm. If coefficient of friction is 0.1, then the
maximum possible reduction (in mm) during rolling of a 250 mm thick plate is
___________
Q. 26 ? Q. 55 carry two marks each.
Q.26 A hot body cools according to the following equation
where, T is the instantaneous temperature at time t, and the constant c = 0.05 s
-1
. Reduce
the differential equation into its finite difference form using forward difference.
For
maintaining numerical stability, the maximum value of the time step ?t (in seconds) is
________
Q.27 Solve the equation e
using Newton-Raphson method. Starting with an initial guess
value x
0
= 0, the value of x after the first iteration is ____________
Q.28 A coin is tossed three times. It is known that out of the three tosses, one is a HEAD. The
probability of the other two tosses also being HEADs is _____________
GATE 2016 MT
MT 6/12
Q.29 The vector parallel to the plane 3x ? 2y + z = ?1 is
(A) ? ?
(B) 3 ? 2 ?
(C) ? ?
(D) 3 ? 2 ? 2
Q.30 The value of the integral
?
?/2
0
dx sinx x = __________
Q.31 The grain sizes (in ?m) measured at five locations in an alloy sample are: 16, 14, 18, 15
and 13. The mean, median and standard deviation of grain sizes respectively are (in ?m)
(A) 15.2, 15 and 1.7
(B) 15.2, 15 and 1.9
(C) 15.8, 15 and 1.9
(D) 15.2, 16 and 1.7
Q.32 The change of standard state from pure liquid to 1 wt.% for Si dissolved in liquid Fe at
1873 K is expressed as
Si (liq.) = Si (1 wt.%)
Given that the activity coefficient of Si at infinite dilution in Fe is 10
-3
, the standard Gibbs
free energy change (in kJ) for this equilibrium is_____________
Q.33 The following experimental data are available for a hypothetical binary liquid system A-B
at 1073 K
Atom fraction of A
0.2 0.4 0.5 0.7 1.0
Partial pressure of A (bar) 0.01 0.04 0.06 0.07 0.08
When the atom fraction of A is 0.4, the activity of A in the liquid is ______________
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GATE 2016 General Aptitude ? GA Set-7
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 If I were you, I __________ that laptop. It?s much too expensive.
(A) won?t buy (B) shan?t buy
(C) wouldn?t buy (D) would buy
Q.2 He turned a deaf ear to my request.
What does the underlined phrasal verb mean?
(A) ignored (B) appreciated (C) twisted (D) returned
Q.3 Choose the most appropriate set of words from the options given below to complete the following
sentence.
_________ ___________ is a will, _________ is a way.
(A) Wear, there, their (B) Were, their, there
(C) Where, there, there (D) Where, their, their
Q.4 (x % of y) + (y % of x) is equivalent to .
(A) 2 % of xy (B) 2 % of (xy/100) (C) xy % of 100 (D) 100 % of xy
Q.5 The sum of the digits of a two digit number is 12. If the new number formed by reversing the digits
is greater than the original number by 54, find the original number.
(A) 39 (B) 57 (C) 66 (D) 93
GATE 2016 General Aptitude ? GA Set-7
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 Two finance companies, P and Q, declared fixed annual rates of interest on the amounts invested
with them. The rates of interest offered by these companies may differ from year to year. Year-wise
annual rates of interest offered by these companies are shown by the line graph provided below.
If the amounts invested in the companies, P and Q, in 2006 are in the ratio 8:9, then the amounts
received after one year as interests from companies P and Q would be in the ratio:
(A) 2:3
(B) 3:4
(C) 6:7
(D) 4:3
Q.7 Today, we consider Ashoka as a great ruler because of the copious evidence he left behind in the
form of stone carved edicts. Historians tend to correlate greatness of a king at his time with the
availability of evidence today.
Which of the following can be logically inferred from the above sentences?
(A) Emperors who do not leave significant sculpted evidence are completely forgotten.
(B) Ashoka produced stone carved edicts to ensure that later historians will respect him.
(C) Statues of kings are a reminder of their greatness.
(D) A king?s greatness, as we know him today, is interpreted by historians.
7
9
8
10
7.5
6.5
6
6.5
8
9.5
8
9
8
4
2000 2001 2002 2003 2004 2005 2006
P Q
GATE 2016 General Aptitude ? GA Set-7
3/3
Q.8 Fact 1: Humans are mammals.
Fact 2: Some humans are engineers.
Fact 3: Engineers build houses.
If the above statements are facts, which of the following can be logically inferred?
I. All mammals build houses.
II. Engineers are mammals.
III. Some humans are not engineers.
(A) II only. (B) III only.
(C) I, II and III. (D) I only.
Q.9 A square pyramid has a base perimeter x, and the slant height is half of the perimeter. What is the
lateral surface area of the pyramid?
(A) x
2
(B) 0.75 x
2
(C) 0.50 x
2
(D) 0.25 x
2
END OF THE QUESTION PAPER
Q.10 Ananth takes 6 hours and Bharath takes 4 hours to read a book. Both started reading copies of the
book at the same time. After how many hours is the number of pages to be read by Ananth, twice
that to be read by Bharath? Assume Ananth and Bharath read all the pages with constant pace.
(A) 1 (B) 2 (C) 3 (D) 4
GATE 2016 MT
MT 1/12
Useful Data:
Gas constant (R) 8.314 J.mol
-1
K
-1
Acceleration due to gravity (g) 9.81 m
2
.s
-1
Atomic weight of oxygen 16 g.mol
-1
Atomic weight of silicon 28 g.mol
-1
Atomic weight of iron 56 g.mol
-1
Q. 1 ? Q. 25 carry one mark each.
Q.1 For the transformation shown below, if one of the eigenvalues is 6, the other eigenvalue of
the matrix is ______
52
2 2
Q.2 The solution of the differential equation
is
(A) C (B)
C
(C)
(D)
[where, C, C
1
and C
2
are constants]
Q.3
If
, the divergence of is
(A)
(B)
(C) 5
(D) 0
Q.4 The first law of thermodynamics can be stated as
(A) dE = ?Q ? ?W
(B) dQ = dE ? ?W
(C) ?W = dQ + dE
(D) dW = ?Q ? ?E
[where, E, Q and W denote internal energy, heat and work, respectively]
Q.5 In a typical Ellingham diagram for the oxides, the C + O
2
= CO
2
line is nearly horizontal
because
(A) The slope of the line is equal to the enthalpy change at standard state, which is
approximately zero in this case
(B) The slope of the line is equal to the entropy change at standard state, which is
approximately zero in this case
(C) CO
2
shows non-ideal behaviour
(D) CO
2
is a gaseous oxide
GATE 2016 MT
MT 2/12
Q.6 Activation energy of a chemical reaction, homogeneous or heterogeneous, is graphically
estimated from a plot between
(A) k versus T (B) 1/k versus T
(C) 1/k versus ln T (D) ln k versus 1/T
[where, k is the rate constant and T is the absolute temperature]
Q.7 The passive film in stainless steel forms above the
(A) Primary passive potential
(B) Breakdown potential
(C) Trans-passive potential
(D) Pitting potential
Q.8 During the roasting of a sulfide ore of a metal M, the possible solid phases are M, MS, MO
and MSO
4
. Assuming that both SO
2
and O
2
are always present in the roaster, the solid
phases that can co-exist at thermodynamic equilibrium are
(A) M, MS, MO, MSO
4
(B) M, MO, MSO
4
(C) MS, MO, MSO
4
(D) M, MSO
4
Q.9 Match the entities in Column I with the corresponding processes in Column II.
Column I Column II
[P] Xanthate salts [1] Extraction of Al
[Q] Thiobacillus Ferrooxidans [2] Flotation
[R] Hydrocyclone [3] Classification
[S] Anode effect [4] Bacterial Leaching
(A) P-4, Q-2, R-3, S-1
(B) P-2, Q-4, R-3, S-1
(C) P-3, Q-4, R-1, S-2
(D) P-4, Q-1, R-2, S-3
Q.10 A sub-lance is used to monitor composition and temperature in
(A) BOF (B) Ladle refining furnace
(C) Continuous casting mould (D) Blast furnace
Q.11 The chemical formula of w?stite is
(A) FeS
2
(B) Fe
2
O
3
(C) Fe
3
O
4
(D) Fe
1-x
O
Q.12 The lattice parameter of face-centered cubic iron ( ?-Fe) is 0.3571 nm. The radius (in nm) of
the octahedral void in ?-Fe is ___________
GATE 2016 MT
MT 3/12
Q.13 For an ideal hexagonal-closed packed structure, the c/a ratio and packing efficiency
respectively are
(A) 1.633 and 52% (B) 1.633 and 74%
(C) 1.733 and 68% (D) 1.733 and 74%
Q.14 A schematic of X-ray diffraction pattern of a single phase cubic polycrystal is given below.
The miller indices of peak A is
(A) 210 (B) 220
(C) 222 (D) 310
Q.15 Which of the following cooling curves (shown in schematic) in an eutectoid steel will
produce 50% bainitic structure?
(A) P (B) Q (C) R (D) S
2 ?
Intensity?(a.u.)
110
200
211
A
Ms
Ac
1
time?
Temperature
Pearlite
Bainite
Martensite
Austenite
Q
S
R
P
GATE 2016 MT
MT 4/12
Q.16
The Burger?s vector of a dislocation in a cubic crystal (with lattice parameter a) is
11 0
and dislocation line is along [112] direction. The angle (in degrees) between the dislocation
line and its Burger?s vector is_______
Q.17 For the tensile stress-strain curve of a material shown in the schematic, the resilience (in
MPa) is _________
Q.18 A plastically deformed metal crystal at low temperature exhibits wavy slip line pattern due
to
(A) Dislocation pile-up
(B) Large number of slip systems
(C) Low stacking fault energy
(D) Dislocation climb
Q.19 Creep resistance decreases due to
(A) Small grain size
(B) Fine dispersoid size
(C) Low stacking fault energy
(D) High melting point
Q.20 The operation NOT associated with casting is
(A) Gating (B) Fettling
(C) Stack Moulding (D) Calendaring
0
20
40
60
80
100
120
140
160
180
200
0.00 0.01 0.02 0.03 0.04 0.05 0.06
Stress,?MPa
Strain
0.01
0.1
360
510
GATE 2016 MT
MT 5/12
Q.21 Of the following welding processes
[P] Laser Beam Welding
[Q] Submerged Arc Welding
[R] Metal Inert Gas Welding
the width of the heat-affected zone in decreasing order is
(A) P > Q > R (B) Q > R > P
(C) R > P > Q (D) P > R > Q
Q.22 Railway tracks are typically manufactured using
(A) Forging (B) Extrusion
(C) Deep Drawing (D) Rolling
Q.23 For dye-penetrant test, identify the CORRECT statement
(A) Pre- and post-cleaning of parts are not required
(B) Internal defects can be detected
(C) Surface oxides helps in crack identification
(D) Dye with low contact angle is required
Q.24 Aluminium powder having an apparent density of 810 kg.m
-3
is compacted in a cylindrical
die at 600 MPa. The density of the as-pressed aluminium compact is 1755 kg.m
-3
. If the
height of the as-pressed compact is 12 mm, the fill height (in mm) required is
___________
Q.25 A rolling mill has a roll diameter of 200 mm. If coefficient of friction is 0.1, then the
maximum possible reduction (in mm) during rolling of a 250 mm thick plate is
___________
Q. 26 ? Q. 55 carry two marks each.
Q.26 A hot body cools according to the following equation
where, T is the instantaneous temperature at time t, and the constant c = 0.05 s
-1
. Reduce
the differential equation into its finite difference form using forward difference.
For
maintaining numerical stability, the maximum value of the time step ?t (in seconds) is
________
Q.27 Solve the equation e
using Newton-Raphson method. Starting with an initial guess
value x
0
= 0, the value of x after the first iteration is ____________
Q.28 A coin is tossed three times. It is known that out of the three tosses, one is a HEAD. The
probability of the other two tosses also being HEADs is _____________
GATE 2016 MT
MT 6/12
Q.29 The vector parallel to the plane 3x ? 2y + z = ?1 is
(A) ? ?
(B) 3 ? 2 ?
(C) ? ?
(D) 3 ? 2 ? 2
Q.30 The value of the integral
?
?/2
0
dx sinx x = __________
Q.31 The grain sizes (in ?m) measured at five locations in an alloy sample are: 16, 14, 18, 15
and 13. The mean, median and standard deviation of grain sizes respectively are (in ?m)
(A) 15.2, 15 and 1.7
(B) 15.2, 15 and 1.9
(C) 15.8, 15 and 1.9
(D) 15.2, 16 and 1.7
Q.32 The change of standard state from pure liquid to 1 wt.% for Si dissolved in liquid Fe at
1873 K is expressed as
Si (liq.) = Si (1 wt.%)
Given that the activity coefficient of Si at infinite dilution in Fe is 10
-3
, the standard Gibbs
free energy change (in kJ) for this equilibrium is_____________
Q.33 The following experimental data are available for a hypothetical binary liquid system A-B
at 1073 K
Atom fraction of A
0.2 0.4 0.5 0.7 1.0
Partial pressure of A (bar) 0.01 0.04 0.06 0.07 0.08
When the atom fraction of A is 0.4, the activity of A in the liquid is ______________
GATE 2016 MT
MT 7/12
Q.34 The lining of a box-type furnace is made up of a refractory layer and steel plate as shown in
the figure. Steady state temperature at the surface of the refractory is 1273 K and that at the
outer steel surface is 473 K. If the steady-state heat flux through the refractory-steel plate
composite is 1600 W.m
-2
, and heat flow is along x-direction, the thermal contact resistance
(W
-1
.m
2
.K) between refractory and steel is _____________
Given data:
Thermal conductivity of refractory = 1.2 W.m
-1
K
-1
Thickness of refractory lining = 80 mm
Thermal conductivity of steel = 32 W.m
-1
K
-1
Thickness of steel plate = 4 mm
Q.35 The height of a liquid metal column in a cylindrical vessel is 3.2 m. At time t=0, liquid
metal is drained out from the vessel through a small nozzle located at the base of the vessel.
Neglecting frictional losses, the initial mass flow rate (in kg.s
-1
) through the
nozzle is ________________
Given data:
Density of liquid metal = 7000 kg.m
-3
Nozzle diameter = 30 mm
Nozzle discharge coefficient = 0.80
Q.36 Match entities listed in Column I with their correct dimensions given in Column II:
Column I Column II
[P] Drag coefficient [1] ML
-1
T
-1
[Q] Mass transfer coefficient [2] ML
-2
T
-1
[R] Viscosity [3] M
0
L
0
T
0
[S] Mass flux [4] M
0
LT
-1
(A) P-3, Q-4, R-1, S-2 (B) P-3, Q-1, R-2, S-4
(C) P-1, Q-4, R-2, S-3 (D) P-4, Q-3, R-1, S-2
Q.37 Direct Reduced Iron (DRI) produced from a gas based process contains Fe, FeO, C and
remainder being gangue. The chemical composition of DRI is: Total Fe = 92 wt.% and
Metallic Fe = 84 wt.%. The weight percent of FeO in DRI is _________________
1273 K 473 K
refractory
steel plate
Furnace
Ambient
x
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude ? GA Set-7
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 If I were you, I __________ that laptop. It?s much too expensive.
(A) won?t buy (B) shan?t buy
(C) wouldn?t buy (D) would buy
Q.2 He turned a deaf ear to my request.
What does the underlined phrasal verb mean?
(A) ignored (B) appreciated (C) twisted (D) returned
Q.3 Choose the most appropriate set of words from the options given below to complete the following
sentence.
_________ ___________ is a will, _________ is a way.
(A) Wear, there, their (B) Were, their, there
(C) Where, there, there (D) Where, their, their
Q.4 (x % of y) + (y % of x) is equivalent to .
(A) 2 % of xy (B) 2 % of (xy/100) (C) xy % of 100 (D) 100 % of xy
Q.5 The sum of the digits of a two digit number is 12. If the new number formed by reversing the digits
is greater than the original number by 54, find the original number.
(A) 39 (B) 57 (C) 66 (D) 93
GATE 2016 General Aptitude ? GA Set-7
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 Two finance companies, P and Q, declared fixed annual rates of interest on the amounts invested
with them. The rates of interest offered by these companies may differ from year to year. Year-wise
annual rates of interest offered by these companies are shown by the line graph provided below.
If the amounts invested in the companies, P and Q, in 2006 are in the ratio 8:9, then the amounts
received after one year as interests from companies P and Q would be in the ratio:
(A) 2:3
(B) 3:4
(C) 6:7
(D) 4:3
Q.7 Today, we consider Ashoka as a great ruler because of the copious evidence he left behind in the
form of stone carved edicts. Historians tend to correlate greatness of a king at his time with the
availability of evidence today.
Which of the following can be logically inferred from the above sentences?
(A) Emperors who do not leave significant sculpted evidence are completely forgotten.
(B) Ashoka produced stone carved edicts to ensure that later historians will respect him.
(C) Statues of kings are a reminder of their greatness.
(D) A king?s greatness, as we know him today, is interpreted by historians.
7
9
8
10
7.5
6.5
6
6.5
8
9.5
8
9
8
4
2000 2001 2002 2003 2004 2005 2006
P Q
GATE 2016 General Aptitude ? GA Set-7
3/3
Q.8 Fact 1: Humans are mammals.
Fact 2: Some humans are engineers.
Fact 3: Engineers build houses.
If the above statements are facts, which of the following can be logically inferred?
I. All mammals build houses.
II. Engineers are mammals.
III. Some humans are not engineers.
(A) II only. (B) III only.
(C) I, II and III. (D) I only.
Q.9 A square pyramid has a base perimeter x, and the slant height is half of the perimeter. What is the
lateral surface area of the pyramid?
(A) x
2
(B) 0.75 x
2
(C) 0.50 x
2
(D) 0.25 x
2
END OF THE QUESTION PAPER
Q.10 Ananth takes 6 hours and Bharath takes 4 hours to read a book. Both started reading copies of the
book at the same time. After how many hours is the number of pages to be read by Ananth, twice
that to be read by Bharath? Assume Ananth and Bharath read all the pages with constant pace.
(A) 1 (B) 2 (C) 3 (D) 4
GATE 2016 MT
MT 1/12
Useful Data:
Gas constant (R) 8.314 J.mol
-1
K
-1
Acceleration due to gravity (g) 9.81 m
2
.s
-1
Atomic weight of oxygen 16 g.mol
-1
Atomic weight of silicon 28 g.mol
-1
Atomic weight of iron 56 g.mol
-1
Q. 1 ? Q. 25 carry one mark each.
Q.1 For the transformation shown below, if one of the eigenvalues is 6, the other eigenvalue of
the matrix is ______
52
2 2
Q.2 The solution of the differential equation
is
(A) C (B)
C
(C)
(D)
[where, C, C
1
and C
2
are constants]
Q.3
If
, the divergence of is
(A)
(B)
(C) 5
(D) 0
Q.4 The first law of thermodynamics can be stated as
(A) dE = ?Q ? ?W
(B) dQ = dE ? ?W
(C) ?W = dQ + dE
(D) dW = ?Q ? ?E
[where, E, Q and W denote internal energy, heat and work, respectively]
Q.5 In a typical Ellingham diagram for the oxides, the C + O
2
= CO
2
line is nearly horizontal
because
(A) The slope of the line is equal to the enthalpy change at standard state, which is
approximately zero in this case
(B) The slope of the line is equal to the entropy change at standard state, which is
approximately zero in this case
(C) CO
2
shows non-ideal behaviour
(D) CO
2
is a gaseous oxide
GATE 2016 MT
MT 2/12
Q.6 Activation energy of a chemical reaction, homogeneous or heterogeneous, is graphically
estimated from a plot between
(A) k versus T (B) 1/k versus T
(C) 1/k versus ln T (D) ln k versus 1/T
[where, k is the rate constant and T is the absolute temperature]
Q.7 The passive film in stainless steel forms above the
(A) Primary passive potential
(B) Breakdown potential
(C) Trans-passive potential
(D) Pitting potential
Q.8 During the roasting of a sulfide ore of a metal M, the possible solid phases are M, MS, MO
and MSO
4
. Assuming that both SO
2
and O
2
are always present in the roaster, the solid
phases that can co-exist at thermodynamic equilibrium are
(A) M, MS, MO, MSO
4
(B) M, MO, MSO
4
(C) MS, MO, MSO
4
(D) M, MSO
4
Q.9 Match the entities in Column I with the corresponding processes in Column II.
Column I Column II
[P] Xanthate salts [1] Extraction of Al
[Q] Thiobacillus Ferrooxidans [2] Flotation
[R] Hydrocyclone [3] Classification
[S] Anode effect [4] Bacterial Leaching
(A) P-4, Q-2, R-3, S-1
(B) P-2, Q-4, R-3, S-1
(C) P-3, Q-4, R-1, S-2
(D) P-4, Q-1, R-2, S-3
Q.10 A sub-lance is used to monitor composition and temperature in
(A) BOF (B) Ladle refining furnace
(C) Continuous casting mould (D) Blast furnace
Q.11 The chemical formula of w?stite is
(A) FeS
2
(B) Fe
2
O
3
(C) Fe
3
O
4
(D) Fe
1-x
O
Q.12 The lattice parameter of face-centered cubic iron ( ?-Fe) is 0.3571 nm. The radius (in nm) of
the octahedral void in ?-Fe is ___________
GATE 2016 MT
MT 3/12
Q.13 For an ideal hexagonal-closed packed structure, the c/a ratio and packing efficiency
respectively are
(A) 1.633 and 52% (B) 1.633 and 74%
(C) 1.733 and 68% (D) 1.733 and 74%
Q.14 A schematic of X-ray diffraction pattern of a single phase cubic polycrystal is given below.
The miller indices of peak A is
(A) 210 (B) 220
(C) 222 (D) 310
Q.15 Which of the following cooling curves (shown in schematic) in an eutectoid steel will
produce 50% bainitic structure?
(A) P (B) Q (C) R (D) S
2 ?
Intensity?(a.u.)
110
200
211
A
Ms
Ac
1
time?
Temperature
Pearlite
Bainite
Martensite
Austenite
Q
S
R
P
GATE 2016 MT
MT 4/12
Q.16
The Burger?s vector of a dislocation in a cubic crystal (with lattice parameter a) is
11 0
and dislocation line is along [112] direction. The angle (in degrees) between the dislocation
line and its Burger?s vector is_______
Q.17 For the tensile stress-strain curve of a material shown in the schematic, the resilience (in
MPa) is _________
Q.18 A plastically deformed metal crystal at low temperature exhibits wavy slip line pattern due
to
(A) Dislocation pile-up
(B) Large number of slip systems
(C) Low stacking fault energy
(D) Dislocation climb
Q.19 Creep resistance decreases due to
(A) Small grain size
(B) Fine dispersoid size
(C) Low stacking fault energy
(D) High melting point
Q.20 The operation NOT associated with casting is
(A) Gating (B) Fettling
(C) Stack Moulding (D) Calendaring
0
20
40
60
80
100
120
140
160
180
200
0.00 0.01 0.02 0.03 0.04 0.05 0.06
Stress,?MPa
Strain
0.01
0.1
360
510
GATE 2016 MT
MT 5/12
Q.21 Of the following welding processes
[P] Laser Beam Welding
[Q] Submerged Arc Welding
[R] Metal Inert Gas Welding
the width of the heat-affected zone in decreasing order is
(A) P > Q > R (B) Q > R > P
(C) R > P > Q (D) P > R > Q
Q.22 Railway tracks are typically manufactured using
(A) Forging (B) Extrusion
(C) Deep Drawing (D) Rolling
Q.23 For dye-penetrant test, identify the CORRECT statement
(A) Pre- and post-cleaning of parts are not required
(B) Internal defects can be detected
(C) Surface oxides helps in crack identification
(D) Dye with low contact angle is required
Q.24 Aluminium powder having an apparent density of 810 kg.m
-3
is compacted in a cylindrical
die at 600 MPa. The density of the as-pressed aluminium compact is 1755 kg.m
-3
. If the
height of the as-pressed compact is 12 mm, the fill height (in mm) required is
___________
Q.25 A rolling mill has a roll diameter of 200 mm. If coefficient of friction is 0.1, then the
maximum possible reduction (in mm) during rolling of a 250 mm thick plate is
___________
Q. 26 ? Q. 55 carry two marks each.
Q.26 A hot body cools according to the following equation
where, T is the instantaneous temperature at time t, and the constant c = 0.05 s
-1
. Reduce
the differential equation into its finite difference form using forward difference.
For
maintaining numerical stability, the maximum value of the time step ?t (in seconds) is
________
Q.27 Solve the equation e
using Newton-Raphson method. Starting with an initial guess
value x
0
= 0, the value of x after the first iteration is ____________
Q.28 A coin is tossed three times. It is known that out of the three tosses, one is a HEAD. The
probability of the other two tosses also being HEADs is _____________
GATE 2016 MT
MT 6/12
Q.29 The vector parallel to the plane 3x ? 2y + z = ?1 is
(A) ? ?
(B) 3 ? 2 ?
(C) ? ?
(D) 3 ? 2 ? 2
Q.30 The value of the integral
?
?/2
0
dx sinx x = __________
Q.31 The grain sizes (in ?m) measured at five locations in an alloy sample are: 16, 14, 18, 15
and 13. The mean, median and standard deviation of grain sizes respectively are (in ?m)
(A) 15.2, 15 and 1.7
(B) 15.2, 15 and 1.9
(C) 15.8, 15 and 1.9
(D) 15.2, 16 and 1.7
Q.32 The change of standard state from pure liquid to 1 wt.% for Si dissolved in liquid Fe at
1873 K is expressed as
Si (liq.) = Si (1 wt.%)
Given that the activity coefficient of Si at infinite dilution in Fe is 10
-3
, the standard Gibbs
free energy change (in kJ) for this equilibrium is_____________
Q.33 The following experimental data are available for a hypothetical binary liquid system A-B
at 1073 K
Atom fraction of A
0.2 0.4 0.5 0.7 1.0
Partial pressure of A (bar) 0.01 0.04 0.06 0.07 0.08
When the atom fraction of A is 0.4, the activity of A in the liquid is ______________
GATE 2016 MT
MT 7/12
Q.34 The lining of a box-type furnace is made up of a refractory layer and steel plate as shown in
the figure. Steady state temperature at the surface of the refractory is 1273 K and that at the
outer steel surface is 473 K. If the steady-state heat flux through the refractory-steel plate
composite is 1600 W.m
-2
, and heat flow is along x-direction, the thermal contact resistance
(W
-1
.m
2
.K) between refractory and steel is _____________
Given data:
Thermal conductivity of refractory = 1.2 W.m
-1
K
-1
Thickness of refractory lining = 80 mm
Thermal conductivity of steel = 32 W.m
-1
K
-1
Thickness of steel plate = 4 mm
Q.35 The height of a liquid metal column in a cylindrical vessel is 3.2 m. At time t=0, liquid
metal is drained out from the vessel through a small nozzle located at the base of the vessel.
Neglecting frictional losses, the initial mass flow rate (in kg.s
-1
) through the
nozzle is ________________
Given data:
Density of liquid metal = 7000 kg.m
-3
Nozzle diameter = 30 mm
Nozzle discharge coefficient = 0.80
Q.36 Match entities listed in Column I with their correct dimensions given in Column II:
Column I Column II
[P] Drag coefficient [1] ML
-1
T
-1
[Q] Mass transfer coefficient [2] ML
-2
T
-1
[R] Viscosity [3] M
0
L
0
T
0
[S] Mass flux [4] M
0
LT
-1
(A) P-3, Q-4, R-1, S-2 (B) P-3, Q-1, R-2, S-4
(C) P-1, Q-4, R-2, S-3 (D) P-4, Q-3, R-1, S-2
Q.37 Direct Reduced Iron (DRI) produced from a gas based process contains Fe, FeO, C and
remainder being gangue. The chemical composition of DRI is: Total Fe = 92 wt.% and
Metallic Fe = 84 wt.%. The weight percent of FeO in DRI is _________________
1273 K 473 K
refractory
steel plate
Furnace
Ambient
x
GATE 2016 MT
MT 8/12
Q.38 Mould heat flux (q
m
) for billet casters is expressed (in SI unit) as a function of distance
below the meniscus (z)
6
c
m
10
U
z
33 . 0 67 . 2 ) z ( q ?
?
?
?
?
?
?
? ? ( ) 0
m
L z ? ?
If mould length (L
m
) is 0.8 m and casting speed (U
c
) is 0.2 m.s
-1
, the average mould flux
(in MW.m
-2
) is ________________
Q.39 In BOF steelmaking, 5 metric ton of lime containing 90 wt.% CaO is used to refine 100
metric ton of hot metal containing 93.2 wt.% Fe. The slag produced during refining
contains 40 wt.% CaO and 22 wt.% FeO. Neglecting material losses, the yield of Fe (in %)
is _________________
Q.40 In vacuum degassing of steel, 14 ppm of dissolved nitrogen is in equilibrium with 1 mbar
of nitrogen gas at 1873 K. At the same temperature, if the pressure is lowered to 0.7 mbar,
the equilibrium nitrogen content (in ppm) is _____________
Q.41 During isothermal phase transformation (in solid-state), fraction transformed is measured at
two different transformation times:
___________________________________________
Transformation Time, t (s) Fraction Transformed, f
___________________________________________
75 0.11
150 0.37
____________________________________________
Assuming Avrami kinetics [f = 1 ? exp (?kt
n
)], the fraction transformed in
300 seconds is _______________
Q.42 Zinc oxide is reduced at a constant temperature in a closed reactor using ZnO(s) and C(s)
as the only starting materials. The following reactions are assumed to be at thermodynamic
equilibrium:
ZnO(s) + C(s) = Zn(g) + CO(g)
2CO(g) = CO
2
(g) + C(s)
Assume ideal gas behaviour. Based on mole balance, the relationship applicable to the
system at equilibrium is
(A)
2
(B)
2
(C)
(D)
0.5
2
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GATE 2016 General Aptitude ? GA Set-7
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 If I were you, I __________ that laptop. It?s much too expensive.
(A) won?t buy (B) shan?t buy
(C) wouldn?t buy (D) would buy
Q.2 He turned a deaf ear to my request.
What does the underlined phrasal verb mean?
(A) ignored (B) appreciated (C) twisted (D) returned
Q.3 Choose the most appropriate set of words from the options given below to complete the following
sentence.
_________ ___________ is a will, _________ is a way.
(A) Wear, there, their (B) Were, their, there
(C) Where, there, there (D) Where, their, their
Q.4 (x % of y) + (y % of x) is equivalent to .
(A) 2 % of xy (B) 2 % of (xy/100) (C) xy % of 100 (D) 100 % of xy
Q.5 The sum of the digits of a two digit number is 12. If the new number formed by reversing the digits
is greater than the original number by 54, find the original number.
(A) 39 (B) 57 (C) 66 (D) 93
GATE 2016 General Aptitude ? GA Set-7
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 Two finance companies, P and Q, declared fixed annual rates of interest on the amounts invested
with them. The rates of interest offered by these companies may differ from year to year. Year-wise
annual rates of interest offered by these companies are shown by the line graph provided below.
If the amounts invested in the companies, P and Q, in 2006 are in the ratio 8:9, then the amounts
received after one year as interests from companies P and Q would be in the ratio:
(A) 2:3
(B) 3:4
(C) 6:7
(D) 4:3
Q.7 Today, we consider Ashoka as a great ruler because of the copious evidence he left behind in the
form of stone carved edicts. Historians tend to correlate greatness of a king at his time with the
availability of evidence today.
Which of the following can be logically inferred from the above sentences?
(A) Emperors who do not leave significant sculpted evidence are completely forgotten.
(B) Ashoka produced stone carved edicts to ensure that later historians will respect him.
(C) Statues of kings are a reminder of their greatness.
(D) A king?s greatness, as we know him today, is interpreted by historians.
7
9
8
10
7.5
6.5
6
6.5
8
9.5
8
9
8
4
2000 2001 2002 2003 2004 2005 2006
P Q
GATE 2016 General Aptitude ? GA Set-7
3/3
Q.8 Fact 1: Humans are mammals.
Fact 2: Some humans are engineers.
Fact 3: Engineers build houses.
If the above statements are facts, which of the following can be logically inferred?
I. All mammals build houses.
II. Engineers are mammals.
III. Some humans are not engineers.
(A) II only. (B) III only.
(C) I, II and III. (D) I only.
Q.9 A square pyramid has a base perimeter x, and the slant height is half of the perimeter. What is the
lateral surface area of the pyramid?
(A) x
2
(B) 0.75 x
2
(C) 0.50 x
2
(D) 0.25 x
2
END OF THE QUESTION PAPER
Q.10 Ananth takes 6 hours and Bharath takes 4 hours to read a book. Both started reading copies of the
book at the same time. After how many hours is the number of pages to be read by Ananth, twice
that to be read by Bharath? Assume Ananth and Bharath read all the pages with constant pace.
(A) 1 (B) 2 (C) 3 (D) 4
GATE 2016 MT
MT 1/12
Useful Data:
Gas constant (R) 8.314 J.mol
-1
K
-1
Acceleration due to gravity (g) 9.81 m
2
.s
-1
Atomic weight of oxygen 16 g.mol
-1
Atomic weight of silicon 28 g.mol
-1
Atomic weight of iron 56 g.mol
-1
Q. 1 ? Q. 25 carry one mark each.
Q.1 For the transformation shown below, if one of the eigenvalues is 6, the other eigenvalue of
the matrix is ______
52
2 2
Q.2 The solution of the differential equation
is
(A) C (B)
C
(C)
(D)
[where, C, C
1
and C
2
are constants]
Q.3
If
, the divergence of is
(A)
(B)
(C) 5
(D) 0
Q.4 The first law of thermodynamics can be stated as
(A) dE = ?Q ? ?W
(B) dQ = dE ? ?W
(C) ?W = dQ + dE
(D) dW = ?Q ? ?E
[where, E, Q and W denote internal energy, heat and work, respectively]
Q.5 In a typical Ellingham diagram for the oxides, the C + O
2
= CO
2
line is nearly horizontal
because
(A) The slope of the line is equal to the enthalpy change at standard state, which is
approximately zero in this case
(B) The slope of the line is equal to the entropy change at standard state, which is
approximately zero in this case
(C) CO
2
shows non-ideal behaviour
(D) CO
2
is a gaseous oxide
GATE 2016 MT
MT 2/12
Q.6 Activation energy of a chemical reaction, homogeneous or heterogeneous, is graphically
estimated from a plot between
(A) k versus T (B) 1/k versus T
(C) 1/k versus ln T (D) ln k versus 1/T
[where, k is the rate constant and T is the absolute temperature]
Q.7 The passive film in stainless steel forms above the
(A) Primary passive potential
(B) Breakdown potential
(C) Trans-passive potential
(D) Pitting potential
Q.8 During the roasting of a sulfide ore of a metal M, the possible solid phases are M, MS, MO
and MSO
4
. Assuming that both SO
2
and O
2
are always present in the roaster, the solid
phases that can co-exist at thermodynamic equilibrium are
(A) M, MS, MO, MSO
4
(B) M, MO, MSO
4
(C) MS, MO, MSO
4
(D) M, MSO
4
Q.9 Match the entities in Column I with the corresponding processes in Column II.
Column I Column II
[P] Xanthate salts [1] Extraction of Al
[Q] Thiobacillus Ferrooxidans [2] Flotation
[R] Hydrocyclone [3] Classification
[S] Anode effect [4] Bacterial Leaching
(A) P-4, Q-2, R-3, S-1
(B) P-2, Q-4, R-3, S-1
(C) P-3, Q-4, R-1, S-2
(D) P-4, Q-1, R-2, S-3
Q.10 A sub-lance is used to monitor composition and temperature in
(A) BOF (B) Ladle refining furnace
(C) Continuous casting mould (D) Blast furnace
Q.11 The chemical formula of w?stite is
(A) FeS
2
(B) Fe
2
O
3
(C) Fe
3
O
4
(D) Fe
1-x
O
Q.12 The lattice parameter of face-centered cubic iron ( ?-Fe) is 0.3571 nm. The radius (in nm) of
the octahedral void in ?-Fe is ___________
GATE 2016 MT
MT 3/12
Q.13 For an ideal hexagonal-closed packed structure, the c/a ratio and packing efficiency
respectively are
(A) 1.633 and 52% (B) 1.633 and 74%
(C) 1.733 and 68% (D) 1.733 and 74%
Q.14 A schematic of X-ray diffraction pattern of a single phase cubic polycrystal is given below.
The miller indices of peak A is
(A) 210 (B) 220
(C) 222 (D) 310
Q.15 Which of the following cooling curves (shown in schematic) in an eutectoid steel will
produce 50% bainitic structure?
(A) P (B) Q (C) R (D) S
2 ?
Intensity?(a.u.)
110
200
211
A
Ms
Ac
1
time?
Temperature
Pearlite
Bainite
Martensite
Austenite
Q
S
R
P
GATE 2016 MT
MT 4/12
Q.16
The Burger?s vector of a dislocation in a cubic crystal (with lattice parameter a) is
11 0
and dislocation line is along [112] direction. The angle (in degrees) between the dislocation
line and its Burger?s vector is_______
Q.17 For the tensile stress-strain curve of a material shown in the schematic, the resilience (in
MPa) is _________
Q.18 A plastically deformed metal crystal at low temperature exhibits wavy slip line pattern due
to
(A) Dislocation pile-up
(B) Large number of slip systems
(C) Low stacking fault energy
(D) Dislocation climb
Q.19 Creep resistance decreases due to
(A) Small grain size
(B) Fine dispersoid size
(C) Low stacking fault energy
(D) High melting point
Q.20 The operation NOT associated with casting is
(A) Gating (B) Fettling
(C) Stack Moulding (D) Calendaring
0
20
40
60
80
100
120
140
160
180
200
0.00 0.01 0.02 0.03 0.04 0.05 0.06
Stress,?MPa
Strain
0.01
0.1
360
510
GATE 2016 MT
MT 5/12
Q.21 Of the following welding processes
[P] Laser Beam Welding
[Q] Submerged Arc Welding
[R] Metal Inert Gas Welding
the width of the heat-affected zone in decreasing order is
(A) P > Q > R (B) Q > R > P
(C) R > P > Q (D) P > R > Q
Q.22 Railway tracks are typically manufactured using
(A) Forging (B) Extrusion
(C) Deep Drawing (D) Rolling
Q.23 For dye-penetrant test, identify the CORRECT statement
(A) Pre- and post-cleaning of parts are not required
(B) Internal defects can be detected
(C) Surface oxides helps in crack identification
(D) Dye with low contact angle is required
Q.24 Aluminium powder having an apparent density of 810 kg.m
-3
is compacted in a cylindrical
die at 600 MPa. The density of the as-pressed aluminium compact is 1755 kg.m
-3
. If the
height of the as-pressed compact is 12 mm, the fill height (in mm) required is
___________
Q.25 A rolling mill has a roll diameter of 200 mm. If coefficient of friction is 0.1, then the
maximum possible reduction (in mm) during rolling of a 250 mm thick plate is
___________
Q. 26 ? Q. 55 carry two marks each.
Q.26 A hot body cools according to the following equation
where, T is the instantaneous temperature at time t, and the constant c = 0.05 s
-1
. Reduce
the differential equation into its finite difference form using forward difference.
For
maintaining numerical stability, the maximum value of the time step ?t (in seconds) is
________
Q.27 Solve the equation e
using Newton-Raphson method. Starting with an initial guess
value x
0
= 0, the value of x after the first iteration is ____________
Q.28 A coin is tossed three times. It is known that out of the three tosses, one is a HEAD. The
probability of the other two tosses also being HEADs is _____________
GATE 2016 MT
MT 6/12
Q.29 The vector parallel to the plane 3x ? 2y + z = ?1 is
(A) ? ?
(B) 3 ? 2 ?
(C) ? ?
(D) 3 ? 2 ? 2
Q.30 The value of the integral
?
?/2
0
dx sinx x = __________
Q.31 The grain sizes (in ?m) measured at five locations in an alloy sample are: 16, 14, 18, 15
and 13. The mean, median and standard deviation of grain sizes respectively are (in ?m)
(A) 15.2, 15 and 1.7
(B) 15.2, 15 and 1.9
(C) 15.8, 15 and 1.9
(D) 15.2, 16 and 1.7
Q.32 The change of standard state from pure liquid to 1 wt.% for Si dissolved in liquid Fe at
1873 K is expressed as
Si (liq.) = Si (1 wt.%)
Given that the activity coefficient of Si at infinite dilution in Fe is 10
-3
, the standard Gibbs
free energy change (in kJ) for this equilibrium is_____________
Q.33 The following experimental data are available for a hypothetical binary liquid system A-B
at 1073 K
Atom fraction of A
0.2 0.4 0.5 0.7 1.0
Partial pressure of A (bar) 0.01 0.04 0.06 0.07 0.08
When the atom fraction of A is 0.4, the activity of A in the liquid is ______________
GATE 2016 MT
MT 7/12
Q.34 The lining of a box-type furnace is made up of a refractory layer and steel plate as shown in
the figure. Steady state temperature at the surface of the refractory is 1273 K and that at the
outer steel surface is 473 K. If the steady-state heat flux through the refractory-steel plate
composite is 1600 W.m
-2
, and heat flow is along x-direction, the thermal contact resistance
(W
-1
.m
2
.K) between refractory and steel is _____________
Given data:
Thermal conductivity of refractory = 1.2 W.m
-1
K
-1
Thickness of refractory lining = 80 mm
Thermal conductivity of steel = 32 W.m
-1
K
-1
Thickness of steel plate = 4 mm
Q.35 The height of a liquid metal column in a cylindrical vessel is 3.2 m. At time t=0, liquid
metal is drained out from the vessel through a small nozzle located at the base of the vessel.
Neglecting frictional losses, the initial mass flow rate (in kg.s
-1
) through the
nozzle is ________________
Given data:
Density of liquid metal = 7000 kg.m
-3
Nozzle diameter = 30 mm
Nozzle discharge coefficient = 0.80
Q.36 Match entities listed in Column I with their correct dimensions given in Column II:
Column I Column II
[P] Drag coefficient [1] ML
-1
T
-1
[Q] Mass transfer coefficient [2] ML
-2
T
-1
[R] Viscosity [3] M
0
L
0
T
0
[S] Mass flux [4] M
0
LT
-1
(A) P-3, Q-4, R-1, S-2 (B) P-3, Q-1, R-2, S-4
(C) P-1, Q-4, R-2, S-3 (D) P-4, Q-3, R-1, S-2
Q.37 Direct Reduced Iron (DRI) produced from a gas based process contains Fe, FeO, C and
remainder being gangue. The chemical composition of DRI is: Total Fe = 92 wt.% and
Metallic Fe = 84 wt.%. The weight percent of FeO in DRI is _________________
1273 K 473 K
refractory
steel plate
Furnace
Ambient
x
GATE 2016 MT
MT 8/12
Q.38 Mould heat flux (q
m
) for billet casters is expressed (in SI unit) as a function of distance
below the meniscus (z)
6
c
m
10
U
z
33 . 0 67 . 2 ) z ( q ?
?
?
?
?
?
?
? ? ( ) 0
m
L z ? ?
If mould length (L
m
) is 0.8 m and casting speed (U
c
) is 0.2 m.s
-1
, the average mould flux
(in MW.m
-2
) is ________________
Q.39 In BOF steelmaking, 5 metric ton of lime containing 90 wt.% CaO is used to refine 100
metric ton of hot metal containing 93.2 wt.% Fe. The slag produced during refining
contains 40 wt.% CaO and 22 wt.% FeO. Neglecting material losses, the yield of Fe (in %)
is _________________
Q.40 In vacuum degassing of steel, 14 ppm of dissolved nitrogen is in equilibrium with 1 mbar
of nitrogen gas at 1873 K. At the same temperature, if the pressure is lowered to 0.7 mbar,
the equilibrium nitrogen content (in ppm) is _____________
Q.41 During isothermal phase transformation (in solid-state), fraction transformed is measured at
two different transformation times:
___________________________________________
Transformation Time, t (s) Fraction Transformed, f
___________________________________________
75 0.11
150 0.37
____________________________________________
Assuming Avrami kinetics [f = 1 ? exp (?kt
n
)], the fraction transformed in
300 seconds is _______________
Q.42 Zinc oxide is reduced at a constant temperature in a closed reactor using ZnO(s) and C(s)
as the only starting materials. The following reactions are assumed to be at thermodynamic
equilibrium:
ZnO(s) + C(s) = Zn(g) + CO(g)
2CO(g) = CO
2
(g) + C(s)
Assume ideal gas behaviour. Based on mole balance, the relationship applicable to the
system at equilibrium is
(A)
2
(B)
2
(C)
(D)
0.5
2
GATE 2016 MT
MT 9/12
Q.43 The critical nucleus size (in nm) when copper melt is under-cooled by 100 K is
Given data:
Melting point: 1356 K
Density: 8900 kg.m
-3
Solid-liquid interfacial energy: 0.5 Jm
-2
Latent heat of freezing: 13000 J.mol
-1
Molar volume: 7 ?10
-6
m
-3
mol
-1
(A) 0.36 (B) 1.55 (C) 3.65 (D) 7.30
Q.44 The density and corresponding crystallinity of two poly-propylene material are given
below
________________________________________
Density, kg.m
-3
Crystallinity, %
________________________________________
904 62.8
895 54.4
_________________________________________
The density of totally amorphous poly-propylene (in kg.m
-3
) is:
(A) 723 (B) 841 (C) 905 (D) 956
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude ? GA Set-7
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 If I were you, I __________ that laptop. It?s much too expensive.
(A) won?t buy (B) shan?t buy
(C) wouldn?t buy (D) would buy
Q.2 He turned a deaf ear to my request.
What does the underlined phrasal verb mean?
(A) ignored (B) appreciated (C) twisted (D) returned
Q.3 Choose the most appropriate set of words from the options given below to complete the following
sentence.
_________ ___________ is a will, _________ is a way.
(A) Wear, there, their (B) Were, their, there
(C) Where, there, there (D) Where, their, their
Q.4 (x % of y) + (y % of x) is equivalent to .
(A) 2 % of xy (B) 2 % of (xy/100) (C) xy % of 100 (D) 100 % of xy
Q.5 The sum of the digits of a two digit number is 12. If the new number formed by reversing the digits
is greater than the original number by 54, find the original number.
(A) 39 (B) 57 (C) 66 (D) 93
GATE 2016 General Aptitude ? GA Set-7
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 Two finance companies, P and Q, declared fixed annual rates of interest on the amounts invested
with them. The rates of interest offered by these companies may differ from year to year. Year-wise
annual rates of interest offered by these companies are shown by the line graph provided below.
If the amounts invested in the companies, P and Q, in 2006 are in the ratio 8:9, then the amounts
received after one year as interests from companies P and Q would be in the ratio:
(A) 2:3
(B) 3:4
(C) 6:7
(D) 4:3
Q.7 Today, we consider Ashoka as a great ruler because of the copious evidence he left behind in the
form of stone carved edicts. Historians tend to correlate greatness of a king at his time with the
availability of evidence today.
Which of the following can be logically inferred from the above sentences?
(A) Emperors who do not leave significant sculpted evidence are completely forgotten.
(B) Ashoka produced stone carved edicts to ensure that later historians will respect him.
(C) Statues of kings are a reminder of their greatness.
(D) A king?s greatness, as we know him today, is interpreted by historians.
7
9
8
10
7.5
6.5
6
6.5
8
9.5
8
9
8
4
2000 2001 2002 2003 2004 2005 2006
P Q
GATE 2016 General Aptitude ? GA Set-7
3/3
Q.8 Fact 1: Humans are mammals.
Fact 2: Some humans are engineers.
Fact 3: Engineers build houses.
If the above statements are facts, which of the following can be logically inferred?
I. All mammals build houses.
II. Engineers are mammals.
III. Some humans are not engineers.
(A) II only. (B) III only.
(C) I, II and III. (D) I only.
Q.9 A square pyramid has a base perimeter x, and the slant height is half of the perimeter. What is the
lateral surface area of the pyramid?
(A) x
2
(B) 0.75 x
2
(C) 0.50 x
2
(D) 0.25 x
2
END OF THE QUESTION PAPER
Q.10 Ananth takes 6 hours and Bharath takes 4 hours to read a book. Both started reading copies of the
book at the same time. After how many hours is the number of pages to be read by Ananth, twice
that to be read by Bharath? Assume Ananth and Bharath read all the pages with constant pace.
(A) 1 (B) 2 (C) 3 (D) 4
GATE 2016 MT
MT 1/12
Useful Data:
Gas constant (R) 8.314 J.mol
-1
K
-1
Acceleration due to gravity (g) 9.81 m
2
.s
-1
Atomic weight of oxygen 16 g.mol
-1
Atomic weight of silicon 28 g.mol
-1
Atomic weight of iron 56 g.mol
-1
Q. 1 ? Q. 25 carry one mark each.
Q.1 For the transformation shown below, if one of the eigenvalues is 6, the other eigenvalue of
the matrix is ______
52
2 2
Q.2 The solution of the differential equation
is
(A) C (B)
C
(C)
(D)
[where, C, C
1
and C
2
are constants]
Q.3
If
, the divergence of is
(A)
(B)
(C) 5
(D) 0
Q.4 The first law of thermodynamics can be stated as
(A) dE = ?Q ? ?W
(B) dQ = dE ? ?W
(C) ?W = dQ + dE
(D) dW = ?Q ? ?E
[where, E, Q and W denote internal energy, heat and work, respectively]
Q.5 In a typical Ellingham diagram for the oxides, the C + O
2
= CO
2
line is nearly horizontal
because
(A) The slope of the line is equal to the enthalpy change at standard state, which is
approximately zero in this case
(B) The slope of the line is equal to the entropy change at standard state, which is
approximately zero in this case
(C) CO
2
shows non-ideal behaviour
(D) CO
2
is a gaseous oxide
GATE 2016 MT
MT 2/12
Q.6 Activation energy of a chemical reaction, homogeneous or heterogeneous, is graphically
estimated from a plot between
(A) k versus T (B) 1/k versus T
(C) 1/k versus ln T (D) ln k versus 1/T
[where, k is the rate constant and T is the absolute temperature]
Q.7 The passive film in stainless steel forms above the
(A) Primary passive potential
(B) Breakdown potential
(C) Trans-passive potential
(D) Pitting potential
Q.8 During the roasting of a sulfide ore of a metal M, the possible solid phases are M, MS, MO
and MSO
4
. Assuming that both SO
2
and O
2
are always present in the roaster, the solid
phases that can co-exist at thermodynamic equilibrium are
(A) M, MS, MO, MSO
4
(B) M, MO, MSO
4
(C) MS, MO, MSO
4
(D) M, MSO
4
Q.9 Match the entities in Column I with the corresponding processes in Column II.
Column I Column II
[P] Xanthate salts [1] Extraction of Al
[Q] Thiobacillus Ferrooxidans [2] Flotation
[R] Hydrocyclone [3] Classification
[S] Anode effect [4] Bacterial Leaching
(A) P-4, Q-2, R-3, S-1
(B) P-2, Q-4, R-3, S-1
(C) P-3, Q-4, R-1, S-2
(D) P-4, Q-1, R-2, S-3
Q.10 A sub-lance is used to monitor composition and temperature in
(A) BOF (B) Ladle refining furnace
(C) Continuous casting mould (D) Blast furnace
Q.11 The chemical formula of w?stite is
(A) FeS
2
(B) Fe
2
O
3
(C) Fe
3
O
4
(D) Fe
1-x
O
Q.12 The lattice parameter of face-centered cubic iron ( ?-Fe) is 0.3571 nm. The radius (in nm) of
the octahedral void in ?-Fe is ___________
GATE 2016 MT
MT 3/12
Q.13 For an ideal hexagonal-closed packed structure, the c/a ratio and packing efficiency
respectively are
(A) 1.633 and 52% (B) 1.633 and 74%
(C) 1.733 and 68% (D) 1.733 and 74%
Q.14 A schematic of X-ray diffraction pattern of a single phase cubic polycrystal is given below.
The miller indices of peak A is
(A) 210 (B) 220
(C) 222 (D) 310
Q.15 Which of the following cooling curves (shown in schematic) in an eutectoid steel will
produce 50% bainitic structure?
(A) P (B) Q (C) R (D) S
2 ?
Intensity?(a.u.)
110
200
211
A
Ms
Ac
1
time?
Temperature
Pearlite
Bainite
Martensite
Austenite
Q
S
R
P
GATE 2016 MT
MT 4/12
Q.16
The Burger?s vector of a dislocation in a cubic crystal (with lattice parameter a) is
11 0
and dislocation line is along [112] direction. The angle (in degrees) between the dislocation
line and its Burger?s vector is_______
Q.17 For the tensile stress-strain curve of a material shown in the schematic, the resilience (in
MPa) is _________
Q.18 A plastically deformed metal crystal at low temperature exhibits wavy slip line pattern due
to
(A) Dislocation pile-up
(B) Large number of slip systems
(C) Low stacking fault energy
(D) Dislocation climb
Q.19 Creep resistance decreases due to
(A) Small grain size
(B) Fine dispersoid size
(C) Low stacking fault energy
(D) High melting point
Q.20 The operation NOT associated with casting is
(A) Gating (B) Fettling
(C) Stack Moulding (D) Calendaring
0
20
40
60
80
100
120
140
160
180
200
0.00 0.01 0.02 0.03 0.04 0.05 0.06
Stress,?MPa
Strain
0.01
0.1
360
510
GATE 2016 MT
MT 5/12
Q.21 Of the following welding processes
[P] Laser Beam Welding
[Q] Submerged Arc Welding
[R] Metal Inert Gas Welding
the width of the heat-affected zone in decreasing order is
(A) P > Q > R (B) Q > R > P
(C) R > P > Q (D) P > R > Q
Q.22 Railway tracks are typically manufactured using
(A) Forging (B) Extrusion
(C) Deep Drawing (D) Rolling
Q.23 For dye-penetrant test, identify the CORRECT statement
(A) Pre- and post-cleaning of parts are not required
(B) Internal defects can be detected
(C) Surface oxides helps in crack identification
(D) Dye with low contact angle is required
Q.24 Aluminium powder having an apparent density of 810 kg.m
-3
is compacted in a cylindrical
die at 600 MPa. The density of the as-pressed aluminium compact is 1755 kg.m
-3
. If the
height of the as-pressed compact is 12 mm, the fill height (in mm) required is
___________
Q.25 A rolling mill has a roll diameter of 200 mm. If coefficient of friction is 0.1, then the
maximum possible reduction (in mm) during rolling of a 250 mm thick plate is
___________
Q. 26 ? Q. 55 carry two marks each.
Q.26 A hot body cools according to the following equation
where, T is the instantaneous temperature at time t, and the constant c = 0.05 s
-1
. Reduce
the differential equation into its finite difference form using forward difference.
For
maintaining numerical stability, the maximum value of the time step ?t (in seconds) is
________
Q.27 Solve the equation e
using Newton-Raphson method. Starting with an initial guess
value x
0
= 0, the value of x after the first iteration is ____________
Q.28 A coin is tossed three times. It is known that out of the three tosses, one is a HEAD. The
probability of the other two tosses also being HEADs is _____________
GATE 2016 MT
MT 6/12
Q.29 The vector parallel to the plane 3x ? 2y + z = ?1 is
(A) ? ?
(B) 3 ? 2 ?
(C) ? ?
(D) 3 ? 2 ? 2
Q.30 The value of the integral
?
?/2
0
dx sinx x = __________
Q.31 The grain sizes (in ?m) measured at five locations in an alloy sample are: 16, 14, 18, 15
and 13. The mean, median and standard deviation of grain sizes respectively are (in ?m)
(A) 15.2, 15 and 1.7
(B) 15.2, 15 and 1.9
(C) 15.8, 15 and 1.9
(D) 15.2, 16 and 1.7
Q.32 The change of standard state from pure liquid to 1 wt.% for Si dissolved in liquid Fe at
1873 K is expressed as
Si (liq.) = Si (1 wt.%)
Given that the activity coefficient of Si at infinite dilution in Fe is 10
-3
, the standard Gibbs
free energy change (in kJ) for this equilibrium is_____________
Q.33 The following experimental data are available for a hypothetical binary liquid system A-B
at 1073 K
Atom fraction of A
0.2 0.4 0.5 0.7 1.0
Partial pressure of A (bar) 0.01 0.04 0.06 0.07 0.08
When the atom fraction of A is 0.4, the activity of A in the liquid is ______________
GATE 2016 MT
MT 7/12
Q.34 The lining of a box-type furnace is made up of a refractory layer and steel plate as shown in
the figure. Steady state temperature at the surface of the refractory is 1273 K and that at the
outer steel surface is 473 K. If the steady-state heat flux through the refractory-steel plate
composite is 1600 W.m
-2
, and heat flow is along x-direction, the thermal contact resistance
(W
-1
.m
2
.K) between refractory and steel is _____________
Given data:
Thermal conductivity of refractory = 1.2 W.m
-1
K
-1
Thickness of refractory lining = 80 mm
Thermal conductivity of steel = 32 W.m
-1
K
-1
Thickness of steel plate = 4 mm
Q.35 The height of a liquid metal column in a cylindrical vessel is 3.2 m. At time t=0, liquid
metal is drained out from the vessel through a small nozzle located at the base of the vessel.
Neglecting frictional losses, the initial mass flow rate (in kg.s
-1
) through the
nozzle is ________________
Given data:
Density of liquid metal = 7000 kg.m
-3
Nozzle diameter = 30 mm
Nozzle discharge coefficient = 0.80
Q.36 Match entities listed in Column I with their correct dimensions given in Column II:
Column I Column II
[P] Drag coefficient [1] ML
-1
T
-1
[Q] Mass transfer coefficient [2] ML
-2
T
-1
[R] Viscosity [3] M
0
L
0
T
0
[S] Mass flux [4] M
0
LT
-1
(A) P-3, Q-4, R-1, S-2 (B) P-3, Q-1, R-2, S-4
(C) P-1, Q-4, R-2, S-3 (D) P-4, Q-3, R-1, S-2
Q.37 Direct Reduced Iron (DRI) produced from a gas based process contains Fe, FeO, C and
remainder being gangue. The chemical composition of DRI is: Total Fe = 92 wt.% and
Metallic Fe = 84 wt.%. The weight percent of FeO in DRI is _________________
1273 K 473 K
refractory
steel plate
Furnace
Ambient
x
GATE 2016 MT
MT 8/12
Q.38 Mould heat flux (q
m
) for billet casters is expressed (in SI unit) as a function of distance
below the meniscus (z)
6
c
m
10
U
z
33 . 0 67 . 2 ) z ( q ?
?
?
?
?
?
?
? ? ( ) 0
m
L z ? ?
If mould length (L
m
) is 0.8 m and casting speed (U
c
) is 0.2 m.s
-1
, the average mould flux
(in MW.m
-2
) is ________________
Q.39 In BOF steelmaking, 5 metric ton of lime containing 90 wt.% CaO is used to refine 100
metric ton of hot metal containing 93.2 wt.% Fe. The slag produced during refining
contains 40 wt.% CaO and 22 wt.% FeO. Neglecting material losses, the yield of Fe (in %)
is _________________
Q.40 In vacuum degassing of steel, 14 ppm of dissolved nitrogen is in equilibrium with 1 mbar
of nitrogen gas at 1873 K. At the same temperature, if the pressure is lowered to 0.7 mbar,
the equilibrium nitrogen content (in ppm) is _____________
Q.41 During isothermal phase transformation (in solid-state), fraction transformed is measured at
two different transformation times:
___________________________________________
Transformation Time, t (s) Fraction Transformed, f
___________________________________________
75 0.11
150 0.37
____________________________________________
Assuming Avrami kinetics [f = 1 ? exp (?kt
n
)], the fraction transformed in
300 seconds is _______________
Q.42 Zinc oxide is reduced at a constant temperature in a closed reactor using ZnO(s) and C(s)
as the only starting materials. The following reactions are assumed to be at thermodynamic
equilibrium:
ZnO(s) + C(s) = Zn(g) + CO(g)
2CO(g) = CO
2
(g) + C(s)
Assume ideal gas behaviour. Based on mole balance, the relationship applicable to the
system at equilibrium is
(A)
2
(B)
2
(C)
(D)
0.5
2
GATE 2016 MT
MT 9/12
Q.43 The critical nucleus size (in nm) when copper melt is under-cooled by 100 K is
Given data:
Melting point: 1356 K
Density: 8900 kg.m
-3
Solid-liquid interfacial energy: 0.5 Jm
-2
Latent heat of freezing: 13000 J.mol
-1
Molar volume: 7 ?10
-6
m
-3
mol
-1
(A) 0.36 (B) 1.55 (C) 3.65 (D) 7.30
Q.44 The density and corresponding crystallinity of two poly-propylene material are given
below
________________________________________
Density, kg.m
-3
Crystallinity, %
________________________________________
904 62.8
895 54.4
_________________________________________
The density of totally amorphous poly-propylene (in kg.m
-3
) is:
(A) 723 (B) 841 (C) 905 (D) 956
GATE 2016 MT
MT 10/12
Q.45 A simplified energy band-diagram of an intrinsic semiconductor at thermal equilibrium
(300 K) is shown. In the accompanying table, which one of the four columns correctly
represents the listed parameters? Assume same effective mass for electrons and holes.
Parameter
Energy-difference
Column 1 Column 2 Column 3 Column 4
Band-gap ?E
2
?E
1
?E
2
?E
1
Electron affinity ?E
1
/2 ?E
2
? ?E
1
?E
2
/2 ?E
2
? ( ?E
1
/2)
Work function ?E
1
+ ?E
2
?E
2
? ( ?E
1
/2) ?E
1
? ?E
2
/2 ?E
2
+ ( ?E
1
/2)
(A) Column 1 (B) Column 2 (C) Column 3 (D) Column 4
Q.46 A binary phase diagram is shown in the schematic.
Upon complete solidification of a binary alloy system A-B, the fraction of pro-eutectic ?-
phase present is 0.50. The alloy composition in terms of wt%. B is _________________
Fermi
level
Vacuum
level
Electron Energy(E)
?E
1
?E
2
L
?+?L
?+?L
?
?
?+? ?
18.3
61.9
97.8
A
B
Wt%?B
Temperature
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude ? GA Set-7
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 If I were you, I __________ that laptop. It?s much too expensive.
(A) won?t buy (B) shan?t buy
(C) wouldn?t buy (D) would buy
Q.2 He turned a deaf ear to my request.
What does the underlined phrasal verb mean?
(A) ignored (B) appreciated (C) twisted (D) returned
Q.3 Choose the most appropriate set of words from the options given below to complete the following
sentence.
_________ ___________ is a will, _________ is a way.
(A) Wear, there, their (B) Were, their, there
(C) Where, there, there (D) Where, their, their
Q.4 (x % of y) + (y % of x) is equivalent to .
(A) 2 % of xy (B) 2 % of (xy/100) (C) xy % of 100 (D) 100 % of xy
Q.5 The sum of the digits of a two digit number is 12. If the new number formed by reversing the digits
is greater than the original number by 54, find the original number.
(A) 39 (B) 57 (C) 66 (D) 93
GATE 2016 General Aptitude ? GA Set-7
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 Two finance companies, P and Q, declared fixed annual rates of interest on the amounts invested
with them. The rates of interest offered by these companies may differ from year to year. Year-wise
annual rates of interest offered by these companies are shown by the line graph provided below.
If the amounts invested in the companies, P and Q, in 2006 are in the ratio 8:9, then the amounts
received after one year as interests from companies P and Q would be in the ratio:
(A) 2:3
(B) 3:4
(C) 6:7
(D) 4:3
Q.7 Today, we consider Ashoka as a great ruler because of the copious evidence he left behind in the
form of stone carved edicts. Historians tend to correlate greatness of a king at his time with the
availability of evidence today.
Which of the following can be logically inferred from the above sentences?
(A) Emperors who do not leave significant sculpted evidence are completely forgotten.
(B) Ashoka produced stone carved edicts to ensure that later historians will respect him.
(C) Statues of kings are a reminder of their greatness.
(D) A king?s greatness, as we know him today, is interpreted by historians.
7
9
8
10
7.5
6.5
6
6.5
8
9.5
8
9
8
4
2000 2001 2002 2003 2004 2005 2006
P Q
GATE 2016 General Aptitude ? GA Set-7
3/3
Q.8 Fact 1: Humans are mammals.
Fact 2: Some humans are engineers.
Fact 3: Engineers build houses.
If the above statements are facts, which of the following can be logically inferred?
I. All mammals build houses.
II. Engineers are mammals.
III. Some humans are not engineers.
(A) II only. (B) III only.
(C) I, II and III. (D) I only.
Q.9 A square pyramid has a base perimeter x, and the slant height is half of the perimeter. What is the
lateral surface area of the pyramid?
(A) x
2
(B) 0.75 x
2
(C) 0.50 x
2
(D) 0.25 x
2
END OF THE QUESTION PAPER
Q.10 Ananth takes 6 hours and Bharath takes 4 hours to read a book. Both started reading copies of the
book at the same time. After how many hours is the number of pages to be read by Ananth, twice
that to be read by Bharath? Assume Ananth and Bharath read all the pages with constant pace.
(A) 1 (B) 2 (C) 3 (D) 4
GATE 2016 MT
MT 1/12
Useful Data:
Gas constant (R) 8.314 J.mol
-1
K
-1
Acceleration due to gravity (g) 9.81 m
2
.s
-1
Atomic weight of oxygen 16 g.mol
-1
Atomic weight of silicon 28 g.mol
-1
Atomic weight of iron 56 g.mol
-1
Q. 1 ? Q. 25 carry one mark each.
Q.1 For the transformation shown below, if one of the eigenvalues is 6, the other eigenvalue of
the matrix is ______
52
2 2
Q.2 The solution of the differential equation
is
(A) C (B)
C
(C)
(D)
[where, C, C
1
and C
2
are constants]
Q.3
If
, the divergence of is
(A)
(B)
(C) 5
(D) 0
Q.4 The first law of thermodynamics can be stated as
(A) dE = ?Q ? ?W
(B) dQ = dE ? ?W
(C) ?W = dQ + dE
(D) dW = ?Q ? ?E
[where, E, Q and W denote internal energy, heat and work, respectively]
Q.5 In a typical Ellingham diagram for the oxides, the C + O
2
= CO
2
line is nearly horizontal
because
(A) The slope of the line is equal to the enthalpy change at standard state, which is
approximately zero in this case
(B) The slope of the line is equal to the entropy change at standard state, which is
approximately zero in this case
(C) CO
2
shows non-ideal behaviour
(D) CO
2
is a gaseous oxide
GATE 2016 MT
MT 2/12
Q.6 Activation energy of a chemical reaction, homogeneous or heterogeneous, is graphically
estimated from a plot between
(A) k versus T (B) 1/k versus T
(C) 1/k versus ln T (D) ln k versus 1/T
[where, k is the rate constant and T is the absolute temperature]
Q.7 The passive film in stainless steel forms above the
(A) Primary passive potential
(B) Breakdown potential
(C) Trans-passive potential
(D) Pitting potential
Q.8 During the roasting of a sulfide ore of a metal M, the possible solid phases are M, MS, MO
and MSO
4
. Assuming that both SO
2
and O
2
are always present in the roaster, the solid
phases that can co-exist at thermodynamic equilibrium are
(A) M, MS, MO, MSO
4
(B) M, MO, MSO
4
(C) MS, MO, MSO
4
(D) M, MSO
4
Q.9 Match the entities in Column I with the corresponding processes in Column II.
Column I Column II
[P] Xanthate salts [1] Extraction of Al
[Q] Thiobacillus Ferrooxidans [2] Flotation
[R] Hydrocyclone [3] Classification
[S] Anode effect [4] Bacterial Leaching
(A) P-4, Q-2, R-3, S-1
(B) P-2, Q-4, R-3, S-1
(C) P-3, Q-4, R-1, S-2
(D) P-4, Q-1, R-2, S-3
Q.10 A sub-lance is used to monitor composition and temperature in
(A) BOF (B) Ladle refining furnace
(C) Continuous casting mould (D) Blast furnace
Q.11 The chemical formula of w?stite is
(A) FeS
2
(B) Fe
2
O
3
(C) Fe
3
O
4
(D) Fe
1-x
O
Q.12 The lattice parameter of face-centered cubic iron ( ?-Fe) is 0.3571 nm. The radius (in nm) of
the octahedral void in ?-Fe is ___________
GATE 2016 MT
MT 3/12
Q.13 For an ideal hexagonal-closed packed structure, the c/a ratio and packing efficiency
respectively are
(A) 1.633 and 52% (B) 1.633 and 74%
(C) 1.733 and 68% (D) 1.733 and 74%
Q.14 A schematic of X-ray diffraction pattern of a single phase cubic polycrystal is given below.
The miller indices of peak A is
(A) 210 (B) 220
(C) 222 (D) 310
Q.15 Which of the following cooling curves (shown in schematic) in an eutectoid steel will
produce 50% bainitic structure?
(A) P (B) Q (C) R (D) S
2 ?
Intensity?(a.u.)
110
200
211
A
Ms
Ac
1
time?
Temperature
Pearlite
Bainite
Martensite
Austenite
Q
S
R
P
GATE 2016 MT
MT 4/12
Q.16
The Burger?s vector of a dislocation in a cubic crystal (with lattice parameter a) is
11 0
and dislocation line is along [112] direction. The angle (in degrees) between the dislocation
line and its Burger?s vector is_______
Q.17 For the tensile stress-strain curve of a material shown in the schematic, the resilience (in
MPa) is _________
Q.18 A plastically deformed metal crystal at low temperature exhibits wavy slip line pattern due
to
(A) Dislocation pile-up
(B) Large number of slip systems
(C) Low stacking fault energy
(D) Dislocation climb
Q.19 Creep resistance decreases due to
(A) Small grain size
(B) Fine dispersoid size
(C) Low stacking fault energy
(D) High melting point
Q.20 The operation NOT associated with casting is
(A) Gating (B) Fettling
(C) Stack Moulding (D) Calendaring
0
20
40
60
80
100
120
140
160
180
200
0.00 0.01 0.02 0.03 0.04 0.05 0.06
Stress,?MPa
Strain
0.01
0.1
360
510
GATE 2016 MT
MT 5/12
Q.21 Of the following welding processes
[P] Laser Beam Welding
[Q] Submerged Arc Welding
[R] Metal Inert Gas Welding
the width of the heat-affected zone in decreasing order is
(A) P > Q > R (B) Q > R > P
(C) R > P > Q (D) P > R > Q
Q.22 Railway tracks are typically manufactured using
(A) Forging (B) Extrusion
(C) Deep Drawing (D) Rolling
Q.23 For dye-penetrant test, identify the CORRECT statement
(A) Pre- and post-cleaning of parts are not required
(B) Internal defects can be detected
(C) Surface oxides helps in crack identification
(D) Dye with low contact angle is required
Q.24 Aluminium powder having an apparent density of 810 kg.m
-3
is compacted in a cylindrical
die at 600 MPa. The density of the as-pressed aluminium compact is 1755 kg.m
-3
. If the
height of the as-pressed compact is 12 mm, the fill height (in mm) required is
___________
Q.25 A rolling mill has a roll diameter of 200 mm. If coefficient of friction is 0.1, then the
maximum possible reduction (in mm) during rolling of a 250 mm thick plate is
___________
Q. 26 ? Q. 55 carry two marks each.
Q.26 A hot body cools according to the following equation
where, T is the instantaneous temperature at time t, and the constant c = 0.05 s
-1
. Reduce
the differential equation into its finite difference form using forward difference.
For
maintaining numerical stability, the maximum value of the time step ?t (in seconds) is
________
Q.27 Solve the equation e
using Newton-Raphson method. Starting with an initial guess
value x
0
= 0, the value of x after the first iteration is ____________
Q.28 A coin is tossed three times. It is known that out of the three tosses, one is a HEAD. The
probability of the other two tosses also being HEADs is _____________
GATE 2016 MT
MT 6/12
Q.29 The vector parallel to the plane 3x ? 2y + z = ?1 is
(A) ? ?
(B) 3 ? 2 ?
(C) ? ?
(D) 3 ? 2 ? 2
Q.30 The value of the integral
?
?/2
0
dx sinx x = __________
Q.31 The grain sizes (in ?m) measured at five locations in an alloy sample are: 16, 14, 18, 15
and 13. The mean, median and standard deviation of grain sizes respectively are (in ?m)
(A) 15.2, 15 and 1.7
(B) 15.2, 15 and 1.9
(C) 15.8, 15 and 1.9
(D) 15.2, 16 and 1.7
Q.32 The change of standard state from pure liquid to 1 wt.% for Si dissolved in liquid Fe at
1873 K is expressed as
Si (liq.) = Si (1 wt.%)
Given that the activity coefficient of Si at infinite dilution in Fe is 10
-3
, the standard Gibbs
free energy change (in kJ) for this equilibrium is_____________
Q.33 The following experimental data are available for a hypothetical binary liquid system A-B
at 1073 K
Atom fraction of A
0.2 0.4 0.5 0.7 1.0
Partial pressure of A (bar) 0.01 0.04 0.06 0.07 0.08
When the atom fraction of A is 0.4, the activity of A in the liquid is ______________
GATE 2016 MT
MT 7/12
Q.34 The lining of a box-type furnace is made up of a refractory layer and steel plate as shown in
the figure. Steady state temperature at the surface of the refractory is 1273 K and that at the
outer steel surface is 473 K. If the steady-state heat flux through the refractory-steel plate
composite is 1600 W.m
-2
, and heat flow is along x-direction, the thermal contact resistance
(W
-1
.m
2
.K) between refractory and steel is _____________
Given data:
Thermal conductivity of refractory = 1.2 W.m
-1
K
-1
Thickness of refractory lining = 80 mm
Thermal conductivity of steel = 32 W.m
-1
K
-1
Thickness of steel plate = 4 mm
Q.35 The height of a liquid metal column in a cylindrical vessel is 3.2 m. At time t=0, liquid
metal is drained out from the vessel through a small nozzle located at the base of the vessel.
Neglecting frictional losses, the initial mass flow rate (in kg.s
-1
) through the
nozzle is ________________
Given data:
Density of liquid metal = 7000 kg.m
-3
Nozzle diameter = 30 mm
Nozzle discharge coefficient = 0.80
Q.36 Match entities listed in Column I with their correct dimensions given in Column II:
Column I Column II
[P] Drag coefficient [1] ML
-1
T
-1
[Q] Mass transfer coefficient [2] ML
-2
T
-1
[R] Viscosity [3] M
0
L
0
T
0
[S] Mass flux [4] M
0
LT
-1
(A) P-3, Q-4, R-1, S-2 (B) P-3, Q-1, R-2, S-4
(C) P-1, Q-4, R-2, S-3 (D) P-4, Q-3, R-1, S-2
Q.37 Direct Reduced Iron (DRI) produced from a gas based process contains Fe, FeO, C and
remainder being gangue. The chemical composition of DRI is: Total Fe = 92 wt.% and
Metallic Fe = 84 wt.%. The weight percent of FeO in DRI is _________________
1273 K 473 K
refractory
steel plate
Furnace
Ambient
x
GATE 2016 MT
MT 8/12
Q.38 Mould heat flux (q
m
) for billet casters is expressed (in SI unit) as a function of distance
below the meniscus (z)
6
c
m
10
U
z
33 . 0 67 . 2 ) z ( q ?
?
?
?
?
?
?
? ? ( ) 0
m
L z ? ?
If mould length (L
m
) is 0.8 m and casting speed (U
c
) is 0.2 m.s
-1
, the average mould flux
(in MW.m
-2
) is ________________
Q.39 In BOF steelmaking, 5 metric ton of lime containing 90 wt.% CaO is used to refine 100
metric ton of hot metal containing 93.2 wt.% Fe. The slag produced during refining
contains 40 wt.% CaO and 22 wt.% FeO. Neglecting material losses, the yield of Fe (in %)
is _________________
Q.40 In vacuum degassing of steel, 14 ppm of dissolved nitrogen is in equilibrium with 1 mbar
of nitrogen gas at 1873 K. At the same temperature, if the pressure is lowered to 0.7 mbar,
the equilibrium nitrogen content (in ppm) is _____________
Q.41 During isothermal phase transformation (in solid-state), fraction transformed is measured at
two different transformation times:
___________________________________________
Transformation Time, t (s) Fraction Transformed, f
___________________________________________
75 0.11
150 0.37
____________________________________________
Assuming Avrami kinetics [f = 1 ? exp (?kt
n
)], the fraction transformed in
300 seconds is _______________
Q.42 Zinc oxide is reduced at a constant temperature in a closed reactor using ZnO(s) and C(s)
as the only starting materials. The following reactions are assumed to be at thermodynamic
equilibrium:
ZnO(s) + C(s) = Zn(g) + CO(g)
2CO(g) = CO
2
(g) + C(s)
Assume ideal gas behaviour. Based on mole balance, the relationship applicable to the
system at equilibrium is
(A)
2
(B)
2
(C)
(D)
0.5
2
GATE 2016 MT
MT 9/12
Q.43 The critical nucleus size (in nm) when copper melt is under-cooled by 100 K is
Given data:
Melting point: 1356 K
Density: 8900 kg.m
-3
Solid-liquid interfacial energy: 0.5 Jm
-2
Latent heat of freezing: 13000 J.mol
-1
Molar volume: 7 ?10
-6
m
-3
mol
-1
(A) 0.36 (B) 1.55 (C) 3.65 (D) 7.30
Q.44 The density and corresponding crystallinity of two poly-propylene material are given
below
________________________________________
Density, kg.m
-3
Crystallinity, %
________________________________________
904 62.8
895 54.4
_________________________________________
The density of totally amorphous poly-propylene (in kg.m
-3
) is:
(A) 723 (B) 841 (C) 905 (D) 956
GATE 2016 MT
MT 10/12
Q.45 A simplified energy band-diagram of an intrinsic semiconductor at thermal equilibrium
(300 K) is shown. In the accompanying table, which one of the four columns correctly
represents the listed parameters? Assume same effective mass for electrons and holes.
Parameter
Energy-difference
Column 1 Column 2 Column 3 Column 4
Band-gap ?E
2
?E
1
?E
2
?E
1
Electron affinity ?E
1
/2 ?E
2
? ?E
1
?E
2
/2 ?E
2
? ( ?E
1
/2)
Work function ?E
1
+ ?E
2
?E
2
? ( ?E
1
/2) ?E
1
? ?E
2
/2 ?E
2
+ ( ?E
1
/2)
(A) Column 1 (B) Column 2 (C) Column 3 (D) Column 4
Q.46 A binary phase diagram is shown in the schematic.
Upon complete solidification of a binary alloy system A-B, the fraction of pro-eutectic ?-
phase present is 0.50. The alloy composition in terms of wt%. B is _________________
Fermi
level
Vacuum
level
Electron Energy(E)
?E
1
?E
2
L
?+?L
?+?L
?
?
?+? ?
18.3
61.9
97.8
A
B
Wt%?B
Temperature
GATE 2016 MT
MT 11/12
Q.47 Fatigue behaviour of an aluminium alloy is shown in the S-N plot. A piston rod made of
this material is subjected to: (i) 1000 cycles at 420 MPa, followed by (ii) 1000 cycles at
300 MPa. Using Miner?s rule of cumulative damage, the remaining fatigue life (in terms of
number of cycles) at stress of 250 MPa is _______________
Q.48 A glass plate has two parallel cracks. One of them is an internal crack of length 5 ?m and
the other is a surface crack of length 3 ?m. A tensile stress is applied perpendicular to the
crack surfaces. The fracture stress (in MPa) is ___________
Given data (for glass plate):
Young?s Modulus = 70 GPa
Surface energy per unit area = 1 J.m
-2
Q.49 A tensile stress is applied along the [100] direction in a FCC metal crystal. The critical
resolved shear stress is 6 MPa. The tensile stress (in MPa) required for initiating slip on the
(111) slip plane is_____________
Q.50 For a bcc metal the ratio of the surface energy per unit area of the (100) plane to that of the
(110) plane is ______________
Q.51 For a polymer reinforced with 40 vol.% glass fiber, the elastic modulus (in GPa) along the
transverse direction is
(A) 5.6 (B) 8.1
(C) 30.1 (D) 43.4
[E
glass fiber
= 70 GPa; E
polymer
= 3.5 GPa]
0
200
400
600
800
0 2000 4000 6000 8000 10000
S,??MPa
N
420?MPa
300?MPa
250?MPa
2000 5000
8800
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude ? GA Set-7
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 If I were you, I __________ that laptop. It?s much too expensive.
(A) won?t buy (B) shan?t buy
(C) wouldn?t buy (D) would buy
Q.2 He turned a deaf ear to my request.
What does the underlined phrasal verb mean?
(A) ignored (B) appreciated (C) twisted (D) returned
Q.3 Choose the most appropriate set of words from the options given below to complete the following
sentence.
_________ ___________ is a will, _________ is a way.
(A) Wear, there, their (B) Were, their, there
(C) Where, there, there (D) Where, their, their
Q.4 (x % of y) + (y % of x) is equivalent to .
(A) 2 % of xy (B) 2 % of (xy/100) (C) xy % of 100 (D) 100 % of xy
Q.5 The sum of the digits of a two digit number is 12. If the new number formed by reversing the digits
is greater than the original number by 54, find the original number.
(A) 39 (B) 57 (C) 66 (D) 93
GATE 2016 General Aptitude ? GA Set-7
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 Two finance companies, P and Q, declared fixed annual rates of interest on the amounts invested
with them. The rates of interest offered by these companies may differ from year to year. Year-wise
annual rates of interest offered by these companies are shown by the line graph provided below.
If the amounts invested in the companies, P and Q, in 2006 are in the ratio 8:9, then the amounts
received after one year as interests from companies P and Q would be in the ratio:
(A) 2:3
(B) 3:4
(C) 6:7
(D) 4:3
Q.7 Today, we consider Ashoka as a great ruler because of the copious evidence he left behind in the
form of stone carved edicts. Historians tend to correlate greatness of a king at his time with the
availability of evidence today.
Which of the following can be logically inferred from the above sentences?
(A) Emperors who do not leave significant sculpted evidence are completely forgotten.
(B) Ashoka produced stone carved edicts to ensure that later historians will respect him.
(C) Statues of kings are a reminder of their greatness.
(D) A king?s greatness, as we know him today, is interpreted by historians.
7
9
8
10
7.5
6.5
6
6.5
8
9.5
8
9
8
4
2000 2001 2002 2003 2004 2005 2006
P Q
GATE 2016 General Aptitude ? GA Set-7
3/3
Q.8 Fact 1: Humans are mammals.
Fact 2: Some humans are engineers.
Fact 3: Engineers build houses.
If the above statements are facts, which of the following can be logically inferred?
I. All mammals build houses.
II. Engineers are mammals.
III. Some humans are not engineers.
(A) II only. (B) III only.
(C) I, II and III. (D) I only.
Q.9 A square pyramid has a base perimeter x, and the slant height is half of the perimeter. What is the
lateral surface area of the pyramid?
(A) x
2
(B) 0.75 x
2
(C) 0.50 x
2
(D) 0.25 x
2
END OF THE QUESTION PAPER
Q.10 Ananth takes 6 hours and Bharath takes 4 hours to read a book. Both started reading copies of the
book at the same time. After how many hours is the number of pages to be read by Ananth, twice
that to be read by Bharath? Assume Ananth and Bharath read all the pages with constant pace.
(A) 1 (B) 2 (C) 3 (D) 4
GATE 2016 MT
MT 1/12
Useful Data:
Gas constant (R) 8.314 J.mol
-1
K
-1
Acceleration due to gravity (g) 9.81 m
2
.s
-1
Atomic weight of oxygen 16 g.mol
-1
Atomic weight of silicon 28 g.mol
-1
Atomic weight of iron 56 g.mol
-1
Q. 1 ? Q. 25 carry one mark each.
Q.1 For the transformation shown below, if one of the eigenvalues is 6, the other eigenvalue of
the matrix is ______
52
2 2
Q.2 The solution of the differential equation
is
(A) C (B)
C
(C)
(D)
[where, C, C
1
and C
2
are constants]
Q.3
If
, the divergence of is
(A)
(B)
(C) 5
(D) 0
Q.4 The first law of thermodynamics can be stated as
(A) dE = ?Q ? ?W
(B) dQ = dE ? ?W
(C) ?W = dQ + dE
(D) dW = ?Q ? ?E
[where, E, Q and W denote internal energy, heat and work, respectively]
Q.5 In a typical Ellingham diagram for the oxides, the C + O
2
= CO
2
line is nearly horizontal
because
(A) The slope of the line is equal to the enthalpy change at standard state, which is
approximately zero in this case
(B) The slope of the line is equal to the entropy change at standard state, which is
approximately zero in this case
(C) CO
2
shows non-ideal behaviour
(D) CO
2
is a gaseous oxide
GATE 2016 MT
MT 2/12
Q.6 Activation energy of a chemical reaction, homogeneous or heterogeneous, is graphically
estimated from a plot between
(A) k versus T (B) 1/k versus T
(C) 1/k versus ln T (D) ln k versus 1/T
[where, k is the rate constant and T is the absolute temperature]
Q.7 The passive film in stainless steel forms above the
(A) Primary passive potential
(B) Breakdown potential
(C) Trans-passive potential
(D) Pitting potential
Q.8 During the roasting of a sulfide ore of a metal M, the possible solid phases are M, MS, MO
and MSO
4
. Assuming that both SO
2
and O
2
are always present in the roaster, the solid
phases that can co-exist at thermodynamic equilibrium are
(A) M, MS, MO, MSO
4
(B) M, MO, MSO
4
(C) MS, MO, MSO
4
(D) M, MSO
4
Q.9 Match the entities in Column I with the corresponding processes in Column II.
Column I Column II
[P] Xanthate salts [1] Extraction of Al
[Q] Thiobacillus Ferrooxidans [2] Flotation
[R] Hydrocyclone [3] Classification
[S] Anode effect [4] Bacterial Leaching
(A) P-4, Q-2, R-3, S-1
(B) P-2, Q-4, R-3, S-1
(C) P-3, Q-4, R-1, S-2
(D) P-4, Q-1, R-2, S-3
Q.10 A sub-lance is used to monitor composition and temperature in
(A) BOF (B) Ladle refining furnace
(C) Continuous casting mould (D) Blast furnace
Q.11 The chemical formula of w?stite is
(A) FeS
2
(B) Fe
2
O
3
(C) Fe
3
O
4
(D) Fe
1-x
O
Q.12 The lattice parameter of face-centered cubic iron ( ?-Fe) is 0.3571 nm. The radius (in nm) of
the octahedral void in ?-Fe is ___________
GATE 2016 MT
MT 3/12
Q.13 For an ideal hexagonal-closed packed structure, the c/a ratio and packing efficiency
respectively are
(A) 1.633 and 52% (B) 1.633 and 74%
(C) 1.733 and 68% (D) 1.733 and 74%
Q.14 A schematic of X-ray diffraction pattern of a single phase cubic polycrystal is given below.
The miller indices of peak A is
(A) 210 (B) 220
(C) 222 (D) 310
Q.15 Which of the following cooling curves (shown in schematic) in an eutectoid steel will
produce 50% bainitic structure?
(A) P (B) Q (C) R (D) S
2 ?
Intensity?(a.u.)
110
200
211
A
Ms
Ac
1
time?
Temperature
Pearlite
Bainite
Martensite
Austenite
Q
S
R
P
GATE 2016 MT
MT 4/12
Q.16
The Burger?s vector of a dislocation in a cubic crystal (with lattice parameter a) is
11 0
and dislocation line is along [112] direction. The angle (in degrees) between the dislocation
line and its Burger?s vector is_______
Q.17 For the tensile stress-strain curve of a material shown in the schematic, the resilience (in
MPa) is _________
Q.18 A plastically deformed metal crystal at low temperature exhibits wavy slip line pattern due
to
(A) Dislocation pile-up
(B) Large number of slip systems
(C) Low stacking fault energy
(D) Dislocation climb
Q.19 Creep resistance decreases due to
(A) Small grain size
(B) Fine dispersoid size
(C) Low stacking fault energy
(D) High melting point
Q.20 The operation NOT associated with casting is
(A) Gating (B) Fettling
(C) Stack Moulding (D) Calendaring
0
20
40
60
80
100
120
140
160
180
200
0.00 0.01 0.02 0.03 0.04 0.05 0.06
Stress,?MPa
Strain
0.01
0.1
360
510
GATE 2016 MT
MT 5/12
Q.21 Of the following welding processes
[P] Laser Beam Welding
[Q] Submerged Arc Welding
[R] Metal Inert Gas Welding
the width of the heat-affected zone in decreasing order is
(A) P > Q > R (B) Q > R > P
(C) R > P > Q (D) P > R > Q
Q.22 Railway tracks are typically manufactured using
(A) Forging (B) Extrusion
(C) Deep Drawing (D) Rolling
Q.23 For dye-penetrant test, identify the CORRECT statement
(A) Pre- and post-cleaning of parts are not required
(B) Internal defects can be detected
(C) Surface oxides helps in crack identification
(D) Dye with low contact angle is required
Q.24 Aluminium powder having an apparent density of 810 kg.m
-3
is compacted in a cylindrical
die at 600 MPa. The density of the as-pressed aluminium compact is 1755 kg.m
-3
. If the
height of the as-pressed compact is 12 mm, the fill height (in mm) required is
___________
Q.25 A rolling mill has a roll diameter of 200 mm. If coefficient of friction is 0.1, then the
maximum possible reduction (in mm) during rolling of a 250 mm thick plate is
___________
Q. 26 ? Q. 55 carry two marks each.
Q.26 A hot body cools according to the following equation
where, T is the instantaneous temperature at time t, and the constant c = 0.05 s
-1
. Reduce
the differential equation into its finite difference form using forward difference.
For
maintaining numerical stability, the maximum value of the time step ?t (in seconds) is
________
Q.27 Solve the equation e
using Newton-Raphson method. Starting with an initial guess
value x
0
= 0, the value of x after the first iteration is ____________
Q.28 A coin is tossed three times. It is known that out of the three tosses, one is a HEAD. The
probability of the other two tosses also being HEADs is _____________
GATE 2016 MT
MT 6/12
Q.29 The vector parallel to the plane 3x ? 2y + z = ?1 is
(A) ? ?
(B) 3 ? 2 ?
(C) ? ?
(D) 3 ? 2 ? 2
Q.30 The value of the integral
?
?/2
0
dx sinx x = __________
Q.31 The grain sizes (in ?m) measured at five locations in an alloy sample are: 16, 14, 18, 15
and 13. The mean, median and standard deviation of grain sizes respectively are (in ?m)
(A) 15.2, 15 and 1.7
(B) 15.2, 15 and 1.9
(C) 15.8, 15 and 1.9
(D) 15.2, 16 and 1.7
Q.32 The change of standard state from pure liquid to 1 wt.% for Si dissolved in liquid Fe at
1873 K is expressed as
Si (liq.) = Si (1 wt.%)
Given that the activity coefficient of Si at infinite dilution in Fe is 10
-3
, the standard Gibbs
free energy change (in kJ) for this equilibrium is_____________
Q.33 The following experimental data are available for a hypothetical binary liquid system A-B
at 1073 K
Atom fraction of A
0.2 0.4 0.5 0.7 1.0
Partial pressure of A (bar) 0.01 0.04 0.06 0.07 0.08
When the atom fraction of A is 0.4, the activity of A in the liquid is ______________
GATE 2016 MT
MT 7/12
Q.34 The lining of a box-type furnace is made up of a refractory layer and steel plate as shown in
the figure. Steady state temperature at the surface of the refractory is 1273 K and that at the
outer steel surface is 473 K. If the steady-state heat flux through the refractory-steel plate
composite is 1600 W.m
-2
, and heat flow is along x-direction, the thermal contact resistance
(W
-1
.m
2
.K) between refractory and steel is _____________
Given data:
Thermal conductivity of refractory = 1.2 W.m
-1
K
-1
Thickness of refractory lining = 80 mm
Thermal conductivity of steel = 32 W.m
-1
K
-1
Thickness of steel plate = 4 mm
Q.35 The height of a liquid metal column in a cylindrical vessel is 3.2 m. At time t=0, liquid
metal is drained out from the vessel through a small nozzle located at the base of the vessel.
Neglecting frictional losses, the initial mass flow rate (in kg.s
-1
) through the
nozzle is ________________
Given data:
Density of liquid metal = 7000 kg.m
-3
Nozzle diameter = 30 mm
Nozzle discharge coefficient = 0.80
Q.36 Match entities listed in Column I with their correct dimensions given in Column II:
Column I Column II
[P] Drag coefficient [1] ML
-1
T
-1
[Q] Mass transfer coefficient [2] ML
-2
T
-1
[R] Viscosity [3] M
0
L
0
T
0
[S] Mass flux [4] M
0
LT
-1
(A) P-3, Q-4, R-1, S-2 (B) P-3, Q-1, R-2, S-4
(C) P-1, Q-4, R-2, S-3 (D) P-4, Q-3, R-1, S-2
Q.37 Direct Reduced Iron (DRI) produced from a gas based process contains Fe, FeO, C and
remainder being gangue. The chemical composition of DRI is: Total Fe = 92 wt.% and
Metallic Fe = 84 wt.%. The weight percent of FeO in DRI is _________________
1273 K 473 K
refractory
steel plate
Furnace
Ambient
x
GATE 2016 MT
MT 8/12
Q.38 Mould heat flux (q
m
) for billet casters is expressed (in SI unit) as a function of distance
below the meniscus (z)
6
c
m
10
U
z
33 . 0 67 . 2 ) z ( q ?
?
?
?
?
?
?
? ? ( ) 0
m
L z ? ?
If mould length (L
m
) is 0.8 m and casting speed (U
c
) is 0.2 m.s
-1
, the average mould flux
(in MW.m
-2
) is ________________
Q.39 In BOF steelmaking, 5 metric ton of lime containing 90 wt.% CaO is used to refine 100
metric ton of hot metal containing 93.2 wt.% Fe. The slag produced during refining
contains 40 wt.% CaO and 22 wt.% FeO. Neglecting material losses, the yield of Fe (in %)
is _________________
Q.40 In vacuum degassing of steel, 14 ppm of dissolved nitrogen is in equilibrium with 1 mbar
of nitrogen gas at 1873 K. At the same temperature, if the pressure is lowered to 0.7 mbar,
the equilibrium nitrogen content (in ppm) is _____________
Q.41 During isothermal phase transformation (in solid-state), fraction transformed is measured at
two different transformation times:
___________________________________________
Transformation Time, t (s) Fraction Transformed, f
___________________________________________
75 0.11
150 0.37
____________________________________________
Assuming Avrami kinetics [f = 1 ? exp (?kt
n
)], the fraction transformed in
300 seconds is _______________
Q.42 Zinc oxide is reduced at a constant temperature in a closed reactor using ZnO(s) and C(s)
as the only starting materials. The following reactions are assumed to be at thermodynamic
equilibrium:
ZnO(s) + C(s) = Zn(g) + CO(g)
2CO(g) = CO
2
(g) + C(s)
Assume ideal gas behaviour. Based on mole balance, the relationship applicable to the
system at equilibrium is
(A)
2
(B)
2
(C)
(D)
0.5
2
GATE 2016 MT
MT 9/12
Q.43 The critical nucleus size (in nm) when copper melt is under-cooled by 100 K is
Given data:
Melting point: 1356 K
Density: 8900 kg.m
-3
Solid-liquid interfacial energy: 0.5 Jm
-2
Latent heat of freezing: 13000 J.mol
-1
Molar volume: 7 ?10
-6
m
-3
mol
-1
(A) 0.36 (B) 1.55 (C) 3.65 (D) 7.30
Q.44 The density and corresponding crystallinity of two poly-propylene material are given
below
________________________________________
Density, kg.m
-3
Crystallinity, %
________________________________________
904 62.8
895 54.4
_________________________________________
The density of totally amorphous poly-propylene (in kg.m
-3
) is:
(A) 723 (B) 841 (C) 905 (D) 956
GATE 2016 MT
MT 10/12
Q.45 A simplified energy band-diagram of an intrinsic semiconductor at thermal equilibrium
(300 K) is shown. In the accompanying table, which one of the four columns correctly
represents the listed parameters? Assume same effective mass for electrons and holes.
Parameter
Energy-difference
Column 1 Column 2 Column 3 Column 4
Band-gap ?E
2
?E
1
?E
2
?E
1
Electron affinity ?E
1
/2 ?E
2
? ?E
1
?E
2
/2 ?E
2
? ( ?E
1
/2)
Work function ?E
1
+ ?E
2
?E
2
? ( ?E
1
/2) ?E
1
? ?E
2
/2 ?E
2
+ ( ?E
1
/2)
(A) Column 1 (B) Column 2 (C) Column 3 (D) Column 4
Q.46 A binary phase diagram is shown in the schematic.
Upon complete solidification of a binary alloy system A-B, the fraction of pro-eutectic ?-
phase present is 0.50. The alloy composition in terms of wt%. B is _________________
Fermi
level
Vacuum
level
Electron Energy(E)
?E
1
?E
2
L
?+?L
?+?L
?
?
?+? ?
18.3
61.9
97.8
A
B
Wt%?B
Temperature
GATE 2016 MT
MT 11/12
Q.47 Fatigue behaviour of an aluminium alloy is shown in the S-N plot. A piston rod made of
this material is subjected to: (i) 1000 cycles at 420 MPa, followed by (ii) 1000 cycles at
300 MPa. Using Miner?s rule of cumulative damage, the remaining fatigue life (in terms of
number of cycles) at stress of 250 MPa is _______________
Q.48 A glass plate has two parallel cracks. One of them is an internal crack of length 5 ?m and
the other is a surface crack of length 3 ?m. A tensile stress is applied perpendicular to the
crack surfaces. The fracture stress (in MPa) is ___________
Given data (for glass plate):
Young?s Modulus = 70 GPa
Surface energy per unit area = 1 J.m
-2
Q.49 A tensile stress is applied along the [100] direction in a FCC metal crystal. The critical
resolved shear stress is 6 MPa. The tensile stress (in MPa) required for initiating slip on the
(111) slip plane is_____________
Q.50 For a bcc metal the ratio of the surface energy per unit area of the (100) plane to that of the
(110) plane is ______________
Q.51 For a polymer reinforced with 40 vol.% glass fiber, the elastic modulus (in GPa) along the
transverse direction is
(A) 5.6 (B) 8.1
(C) 30.1 (D) 43.4
[E
glass fiber
= 70 GPa; E
polymer
= 3.5 GPa]
0
200
400
600
800
0 2000 4000 6000 8000 10000
S,??MPa
N
420?MPa
300?MPa
250?MPa
2000 5000
8800
GATE 2016 MT
MT 12/12
Q.52 In a sand-mould, a sprue of 0.25 m height and a top cross-section area of 2.2 m
2
is provided
to maintain the melt flow rate at 4 m
3
.s
-1
. To prevent aspiration of molten metal, the
maximum cross-section area (in m
2
) at the base of the sprue is ____________
Q.53 For casting a cylindrical aluminum bloom having a length of 1000 mm and diameter of
750 mm, the approximate solidification time (in minutes) estimated using Chvorinov?s rule
is
(A) 45 (B) 316 (C) 440 (D) 620
[The mould constant is 2 s/mm
2
]
Q.54 A liquid phase sintered SiC-Ni composite has a solid-solid grain boundary energy ( ?
SiC-SiC
)
of 0.80 J.m
-2
and a solid-liquid ( ?
SiC-Ni
) interfacial energy of 0.45 J.m
-2
. For a SiC grain size
of 20 ?m, the average interparticle (SiC-SiC) neck size (in ?m) is:
(A) 3.03 (B) 4.28 (C) 9.16 (D) 18.32
Q.55 Match the deformation processes in Column I with the corresponding stress states listed in
Column II
Column I Column II
[P] Wire Drawing [1] Direct Compression
[Q] Forging [2] Indirect Compression
[R] Stretch Forming [3] Tension
[S] Cutting [4] Shear
(A) P-1; Q-2; R-3; S-4 (B) P-1; Q-2; R-4; S-3
(C) P-2; Q-1; R-3; S-4 (D) P-2; Q-1; R-4; S-3
END OF THE QUESTION PAPER
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This post was last modified on 18 December 2019