Download GATE (Graduate Aptitude Test in Engineering) Last 10 Years 2020, 2019, 2018, 2017, 2016, 2015, 2014, 2013, 2012, 2011 and 2010 PI Production and Industrial 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
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
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
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 Production and Industrial Engineering (PI)
PI
1/13
Q. 1 ? Q. 25 carry one mark each.
Q.1 The eigenvalues of the matrix
01
1 0
are
(A) i and ?i (B) 1 and ?1 (C) 0 and 1 (D) 0 and ?1
Q.2
The number of solutions of the simultaneous algebraic equations 33 and 35 is
(A) zero (B) 1 (C) 2 (D) infinite
Q.3 At x = 0, the function
sin
, ? ?,?????? 0
is
(A) continuous and differentiable.
(B) not continuous and not differentiable.
(C) not continuous but differentiable.
(D) continuous but not differentiable.
Q.4 For the two functions
,
3 and , 3
which one of the following options is correct?
(A)
(B)
(C)
(D)
Q.5 The function
is singular at
(A) 2 (B) 1 (C) (D) 2
Q.6 A fair coin is tossed N times. The probability that head does not turn up in any of the tosses is
(A) (B) 1 (C) (D) 1
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 Production and Industrial Engineering (PI)
PI
1/13
Q. 1 ? Q. 25 carry one mark each.
Q.1 The eigenvalues of the matrix
01
1 0
are
(A) i and ?i (B) 1 and ?1 (C) 0 and 1 (D) 0 and ?1
Q.2
The number of solutions of the simultaneous algebraic equations 33 and 35 is
(A) zero (B) 1 (C) 2 (D) infinite
Q.3 At x = 0, the function
sin
, ? ?,?????? 0
is
(A) continuous and differentiable.
(B) not continuous and not differentiable.
(C) not continuous but differentiable.
(D) continuous but not differentiable.
Q.4 For the two functions
,
3 and , 3
which one of the following options is correct?
(A)
(B)
(C)
(D)
Q.5 The function
is singular at
(A) 2 (B) 1 (C) (D) 2
Q.6 A fair coin is tossed N times. The probability that head does not turn up in any of the tosses is
(A) (B) 1 (C) (D) 1
GATE 2016 Production and Industrial Engineering (PI)
PI
2/13
Q.7 A normal random variable X has the following probability density function
?
,???? ? ?
Then d
(A) 0
(B)
(C) 1
(D) 1
Q.8 The elastic modulus of a rigid perfectly plastic solid is
(A) 0 (B) 1 (C) 100 (D) infinity
Q.9 Consider the following statements:
(P) Hardness is the resistance of a material to indentation.
(Q) Elastic modulus is a measure of ductility.
(R) Deflection depends on stiffness.
(S) The total area under the stress-strain curve is a measure of resilience.
Among the above statements, the correct ones are
(A) P and Q only. (B) Q and S only. (C) P and R only. (D) R and S only.
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 Production and Industrial Engineering (PI)
PI
1/13
Q. 1 ? Q. 25 carry one mark each.
Q.1 The eigenvalues of the matrix
01
1 0
are
(A) i and ?i (B) 1 and ?1 (C) 0 and 1 (D) 0 and ?1
Q.2
The number of solutions of the simultaneous algebraic equations 33 and 35 is
(A) zero (B) 1 (C) 2 (D) infinite
Q.3 At x = 0, the function
sin
, ? ?,?????? 0
is
(A) continuous and differentiable.
(B) not continuous and not differentiable.
(C) not continuous but differentiable.
(D) continuous but not differentiable.
Q.4 For the two functions
,
3 and , 3
which one of the following options is correct?
(A)
(B)
(C)
(D)
Q.5 The function
is singular at
(A) 2 (B) 1 (C) (D) 2
Q.6 A fair coin is tossed N times. The probability that head does not turn up in any of the tosses is
(A) (B) 1 (C) (D) 1
GATE 2016 Production and Industrial Engineering (PI)
PI
2/13
Q.7 A normal random variable X has the following probability density function
?
,???? ? ?
Then d
(A) 0
(B)
(C) 1
(D) 1
Q.8 The elastic modulus of a rigid perfectly plastic solid is
(A) 0 (B) 1 (C) 100 (D) infinity
Q.9 Consider the following statements:
(P) Hardness is the resistance of a material to indentation.
(Q) Elastic modulus is a measure of ductility.
(R) Deflection depends on stiffness.
(S) The total area under the stress-strain curve is a measure of resilience.
Among the above statements, the correct ones are
(A) P and Q only. (B) Q and S only. (C) P and R only. (D) R and S only.
GATE 2016 Production and Industrial Engineering (PI)
PI
3/13
Q.10 A beam is subjected to an inclined concentrated load as shown in the figure below. Neglect the
weight of the beam.
The correct Free Body Diagram of the beam is
(A)
(B)
(C)
(D)
Q.11 Consider a circular cam with a flat face follower as shown in the figure below. The cam is rotated
in the plane of the paper about point P lying 5 mm away from its center. The radius of the cam is 20
mm. The distance (in mm) between the highest and the lowest positions of the flat face follower is
(A) 5 (B) 10 (C) 40 (D) 45
5 mm
P
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 Production and Industrial Engineering (PI)
PI
1/13
Q. 1 ? Q. 25 carry one mark each.
Q.1 The eigenvalues of the matrix
01
1 0
are
(A) i and ?i (B) 1 and ?1 (C) 0 and 1 (D) 0 and ?1
Q.2
The number of solutions of the simultaneous algebraic equations 33 and 35 is
(A) zero (B) 1 (C) 2 (D) infinite
Q.3 At x = 0, the function
sin
, ? ?,?????? 0
is
(A) continuous and differentiable.
(B) not continuous and not differentiable.
(C) not continuous but differentiable.
(D) continuous but not differentiable.
Q.4 For the two functions
,
3 and , 3
which one of the following options is correct?
(A)
(B)
(C)
(D)
Q.5 The function
is singular at
(A) 2 (B) 1 (C) (D) 2
Q.6 A fair coin is tossed N times. The probability that head does not turn up in any of the tosses is
(A) (B) 1 (C) (D) 1
GATE 2016 Production and Industrial Engineering (PI)
PI
2/13
Q.7 A normal random variable X has the following probability density function
?
,???? ? ?
Then d
(A) 0
(B)
(C) 1
(D) 1
Q.8 The elastic modulus of a rigid perfectly plastic solid is
(A) 0 (B) 1 (C) 100 (D) infinity
Q.9 Consider the following statements:
(P) Hardness is the resistance of a material to indentation.
(Q) Elastic modulus is a measure of ductility.
(R) Deflection depends on stiffness.
(S) The total area under the stress-strain curve is a measure of resilience.
Among the above statements, the correct ones are
(A) P and Q only. (B) Q and S only. (C) P and R only. (D) R and S only.
GATE 2016 Production and Industrial Engineering (PI)
PI
3/13
Q.10 A beam is subjected to an inclined concentrated load as shown in the figure below. Neglect the
weight of the beam.
The correct Free Body Diagram of the beam is
(A)
(B)
(C)
(D)
Q.11 Consider a circular cam with a flat face follower as shown in the figure below. The cam is rotated
in the plane of the paper about point P lying 5 mm away from its center. The radius of the cam is 20
mm. The distance (in mm) between the highest and the lowest positions of the flat face follower is
(A) 5 (B) 10 (C) 40 (D) 45
5 mm
P
GATE 2016 Production and Industrial Engineering (PI)
PI
4/13
Q.12 A vertical cylindrical tank of 1 m diameter is filled with water up to a height of 5 m from its
bottom. Top surface of water is exposed to atmosphere. A hole of 5 mm
2
area forms at the bottom
of the tank. Considering the coefficient of discharge of the hole to be unity and the acceleration due
to gravity to be 10 m/s
2
, the rate of leakage of water (in litre/min) through the hole from the tank to
the atmosphere, under the given conditions, is _______.
Q.13 The figure below shows an air standard Diesel cycle in p-V diagram. The cut-off ratio is given by:
(A)?
(B)
(C)
(D)
Q.14 The ratio of press force required to punch a square hole of 30 mm side in a 1 mm thick aluminium
sheet to that needed to punch a square hole of 60 mm side in a 2 mm thick aluminium sheet
is________.
Q.15 Which one of the following is a natural polymer?
(A) Cellulose (B) Nylon (C) Polyester (D) Polyvinyl chloride
Q.16 In powder metallurgy, sintering of the component
(A) increases density and reduces ductility.
(B) increases porosity and reduces density.
(C) increases density and reduces porosity.
(D) increases porosity and reduces brittleness.
Q.17 A single point right handed turning tool is used for straight turning. The feed is 0.25 mm/rev and
the uncut chip thickness is found to be 0.25 mm. The inclination angle of the main cutting edge is
10 ?. The back rake angle (in degrees) is _______.
4
p
V
2
3
1
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 Production and Industrial Engineering (PI)
PI
1/13
Q. 1 ? Q. 25 carry one mark each.
Q.1 The eigenvalues of the matrix
01
1 0
are
(A) i and ?i (B) 1 and ?1 (C) 0 and 1 (D) 0 and ?1
Q.2
The number of solutions of the simultaneous algebraic equations 33 and 35 is
(A) zero (B) 1 (C) 2 (D) infinite
Q.3 At x = 0, the function
sin
, ? ?,?????? 0
is
(A) continuous and differentiable.
(B) not continuous and not differentiable.
(C) not continuous but differentiable.
(D) continuous but not differentiable.
Q.4 For the two functions
,
3 and , 3
which one of the following options is correct?
(A)
(B)
(C)
(D)
Q.5 The function
is singular at
(A) 2 (B) 1 (C) (D) 2
Q.6 A fair coin is tossed N times. The probability that head does not turn up in any of the tosses is
(A) (B) 1 (C) (D) 1
GATE 2016 Production and Industrial Engineering (PI)
PI
2/13
Q.7 A normal random variable X has the following probability density function
?
,???? ? ?
Then d
(A) 0
(B)
(C) 1
(D) 1
Q.8 The elastic modulus of a rigid perfectly plastic solid is
(A) 0 (B) 1 (C) 100 (D) infinity
Q.9 Consider the following statements:
(P) Hardness is the resistance of a material to indentation.
(Q) Elastic modulus is a measure of ductility.
(R) Deflection depends on stiffness.
(S) The total area under the stress-strain curve is a measure of resilience.
Among the above statements, the correct ones are
(A) P and Q only. (B) Q and S only. (C) P and R only. (D) R and S only.
GATE 2016 Production and Industrial Engineering (PI)
PI
3/13
Q.10 A beam is subjected to an inclined concentrated load as shown in the figure below. Neglect the
weight of the beam.
The correct Free Body Diagram of the beam is
(A)
(B)
(C)
(D)
Q.11 Consider a circular cam with a flat face follower as shown in the figure below. The cam is rotated
in the plane of the paper about point P lying 5 mm away from its center. The radius of the cam is 20
mm. The distance (in mm) between the highest and the lowest positions of the flat face follower is
(A) 5 (B) 10 (C) 40 (D) 45
5 mm
P
GATE 2016 Production and Industrial Engineering (PI)
PI
4/13
Q.12 A vertical cylindrical tank of 1 m diameter is filled with water up to a height of 5 m from its
bottom. Top surface of water is exposed to atmosphere. A hole of 5 mm
2
area forms at the bottom
of the tank. Considering the coefficient of discharge of the hole to be unity and the acceleration due
to gravity to be 10 m/s
2
, the rate of leakage of water (in litre/min) through the hole from the tank to
the atmosphere, under the given conditions, is _______.
Q.13 The figure below shows an air standard Diesel cycle in p-V diagram. The cut-off ratio is given by:
(A)?
(B)
(C)
(D)
Q.14 The ratio of press force required to punch a square hole of 30 mm side in a 1 mm thick aluminium
sheet to that needed to punch a square hole of 60 mm side in a 2 mm thick aluminium sheet
is________.
Q.15 Which one of the following is a natural polymer?
(A) Cellulose (B) Nylon (C) Polyester (D) Polyvinyl chloride
Q.16 In powder metallurgy, sintering of the component
(A) increases density and reduces ductility.
(B) increases porosity and reduces density.
(C) increases density and reduces porosity.
(D) increases porosity and reduces brittleness.
Q.17 A single point right handed turning tool is used for straight turning. The feed is 0.25 mm/rev and
the uncut chip thickness is found to be 0.25 mm. The inclination angle of the main cutting edge is
10 ?. The back rake angle (in degrees) is _______.
4
p
V
2
3
1
GATE 2016 Production and Industrial Engineering (PI)
PI
5/13
Q.18 Consider the following statements.
(P) Electrolyte is used in Electro-chemical machining.
(Q) Electrolyte is used in Electrical discharge machining.
(R) Abrasive-slurry is used in Ultrasonic machining.
(S) Abrasive-slurry is used in Abrasive jet machining.
Among the above statements, the correct ones are
(A) P and R only (B) Q and S only (C) Q, R and S only (D) P and Q only
Q.19 Consider the following statements.
(P) Computer aided process planning (CAPP) takes input from material requirement plan (MRP).
(Q) Production flow analysis helps in work cell formation.
(R) Group technology takes input from choice of machining or cutting parameters.
Among the above statements, the correct one(s) is (are)
(A) P only (B) Q and R only (C) P and R only (D) Q only
Q.20 The limits of a shaft designated as 100h5 are 100.000 mm and 100.014 mm. Similarly, the limits of
a shaft designated as 100h8 are 100.000 mm and 100.055 mm. If a shaft is designated as 100h6, the
fundamental deviation (in ?m) for the same is
(A) ?22 (B) zero (C) 22 (D) 24
Q.21 The roughness profile of a surface is depicted below.
The surface roughness parameter R
a
(in ?m) is _______.
2 ?m
5 mm
2 ?m
X
profile height
centre-line of
the profile
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 Production and Industrial Engineering (PI)
PI
1/13
Q. 1 ? Q. 25 carry one mark each.
Q.1 The eigenvalues of the matrix
01
1 0
are
(A) i and ?i (B) 1 and ?1 (C) 0 and 1 (D) 0 and ?1
Q.2
The number of solutions of the simultaneous algebraic equations 33 and 35 is
(A) zero (B) 1 (C) 2 (D) infinite
Q.3 At x = 0, the function
sin
, ? ?,?????? 0
is
(A) continuous and differentiable.
(B) not continuous and not differentiable.
(C) not continuous but differentiable.
(D) continuous but not differentiable.
Q.4 For the two functions
,
3 and , 3
which one of the following options is correct?
(A)
(B)
(C)
(D)
Q.5 The function
is singular at
(A) 2 (B) 1 (C) (D) 2
Q.6 A fair coin is tossed N times. The probability that head does not turn up in any of the tosses is
(A) (B) 1 (C) (D) 1
GATE 2016 Production and Industrial Engineering (PI)
PI
2/13
Q.7 A normal random variable X has the following probability density function
?
,???? ? ?
Then d
(A) 0
(B)
(C) 1
(D) 1
Q.8 The elastic modulus of a rigid perfectly plastic solid is
(A) 0 (B) 1 (C) 100 (D) infinity
Q.9 Consider the following statements:
(P) Hardness is the resistance of a material to indentation.
(Q) Elastic modulus is a measure of ductility.
(R) Deflection depends on stiffness.
(S) The total area under the stress-strain curve is a measure of resilience.
Among the above statements, the correct ones are
(A) P and Q only. (B) Q and S only. (C) P and R only. (D) R and S only.
GATE 2016 Production and Industrial Engineering (PI)
PI
3/13
Q.10 A beam is subjected to an inclined concentrated load as shown in the figure below. Neglect the
weight of the beam.
The correct Free Body Diagram of the beam is
(A)
(B)
(C)
(D)
Q.11 Consider a circular cam with a flat face follower as shown in the figure below. The cam is rotated
in the plane of the paper about point P lying 5 mm away from its center. The radius of the cam is 20
mm. The distance (in mm) between the highest and the lowest positions of the flat face follower is
(A) 5 (B) 10 (C) 40 (D) 45
5 mm
P
GATE 2016 Production and Industrial Engineering (PI)
PI
4/13
Q.12 A vertical cylindrical tank of 1 m diameter is filled with water up to a height of 5 m from its
bottom. Top surface of water is exposed to atmosphere. A hole of 5 mm
2
area forms at the bottom
of the tank. Considering the coefficient of discharge of the hole to be unity and the acceleration due
to gravity to be 10 m/s
2
, the rate of leakage of water (in litre/min) through the hole from the tank to
the atmosphere, under the given conditions, is _______.
Q.13 The figure below shows an air standard Diesel cycle in p-V diagram. The cut-off ratio is given by:
(A)?
(B)
(C)
(D)
Q.14 The ratio of press force required to punch a square hole of 30 mm side in a 1 mm thick aluminium
sheet to that needed to punch a square hole of 60 mm side in a 2 mm thick aluminium sheet
is________.
Q.15 Which one of the following is a natural polymer?
(A) Cellulose (B) Nylon (C) Polyester (D) Polyvinyl chloride
Q.16 In powder metallurgy, sintering of the component
(A) increases density and reduces ductility.
(B) increases porosity and reduces density.
(C) increases density and reduces porosity.
(D) increases porosity and reduces brittleness.
Q.17 A single point right handed turning tool is used for straight turning. The feed is 0.25 mm/rev and
the uncut chip thickness is found to be 0.25 mm. The inclination angle of the main cutting edge is
10 ?. The back rake angle (in degrees) is _______.
4
p
V
2
3
1
GATE 2016 Production and Industrial Engineering (PI)
PI
5/13
Q.18 Consider the following statements.
(P) Electrolyte is used in Electro-chemical machining.
(Q) Electrolyte is used in Electrical discharge machining.
(R) Abrasive-slurry is used in Ultrasonic machining.
(S) Abrasive-slurry is used in Abrasive jet machining.
Among the above statements, the correct ones are
(A) P and R only (B) Q and S only (C) Q, R and S only (D) P and Q only
Q.19 Consider the following statements.
(P) Computer aided process planning (CAPP) takes input from material requirement plan (MRP).
(Q) Production flow analysis helps in work cell formation.
(R) Group technology takes input from choice of machining or cutting parameters.
Among the above statements, the correct one(s) is (are)
(A) P only (B) Q and R only (C) P and R only (D) Q only
Q.20 The limits of a shaft designated as 100h5 are 100.000 mm and 100.014 mm. Similarly, the limits of
a shaft designated as 100h8 are 100.000 mm and 100.055 mm. If a shaft is designated as 100h6, the
fundamental deviation (in ?m) for the same is
(A) ?22 (B) zero (C) 22 (D) 24
Q.21 The roughness profile of a surface is depicted below.
The surface roughness parameter R
a
(in ?m) is _______.
2 ?m
5 mm
2 ?m
X
profile height
centre-line of
the profile
GATE 2016 Production and Industrial Engineering (PI)
PI
6/13
Q.22 The facility layout technique that uses relationship (REL) chart is
(A) CRAFT. (B) Travel chart. (C) Partial Set Covering. (D) ALDEP.
Q.23 For a random variable, X, let be the sample average. The sample size is n. The mean and the
standard deviation of X are ? and ?, respectively. The standard deviation of is
(A) (B)
(C )
(D)
?
Q.24 ST and NT denote the standard time and the normal time, respectively, to complete a job.
Allowance , where 0 1 . Which one of the following relationships is correct?
(A)
(B) 1 )
(C )
(D) 1
Q.25 The throughput rate of a production system is 20 units per hour. The average flow time is 30
minutes and the cycle time is 3 minutes. The average inventory (in units) in the system is
(A) 1.5 (B) 9 (C ) 10 (D) 11.33
Q. 26 ? Q. 55 carry two marks each.
Q.26 The range of values of k for which the function
4 6 8
has a local maxima at point x = 0 is
(A) 2 or 2 (B) 2 or 2
(C) 2 2 (D) 2 2
Q.27
lim
?
is equal to ______.
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 Production and Industrial Engineering (PI)
PI
1/13
Q. 1 ? Q. 25 carry one mark each.
Q.1 The eigenvalues of the matrix
01
1 0
are
(A) i and ?i (B) 1 and ?1 (C) 0 and 1 (D) 0 and ?1
Q.2
The number of solutions of the simultaneous algebraic equations 33 and 35 is
(A) zero (B) 1 (C) 2 (D) infinite
Q.3 At x = 0, the function
sin
, ? ?,?????? 0
is
(A) continuous and differentiable.
(B) not continuous and not differentiable.
(C) not continuous but differentiable.
(D) continuous but not differentiable.
Q.4 For the two functions
,
3 and , 3
which one of the following options is correct?
(A)
(B)
(C)
(D)
Q.5 The function
is singular at
(A) 2 (B) 1 (C) (D) 2
Q.6 A fair coin is tossed N times. The probability that head does not turn up in any of the tosses is
(A) (B) 1 (C) (D) 1
GATE 2016 Production and Industrial Engineering (PI)
PI
2/13
Q.7 A normal random variable X has the following probability density function
?
,???? ? ?
Then d
(A) 0
(B)
(C) 1
(D) 1
Q.8 The elastic modulus of a rigid perfectly plastic solid is
(A) 0 (B) 1 (C) 100 (D) infinity
Q.9 Consider the following statements:
(P) Hardness is the resistance of a material to indentation.
(Q) Elastic modulus is a measure of ductility.
(R) Deflection depends on stiffness.
(S) The total area under the stress-strain curve is a measure of resilience.
Among the above statements, the correct ones are
(A) P and Q only. (B) Q and S only. (C) P and R only. (D) R and S only.
GATE 2016 Production and Industrial Engineering (PI)
PI
3/13
Q.10 A beam is subjected to an inclined concentrated load as shown in the figure below. Neglect the
weight of the beam.
The correct Free Body Diagram of the beam is
(A)
(B)
(C)
(D)
Q.11 Consider a circular cam with a flat face follower as shown in the figure below. The cam is rotated
in the plane of the paper about point P lying 5 mm away from its center. The radius of the cam is 20
mm. The distance (in mm) between the highest and the lowest positions of the flat face follower is
(A) 5 (B) 10 (C) 40 (D) 45
5 mm
P
GATE 2016 Production and Industrial Engineering (PI)
PI
4/13
Q.12 A vertical cylindrical tank of 1 m diameter is filled with water up to a height of 5 m from its
bottom. Top surface of water is exposed to atmosphere. A hole of 5 mm
2
area forms at the bottom
of the tank. Considering the coefficient of discharge of the hole to be unity and the acceleration due
to gravity to be 10 m/s
2
, the rate of leakage of water (in litre/min) through the hole from the tank to
the atmosphere, under the given conditions, is _______.
Q.13 The figure below shows an air standard Diesel cycle in p-V diagram. The cut-off ratio is given by:
(A)?
(B)
(C)
(D)
Q.14 The ratio of press force required to punch a square hole of 30 mm side in a 1 mm thick aluminium
sheet to that needed to punch a square hole of 60 mm side in a 2 mm thick aluminium sheet
is________.
Q.15 Which one of the following is a natural polymer?
(A) Cellulose (B) Nylon (C) Polyester (D) Polyvinyl chloride
Q.16 In powder metallurgy, sintering of the component
(A) increases density and reduces ductility.
(B) increases porosity and reduces density.
(C) increases density and reduces porosity.
(D) increases porosity and reduces brittleness.
Q.17 A single point right handed turning tool is used for straight turning. The feed is 0.25 mm/rev and
the uncut chip thickness is found to be 0.25 mm. The inclination angle of the main cutting edge is
10 ?. The back rake angle (in degrees) is _______.
4
p
V
2
3
1
GATE 2016 Production and Industrial Engineering (PI)
PI
5/13
Q.18 Consider the following statements.
(P) Electrolyte is used in Electro-chemical machining.
(Q) Electrolyte is used in Electrical discharge machining.
(R) Abrasive-slurry is used in Ultrasonic machining.
(S) Abrasive-slurry is used in Abrasive jet machining.
Among the above statements, the correct ones are
(A) P and R only (B) Q and S only (C) Q, R and S only (D) P and Q only
Q.19 Consider the following statements.
(P) Computer aided process planning (CAPP) takes input from material requirement plan (MRP).
(Q) Production flow analysis helps in work cell formation.
(R) Group technology takes input from choice of machining or cutting parameters.
Among the above statements, the correct one(s) is (are)
(A) P only (B) Q and R only (C) P and R only (D) Q only
Q.20 The limits of a shaft designated as 100h5 are 100.000 mm and 100.014 mm. Similarly, the limits of
a shaft designated as 100h8 are 100.000 mm and 100.055 mm. If a shaft is designated as 100h6, the
fundamental deviation (in ?m) for the same is
(A) ?22 (B) zero (C) 22 (D) 24
Q.21 The roughness profile of a surface is depicted below.
The surface roughness parameter R
a
(in ?m) is _______.
2 ?m
5 mm
2 ?m
X
profile height
centre-line of
the profile
GATE 2016 Production and Industrial Engineering (PI)
PI
6/13
Q.22 The facility layout technique that uses relationship (REL) chart is
(A) CRAFT. (B) Travel chart. (C) Partial Set Covering. (D) ALDEP.
Q.23 For a random variable, X, let be the sample average. The sample size is n. The mean and the
standard deviation of X are ? and ?, respectively. The standard deviation of is
(A) (B)
(C )
(D)
?
Q.24 ST and NT denote the standard time and the normal time, respectively, to complete a job.
Allowance , where 0 1 . Which one of the following relationships is correct?
(A)
(B) 1 )
(C )
(D) 1
Q.25 The throughput rate of a production system is 20 units per hour. The average flow time is 30
minutes and the cycle time is 3 minutes. The average inventory (in units) in the system is
(A) 1.5 (B) 9 (C ) 10 (D) 11.33
Q. 26 ? Q. 55 carry two marks each.
Q.26 The range of values of k for which the function
4 6 8
has a local maxima at point x = 0 is
(A) 2 or 2 (B) 2 or 2
(C) 2 2 (D) 2 2
Q.27
lim
?
is equal to ______.
GATE 2016 Production and Industrial Engineering (PI)
PI
7/13
Q.28 To solve the equation
2sin
by Newton-Raphson method, the initial guess was chosen to be x = 2.0. Consider x in radian only.
The value of x (in radian) obtained after one iteration will be closest to
(A) ? 8.101 (B) 1.901 (C) 2.099 (D) 12.101
Q.29 In linear gas tungsten arc welding of two plates of the same material, the peak temperature T (in K)
is given as
, where q is the heat input per unit length (in J/m) of weld, ? is the thermal
diffusivity (in m
2
/s) of the plate materials and is a constant independent of process parameters
and material types. Two welding cases are given below.
Case I: V = 15 V, I = 200 A, v = 5 mm/s, k = 150 W/mK, ? = 3000 kg/m
3
, C = 900 J/kg-K
Case II: V = 15 V, I = 300 A, v = 10 mm/s, k = 50 W/mK, ? = 8000 kg/m
3
, C = 450 J/kg-K
where, V is welding voltage, I is welding current, v is welding speed, and k, ? and C refer to the
thermal conductivity, the density and the specific heat of the plate materials, respectively. Consider
that electrical energy is completely converted to thermal energy. All other conditions remain same.
The ratio of the peak temperature in Case I to that in Case II is
(A)
(B)
(C) 1 (D) 2
Q.30 A bar of rectangular cross-sectional area of 50 mm
2
is pulled from both the sides by equal forces of
100 N as shown in the figure below. The shear stress (in MPa) along the plane making an angle 45
o
with the axis, shown as a dashed line in the figure, is ________________.
100 N
100 N
45
o
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 Production and Industrial Engineering (PI)
PI
1/13
Q. 1 ? Q. 25 carry one mark each.
Q.1 The eigenvalues of the matrix
01
1 0
are
(A) i and ?i (B) 1 and ?1 (C) 0 and 1 (D) 0 and ?1
Q.2
The number of solutions of the simultaneous algebraic equations 33 and 35 is
(A) zero (B) 1 (C) 2 (D) infinite
Q.3 At x = 0, the function
sin
, ? ?,?????? 0
is
(A) continuous and differentiable.
(B) not continuous and not differentiable.
(C) not continuous but differentiable.
(D) continuous but not differentiable.
Q.4 For the two functions
,
3 and , 3
which one of the following options is correct?
(A)
(B)
(C)
(D)
Q.5 The function
is singular at
(A) 2 (B) 1 (C) (D) 2
Q.6 A fair coin is tossed N times. The probability that head does not turn up in any of the tosses is
(A) (B) 1 (C) (D) 1
GATE 2016 Production and Industrial Engineering (PI)
PI
2/13
Q.7 A normal random variable X has the following probability density function
?
,???? ? ?
Then d
(A) 0
(B)
(C) 1
(D) 1
Q.8 The elastic modulus of a rigid perfectly plastic solid is
(A) 0 (B) 1 (C) 100 (D) infinity
Q.9 Consider the following statements:
(P) Hardness is the resistance of a material to indentation.
(Q) Elastic modulus is a measure of ductility.
(R) Deflection depends on stiffness.
(S) The total area under the stress-strain curve is a measure of resilience.
Among the above statements, the correct ones are
(A) P and Q only. (B) Q and S only. (C) P and R only. (D) R and S only.
GATE 2016 Production and Industrial Engineering (PI)
PI
3/13
Q.10 A beam is subjected to an inclined concentrated load as shown in the figure below. Neglect the
weight of the beam.
The correct Free Body Diagram of the beam is
(A)
(B)
(C)
(D)
Q.11 Consider a circular cam with a flat face follower as shown in the figure below. The cam is rotated
in the plane of the paper about point P lying 5 mm away from its center. The radius of the cam is 20
mm. The distance (in mm) between the highest and the lowest positions of the flat face follower is
(A) 5 (B) 10 (C) 40 (D) 45
5 mm
P
GATE 2016 Production and Industrial Engineering (PI)
PI
4/13
Q.12 A vertical cylindrical tank of 1 m diameter is filled with water up to a height of 5 m from its
bottom. Top surface of water is exposed to atmosphere. A hole of 5 mm
2
area forms at the bottom
of the tank. Considering the coefficient of discharge of the hole to be unity and the acceleration due
to gravity to be 10 m/s
2
, the rate of leakage of water (in litre/min) through the hole from the tank to
the atmosphere, under the given conditions, is _______.
Q.13 The figure below shows an air standard Diesel cycle in p-V diagram. The cut-off ratio is given by:
(A)?
(B)
(C)
(D)
Q.14 The ratio of press force required to punch a square hole of 30 mm side in a 1 mm thick aluminium
sheet to that needed to punch a square hole of 60 mm side in a 2 mm thick aluminium sheet
is________.
Q.15 Which one of the following is a natural polymer?
(A) Cellulose (B) Nylon (C) Polyester (D) Polyvinyl chloride
Q.16 In powder metallurgy, sintering of the component
(A) increases density and reduces ductility.
(B) increases porosity and reduces density.
(C) increases density and reduces porosity.
(D) increases porosity and reduces brittleness.
Q.17 A single point right handed turning tool is used for straight turning. The feed is 0.25 mm/rev and
the uncut chip thickness is found to be 0.25 mm. The inclination angle of the main cutting edge is
10 ?. The back rake angle (in degrees) is _______.
4
p
V
2
3
1
GATE 2016 Production and Industrial Engineering (PI)
PI
5/13
Q.18 Consider the following statements.
(P) Electrolyte is used in Electro-chemical machining.
(Q) Electrolyte is used in Electrical discharge machining.
(R) Abrasive-slurry is used in Ultrasonic machining.
(S) Abrasive-slurry is used in Abrasive jet machining.
Among the above statements, the correct ones are
(A) P and R only (B) Q and S only (C) Q, R and S only (D) P and Q only
Q.19 Consider the following statements.
(P) Computer aided process planning (CAPP) takes input from material requirement plan (MRP).
(Q) Production flow analysis helps in work cell formation.
(R) Group technology takes input from choice of machining or cutting parameters.
Among the above statements, the correct one(s) is (are)
(A) P only (B) Q and R only (C) P and R only (D) Q only
Q.20 The limits of a shaft designated as 100h5 are 100.000 mm and 100.014 mm. Similarly, the limits of
a shaft designated as 100h8 are 100.000 mm and 100.055 mm. If a shaft is designated as 100h6, the
fundamental deviation (in ?m) for the same is
(A) ?22 (B) zero (C) 22 (D) 24
Q.21 The roughness profile of a surface is depicted below.
The surface roughness parameter R
a
(in ?m) is _______.
2 ?m
5 mm
2 ?m
X
profile height
centre-line of
the profile
GATE 2016 Production and Industrial Engineering (PI)
PI
6/13
Q.22 The facility layout technique that uses relationship (REL) chart is
(A) CRAFT. (B) Travel chart. (C) Partial Set Covering. (D) ALDEP.
Q.23 For a random variable, X, let be the sample average. The sample size is n. The mean and the
standard deviation of X are ? and ?, respectively. The standard deviation of is
(A) (B)
(C )
(D)
?
Q.24 ST and NT denote the standard time and the normal time, respectively, to complete a job.
Allowance , where 0 1 . Which one of the following relationships is correct?
(A)
(B) 1 )
(C )
(D) 1
Q.25 The throughput rate of a production system is 20 units per hour. The average flow time is 30
minutes and the cycle time is 3 minutes. The average inventory (in units) in the system is
(A) 1.5 (B) 9 (C ) 10 (D) 11.33
Q. 26 ? Q. 55 carry two marks each.
Q.26 The range of values of k for which the function
4 6 8
has a local maxima at point x = 0 is
(A) 2 or 2 (B) 2 or 2
(C) 2 2 (D) 2 2
Q.27
lim
?
is equal to ______.
GATE 2016 Production and Industrial Engineering (PI)
PI
7/13
Q.28 To solve the equation
2sin
by Newton-Raphson method, the initial guess was chosen to be x = 2.0. Consider x in radian only.
The value of x (in radian) obtained after one iteration will be closest to
(A) ? 8.101 (B) 1.901 (C) 2.099 (D) 12.101
Q.29 In linear gas tungsten arc welding of two plates of the same material, the peak temperature T (in K)
is given as
, where q is the heat input per unit length (in J/m) of weld, ? is the thermal
diffusivity (in m
2
/s) of the plate materials and is a constant independent of process parameters
and material types. Two welding cases are given below.
Case I: V = 15 V, I = 200 A, v = 5 mm/s, k = 150 W/mK, ? = 3000 kg/m
3
, C = 900 J/kg-K
Case II: V = 15 V, I = 300 A, v = 10 mm/s, k = 50 W/mK, ? = 8000 kg/m
3
, C = 450 J/kg-K
where, V is welding voltage, I is welding current, v is welding speed, and k, ? and C refer to the
thermal conductivity, the density and the specific heat of the plate materials, respectively. Consider
that electrical energy is completely converted to thermal energy. All other conditions remain same.
The ratio of the peak temperature in Case I to that in Case II is
(A)
(B)
(C) 1 (D) 2
Q.30 A bar of rectangular cross-sectional area of 50 mm
2
is pulled from both the sides by equal forces of
100 N as shown in the figure below. The shear stress (in MPa) along the plane making an angle 45
o
with the axis, shown as a dashed line in the figure, is ________________.
100 N
100 N
45
o
GATE 2016 Production and Industrial Engineering (PI)
PI
8/13
Q.31 A 1 m ? 10 mm ? 10 mm cantilever beam is subjected to a uniformly distributed load per unit
length of 100 N/m as shown in the figure below. The normal stress (in MPa) due to bending at point
P is ____________.
Q.32 A thin-walled cylindrical pressure vessel of internal diameter 2 m is designed to withstand an
internal pressure of 500 kPa (gauge). If the allowable normal stress at any point within the
cylindrical portion of the vessel is 100 MPa, the minimum thickness of the plate of the vessel (in
mm) is________.
Q.33 An engine, connected with a flywheel, is designed to operate at an average angular speed of 800
rpm. During operation of the engine, the maximum change in kinetic energy in a cycle is found to
be 6240 J. In order to keep the fluctuation of the angular speed within ?1% of its average value, the
moment of inertia (in kg-m
2
) of the flywheel should be ____________.
Q.34 A 2 m ? 2 m square opening in a vertical wall is covered with a metallic plate of the same
dimensions as shown in the figure below. Consider the acceleration due to gravity to be 10.0 m/s
2
.
The force (in kN) exerted by water on the plate is _____.
2 m
2 m
water
p
atm
p
atm
2 m ? 2 m
square plate
vertical wall
vertical wall
100 N/m
1 m
Point P
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 Production and Industrial Engineering (PI)
PI
1/13
Q. 1 ? Q. 25 carry one mark each.
Q.1 The eigenvalues of the matrix
01
1 0
are
(A) i and ?i (B) 1 and ?1 (C) 0 and 1 (D) 0 and ?1
Q.2
The number of solutions of the simultaneous algebraic equations 33 and 35 is
(A) zero (B) 1 (C) 2 (D) infinite
Q.3 At x = 0, the function
sin
, ? ?,?????? 0
is
(A) continuous and differentiable.
(B) not continuous and not differentiable.
(C) not continuous but differentiable.
(D) continuous but not differentiable.
Q.4 For the two functions
,
3 and , 3
which one of the following options is correct?
(A)
(B)
(C)
(D)
Q.5 The function
is singular at
(A) 2 (B) 1 (C) (D) 2
Q.6 A fair coin is tossed N times. The probability that head does not turn up in any of the tosses is
(A) (B) 1 (C) (D) 1
GATE 2016 Production and Industrial Engineering (PI)
PI
2/13
Q.7 A normal random variable X has the following probability density function
?
,???? ? ?
Then d
(A) 0
(B)
(C) 1
(D) 1
Q.8 The elastic modulus of a rigid perfectly plastic solid is
(A) 0 (B) 1 (C) 100 (D) infinity
Q.9 Consider the following statements:
(P) Hardness is the resistance of a material to indentation.
(Q) Elastic modulus is a measure of ductility.
(R) Deflection depends on stiffness.
(S) The total area under the stress-strain curve is a measure of resilience.
Among the above statements, the correct ones are
(A) P and Q only. (B) Q and S only. (C) P and R only. (D) R and S only.
GATE 2016 Production and Industrial Engineering (PI)
PI
3/13
Q.10 A beam is subjected to an inclined concentrated load as shown in the figure below. Neglect the
weight of the beam.
The correct Free Body Diagram of the beam is
(A)
(B)
(C)
(D)
Q.11 Consider a circular cam with a flat face follower as shown in the figure below. The cam is rotated
in the plane of the paper about point P lying 5 mm away from its center. The radius of the cam is 20
mm. The distance (in mm) between the highest and the lowest positions of the flat face follower is
(A) 5 (B) 10 (C) 40 (D) 45
5 mm
P
GATE 2016 Production and Industrial Engineering (PI)
PI
4/13
Q.12 A vertical cylindrical tank of 1 m diameter is filled with water up to a height of 5 m from its
bottom. Top surface of water is exposed to atmosphere. A hole of 5 mm
2
area forms at the bottom
of the tank. Considering the coefficient of discharge of the hole to be unity and the acceleration due
to gravity to be 10 m/s
2
, the rate of leakage of water (in litre/min) through the hole from the tank to
the atmosphere, under the given conditions, is _______.
Q.13 The figure below shows an air standard Diesel cycle in p-V diagram. The cut-off ratio is given by:
(A)?
(B)
(C)
(D)
Q.14 The ratio of press force required to punch a square hole of 30 mm side in a 1 mm thick aluminium
sheet to that needed to punch a square hole of 60 mm side in a 2 mm thick aluminium sheet
is________.
Q.15 Which one of the following is a natural polymer?
(A) Cellulose (B) Nylon (C) Polyester (D) Polyvinyl chloride
Q.16 In powder metallurgy, sintering of the component
(A) increases density and reduces ductility.
(B) increases porosity and reduces density.
(C) increases density and reduces porosity.
(D) increases porosity and reduces brittleness.
Q.17 A single point right handed turning tool is used for straight turning. The feed is 0.25 mm/rev and
the uncut chip thickness is found to be 0.25 mm. The inclination angle of the main cutting edge is
10 ?. The back rake angle (in degrees) is _______.
4
p
V
2
3
1
GATE 2016 Production and Industrial Engineering (PI)
PI
5/13
Q.18 Consider the following statements.
(P) Electrolyte is used in Electro-chemical machining.
(Q) Electrolyte is used in Electrical discharge machining.
(R) Abrasive-slurry is used in Ultrasonic machining.
(S) Abrasive-slurry is used in Abrasive jet machining.
Among the above statements, the correct ones are
(A) P and R only (B) Q and S only (C) Q, R and S only (D) P and Q only
Q.19 Consider the following statements.
(P) Computer aided process planning (CAPP) takes input from material requirement plan (MRP).
(Q) Production flow analysis helps in work cell formation.
(R) Group technology takes input from choice of machining or cutting parameters.
Among the above statements, the correct one(s) is (are)
(A) P only (B) Q and R only (C) P and R only (D) Q only
Q.20 The limits of a shaft designated as 100h5 are 100.000 mm and 100.014 mm. Similarly, the limits of
a shaft designated as 100h8 are 100.000 mm and 100.055 mm. If a shaft is designated as 100h6, the
fundamental deviation (in ?m) for the same is
(A) ?22 (B) zero (C) 22 (D) 24
Q.21 The roughness profile of a surface is depicted below.
The surface roughness parameter R
a
(in ?m) is _______.
2 ?m
5 mm
2 ?m
X
profile height
centre-line of
the profile
GATE 2016 Production and Industrial Engineering (PI)
PI
6/13
Q.22 The facility layout technique that uses relationship (REL) chart is
(A) CRAFT. (B) Travel chart. (C) Partial Set Covering. (D) ALDEP.
Q.23 For a random variable, X, let be the sample average. The sample size is n. The mean and the
standard deviation of X are ? and ?, respectively. The standard deviation of is
(A) (B)
(C )
(D)
?
Q.24 ST and NT denote the standard time and the normal time, respectively, to complete a job.
Allowance , where 0 1 . Which one of the following relationships is correct?
(A)
(B) 1 )
(C )
(D) 1
Q.25 The throughput rate of a production system is 20 units per hour. The average flow time is 30
minutes and the cycle time is 3 minutes. The average inventory (in units) in the system is
(A) 1.5 (B) 9 (C ) 10 (D) 11.33
Q. 26 ? Q. 55 carry two marks each.
Q.26 The range of values of k for which the function
4 6 8
has a local maxima at point x = 0 is
(A) 2 or 2 (B) 2 or 2
(C) 2 2 (D) 2 2
Q.27
lim
?
is equal to ______.
GATE 2016 Production and Industrial Engineering (PI)
PI
7/13
Q.28 To solve the equation
2sin
by Newton-Raphson method, the initial guess was chosen to be x = 2.0. Consider x in radian only.
The value of x (in radian) obtained after one iteration will be closest to
(A) ? 8.101 (B) 1.901 (C) 2.099 (D) 12.101
Q.29 In linear gas tungsten arc welding of two plates of the same material, the peak temperature T (in K)
is given as
, where q is the heat input per unit length (in J/m) of weld, ? is the thermal
diffusivity (in m
2
/s) of the plate materials and is a constant independent of process parameters
and material types. Two welding cases are given below.
Case I: V = 15 V, I = 200 A, v = 5 mm/s, k = 150 W/mK, ? = 3000 kg/m
3
, C = 900 J/kg-K
Case II: V = 15 V, I = 300 A, v = 10 mm/s, k = 50 W/mK, ? = 8000 kg/m
3
, C = 450 J/kg-K
where, V is welding voltage, I is welding current, v is welding speed, and k, ? and C refer to the
thermal conductivity, the density and the specific heat of the plate materials, respectively. Consider
that electrical energy is completely converted to thermal energy. All other conditions remain same.
The ratio of the peak temperature in Case I to that in Case II is
(A)
(B)
(C) 1 (D) 2
Q.30 A bar of rectangular cross-sectional area of 50 mm
2
is pulled from both the sides by equal forces of
100 N as shown in the figure below. The shear stress (in MPa) along the plane making an angle 45
o
with the axis, shown as a dashed line in the figure, is ________________.
100 N
100 N
45
o
GATE 2016 Production and Industrial Engineering (PI)
PI
8/13
Q.31 A 1 m ? 10 mm ? 10 mm cantilever beam is subjected to a uniformly distributed load per unit
length of 100 N/m as shown in the figure below. The normal stress (in MPa) due to bending at point
P is ____________.
Q.32 A thin-walled cylindrical pressure vessel of internal diameter 2 m is designed to withstand an
internal pressure of 500 kPa (gauge). If the allowable normal stress at any point within the
cylindrical portion of the vessel is 100 MPa, the minimum thickness of the plate of the vessel (in
mm) is________.
Q.33 An engine, connected with a flywheel, is designed to operate at an average angular speed of 800
rpm. During operation of the engine, the maximum change in kinetic energy in a cycle is found to
be 6240 J. In order to keep the fluctuation of the angular speed within ?1% of its average value, the
moment of inertia (in kg-m
2
) of the flywheel should be ____________.
Q.34 A 2 m ? 2 m square opening in a vertical wall is covered with a metallic plate of the same
dimensions as shown in the figure below. Consider the acceleration due to gravity to be 10.0 m/s
2
.
The force (in kN) exerted by water on the plate is _____.
2 m
2 m
water
p
atm
p
atm
2 m ? 2 m
square plate
vertical wall
vertical wall
100 N/m
1 m
Point P
GATE 2016 Production and Industrial Engineering (PI)
PI
9/13
Q.35 An ideal gas of mass m is contained in a rigid tank of volume V at a pressure p. During a reversible
process its pressure reduces to . Following statements are made regarding the process.
(P) Heat is transferred from the gas.
(Q) Work done by the gas is zero.
(R) Entropy of the gas remains constant.
(S) Entropy of the gas decreases.
Among the above statements, the correct ones are
(A) P and R only. (B) P, Q and R only. (C) Q and R only. (D) P, Q and S only.
Q.36 A long slender metallic rod of length L is used as a fin. As shown in the figure below, the left end
of the fin is kept at a constant temperature t
b
. The fin loses heat by convection to the atmosphere
which is at a temperature t
a
(t
a
< t
b
). Four options of temperature profiles are shown. Identify the
correct option.
(A)
(B)
(C)
(D)
L
temperature
t
b
t
a
x
0
t
b
t
a
L
x
temperature
0
L
t
b
t
a
x
0
temperature
atmosphere at t
a
t
b
convection
x x = L
t
b
t
a
L
temperature
x
0
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 Production and Industrial Engineering (PI)
PI
1/13
Q. 1 ? Q. 25 carry one mark each.
Q.1 The eigenvalues of the matrix
01
1 0
are
(A) i and ?i (B) 1 and ?1 (C) 0 and 1 (D) 0 and ?1
Q.2
The number of solutions of the simultaneous algebraic equations 33 and 35 is
(A) zero (B) 1 (C) 2 (D) infinite
Q.3 At x = 0, the function
sin
, ? ?,?????? 0
is
(A) continuous and differentiable.
(B) not continuous and not differentiable.
(C) not continuous but differentiable.
(D) continuous but not differentiable.
Q.4 For the two functions
,
3 and , 3
which one of the following options is correct?
(A)
(B)
(C)
(D)
Q.5 The function
is singular at
(A) 2 (B) 1 (C) (D) 2
Q.6 A fair coin is tossed N times. The probability that head does not turn up in any of the tosses is
(A) (B) 1 (C) (D) 1
GATE 2016 Production and Industrial Engineering (PI)
PI
2/13
Q.7 A normal random variable X has the following probability density function
?
,???? ? ?
Then d
(A) 0
(B)
(C) 1
(D) 1
Q.8 The elastic modulus of a rigid perfectly plastic solid is
(A) 0 (B) 1 (C) 100 (D) infinity
Q.9 Consider the following statements:
(P) Hardness is the resistance of a material to indentation.
(Q) Elastic modulus is a measure of ductility.
(R) Deflection depends on stiffness.
(S) The total area under the stress-strain curve is a measure of resilience.
Among the above statements, the correct ones are
(A) P and Q only. (B) Q and S only. (C) P and R only. (D) R and S only.
GATE 2016 Production and Industrial Engineering (PI)
PI
3/13
Q.10 A beam is subjected to an inclined concentrated load as shown in the figure below. Neglect the
weight of the beam.
The correct Free Body Diagram of the beam is
(A)
(B)
(C)
(D)
Q.11 Consider a circular cam with a flat face follower as shown in the figure below. The cam is rotated
in the plane of the paper about point P lying 5 mm away from its center. The radius of the cam is 20
mm. The distance (in mm) between the highest and the lowest positions of the flat face follower is
(A) 5 (B) 10 (C) 40 (D) 45
5 mm
P
GATE 2016 Production and Industrial Engineering (PI)
PI
4/13
Q.12 A vertical cylindrical tank of 1 m diameter is filled with water up to a height of 5 m from its
bottom. Top surface of water is exposed to atmosphere. A hole of 5 mm
2
area forms at the bottom
of the tank. Considering the coefficient of discharge of the hole to be unity and the acceleration due
to gravity to be 10 m/s
2
, the rate of leakage of water (in litre/min) through the hole from the tank to
the atmosphere, under the given conditions, is _______.
Q.13 The figure below shows an air standard Diesel cycle in p-V diagram. The cut-off ratio is given by:
(A)?
(B)
(C)
(D)
Q.14 The ratio of press force required to punch a square hole of 30 mm side in a 1 mm thick aluminium
sheet to that needed to punch a square hole of 60 mm side in a 2 mm thick aluminium sheet
is________.
Q.15 Which one of the following is a natural polymer?
(A) Cellulose (B) Nylon (C) Polyester (D) Polyvinyl chloride
Q.16 In powder metallurgy, sintering of the component
(A) increases density and reduces ductility.
(B) increases porosity and reduces density.
(C) increases density and reduces porosity.
(D) increases porosity and reduces brittleness.
Q.17 A single point right handed turning tool is used for straight turning. The feed is 0.25 mm/rev and
the uncut chip thickness is found to be 0.25 mm. The inclination angle of the main cutting edge is
10 ?. The back rake angle (in degrees) is _______.
4
p
V
2
3
1
GATE 2016 Production and Industrial Engineering (PI)
PI
5/13
Q.18 Consider the following statements.
(P) Electrolyte is used in Electro-chemical machining.
(Q) Electrolyte is used in Electrical discharge machining.
(R) Abrasive-slurry is used in Ultrasonic machining.
(S) Abrasive-slurry is used in Abrasive jet machining.
Among the above statements, the correct ones are
(A) P and R only (B) Q and S only (C) Q, R and S only (D) P and Q only
Q.19 Consider the following statements.
(P) Computer aided process planning (CAPP) takes input from material requirement plan (MRP).
(Q) Production flow analysis helps in work cell formation.
(R) Group technology takes input from choice of machining or cutting parameters.
Among the above statements, the correct one(s) is (are)
(A) P only (B) Q and R only (C) P and R only (D) Q only
Q.20 The limits of a shaft designated as 100h5 are 100.000 mm and 100.014 mm. Similarly, the limits of
a shaft designated as 100h8 are 100.000 mm and 100.055 mm. If a shaft is designated as 100h6, the
fundamental deviation (in ?m) for the same is
(A) ?22 (B) zero (C) 22 (D) 24
Q.21 The roughness profile of a surface is depicted below.
The surface roughness parameter R
a
(in ?m) is _______.
2 ?m
5 mm
2 ?m
X
profile height
centre-line of
the profile
GATE 2016 Production and Industrial Engineering (PI)
PI
6/13
Q.22 The facility layout technique that uses relationship (REL) chart is
(A) CRAFT. (B) Travel chart. (C) Partial Set Covering. (D) ALDEP.
Q.23 For a random variable, X, let be the sample average. The sample size is n. The mean and the
standard deviation of X are ? and ?, respectively. The standard deviation of is
(A) (B)
(C )
(D)
?
Q.24 ST and NT denote the standard time and the normal time, respectively, to complete a job.
Allowance , where 0 1 . Which one of the following relationships is correct?
(A)
(B) 1 )
(C )
(D) 1
Q.25 The throughput rate of a production system is 20 units per hour. The average flow time is 30
minutes and the cycle time is 3 minutes. The average inventory (in units) in the system is
(A) 1.5 (B) 9 (C ) 10 (D) 11.33
Q. 26 ? Q. 55 carry two marks each.
Q.26 The range of values of k for which the function
4 6 8
has a local maxima at point x = 0 is
(A) 2 or 2 (B) 2 or 2
(C) 2 2 (D) 2 2
Q.27
lim
?
is equal to ______.
GATE 2016 Production and Industrial Engineering (PI)
PI
7/13
Q.28 To solve the equation
2sin
by Newton-Raphson method, the initial guess was chosen to be x = 2.0. Consider x in radian only.
The value of x (in radian) obtained after one iteration will be closest to
(A) ? 8.101 (B) 1.901 (C) 2.099 (D) 12.101
Q.29 In linear gas tungsten arc welding of two plates of the same material, the peak temperature T (in K)
is given as
, where q is the heat input per unit length (in J/m) of weld, ? is the thermal
diffusivity (in m
2
/s) of the plate materials and is a constant independent of process parameters
and material types. Two welding cases are given below.
Case I: V = 15 V, I = 200 A, v = 5 mm/s, k = 150 W/mK, ? = 3000 kg/m
3
, C = 900 J/kg-K
Case II: V = 15 V, I = 300 A, v = 10 mm/s, k = 50 W/mK, ? = 8000 kg/m
3
, C = 450 J/kg-K
where, V is welding voltage, I is welding current, v is welding speed, and k, ? and C refer to the
thermal conductivity, the density and the specific heat of the plate materials, respectively. Consider
that electrical energy is completely converted to thermal energy. All other conditions remain same.
The ratio of the peak temperature in Case I to that in Case II is
(A)
(B)
(C) 1 (D) 2
Q.30 A bar of rectangular cross-sectional area of 50 mm
2
is pulled from both the sides by equal forces of
100 N as shown in the figure below. The shear stress (in MPa) along the plane making an angle 45
o
with the axis, shown as a dashed line in the figure, is ________________.
100 N
100 N
45
o
GATE 2016 Production and Industrial Engineering (PI)
PI
8/13
Q.31 A 1 m ? 10 mm ? 10 mm cantilever beam is subjected to a uniformly distributed load per unit
length of 100 N/m as shown in the figure below. The normal stress (in MPa) due to bending at point
P is ____________.
Q.32 A thin-walled cylindrical pressure vessel of internal diameter 2 m is designed to withstand an
internal pressure of 500 kPa (gauge). If the allowable normal stress at any point within the
cylindrical portion of the vessel is 100 MPa, the minimum thickness of the plate of the vessel (in
mm) is________.
Q.33 An engine, connected with a flywheel, is designed to operate at an average angular speed of 800
rpm. During operation of the engine, the maximum change in kinetic energy in a cycle is found to
be 6240 J. In order to keep the fluctuation of the angular speed within ?1% of its average value, the
moment of inertia (in kg-m
2
) of the flywheel should be ____________.
Q.34 A 2 m ? 2 m square opening in a vertical wall is covered with a metallic plate of the same
dimensions as shown in the figure below. Consider the acceleration due to gravity to be 10.0 m/s
2
.
The force (in kN) exerted by water on the plate is _____.
2 m
2 m
water
p
atm
p
atm
2 m ? 2 m
square plate
vertical wall
vertical wall
100 N/m
1 m
Point P
GATE 2016 Production and Industrial Engineering (PI)
PI
9/13
Q.35 An ideal gas of mass m is contained in a rigid tank of volume V at a pressure p. During a reversible
process its pressure reduces to . Following statements are made regarding the process.
(P) Heat is transferred from the gas.
(Q) Work done by the gas is zero.
(R) Entropy of the gas remains constant.
(S) Entropy of the gas decreases.
Among the above statements, the correct ones are
(A) P and R only. (B) P, Q and R only. (C) Q and R only. (D) P, Q and S only.
Q.36 A long slender metallic rod of length L is used as a fin. As shown in the figure below, the left end
of the fin is kept at a constant temperature t
b
. The fin loses heat by convection to the atmosphere
which is at a temperature t
a
(t
a
< t
b
). Four options of temperature profiles are shown. Identify the
correct option.
(A)
(B)
(C)
(D)
L
temperature
t
b
t
a
x
0
t
b
t
a
L
x
temperature
0
L
t
b
t
a
x
0
temperature
atmosphere at t
a
t
b
convection
x x = L
t
b
t
a
L
temperature
x
0
GATE 2016 Production and Industrial Engineering (PI)
PI
10/13
Q.37 In a fully developed turbulent flow through a circular pipe, a head loss of is observed.
The
diameter of the pipe is increased by 10% for the same flow rate and a head loss of is noted.
Assume friction factor for both the cases of pipe flow is the same. The ratio of
is closest to
(A) 0.34 (B) 0.62 (C) 0.87 (D) 1.00
Q.38 Two cast iron blocks P and Q, each of 500 mm length, have the same cross-sectional area. Block P
has rectangular cross-section of 100 mm ? 200 mm. Block Q is of square cross-section. Both P and
Q were cast under the same conditions with all their surfaces enclosed within the mould. The
solidification time of a casting is proportional to the square of the ratio of its volume to its surface
area. The ratio of solidification time of the block P to that of the block Q is ______.
Q.39 A 300 mm long copper wire of uniform cross-section is pulled in tension so that a maximum tensile
stress of 270 MPa is developed within the wire. The entire deformation of the wire remains linearly
elastic. The elastic modulus of copper is 100 GPa. The resultant elongation (in mm) is ________.
Q.40 In a single-pass rolling operation, a 200 mm wide metallic strip is rolled from a thickness 10 mm to
a thickness 6 mm. The roll radius is 100 mm and it rotates at 200 rpm. The roll-strip contact length
is a function of roll radius and, initial and final thickness of the strip. If the average flow stress in
plane strain of the strip material in the roll gap is 500 MPa, the roll separating force (in kN) is
_______.
Q.41 Two solid cylinders of equal diameter have different heights. They are compressed plastically by a
pair of rigid dies to create the same percentage reduction in their respective heights. Consider that
the die-workpiece interface friction is negligible. The ratio of the final diameter of the shorter
cylinder to that of the longer cylinder is __________.
Q.42 Two flat steel sheets, each of 2.5 mm thickness, are being resistance spot welded using a current of
6000 A and weld time of 0.2 s. The contact resistance at the interface between the two sheets is
200 ?? ?and the specific energy to melt steel is 10?10
9
J/m
3
. A spherical melt pool of diameter 4
mm is formed at the interface due to the current flow. Consider that electrical energy is completely
converted to thermal energy. The ratio of the heat used for melting to the total resistive heat
generated is ______.
Q.43 A cylindrical bar of 100 mm diameter is orthogonally straight turned with cutting velocity, feed and
depth of cut of 120 m/min, 0.25 mm/rev and 4 mm, respectively. The specific cutting energy of the
work material is 1?10
9
J/m
3
. Neglect the contribution of feed force towards cutting power. The
main or tangential cutting force (in N) is ________.
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 Production and Industrial Engineering (PI)
PI
1/13
Q. 1 ? Q. 25 carry one mark each.
Q.1 The eigenvalues of the matrix
01
1 0
are
(A) i and ?i (B) 1 and ?1 (C) 0 and 1 (D) 0 and ?1
Q.2
The number of solutions of the simultaneous algebraic equations 33 and 35 is
(A) zero (B) 1 (C) 2 (D) infinite
Q.3 At x = 0, the function
sin
, ? ?,?????? 0
is
(A) continuous and differentiable.
(B) not continuous and not differentiable.
(C) not continuous but differentiable.
(D) continuous but not differentiable.
Q.4 For the two functions
,
3 and , 3
which one of the following options is correct?
(A)
(B)
(C)
(D)
Q.5 The function
is singular at
(A) 2 (B) 1 (C) (D) 2
Q.6 A fair coin is tossed N times. The probability that head does not turn up in any of the tosses is
(A) (B) 1 (C) (D) 1
GATE 2016 Production and Industrial Engineering (PI)
PI
2/13
Q.7 A normal random variable X has the following probability density function
?
,???? ? ?
Then d
(A) 0
(B)
(C) 1
(D) 1
Q.8 The elastic modulus of a rigid perfectly plastic solid is
(A) 0 (B) 1 (C) 100 (D) infinity
Q.9 Consider the following statements:
(P) Hardness is the resistance of a material to indentation.
(Q) Elastic modulus is a measure of ductility.
(R) Deflection depends on stiffness.
(S) The total area under the stress-strain curve is a measure of resilience.
Among the above statements, the correct ones are
(A) P and Q only. (B) Q and S only. (C) P and R only. (D) R and S only.
GATE 2016 Production and Industrial Engineering (PI)
PI
3/13
Q.10 A beam is subjected to an inclined concentrated load as shown in the figure below. Neglect the
weight of the beam.
The correct Free Body Diagram of the beam is
(A)
(B)
(C)
(D)
Q.11 Consider a circular cam with a flat face follower as shown in the figure below. The cam is rotated
in the plane of the paper about point P lying 5 mm away from its center. The radius of the cam is 20
mm. The distance (in mm) between the highest and the lowest positions of the flat face follower is
(A) 5 (B) 10 (C) 40 (D) 45
5 mm
P
GATE 2016 Production and Industrial Engineering (PI)
PI
4/13
Q.12 A vertical cylindrical tank of 1 m diameter is filled with water up to a height of 5 m from its
bottom. Top surface of water is exposed to atmosphere. A hole of 5 mm
2
area forms at the bottom
of the tank. Considering the coefficient of discharge of the hole to be unity and the acceleration due
to gravity to be 10 m/s
2
, the rate of leakage of water (in litre/min) through the hole from the tank to
the atmosphere, under the given conditions, is _______.
Q.13 The figure below shows an air standard Diesel cycle in p-V diagram. The cut-off ratio is given by:
(A)?
(B)
(C)
(D)
Q.14 The ratio of press force required to punch a square hole of 30 mm side in a 1 mm thick aluminium
sheet to that needed to punch a square hole of 60 mm side in a 2 mm thick aluminium sheet
is________.
Q.15 Which one of the following is a natural polymer?
(A) Cellulose (B) Nylon (C) Polyester (D) Polyvinyl chloride
Q.16 In powder metallurgy, sintering of the component
(A) increases density and reduces ductility.
(B) increases porosity and reduces density.
(C) increases density and reduces porosity.
(D) increases porosity and reduces brittleness.
Q.17 A single point right handed turning tool is used for straight turning. The feed is 0.25 mm/rev and
the uncut chip thickness is found to be 0.25 mm. The inclination angle of the main cutting edge is
10 ?. The back rake angle (in degrees) is _______.
4
p
V
2
3
1
GATE 2016 Production and Industrial Engineering (PI)
PI
5/13
Q.18 Consider the following statements.
(P) Electrolyte is used in Electro-chemical machining.
(Q) Electrolyte is used in Electrical discharge machining.
(R) Abrasive-slurry is used in Ultrasonic machining.
(S) Abrasive-slurry is used in Abrasive jet machining.
Among the above statements, the correct ones are
(A) P and R only (B) Q and S only (C) Q, R and S only (D) P and Q only
Q.19 Consider the following statements.
(P) Computer aided process planning (CAPP) takes input from material requirement plan (MRP).
(Q) Production flow analysis helps in work cell formation.
(R) Group technology takes input from choice of machining or cutting parameters.
Among the above statements, the correct one(s) is (are)
(A) P only (B) Q and R only (C) P and R only (D) Q only
Q.20 The limits of a shaft designated as 100h5 are 100.000 mm and 100.014 mm. Similarly, the limits of
a shaft designated as 100h8 are 100.000 mm and 100.055 mm. If a shaft is designated as 100h6, the
fundamental deviation (in ?m) for the same is
(A) ?22 (B) zero (C) 22 (D) 24
Q.21 The roughness profile of a surface is depicted below.
The surface roughness parameter R
a
(in ?m) is _______.
2 ?m
5 mm
2 ?m
X
profile height
centre-line of
the profile
GATE 2016 Production and Industrial Engineering (PI)
PI
6/13
Q.22 The facility layout technique that uses relationship (REL) chart is
(A) CRAFT. (B) Travel chart. (C) Partial Set Covering. (D) ALDEP.
Q.23 For a random variable, X, let be the sample average. The sample size is n. The mean and the
standard deviation of X are ? and ?, respectively. The standard deviation of is
(A) (B)
(C )
(D)
?
Q.24 ST and NT denote the standard time and the normal time, respectively, to complete a job.
Allowance , where 0 1 . Which one of the following relationships is correct?
(A)
(B) 1 )
(C )
(D) 1
Q.25 The throughput rate of a production system is 20 units per hour. The average flow time is 30
minutes and the cycle time is 3 minutes. The average inventory (in units) in the system is
(A) 1.5 (B) 9 (C ) 10 (D) 11.33
Q. 26 ? Q. 55 carry two marks each.
Q.26 The range of values of k for which the function
4 6 8
has a local maxima at point x = 0 is
(A) 2 or 2 (B) 2 or 2
(C) 2 2 (D) 2 2
Q.27
lim
?
is equal to ______.
GATE 2016 Production and Industrial Engineering (PI)
PI
7/13
Q.28 To solve the equation
2sin
by Newton-Raphson method, the initial guess was chosen to be x = 2.0. Consider x in radian only.
The value of x (in radian) obtained after one iteration will be closest to
(A) ? 8.101 (B) 1.901 (C) 2.099 (D) 12.101
Q.29 In linear gas tungsten arc welding of two plates of the same material, the peak temperature T (in K)
is given as
, where q is the heat input per unit length (in J/m) of weld, ? is the thermal
diffusivity (in m
2
/s) of the plate materials and is a constant independent of process parameters
and material types. Two welding cases are given below.
Case I: V = 15 V, I = 200 A, v = 5 mm/s, k = 150 W/mK, ? = 3000 kg/m
3
, C = 900 J/kg-K
Case II: V = 15 V, I = 300 A, v = 10 mm/s, k = 50 W/mK, ? = 8000 kg/m
3
, C = 450 J/kg-K
where, V is welding voltage, I is welding current, v is welding speed, and k, ? and C refer to the
thermal conductivity, the density and the specific heat of the plate materials, respectively. Consider
that electrical energy is completely converted to thermal energy. All other conditions remain same.
The ratio of the peak temperature in Case I to that in Case II is
(A)
(B)
(C) 1 (D) 2
Q.30 A bar of rectangular cross-sectional area of 50 mm
2
is pulled from both the sides by equal forces of
100 N as shown in the figure below. The shear stress (in MPa) along the plane making an angle 45
o
with the axis, shown as a dashed line in the figure, is ________________.
100 N
100 N
45
o
GATE 2016 Production and Industrial Engineering (PI)
PI
8/13
Q.31 A 1 m ? 10 mm ? 10 mm cantilever beam is subjected to a uniformly distributed load per unit
length of 100 N/m as shown in the figure below. The normal stress (in MPa) due to bending at point
P is ____________.
Q.32 A thin-walled cylindrical pressure vessel of internal diameter 2 m is designed to withstand an
internal pressure of 500 kPa (gauge). If the allowable normal stress at any point within the
cylindrical portion of the vessel is 100 MPa, the minimum thickness of the plate of the vessel (in
mm) is________.
Q.33 An engine, connected with a flywheel, is designed to operate at an average angular speed of 800
rpm. During operation of the engine, the maximum change in kinetic energy in a cycle is found to
be 6240 J. In order to keep the fluctuation of the angular speed within ?1% of its average value, the
moment of inertia (in kg-m
2
) of the flywheel should be ____________.
Q.34 A 2 m ? 2 m square opening in a vertical wall is covered with a metallic plate of the same
dimensions as shown in the figure below. Consider the acceleration due to gravity to be 10.0 m/s
2
.
The force (in kN) exerted by water on the plate is _____.
2 m
2 m
water
p
atm
p
atm
2 m ? 2 m
square plate
vertical wall
vertical wall
100 N/m
1 m
Point P
GATE 2016 Production and Industrial Engineering (PI)
PI
9/13
Q.35 An ideal gas of mass m is contained in a rigid tank of volume V at a pressure p. During a reversible
process its pressure reduces to . Following statements are made regarding the process.
(P) Heat is transferred from the gas.
(Q) Work done by the gas is zero.
(R) Entropy of the gas remains constant.
(S) Entropy of the gas decreases.
Among the above statements, the correct ones are
(A) P and R only. (B) P, Q and R only. (C) Q and R only. (D) P, Q and S only.
Q.36 A long slender metallic rod of length L is used as a fin. As shown in the figure below, the left end
of the fin is kept at a constant temperature t
b
. The fin loses heat by convection to the atmosphere
which is at a temperature t
a
(t
a
< t
b
). Four options of temperature profiles are shown. Identify the
correct option.
(A)
(B)
(C)
(D)
L
temperature
t
b
t
a
x
0
t
b
t
a
L
x
temperature
0
L
t
b
t
a
x
0
temperature
atmosphere at t
a
t
b
convection
x x = L
t
b
t
a
L
temperature
x
0
GATE 2016 Production and Industrial Engineering (PI)
PI
10/13
Q.37 In a fully developed turbulent flow through a circular pipe, a head loss of is observed.
The
diameter of the pipe is increased by 10% for the same flow rate and a head loss of is noted.
Assume friction factor for both the cases of pipe flow is the same. The ratio of
is closest to
(A) 0.34 (B) 0.62 (C) 0.87 (D) 1.00
Q.38 Two cast iron blocks P and Q, each of 500 mm length, have the same cross-sectional area. Block P
has rectangular cross-section of 100 mm ? 200 mm. Block Q is of square cross-section. Both P and
Q were cast under the same conditions with all their surfaces enclosed within the mould. The
solidification time of a casting is proportional to the square of the ratio of its volume to its surface
area. The ratio of solidification time of the block P to that of the block Q is ______.
Q.39 A 300 mm long copper wire of uniform cross-section is pulled in tension so that a maximum tensile
stress of 270 MPa is developed within the wire. The entire deformation of the wire remains linearly
elastic. The elastic modulus of copper is 100 GPa. The resultant elongation (in mm) is ________.
Q.40 In a single-pass rolling operation, a 200 mm wide metallic strip is rolled from a thickness 10 mm to
a thickness 6 mm. The roll radius is 100 mm and it rotates at 200 rpm. The roll-strip contact length
is a function of roll radius and, initial and final thickness of the strip. If the average flow stress in
plane strain of the strip material in the roll gap is 500 MPa, the roll separating force (in kN) is
_______.
Q.41 Two solid cylinders of equal diameter have different heights. They are compressed plastically by a
pair of rigid dies to create the same percentage reduction in their respective heights. Consider that
the die-workpiece interface friction is negligible. The ratio of the final diameter of the shorter
cylinder to that of the longer cylinder is __________.
Q.42 Two flat steel sheets, each of 2.5 mm thickness, are being resistance spot welded using a current of
6000 A and weld time of 0.2 s. The contact resistance at the interface between the two sheets is
200 ?? ?and the specific energy to melt steel is 10?10
9
J/m
3
. A spherical melt pool of diameter 4
mm is formed at the interface due to the current flow. Consider that electrical energy is completely
converted to thermal energy. The ratio of the heat used for melting to the total resistive heat
generated is ______.
Q.43 A cylindrical bar of 100 mm diameter is orthogonally straight turned with cutting velocity, feed and
depth of cut of 120 m/min, 0.25 mm/rev and 4 mm, respectively. The specific cutting energy of the
work material is 1?10
9
J/m
3
. Neglect the contribution of feed force towards cutting power. The
main or tangential cutting force (in N) is ________.
GATE 2016 Production and Industrial Engineering (PI)
PI
11/13
Q.44 A 60 mm wide block of low carbon steel is face milled at a cutting speed of 120 m/min, feed of 0.1
mm/tooth and axial depth of cut of 4 mm. A schematic representation of the face milling process is
shown below. The diameter of the cutter is 120 mm and it has 12 cutting edges. The material
removal rate (in mm
3
/s) is ______.
Q.45 In abrasive water jet machining, the velocity of water at the exit of the orifice, before mixing with
abrasives, is 800 m/s. The mass flow rate of water is 3.4 kg/min. The abrasives are added to the
water jet at a rate of 0.6 kg/min with negligible velocity. Assume that at the end of the focusing
tube, abrasive particles and water come out with equal velocity. Consider that there is no air in the
abrasive water jet. Assuming conservation of momentum, the velocity (in m/s) of the abrasive water
jet at the end of the focusing tube is _________.
Q.46 A single axis CNC table is driven by a DC servo motor that is directly coupled to a lead screw of 5
mm pitch. The circular encoder attached to the lead screw generates 1000 voltage pulses per
revolution of the lead screw. The table moves at a constant speed of 6 m/min. The corresponding
frequency (in kHz) of the voltage pulses generated by the circular encoder is_________.
Q.47 A helical gear with involute tooth profile has been machined with a disc-type form gear milling
cutter. The helical gear has 30 teeth and a helix angle of 30
?
. The module of the gear milling cutter
is 2. The pitch circle diameter (in mm) of the helical gear is_______________.
Q.48 A quality control engineer has collected 5 samples, each of size 30. The numbers of defective items
in the samples are given in the table below.
Sample number I II III IV V
Number of defective items 3 2 4 1 5
The upper three-sigma (3 ?) control limit for the proportion of defective items in any sample is
_____.
cutter
feed
work piece
60 mm
? 120 mm
schematic representation (top view)
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 Production and Industrial Engineering (PI)
PI
1/13
Q. 1 ? Q. 25 carry one mark each.
Q.1 The eigenvalues of the matrix
01
1 0
are
(A) i and ?i (B) 1 and ?1 (C) 0 and 1 (D) 0 and ?1
Q.2
The number of solutions of the simultaneous algebraic equations 33 and 35 is
(A) zero (B) 1 (C) 2 (D) infinite
Q.3 At x = 0, the function
sin
, ? ?,?????? 0
is
(A) continuous and differentiable.
(B) not continuous and not differentiable.
(C) not continuous but differentiable.
(D) continuous but not differentiable.
Q.4 For the two functions
,
3 and , 3
which one of the following options is correct?
(A)
(B)
(C)
(D)
Q.5 The function
is singular at
(A) 2 (B) 1 (C) (D) 2
Q.6 A fair coin is tossed N times. The probability that head does not turn up in any of the tosses is
(A) (B) 1 (C) (D) 1
GATE 2016 Production and Industrial Engineering (PI)
PI
2/13
Q.7 A normal random variable X has the following probability density function
?
,???? ? ?
Then d
(A) 0
(B)
(C) 1
(D) 1
Q.8 The elastic modulus of a rigid perfectly plastic solid is
(A) 0 (B) 1 (C) 100 (D) infinity
Q.9 Consider the following statements:
(P) Hardness is the resistance of a material to indentation.
(Q) Elastic modulus is a measure of ductility.
(R) Deflection depends on stiffness.
(S) The total area under the stress-strain curve is a measure of resilience.
Among the above statements, the correct ones are
(A) P and Q only. (B) Q and S only. (C) P and R only. (D) R and S only.
GATE 2016 Production and Industrial Engineering (PI)
PI
3/13
Q.10 A beam is subjected to an inclined concentrated load as shown in the figure below. Neglect the
weight of the beam.
The correct Free Body Diagram of the beam is
(A)
(B)
(C)
(D)
Q.11 Consider a circular cam with a flat face follower as shown in the figure below. The cam is rotated
in the plane of the paper about point P lying 5 mm away from its center. The radius of the cam is 20
mm. The distance (in mm) between the highest and the lowest positions of the flat face follower is
(A) 5 (B) 10 (C) 40 (D) 45
5 mm
P
GATE 2016 Production and Industrial Engineering (PI)
PI
4/13
Q.12 A vertical cylindrical tank of 1 m diameter is filled with water up to a height of 5 m from its
bottom. Top surface of water is exposed to atmosphere. A hole of 5 mm
2
area forms at the bottom
of the tank. Considering the coefficient of discharge of the hole to be unity and the acceleration due
to gravity to be 10 m/s
2
, the rate of leakage of water (in litre/min) through the hole from the tank to
the atmosphere, under the given conditions, is _______.
Q.13 The figure below shows an air standard Diesel cycle in p-V diagram. The cut-off ratio is given by:
(A)?
(B)
(C)
(D)
Q.14 The ratio of press force required to punch a square hole of 30 mm side in a 1 mm thick aluminium
sheet to that needed to punch a square hole of 60 mm side in a 2 mm thick aluminium sheet
is________.
Q.15 Which one of the following is a natural polymer?
(A) Cellulose (B) Nylon (C) Polyester (D) Polyvinyl chloride
Q.16 In powder metallurgy, sintering of the component
(A) increases density and reduces ductility.
(B) increases porosity and reduces density.
(C) increases density and reduces porosity.
(D) increases porosity and reduces brittleness.
Q.17 A single point right handed turning tool is used for straight turning. The feed is 0.25 mm/rev and
the uncut chip thickness is found to be 0.25 mm. The inclination angle of the main cutting edge is
10 ?. The back rake angle (in degrees) is _______.
4
p
V
2
3
1
GATE 2016 Production and Industrial Engineering (PI)
PI
5/13
Q.18 Consider the following statements.
(P) Electrolyte is used in Electro-chemical machining.
(Q) Electrolyte is used in Electrical discharge machining.
(R) Abrasive-slurry is used in Ultrasonic machining.
(S) Abrasive-slurry is used in Abrasive jet machining.
Among the above statements, the correct ones are
(A) P and R only (B) Q and S only (C) Q, R and S only (D) P and Q only
Q.19 Consider the following statements.
(P) Computer aided process planning (CAPP) takes input from material requirement plan (MRP).
(Q) Production flow analysis helps in work cell formation.
(R) Group technology takes input from choice of machining or cutting parameters.
Among the above statements, the correct one(s) is (are)
(A) P only (B) Q and R only (C) P and R only (D) Q only
Q.20 The limits of a shaft designated as 100h5 are 100.000 mm and 100.014 mm. Similarly, the limits of
a shaft designated as 100h8 are 100.000 mm and 100.055 mm. If a shaft is designated as 100h6, the
fundamental deviation (in ?m) for the same is
(A) ?22 (B) zero (C) 22 (D) 24
Q.21 The roughness profile of a surface is depicted below.
The surface roughness parameter R
a
(in ?m) is _______.
2 ?m
5 mm
2 ?m
X
profile height
centre-line of
the profile
GATE 2016 Production and Industrial Engineering (PI)
PI
6/13
Q.22 The facility layout technique that uses relationship (REL) chart is
(A) CRAFT. (B) Travel chart. (C) Partial Set Covering. (D) ALDEP.
Q.23 For a random variable, X, let be the sample average. The sample size is n. The mean and the
standard deviation of X are ? and ?, respectively. The standard deviation of is
(A) (B)
(C )
(D)
?
Q.24 ST and NT denote the standard time and the normal time, respectively, to complete a job.
Allowance , where 0 1 . Which one of the following relationships is correct?
(A)
(B) 1 )
(C )
(D) 1
Q.25 The throughput rate of a production system is 20 units per hour. The average flow time is 30
minutes and the cycle time is 3 minutes. The average inventory (in units) in the system is
(A) 1.5 (B) 9 (C ) 10 (D) 11.33
Q. 26 ? Q. 55 carry two marks each.
Q.26 The range of values of k for which the function
4 6 8
has a local maxima at point x = 0 is
(A) 2 or 2 (B) 2 or 2
(C) 2 2 (D) 2 2
Q.27
lim
?
is equal to ______.
GATE 2016 Production and Industrial Engineering (PI)
PI
7/13
Q.28 To solve the equation
2sin
by Newton-Raphson method, the initial guess was chosen to be x = 2.0. Consider x in radian only.
The value of x (in radian) obtained after one iteration will be closest to
(A) ? 8.101 (B) 1.901 (C) 2.099 (D) 12.101
Q.29 In linear gas tungsten arc welding of two plates of the same material, the peak temperature T (in K)
is given as
, where q is the heat input per unit length (in J/m) of weld, ? is the thermal
diffusivity (in m
2
/s) of the plate materials and is a constant independent of process parameters
and material types. Two welding cases are given below.
Case I: V = 15 V, I = 200 A, v = 5 mm/s, k = 150 W/mK, ? = 3000 kg/m
3
, C = 900 J/kg-K
Case II: V = 15 V, I = 300 A, v = 10 mm/s, k = 50 W/mK, ? = 8000 kg/m
3
, C = 450 J/kg-K
where, V is welding voltage, I is welding current, v is welding speed, and k, ? and C refer to the
thermal conductivity, the density and the specific heat of the plate materials, respectively. Consider
that electrical energy is completely converted to thermal energy. All other conditions remain same.
The ratio of the peak temperature in Case I to that in Case II is
(A)
(B)
(C) 1 (D) 2
Q.30 A bar of rectangular cross-sectional area of 50 mm
2
is pulled from both the sides by equal forces of
100 N as shown in the figure below. The shear stress (in MPa) along the plane making an angle 45
o
with the axis, shown as a dashed line in the figure, is ________________.
100 N
100 N
45
o
GATE 2016 Production and Industrial Engineering (PI)
PI
8/13
Q.31 A 1 m ? 10 mm ? 10 mm cantilever beam is subjected to a uniformly distributed load per unit
length of 100 N/m as shown in the figure below. The normal stress (in MPa) due to bending at point
P is ____________.
Q.32 A thin-walled cylindrical pressure vessel of internal diameter 2 m is designed to withstand an
internal pressure of 500 kPa (gauge). If the allowable normal stress at any point within the
cylindrical portion of the vessel is 100 MPa, the minimum thickness of the plate of the vessel (in
mm) is________.
Q.33 An engine, connected with a flywheel, is designed to operate at an average angular speed of 800
rpm. During operation of the engine, the maximum change in kinetic energy in a cycle is found to
be 6240 J. In order to keep the fluctuation of the angular speed within ?1% of its average value, the
moment of inertia (in kg-m
2
) of the flywheel should be ____________.
Q.34 A 2 m ? 2 m square opening in a vertical wall is covered with a metallic plate of the same
dimensions as shown in the figure below. Consider the acceleration due to gravity to be 10.0 m/s
2
.
The force (in kN) exerted by water on the plate is _____.
2 m
2 m
water
p
atm
p
atm
2 m ? 2 m
square plate
vertical wall
vertical wall
100 N/m
1 m
Point P
GATE 2016 Production and Industrial Engineering (PI)
PI
9/13
Q.35 An ideal gas of mass m is contained in a rigid tank of volume V at a pressure p. During a reversible
process its pressure reduces to . Following statements are made regarding the process.
(P) Heat is transferred from the gas.
(Q) Work done by the gas is zero.
(R) Entropy of the gas remains constant.
(S) Entropy of the gas decreases.
Among the above statements, the correct ones are
(A) P and R only. (B) P, Q and R only. (C) Q and R only. (D) P, Q and S only.
Q.36 A long slender metallic rod of length L is used as a fin. As shown in the figure below, the left end
of the fin is kept at a constant temperature t
b
. The fin loses heat by convection to the atmosphere
which is at a temperature t
a
(t
a
< t
b
). Four options of temperature profiles are shown. Identify the
correct option.
(A)
(B)
(C)
(D)
L
temperature
t
b
t
a
x
0
t
b
t
a
L
x
temperature
0
L
t
b
t
a
x
0
temperature
atmosphere at t
a
t
b
convection
x x = L
t
b
t
a
L
temperature
x
0
GATE 2016 Production and Industrial Engineering (PI)
PI
10/13
Q.37 In a fully developed turbulent flow through a circular pipe, a head loss of is observed.
The
diameter of the pipe is increased by 10% for the same flow rate and a head loss of is noted.
Assume friction factor for both the cases of pipe flow is the same. The ratio of
is closest to
(A) 0.34 (B) 0.62 (C) 0.87 (D) 1.00
Q.38 Two cast iron blocks P and Q, each of 500 mm length, have the same cross-sectional area. Block P
has rectangular cross-section of 100 mm ? 200 mm. Block Q is of square cross-section. Both P and
Q were cast under the same conditions with all their surfaces enclosed within the mould. The
solidification time of a casting is proportional to the square of the ratio of its volume to its surface
area. The ratio of solidification time of the block P to that of the block Q is ______.
Q.39 A 300 mm long copper wire of uniform cross-section is pulled in tension so that a maximum tensile
stress of 270 MPa is developed within the wire. The entire deformation of the wire remains linearly
elastic. The elastic modulus of copper is 100 GPa. The resultant elongation (in mm) is ________.
Q.40 In a single-pass rolling operation, a 200 mm wide metallic strip is rolled from a thickness 10 mm to
a thickness 6 mm. The roll radius is 100 mm and it rotates at 200 rpm. The roll-strip contact length
is a function of roll radius and, initial and final thickness of the strip. If the average flow stress in
plane strain of the strip material in the roll gap is 500 MPa, the roll separating force (in kN) is
_______.
Q.41 Two solid cylinders of equal diameter have different heights. They are compressed plastically by a
pair of rigid dies to create the same percentage reduction in their respective heights. Consider that
the die-workpiece interface friction is negligible. The ratio of the final diameter of the shorter
cylinder to that of the longer cylinder is __________.
Q.42 Two flat steel sheets, each of 2.5 mm thickness, are being resistance spot welded using a current of
6000 A and weld time of 0.2 s. The contact resistance at the interface between the two sheets is
200 ?? ?and the specific energy to melt steel is 10?10
9
J/m
3
. A spherical melt pool of diameter 4
mm is formed at the interface due to the current flow. Consider that electrical energy is completely
converted to thermal energy. The ratio of the heat used for melting to the total resistive heat
generated is ______.
Q.43 A cylindrical bar of 100 mm diameter is orthogonally straight turned with cutting velocity, feed and
depth of cut of 120 m/min, 0.25 mm/rev and 4 mm, respectively. The specific cutting energy of the
work material is 1?10
9
J/m
3
. Neglect the contribution of feed force towards cutting power. The
main or tangential cutting force (in N) is ________.
GATE 2016 Production and Industrial Engineering (PI)
PI
11/13
Q.44 A 60 mm wide block of low carbon steel is face milled at a cutting speed of 120 m/min, feed of 0.1
mm/tooth and axial depth of cut of 4 mm. A schematic representation of the face milling process is
shown below. The diameter of the cutter is 120 mm and it has 12 cutting edges. The material
removal rate (in mm
3
/s) is ______.
Q.45 In abrasive water jet machining, the velocity of water at the exit of the orifice, before mixing with
abrasives, is 800 m/s. The mass flow rate of water is 3.4 kg/min. The abrasives are added to the
water jet at a rate of 0.6 kg/min with negligible velocity. Assume that at the end of the focusing
tube, abrasive particles and water come out with equal velocity. Consider that there is no air in the
abrasive water jet. Assuming conservation of momentum, the velocity (in m/s) of the abrasive water
jet at the end of the focusing tube is _________.
Q.46 A single axis CNC table is driven by a DC servo motor that is directly coupled to a lead screw of 5
mm pitch. The circular encoder attached to the lead screw generates 1000 voltage pulses per
revolution of the lead screw. The table moves at a constant speed of 6 m/min. The corresponding
frequency (in kHz) of the voltage pulses generated by the circular encoder is_________.
Q.47 A helical gear with involute tooth profile has been machined with a disc-type form gear milling
cutter. The helical gear has 30 teeth and a helix angle of 30
?
. The module of the gear milling cutter
is 2. The pitch circle diameter (in mm) of the helical gear is_______________.
Q.48 A quality control engineer has collected 5 samples, each of size 30. The numbers of defective items
in the samples are given in the table below.
Sample number I II III IV V
Number of defective items 3 2 4 1 5
The upper three-sigma (3 ?) control limit for the proportion of defective items in any sample is
_____.
cutter
feed
work piece
60 mm
? 120 mm
schematic representation (top view)
GATE 2016 Production and Industrial Engineering (PI)
PI
12/13
Q.49 A job consists of two work elements, P and Q. Completion time (in minutes) of each work element
was measured. A pilot study involved collecting a sample of 40 observations. The results of this
pilot study are summarized in the table below.
Work element Mean completion time (in minutes) Standard deviation (in minutes)
P 1 0.50
Q 1 0.05
For the main study, the minimum sample size for the sample mean time of any work element to be
within 0.1 minutes of its true mean time with 95% confidence (corresponding standard normal
value, . 1.96 is ______________.
Q.50 Consider a system with 10 identical components connected in series. The time to failure of each
component is exponentially distributed with a failure rate of 0.10 per 500 days. The reliability of
the system after 400 days of operation is _____.
Q.51 For a process, the quality loss coefficient is 5. The target value on the dimension to be attained
through the process is 50 mm. If the maximum loss permissible (in monetary terms) is INR 80, the
maximum allowable deviation (in mm) from the target is
(A)
(B)
(C) 4
(D) ?10
Q.52 Consider a network with nodes 1, 2, 3, 4, 5 and 6. The nodes are connected with directed arcs as
shown in the table below. The respective costs (in INR) incurred while traversing the directed arcs
are also mentioned.
Directed arcs 1 ? 2 1 ?32 ?42 ?53 ?23 ?43 ?54 ?5 4 ?6 5 ?6
Cost (in INR) 3 9 3 2 2 4 8 7 2 2
The second shortest path from node 1 to node 6 (i.e. the path that has the second least total cost and
does not use any part of the shortest path) has a total cost (in INR) of
(A) 7 (B) 8 (C) 15 (D) 19
Q.53 Five jobs need to be processed on a single machine. All the jobs are available for processing at time
t = 0. Their respective processing times are given below.
Jobs I IIIIIIVV
Processing times (in minutes) 13 4 7 14 11
The average completion time (in minutes) of jobs as per the Shortest Processing Time rule is
(A) 9.8 (B) 24.2 (C) 49.0 (D) 121.0
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 Production and Industrial Engineering (PI)
PI
1/13
Q. 1 ? Q. 25 carry one mark each.
Q.1 The eigenvalues of the matrix
01
1 0
are
(A) i and ?i (B) 1 and ?1 (C) 0 and 1 (D) 0 and ?1
Q.2
The number of solutions of the simultaneous algebraic equations 33 and 35 is
(A) zero (B) 1 (C) 2 (D) infinite
Q.3 At x = 0, the function
sin
, ? ?,?????? 0
is
(A) continuous and differentiable.
(B) not continuous and not differentiable.
(C) not continuous but differentiable.
(D) continuous but not differentiable.
Q.4 For the two functions
,
3 and , 3
which one of the following options is correct?
(A)
(B)
(C)
(D)
Q.5 The function
is singular at
(A) 2 (B) 1 (C) (D) 2
Q.6 A fair coin is tossed N times. The probability that head does not turn up in any of the tosses is
(A) (B) 1 (C) (D) 1
GATE 2016 Production and Industrial Engineering (PI)
PI
2/13
Q.7 A normal random variable X has the following probability density function
?
,???? ? ?
Then d
(A) 0
(B)
(C) 1
(D) 1
Q.8 The elastic modulus of a rigid perfectly plastic solid is
(A) 0 (B) 1 (C) 100 (D) infinity
Q.9 Consider the following statements:
(P) Hardness is the resistance of a material to indentation.
(Q) Elastic modulus is a measure of ductility.
(R) Deflection depends on stiffness.
(S) The total area under the stress-strain curve is a measure of resilience.
Among the above statements, the correct ones are
(A) P and Q only. (B) Q and S only. (C) P and R only. (D) R and S only.
GATE 2016 Production and Industrial Engineering (PI)
PI
3/13
Q.10 A beam is subjected to an inclined concentrated load as shown in the figure below. Neglect the
weight of the beam.
The correct Free Body Diagram of the beam is
(A)
(B)
(C)
(D)
Q.11 Consider a circular cam with a flat face follower as shown in the figure below. The cam is rotated
in the plane of the paper about point P lying 5 mm away from its center. The radius of the cam is 20
mm. The distance (in mm) between the highest and the lowest positions of the flat face follower is
(A) 5 (B) 10 (C) 40 (D) 45
5 mm
P
GATE 2016 Production and Industrial Engineering (PI)
PI
4/13
Q.12 A vertical cylindrical tank of 1 m diameter is filled with water up to a height of 5 m from its
bottom. Top surface of water is exposed to atmosphere. A hole of 5 mm
2
area forms at the bottom
of the tank. Considering the coefficient of discharge of the hole to be unity and the acceleration due
to gravity to be 10 m/s
2
, the rate of leakage of water (in litre/min) through the hole from the tank to
the atmosphere, under the given conditions, is _______.
Q.13 The figure below shows an air standard Diesel cycle in p-V diagram. The cut-off ratio is given by:
(A)?
(B)
(C)
(D)
Q.14 The ratio of press force required to punch a square hole of 30 mm side in a 1 mm thick aluminium
sheet to that needed to punch a square hole of 60 mm side in a 2 mm thick aluminium sheet
is________.
Q.15 Which one of the following is a natural polymer?
(A) Cellulose (B) Nylon (C) Polyester (D) Polyvinyl chloride
Q.16 In powder metallurgy, sintering of the component
(A) increases density and reduces ductility.
(B) increases porosity and reduces density.
(C) increases density and reduces porosity.
(D) increases porosity and reduces brittleness.
Q.17 A single point right handed turning tool is used for straight turning. The feed is 0.25 mm/rev and
the uncut chip thickness is found to be 0.25 mm. The inclination angle of the main cutting edge is
10 ?. The back rake angle (in degrees) is _______.
4
p
V
2
3
1
GATE 2016 Production and Industrial Engineering (PI)
PI
5/13
Q.18 Consider the following statements.
(P) Electrolyte is used in Electro-chemical machining.
(Q) Electrolyte is used in Electrical discharge machining.
(R) Abrasive-slurry is used in Ultrasonic machining.
(S) Abrasive-slurry is used in Abrasive jet machining.
Among the above statements, the correct ones are
(A) P and R only (B) Q and S only (C) Q, R and S only (D) P and Q only
Q.19 Consider the following statements.
(P) Computer aided process planning (CAPP) takes input from material requirement plan (MRP).
(Q) Production flow analysis helps in work cell formation.
(R) Group technology takes input from choice of machining or cutting parameters.
Among the above statements, the correct one(s) is (are)
(A) P only (B) Q and R only (C) P and R only (D) Q only
Q.20 The limits of a shaft designated as 100h5 are 100.000 mm and 100.014 mm. Similarly, the limits of
a shaft designated as 100h8 are 100.000 mm and 100.055 mm. If a shaft is designated as 100h6, the
fundamental deviation (in ?m) for the same is
(A) ?22 (B) zero (C) 22 (D) 24
Q.21 The roughness profile of a surface is depicted below.
The surface roughness parameter R
a
(in ?m) is _______.
2 ?m
5 mm
2 ?m
X
profile height
centre-line of
the profile
GATE 2016 Production and Industrial Engineering (PI)
PI
6/13
Q.22 The facility layout technique that uses relationship (REL) chart is
(A) CRAFT. (B) Travel chart. (C) Partial Set Covering. (D) ALDEP.
Q.23 For a random variable, X, let be the sample average. The sample size is n. The mean and the
standard deviation of X are ? and ?, respectively. The standard deviation of is
(A) (B)
(C )
(D)
?
Q.24 ST and NT denote the standard time and the normal time, respectively, to complete a job.
Allowance , where 0 1 . Which one of the following relationships is correct?
(A)
(B) 1 )
(C )
(D) 1
Q.25 The throughput rate of a production system is 20 units per hour. The average flow time is 30
minutes and the cycle time is 3 minutes. The average inventory (in units) in the system is
(A) 1.5 (B) 9 (C ) 10 (D) 11.33
Q. 26 ? Q. 55 carry two marks each.
Q.26 The range of values of k for which the function
4 6 8
has a local maxima at point x = 0 is
(A) 2 or 2 (B) 2 or 2
(C) 2 2 (D) 2 2
Q.27
lim
?
is equal to ______.
GATE 2016 Production and Industrial Engineering (PI)
PI
7/13
Q.28 To solve the equation
2sin
by Newton-Raphson method, the initial guess was chosen to be x = 2.0. Consider x in radian only.
The value of x (in radian) obtained after one iteration will be closest to
(A) ? 8.101 (B) 1.901 (C) 2.099 (D) 12.101
Q.29 In linear gas tungsten arc welding of two plates of the same material, the peak temperature T (in K)
is given as
, where q is the heat input per unit length (in J/m) of weld, ? is the thermal
diffusivity (in m
2
/s) of the plate materials and is a constant independent of process parameters
and material types. Two welding cases are given below.
Case I: V = 15 V, I = 200 A, v = 5 mm/s, k = 150 W/mK, ? = 3000 kg/m
3
, C = 900 J/kg-K
Case II: V = 15 V, I = 300 A, v = 10 mm/s, k = 50 W/mK, ? = 8000 kg/m
3
, C = 450 J/kg-K
where, V is welding voltage, I is welding current, v is welding speed, and k, ? and C refer to the
thermal conductivity, the density and the specific heat of the plate materials, respectively. Consider
that electrical energy is completely converted to thermal energy. All other conditions remain same.
The ratio of the peak temperature in Case I to that in Case II is
(A)
(B)
(C) 1 (D) 2
Q.30 A bar of rectangular cross-sectional area of 50 mm
2
is pulled from both the sides by equal forces of
100 N as shown in the figure below. The shear stress (in MPa) along the plane making an angle 45
o
with the axis, shown as a dashed line in the figure, is ________________.
100 N
100 N
45
o
GATE 2016 Production and Industrial Engineering (PI)
PI
8/13
Q.31 A 1 m ? 10 mm ? 10 mm cantilever beam is subjected to a uniformly distributed load per unit
length of 100 N/m as shown in the figure below. The normal stress (in MPa) due to bending at point
P is ____________.
Q.32 A thin-walled cylindrical pressure vessel of internal diameter 2 m is designed to withstand an
internal pressure of 500 kPa (gauge). If the allowable normal stress at any point within the
cylindrical portion of the vessel is 100 MPa, the minimum thickness of the plate of the vessel (in
mm) is________.
Q.33 An engine, connected with a flywheel, is designed to operate at an average angular speed of 800
rpm. During operation of the engine, the maximum change in kinetic energy in a cycle is found to
be 6240 J. In order to keep the fluctuation of the angular speed within ?1% of its average value, the
moment of inertia (in kg-m
2
) of the flywheel should be ____________.
Q.34 A 2 m ? 2 m square opening in a vertical wall is covered with a metallic plate of the same
dimensions as shown in the figure below. Consider the acceleration due to gravity to be 10.0 m/s
2
.
The force (in kN) exerted by water on the plate is _____.
2 m
2 m
water
p
atm
p
atm
2 m ? 2 m
square plate
vertical wall
vertical wall
100 N/m
1 m
Point P
GATE 2016 Production and Industrial Engineering (PI)
PI
9/13
Q.35 An ideal gas of mass m is contained in a rigid tank of volume V at a pressure p. During a reversible
process its pressure reduces to . Following statements are made regarding the process.
(P) Heat is transferred from the gas.
(Q) Work done by the gas is zero.
(R) Entropy of the gas remains constant.
(S) Entropy of the gas decreases.
Among the above statements, the correct ones are
(A) P and R only. (B) P, Q and R only. (C) Q and R only. (D) P, Q and S only.
Q.36 A long slender metallic rod of length L is used as a fin. As shown in the figure below, the left end
of the fin is kept at a constant temperature t
b
. The fin loses heat by convection to the atmosphere
which is at a temperature t
a
(t
a
< t
b
). Four options of temperature profiles are shown. Identify the
correct option.
(A)
(B)
(C)
(D)
L
temperature
t
b
t
a
x
0
t
b
t
a
L
x
temperature
0
L
t
b
t
a
x
0
temperature
atmosphere at t
a
t
b
convection
x x = L
t
b
t
a
L
temperature
x
0
GATE 2016 Production and Industrial Engineering (PI)
PI
10/13
Q.37 In a fully developed turbulent flow through a circular pipe, a head loss of is observed.
The
diameter of the pipe is increased by 10% for the same flow rate and a head loss of is noted.
Assume friction factor for both the cases of pipe flow is the same. The ratio of
is closest to
(A) 0.34 (B) 0.62 (C) 0.87 (D) 1.00
Q.38 Two cast iron blocks P and Q, each of 500 mm length, have the same cross-sectional area. Block P
has rectangular cross-section of 100 mm ? 200 mm. Block Q is of square cross-section. Both P and
Q were cast under the same conditions with all their surfaces enclosed within the mould. The
solidification time of a casting is proportional to the square of the ratio of its volume to its surface
area. The ratio of solidification time of the block P to that of the block Q is ______.
Q.39 A 300 mm long copper wire of uniform cross-section is pulled in tension so that a maximum tensile
stress of 270 MPa is developed within the wire. The entire deformation of the wire remains linearly
elastic. The elastic modulus of copper is 100 GPa. The resultant elongation (in mm) is ________.
Q.40 In a single-pass rolling operation, a 200 mm wide metallic strip is rolled from a thickness 10 mm to
a thickness 6 mm. The roll radius is 100 mm and it rotates at 200 rpm. The roll-strip contact length
is a function of roll radius and, initial and final thickness of the strip. If the average flow stress in
plane strain of the strip material in the roll gap is 500 MPa, the roll separating force (in kN) is
_______.
Q.41 Two solid cylinders of equal diameter have different heights. They are compressed plastically by a
pair of rigid dies to create the same percentage reduction in their respective heights. Consider that
the die-workpiece interface friction is negligible. The ratio of the final diameter of the shorter
cylinder to that of the longer cylinder is __________.
Q.42 Two flat steel sheets, each of 2.5 mm thickness, are being resistance spot welded using a current of
6000 A and weld time of 0.2 s. The contact resistance at the interface between the two sheets is
200 ?? ?and the specific energy to melt steel is 10?10
9
J/m
3
. A spherical melt pool of diameter 4
mm is formed at the interface due to the current flow. Consider that electrical energy is completely
converted to thermal energy. The ratio of the heat used for melting to the total resistive heat
generated is ______.
Q.43 A cylindrical bar of 100 mm diameter is orthogonally straight turned with cutting velocity, feed and
depth of cut of 120 m/min, 0.25 mm/rev and 4 mm, respectively. The specific cutting energy of the
work material is 1?10
9
J/m
3
. Neglect the contribution of feed force towards cutting power. The
main or tangential cutting force (in N) is ________.
GATE 2016 Production and Industrial Engineering (PI)
PI
11/13
Q.44 A 60 mm wide block of low carbon steel is face milled at a cutting speed of 120 m/min, feed of 0.1
mm/tooth and axial depth of cut of 4 mm. A schematic representation of the face milling process is
shown below. The diameter of the cutter is 120 mm and it has 12 cutting edges. The material
removal rate (in mm
3
/s) is ______.
Q.45 In abrasive water jet machining, the velocity of water at the exit of the orifice, before mixing with
abrasives, is 800 m/s. The mass flow rate of water is 3.4 kg/min. The abrasives are added to the
water jet at a rate of 0.6 kg/min with negligible velocity. Assume that at the end of the focusing
tube, abrasive particles and water come out with equal velocity. Consider that there is no air in the
abrasive water jet. Assuming conservation of momentum, the velocity (in m/s) of the abrasive water
jet at the end of the focusing tube is _________.
Q.46 A single axis CNC table is driven by a DC servo motor that is directly coupled to a lead screw of 5
mm pitch. The circular encoder attached to the lead screw generates 1000 voltage pulses per
revolution of the lead screw. The table moves at a constant speed of 6 m/min. The corresponding
frequency (in kHz) of the voltage pulses generated by the circular encoder is_________.
Q.47 A helical gear with involute tooth profile has been machined with a disc-type form gear milling
cutter. The helical gear has 30 teeth and a helix angle of 30
?
. The module of the gear milling cutter
is 2. The pitch circle diameter (in mm) of the helical gear is_______________.
Q.48 A quality control engineer has collected 5 samples, each of size 30. The numbers of defective items
in the samples are given in the table below.
Sample number I II III IV V
Number of defective items 3 2 4 1 5
The upper three-sigma (3 ?) control limit for the proportion of defective items in any sample is
_____.
cutter
feed
work piece
60 mm
? 120 mm
schematic representation (top view)
GATE 2016 Production and Industrial Engineering (PI)
PI
12/13
Q.49 A job consists of two work elements, P and Q. Completion time (in minutes) of each work element
was measured. A pilot study involved collecting a sample of 40 observations. The results of this
pilot study are summarized in the table below.
Work element Mean completion time (in minutes) Standard deviation (in minutes)
P 1 0.50
Q 1 0.05
For the main study, the minimum sample size for the sample mean time of any work element to be
within 0.1 minutes of its true mean time with 95% confidence (corresponding standard normal
value, . 1.96 is ______________.
Q.50 Consider a system with 10 identical components connected in series. The time to failure of each
component is exponentially distributed with a failure rate of 0.10 per 500 days. The reliability of
the system after 400 days of operation is _____.
Q.51 For a process, the quality loss coefficient is 5. The target value on the dimension to be attained
through the process is 50 mm. If the maximum loss permissible (in monetary terms) is INR 80, the
maximum allowable deviation (in mm) from the target is
(A)
(B)
(C) 4
(D) ?10
Q.52 Consider a network with nodes 1, 2, 3, 4, 5 and 6. The nodes are connected with directed arcs as
shown in the table below. The respective costs (in INR) incurred while traversing the directed arcs
are also mentioned.
Directed arcs 1 ? 2 1 ?32 ?42 ?53 ?23 ?43 ?54 ?5 4 ?6 5 ?6
Cost (in INR) 3 9 3 2 2 4 8 7 2 2
The second shortest path from node 1 to node 6 (i.e. the path that has the second least total cost and
does not use any part of the shortest path) has a total cost (in INR) of
(A) 7 (B) 8 (C) 15 (D) 19
Q.53 Five jobs need to be processed on a single machine. All the jobs are available for processing at time
t = 0. Their respective processing times are given below.
Jobs I IIIIIIVV
Processing times (in minutes) 13 4 7 14 11
The average completion time (in minutes) of jobs as per the Shortest Processing Time rule is
(A) 9.8 (B) 24.2 (C) 49.0 (D) 121.0
GATE 2016 Production and Industrial Engineering (PI)
PI
13/13
Q.54 Transportation costs (in INR/unit) from factories to respective markets are given in the table below.
The market requirements and factory capacities are also given. Using the North-West Corner
method, the quantity (in units) to be transported from factory R to market II is
Factory Requirements
(in units) P Q R S
Market
I 3 3 2 1 50
II 4 2 5 9 20
III 1 2 1 4 30
Factory Capacity
(in units)
20 40 30 10
(A) 30 (B) 20 (C) 10 (D) 0
Q.55 In a given year, a restaurant earned INR 38,500 in revenues. In that year, total expenses incurred
were INR 30,000 and the depreciation amount was INR 3,200. At 40% tax rate, the net cash flow
(in INR) for that year was _____.
END OF THE QUESTION PAPER
FirstRanker.com - FirstRanker's Choice
This post was last modified on 18 December 2019