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Production and Industrial Engineering (PI) 2015 GATE Paper without solution (unsolved) GATE Notes | EduRev

GATE : Production and Industrial Engineering (PI) 2015 GATE Paper without solution (unsolved) GATE Notes | EduRev

``` Page 1

GATE 2015                                                                                                                                                 PRODUCTION & INDUSTRIAL ENGG.   – PI
PI 1/9
Q. 1 – Q. 25 carry one mark each.
Q.1  In numerical integration using Simpson’s rule, the approximating function in the interval is a
(A) constant (B) straight line

(C) cubic B-Spline (D) parabola

Q.2
If a constant force f
?
applied on an object P, displaces it by a distance , d
?
inclined at an angle ? to
the direction of force , f
?
then the work done by the force f
?
is

(A) div( ) fd ×
? ?
(B) (curl ) fd ×
? ?
(C) fd ×
? ?
(D) . fd
? ?

Q.3  A product is an assembly of 5 different components. The product can be sequentially assembled in
two possible ways. If the 5 components are placed in a box and these are drawn at random from the
box, then the probability of getting a correct sequence is
(A)
2
5!
(B)
2
5

(C)
2
(5 2)! -
(D)
2
(5 3)! -

Q.4
2
The function ( ) times, is defined f x x xxx x = = +++ ?
(A) at all real values of x
(B) only at positive integer values of x
(C) only at negative integer values of x
(D) only at rational values of x

Q.5  The room-temperature stress ( s)-strain ( e) curves of four materials P, Q, R, and S are shown in the
figure below. The material that behaves as a rigid perfectly plastic material is

(A) P (B) Q (C) R (D) S

Page 2

GATE 2015                                                                                                                                                 PRODUCTION & INDUSTRIAL ENGG.   – PI
PI 1/9
Q. 1 – Q. 25 carry one mark each.
Q.1  In numerical integration using Simpson’s rule, the approximating function in the interval is a
(A) constant (B) straight line

(C) cubic B-Spline (D) parabola

Q.2
If a constant force f
?
applied on an object P, displaces it by a distance , d
?
inclined at an angle ? to
the direction of force , f
?
then the work done by the force f
?
is

(A) div( ) fd ×
? ?
(B) (curl ) fd ×
? ?
(C) fd ×
? ?
(D) . fd
? ?

Q.3  A product is an assembly of 5 different components. The product can be sequentially assembled in
two possible ways. If the 5 components are placed in a box and these are drawn at random from the
box, then the probability of getting a correct sequence is
(A)
2
5!
(B)
2
5

(C)
2
(5 2)! -
(D)
2
(5 3)! -

Q.4
2
The function ( ) times, is defined f x x xxx x = = +++ ?
(A) at all real values of x
(B) only at positive integer values of x
(C) only at negative integer values of x
(D) only at rational values of x

Q.5  The room-temperature stress ( s)-strain ( e) curves of four materials P, Q, R, and S are shown in the
figure below. The material that behaves as a rigid perfectly plastic material is

(A) P (B) Q (C) R (D) S

GATE 2015                                                                                                                                                 PRODUCTION & INDUSTRIAL ENGG.   – PI
PI 2/9
Q.6  The true stress at fracture of a tensile tested specimen, having an initial diameter of 13 mm, is
700 MPa.  If the diameter of specimen at fracture is 10 mm, then the engineering stress, in MPa, at
fracture is _________________.

Q.7  If the principal stress values are 120 MPa, –50 MPa and 10 MPa in a given state of stress, then
maximum shear stress in the material, in MPa, is ___________________.

Q.8  Match the items in the first column to their functions in the second column.

P.     Sprue 1.     regulates flow of molten metal into mould cavity
Q.     Riser 2.     feeds molten metal from pouring basin to gate
R.     Gate 3.     acts as a reservoir for molten metal
S.     Pouring basin 4.     supplies molten metal to compensate for liquid shrinkage

(A) P-1, Q-2, R-3, S-4 (B) P-2, Q-4, R-1, S-3
(C) P-4, Q-2, R-1, S-3 (D) P-2, Q-4, R-3, S-1

Q.9  In rolling of a flat strip, the  relative velocity of strip with respect to the roller is
(A) positive at entry plane, negative at exit plane
(B) negative at entry plane, positive at exit plane
(C) positive throughout from entry to exit plane
(D) negative throughout from entry to exit plane

Q.10  The maximum reduction per pass during wire drawing of an aluminum alloy ignoring friction and
redundant work is 77%. The strain hardening exponent of the material is ____________.

Q.11  Built-up edge formation decreases under the conditions listed below EXCEPT
(A) at low cutting speeds (B) using large positive rake angle
(C) with sharper tool (D) using cutting fluid

Q.12  During turning of mild steel work material, the maximum temperature is observed at
(A) primary deformation zone (B) tool and chip interface
(C) tool-flank and work interface (D) machined sub-surface

Q.13  Which one of the following statements related to grinding process is INCORRECT?
(A) Grinding wheels made of finer abrasive grains produce better surface finish.
(B) Abrasive grains tend to fracture frequently during the grinding process.
(C) Specific energy in grinding is higher than that in turning.
(D) Cutting speed in grinding process is much lower than that in face milling.

Q.14  For an assembly made of n components, the dimensions on each component i follow a normal
distribution and have tolerance T
i
. Overall dimension of the assembly is L
a
with tolerance T
a
. The
relationship between T
a
and T
i
is
(A)  (B)

(C)  (D)

Page 3

GATE 2015                                                                                                                                                 PRODUCTION & INDUSTRIAL ENGG.   – PI
PI 1/9
Q. 1 – Q. 25 carry one mark each.
Q.1  In numerical integration using Simpson’s rule, the approximating function in the interval is a
(A) constant (B) straight line

(C) cubic B-Spline (D) parabola

Q.2
If a constant force f
?
applied on an object P, displaces it by a distance , d
?
inclined at an angle ? to
the direction of force , f
?
then the work done by the force f
?
is

(A) div( ) fd ×
? ?
(B) (curl ) fd ×
? ?
(C) fd ×
? ?
(D) . fd
? ?

Q.3  A product is an assembly of 5 different components. The product can be sequentially assembled in
two possible ways. If the 5 components are placed in a box and these are drawn at random from the
box, then the probability of getting a correct sequence is
(A)
2
5!
(B)
2
5

(C)
2
(5 2)! -
(D)
2
(5 3)! -

Q.4
2
The function ( ) times, is defined f x x xxx x = = +++ ?
(A) at all real values of x
(B) only at positive integer values of x
(C) only at negative integer values of x
(D) only at rational values of x

Q.5  The room-temperature stress ( s)-strain ( e) curves of four materials P, Q, R, and S are shown in the
figure below. The material that behaves as a rigid perfectly plastic material is

(A) P (B) Q (C) R (D) S

GATE 2015                                                                                                                                                 PRODUCTION & INDUSTRIAL ENGG.   – PI
PI 2/9
Q.6  The true stress at fracture of a tensile tested specimen, having an initial diameter of 13 mm, is
700 MPa.  If the diameter of specimen at fracture is 10 mm, then the engineering stress, in MPa, at
fracture is _________________.

Q.7  If the principal stress values are 120 MPa, –50 MPa and 10 MPa in a given state of stress, then
maximum shear stress in the material, in MPa, is ___________________.

Q.8  Match the items in the first column to their functions in the second column.

P.     Sprue 1.     regulates flow of molten metal into mould cavity
Q.     Riser 2.     feeds molten metal from pouring basin to gate
R.     Gate 3.     acts as a reservoir for molten metal
S.     Pouring basin 4.     supplies molten metal to compensate for liquid shrinkage

(A) P-1, Q-2, R-3, S-4 (B) P-2, Q-4, R-1, S-3
(C) P-4, Q-2, R-1, S-3 (D) P-2, Q-4, R-3, S-1

Q.9  In rolling of a flat strip, the  relative velocity of strip with respect to the roller is
(A) positive at entry plane, negative at exit plane
(B) negative at entry plane, positive at exit plane
(C) positive throughout from entry to exit plane
(D) negative throughout from entry to exit plane

Q.10  The maximum reduction per pass during wire drawing of an aluminum alloy ignoring friction and
redundant work is 77%. The strain hardening exponent of the material is ____________.

Q.11  Built-up edge formation decreases under the conditions listed below EXCEPT
(A) at low cutting speeds (B) using large positive rake angle
(C) with sharper tool (D) using cutting fluid

Q.12  During turning of mild steel work material, the maximum temperature is observed at
(A) primary deformation zone (B) tool and chip interface
(C) tool-flank and work interface (D) machined sub-surface

Q.13  Which one of the following statements related to grinding process is INCORRECT?
(A) Grinding wheels made of finer abrasive grains produce better surface finish.
(B) Abrasive grains tend to fracture frequently during the grinding process.
(C) Specific energy in grinding is higher than that in turning.
(D) Cutting speed in grinding process is much lower than that in face milling.

Q.14  For an assembly made of n components, the dimensions on each component i follow a normal
distribution and have tolerance T
i
. Overall dimension of the assembly is L
a
with tolerance T
a
. The
relationship between T
a
and T
i
is
(A)  (B)

(C)  (D)

GATE 2015                                                                                                                                                 PRODUCTION & INDUSTRIAL ENGG.   – PI
PI 3/9
Q.15  Which of the following DO NOT influence the material removal rate in Electrical Discharge
Machining process?

(i) Hardness of work piece material
(ii) Melting temperature of work piece material
(iii) Hardness of tool material
(iv) Discharge current and frequency
(A) (i) and (ii) (B) (i) and (iii) (C)  (iii) and (iv) (D) (i), (ii) and (iii)

Q.16  In Computer Aided Process Planning, determination of process sequence for manufacture of any
part design without predefined standard plans is known as
(A) variant type process planning
(B) retrieval type process planning
(C) generative type process planning
(D) group technology based process planning

Q.17  The angle of a twist drill that determines its rake angle is
(A) lip relief angle (B)  chisel edge angle (C)  helix angle (D)  point angle

Q.18  A line balancing problem is solved in the context of
(A) process layout (B) fixed position layout
(C) product layout (D) production schedule

Q.19  Solution to the balanced assignment problem is binary due to
(A) linear formulation (B) non-empty feasible region
(C) approximation algorithms (D) uni-modularity property

Q.20  Material Requirements Planning DOES NOT include
(A) material price (B) bill of material
(C) inventory level (D) production schedule

Q.21  Ishikawa diagram represents
(A) different types of quality defects
(B) quantitative relation between the extent of defect and a process parameter
(C) relation between defects and their causes
(D) prioritized quality defects

Q.22  As per the principles of motion economy, which one of the following is NOT a pivot for a
classified movement of human body?
(A) Knee  (B) Elbow  (C) Torso   (D) Wrist

Q.23  For air travel over a distance of 500 km, the ticket price is Rs. 4000. The comfort of the air travel
can be monetized at Rs.3000, and the monetary value of time saved because of air travel is Rs.3000.
The value of air travel is ____________.

Q.24  Which one of the following is NOT in the scope of Enterprise Resource Planning (ERP) system?
(A) General ledger entries (B) Materials management system
(C) Order management system (D) Employee promotion policy

Page 4

GATE 2015                                                                                                                                                 PRODUCTION & INDUSTRIAL ENGG.   – PI
PI 1/9
Q. 1 – Q. 25 carry one mark each.
Q.1  In numerical integration using Simpson’s rule, the approximating function in the interval is a
(A) constant (B) straight line

(C) cubic B-Spline (D) parabola

Q.2
If a constant force f
?
applied on an object P, displaces it by a distance , d
?
inclined at an angle ? to
the direction of force , f
?
then the work done by the force f
?
is

(A) div( ) fd ×
? ?
(B) (curl ) fd ×
? ?
(C) fd ×
? ?
(D) . fd
? ?

Q.3  A product is an assembly of 5 different components. The product can be sequentially assembled in
two possible ways. If the 5 components are placed in a box and these are drawn at random from the
box, then the probability of getting a correct sequence is
(A)
2
5!
(B)
2
5

(C)
2
(5 2)! -
(D)
2
(5 3)! -

Q.4
2
The function ( ) times, is defined f x x xxx x = = +++ ?
(A) at all real values of x
(B) only at positive integer values of x
(C) only at negative integer values of x
(D) only at rational values of x

Q.5  The room-temperature stress ( s)-strain ( e) curves of four materials P, Q, R, and S are shown in the
figure below. The material that behaves as a rigid perfectly plastic material is

(A) P (B) Q (C) R (D) S

GATE 2015                                                                                                                                                 PRODUCTION & INDUSTRIAL ENGG.   – PI
PI 2/9
Q.6  The true stress at fracture of a tensile tested specimen, having an initial diameter of 13 mm, is
700 MPa.  If the diameter of specimen at fracture is 10 mm, then the engineering stress, in MPa, at
fracture is _________________.

Q.7  If the principal stress values are 120 MPa, –50 MPa and 10 MPa in a given state of stress, then
maximum shear stress in the material, in MPa, is ___________________.

Q.8  Match the items in the first column to their functions in the second column.

P.     Sprue 1.     regulates flow of molten metal into mould cavity
Q.     Riser 2.     feeds molten metal from pouring basin to gate
R.     Gate 3.     acts as a reservoir for molten metal
S.     Pouring basin 4.     supplies molten metal to compensate for liquid shrinkage

(A) P-1, Q-2, R-3, S-4 (B) P-2, Q-4, R-1, S-3
(C) P-4, Q-2, R-1, S-3 (D) P-2, Q-4, R-3, S-1

Q.9  In rolling of a flat strip, the  relative velocity of strip with respect to the roller is
(A) positive at entry plane, negative at exit plane
(B) negative at entry plane, positive at exit plane
(C) positive throughout from entry to exit plane
(D) negative throughout from entry to exit plane

Q.10  The maximum reduction per pass during wire drawing of an aluminum alloy ignoring friction and
redundant work is 77%. The strain hardening exponent of the material is ____________.

Q.11  Built-up edge formation decreases under the conditions listed below EXCEPT
(A) at low cutting speeds (B) using large positive rake angle
(C) with sharper tool (D) using cutting fluid

Q.12  During turning of mild steel work material, the maximum temperature is observed at
(A) primary deformation zone (B) tool and chip interface
(C) tool-flank and work interface (D) machined sub-surface

Q.13  Which one of the following statements related to grinding process is INCORRECT?
(A) Grinding wheels made of finer abrasive grains produce better surface finish.
(B) Abrasive grains tend to fracture frequently during the grinding process.
(C) Specific energy in grinding is higher than that in turning.
(D) Cutting speed in grinding process is much lower than that in face milling.

Q.14  For an assembly made of n components, the dimensions on each component i follow a normal
distribution and have tolerance T
i
. Overall dimension of the assembly is L
a
with tolerance T
a
. The
relationship between T
a
and T
i
is
(A)  (B)

(C)  (D)

GATE 2015                                                                                                                                                 PRODUCTION & INDUSTRIAL ENGG.   – PI
PI 3/9
Q.15  Which of the following DO NOT influence the material removal rate in Electrical Discharge
Machining process?

(i) Hardness of work piece material
(ii) Melting temperature of work piece material
(iii) Hardness of tool material
(iv) Discharge current and frequency
(A) (i) and (ii) (B) (i) and (iii) (C)  (iii) and (iv) (D) (i), (ii) and (iii)

Q.16  In Computer Aided Process Planning, determination of process sequence for manufacture of any
part design without predefined standard plans is known as
(A) variant type process planning
(B) retrieval type process planning
(C) generative type process planning
(D) group technology based process planning

Q.17  The angle of a twist drill that determines its rake angle is
(A) lip relief angle (B)  chisel edge angle (C)  helix angle (D)  point angle

Q.18  A line balancing problem is solved in the context of
(A) process layout (B) fixed position layout
(C) product layout (D) production schedule

Q.19  Solution to the balanced assignment problem is binary due to
(A) linear formulation (B) non-empty feasible region
(C) approximation algorithms (D) uni-modularity property

Q.20  Material Requirements Planning DOES NOT include
(A) material price (B) bill of material
(C) inventory level (D) production schedule

Q.21  Ishikawa diagram represents
(A) different types of quality defects
(B) quantitative relation between the extent of defect and a process parameter
(C) relation between defects and their causes
(D) prioritized quality defects

Q.22  As per the principles of motion economy, which one of the following is NOT a pivot for a
classified movement of human body?
(A) Knee  (B) Elbow  (C) Torso   (D) Wrist

Q.23  For air travel over a distance of 500 km, the ticket price is Rs. 4000. The comfort of the air travel
can be monetized at Rs.3000, and the monetary value of time saved because of air travel is Rs.3000.
The value of air travel is ____________.

Q.24  Which one of the following is NOT in the scope of Enterprise Resource Planning (ERP) system?
(A) General ledger entries (B) Materials management system
(C) Order management system (D) Employee promotion policy

GATE 2015                                                                                                                                                 PRODUCTION & INDUSTRIAL ENGG.   – PI
PI 4/9
Q.25  If standard production is 20 units, a worker’s actual output is 18 units, piece rate is Rs. 500 per unit,
and over-achievement rate is Rs. 750 per unit, then the wage paid to the worker, in Rs., as per
Taylor’s differential price rate wage incentive plan, is ______________.

Q. 26 – Q. 55 carry two marks each.
Q.26  The solution to  represents a
(A) family of circles (B) family of ellipses
(C) family of parabolas (D) family of hyperbolas

Q.27  The solution to   is

(A)
2 3
12
y c x c x
-
= + (B)
2
12
y c c x
-
= + (C)
2
1
c
y c x
x
= +  (D)
4
12
y c x c x = +

Q.28  Match the linear transformation matrices listed in the first column to their interpretations in the
second column.

P.
10
00
??
??
??
1.        Stretch in the y-axis
Q.
00
01
??
??
??
2.        Uniform stretch in x and y-axes
R.
10
03
??
??
??
3.        Projection in x-axis
S.
40
04
??
??
??
4.        Projection in y-axis

(A) P-1, Q-2, R-3, S-4 (B) P-2, Q-3, R-4, S-1
(C) P-3, Q-4, R-1, S-2 (D) P-4, Q-1, R-2, S-3.

Q.29
The value of
2
( , ) (0,0)
lim
x y
x xy
xy
?
-
-
is
(A) 0 (B)
1
2
(C) 1  (D) 8

Q.30  The curve y = x
4
is
(A) concave up for all values of x
(B) concave down for all values of x
(C) concave up only for positive values of x
(D) concave up only for negative values of x

Q.31  A metallic bar of uniform cross-section with specific weight of 100 kN/m
3
is hung vertically down.
The length and Young’s modulus of the bar are 100 m and 200 GPa, respectively. The elongation
of the bar, in mm, due to its own weight is ____________.

Page 5

GATE 2015                                                                                                                                                 PRODUCTION & INDUSTRIAL ENGG.   – PI
PI 1/9
Q. 1 – Q. 25 carry one mark each.
Q.1  In numerical integration using Simpson’s rule, the approximating function in the interval is a
(A) constant (B) straight line

(C) cubic B-Spline (D) parabola

Q.2
If a constant force f
?
applied on an object P, displaces it by a distance , d
?
inclined at an angle ? to
the direction of force , f
?
then the work done by the force f
?
is

(A) div( ) fd ×
? ?
(B) (curl ) fd ×
? ?
(C) fd ×
? ?
(D) . fd
? ?

Q.3  A product is an assembly of 5 different components. The product can be sequentially assembled in
two possible ways. If the 5 components are placed in a box and these are drawn at random from the
box, then the probability of getting a correct sequence is
(A)
2
5!
(B)
2
5

(C)
2
(5 2)! -
(D)
2
(5 3)! -

Q.4
2
The function ( ) times, is defined f x x xxx x = = +++ ?
(A) at all real values of x
(B) only at positive integer values of x
(C) only at negative integer values of x
(D) only at rational values of x

Q.5  The room-temperature stress ( s)-strain ( e) curves of four materials P, Q, R, and S are shown in the
figure below. The material that behaves as a rigid perfectly plastic material is

(A) P (B) Q (C) R (D) S

GATE 2015                                                                                                                                                 PRODUCTION & INDUSTRIAL ENGG.   – PI
PI 2/9
Q.6  The true stress at fracture of a tensile tested specimen, having an initial diameter of 13 mm, is
700 MPa.  If the diameter of specimen at fracture is 10 mm, then the engineering stress, in MPa, at
fracture is _________________.

Q.7  If the principal stress values are 120 MPa, –50 MPa and 10 MPa in a given state of stress, then
maximum shear stress in the material, in MPa, is ___________________.

Q.8  Match the items in the first column to their functions in the second column.

P.     Sprue 1.     regulates flow of molten metal into mould cavity
Q.     Riser 2.     feeds molten metal from pouring basin to gate
R.     Gate 3.     acts as a reservoir for molten metal
S.     Pouring basin 4.     supplies molten metal to compensate for liquid shrinkage

(A) P-1, Q-2, R-3, S-4 (B) P-2, Q-4, R-1, S-3
(C) P-4, Q-2, R-1, S-3 (D) P-2, Q-4, R-3, S-1

Q.9  In rolling of a flat strip, the  relative velocity of strip with respect to the roller is
(A) positive at entry plane, negative at exit plane
(B) negative at entry plane, positive at exit plane
(C) positive throughout from entry to exit plane
(D) negative throughout from entry to exit plane

Q.10  The maximum reduction per pass during wire drawing of an aluminum alloy ignoring friction and
redundant work is 77%. The strain hardening exponent of the material is ____________.

Q.11  Built-up edge formation decreases under the conditions listed below EXCEPT
(A) at low cutting speeds (B) using large positive rake angle
(C) with sharper tool (D) using cutting fluid

Q.12  During turning of mild steel work material, the maximum temperature is observed at
(A) primary deformation zone (B) tool and chip interface
(C) tool-flank and work interface (D) machined sub-surface

Q.13  Which one of the following statements related to grinding process is INCORRECT?
(A) Grinding wheels made of finer abrasive grains produce better surface finish.
(B) Abrasive grains tend to fracture frequently during the grinding process.
(C) Specific energy in grinding is higher than that in turning.
(D) Cutting speed in grinding process is much lower than that in face milling.

Q.14  For an assembly made of n components, the dimensions on each component i follow a normal
distribution and have tolerance T
i
. Overall dimension of the assembly is L
a
with tolerance T
a
. The
relationship between T
a
and T
i
is
(A)  (B)

(C)  (D)

GATE 2015                                                                                                                                                 PRODUCTION & INDUSTRIAL ENGG.   – PI
PI 3/9
Q.15  Which of the following DO NOT influence the material removal rate in Electrical Discharge
Machining process?

(i) Hardness of work piece material
(ii) Melting temperature of work piece material
(iii) Hardness of tool material
(iv) Discharge current and frequency
(A) (i) and (ii) (B) (i) and (iii) (C)  (iii) and (iv) (D) (i), (ii) and (iii)

Q.16  In Computer Aided Process Planning, determination of process sequence for manufacture of any
part design without predefined standard plans is known as
(A) variant type process planning
(B) retrieval type process planning
(C) generative type process planning
(D) group technology based process planning

Q.17  The angle of a twist drill that determines its rake angle is
(A) lip relief angle (B)  chisel edge angle (C)  helix angle (D)  point angle

Q.18  A line balancing problem is solved in the context of
(A) process layout (B) fixed position layout
(C) product layout (D) production schedule

Q.19  Solution to the balanced assignment problem is binary due to
(A) linear formulation (B) non-empty feasible region
(C) approximation algorithms (D) uni-modularity property

Q.20  Material Requirements Planning DOES NOT include
(A) material price (B) bill of material
(C) inventory level (D) production schedule

Q.21  Ishikawa diagram represents
(A) different types of quality defects
(B) quantitative relation between the extent of defect and a process parameter
(C) relation between defects and their causes
(D) prioritized quality defects

Q.22  As per the principles of motion economy, which one of the following is NOT a pivot for a
classified movement of human body?
(A) Knee  (B) Elbow  (C) Torso   (D) Wrist

Q.23  For air travel over a distance of 500 km, the ticket price is Rs. 4000. The comfort of the air travel
can be monetized at Rs.3000, and the monetary value of time saved because of air travel is Rs.3000.
The value of air travel is ____________.

Q.24  Which one of the following is NOT in the scope of Enterprise Resource Planning (ERP) system?
(A) General ledger entries (B) Materials management system
(C) Order management system (D) Employee promotion policy

GATE 2015                                                                                                                                                 PRODUCTION & INDUSTRIAL ENGG.   – PI
PI 4/9
Q.25  If standard production is 20 units, a worker’s actual output is 18 units, piece rate is Rs. 500 per unit,
and over-achievement rate is Rs. 750 per unit, then the wage paid to the worker, in Rs., as per
Taylor’s differential price rate wage incentive plan, is ______________.

Q. 26 – Q. 55 carry two marks each.
Q.26  The solution to  represents a
(A) family of circles (B) family of ellipses
(C) family of parabolas (D) family of hyperbolas

Q.27  The solution to   is

(A)
2 3
12
y c x c x
-
= + (B)
2
12
y c c x
-
= + (C)
2
1
c
y c x
x
= +  (D)
4
12
y c x c x = +

Q.28  Match the linear transformation matrices listed in the first column to their interpretations in the
second column.

P.
10
00
??
??
??
1.        Stretch in the y-axis
Q.
00
01
??
??
??
2.        Uniform stretch in x and y-axes
R.
10
03
??
??
??
3.        Projection in x-axis
S.
40
04
??
??
??
4.        Projection in y-axis

(A) P-1, Q-2, R-3, S-4 (B) P-2, Q-3, R-4, S-1
(C) P-3, Q-4, R-1, S-2 (D) P-4, Q-1, R-2, S-3.

Q.29
The value of
2
( , ) (0,0)
lim
x y
x xy
xy
?
-
-
is
(A) 0 (B)
1
2
(C) 1  (D) 8

Q.30  The curve y = x
4
is
(A) concave up for all values of x
(B) concave down for all values of x
(C) concave up only for positive values of x
(D) concave up only for negative values of x

Q.31  A metallic bar of uniform cross-section with specific weight of 100 kN/m
3
is hung vertically down.
The length and Young’s modulus of the bar are 100 m and 200 GPa, respectively. The elongation
of the bar, in mm, due to its own weight is ____________.

GATE 2015                                                                                                                                                 PRODUCTION & INDUSTRIAL ENGG.   – PI
PI 5/9
Q.32  A beam is loaded as shown in the figure.

The bending moment, in Nm, at point R is  __________.

Q.33  In an off-set slider crank mechanism, shown in figure, the crank is rotated at a constant speed of 150
rpm. The value of the angle ? shown in the figure is 20
0
. What is the ratio of forward to return stroke
time? Can this mechanism be used in an application involving quick return?

(A) 3.33, No (B) 0.73, Yes (C) 1.25, Yes (D) 0.73, No

Q.34  In a 1 m thick wall, the temperature distribution at a given instant is T(x) = c
0
+ c
1
x + c
2
x
2
where T
is in
o
C and x is in m. The constants are: c
0
= 800
o
C, c
1
= –250
o
C/m and c
2
= –40
o
C/m
2
. The
thermal conductivity of the wall is 50 W/mK and wall area is 5 m
2
. If there is a heat source
generating uniform volumetric heating at the rate of 500 W/m
3
inside the wall, then the rate of
change of energy storage in the wall, in kW, is ________.

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