Production and Industrial Engineering (PI) 2013 GATE Paper (Set A) without solution GATE Notes | EduRev

 Page 1


2013                                                                                                                           Question Booklet Code                                                                           
 
PI-A 
 
1/16
PI : PRODUCTION AND INDUSTRIAL ENGINEERING 
 
Duration: Three Hours                                                                                                                          Maximum Marks: 100 
Read the following instructions carefully. 
 
1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator. 
2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal 
and read the instructions printed on the ORS carefully. If you find that either 
a. The Question Booklet Code printed at the right hand top corner of this page does not match with 
the Question Booklet Code at the right hand top corner of the ORS or 
b. The Question Paper Code preceding the Registration number on the ORS is not PI,  
            then exchange the booklet immediately with a new sealed Question Booklet.  
3. On the right hand side of the ORS, using ONLY a black ink ballpoint pen, (i) darken the appropriate 
bubble under each digit of your registration number and (ii) write your registration number, your name 
and name of the examination centre and put your signature at the specified location. 
4. This Question Booklet contains 16 pages including blank pages for rough work. After you are 
permitted to open the seal, check all pages and report discrepancies, if any, to the invigilator.  
5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each 
question has only one correct answer. Questions must be answered on the left hand side of the ORS 
by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ballpoint pen 
against the question number. For each question darken the bubble of the correct answer. More 
than one answer bubbled against a question will be treated as an incorrect response. 
6. Since bubbles darkened by the black ink ballpoint pen cannot be erased, candidates should darken the 
bubbles in the ORS very carefully. 
7. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks 
questions include two pairs of common data questions and two pairs of linked answer questions. The 
answer to the second question of the linked answer questions depends on the answer to the first 
question of the pair. If the first question in the linked pair is wrongly answered or is not attempted, 
then the answer to the second question in the pair will not be evaluated. 
8. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks. 
Questions Q.56 – Q.60 carry 1 mark each, and questions Q.61 – Q.65 carry 2 marks each. 
9. Questions not attempted will result in zero mark and wrong answers will result in NEGATIVE 
marks.  For all 1 mark questions, ? mark will be deducted for each wrong answer. For all 2 marks 
questions, ? mark will be deducted for each wrong answer.  However, in the case of the linked 
answer question pair, there will be negative marks only for wrong answer to the first question and no 
negative marks for wrong answer to the second question.  
10. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall. 
11. Rough work can be done on the Question Booklet itself. Blank pages are provided at the end of the 
Question Booklet for rough work. 
12. Before the start of the examination, write your name and registration number in the space provided 
below using a black ink ballpoint pen. 
 
 
Name 
 
 
Registration Number 
PI 
       
 
 
A 
Page 2


2013                                                                                                                           Question Booklet Code                                                                           
 
PI-A 
 
1/16
PI : PRODUCTION AND INDUSTRIAL ENGINEERING 
 
Duration: Three Hours                                                                                                                          Maximum Marks: 100 
Read the following instructions carefully. 
 
1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator. 
2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal 
and read the instructions printed on the ORS carefully. If you find that either 
a. The Question Booklet Code printed at the right hand top corner of this page does not match with 
the Question Booklet Code at the right hand top corner of the ORS or 
b. The Question Paper Code preceding the Registration number on the ORS is not PI,  
            then exchange the booklet immediately with a new sealed Question Booklet.  
3. On the right hand side of the ORS, using ONLY a black ink ballpoint pen, (i) darken the appropriate 
bubble under each digit of your registration number and (ii) write your registration number, your name 
and name of the examination centre and put your signature at the specified location. 
4. This Question Booklet contains 16 pages including blank pages for rough work. After you are 
permitted to open the seal, check all pages and report discrepancies, if any, to the invigilator.  
5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each 
question has only one correct answer. Questions must be answered on the left hand side of the ORS 
by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ballpoint pen 
against the question number. For each question darken the bubble of the correct answer. More 
than one answer bubbled against a question will be treated as an incorrect response. 
6. Since bubbles darkened by the black ink ballpoint pen cannot be erased, candidates should darken the 
bubbles in the ORS very carefully. 
7. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks 
questions include two pairs of common data questions and two pairs of linked answer questions. The 
answer to the second question of the linked answer questions depends on the answer to the first 
question of the pair. If the first question in the linked pair is wrongly answered or is not attempted, 
then the answer to the second question in the pair will not be evaluated. 
8. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks. 
Questions Q.56 – Q.60 carry 1 mark each, and questions Q.61 – Q.65 carry 2 marks each. 
9. Questions not attempted will result in zero mark and wrong answers will result in NEGATIVE 
marks.  For all 1 mark questions, ? mark will be deducted for each wrong answer. For all 2 marks 
questions, ? mark will be deducted for each wrong answer.  However, in the case of the linked 
answer question pair, there will be negative marks only for wrong answer to the first question and no 
negative marks for wrong answer to the second question.  
10. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall. 
11. Rough work can be done on the Question Booklet itself. Blank pages are provided at the end of the 
Question Booklet for rough work. 
12. Before the start of the examination, write your name and registration number in the space provided 
below using a black ink ballpoint pen. 
 
 
Name 
 
 
Registration Number 
PI 
       
 
 
A 
2013                                                                                                                            PRODUCTION & INDUSTRIAL ENGG - PI                                                                                                   
 
PI- A 2/16
Q.1  to Q.25 carry one mark each. 
Q.1 The fixed cost and the variable cost of production of a product are Rs. 20000 and Rs. 50 per unit, 
respectively. The demand for the item is 500 units. To break even, the unit price of the items in  
Rs. should be 
(A) 50 (B) 75 (C) 90 (D) 100 
 
Q.2 Therbligs refer to the 
(A) basic types of fixtures used in machining. 
(B) fundamental motions used in manual work. 
(C) basic types of waste in manufacturing process. 
(D) fundamental types of material handling systems. 
 
Q.3 Customers arrive at a ticket counter at a rate of 50 per hr and tickets are issued in the order of their 
arrival. The average time taken for issuing a ticket is 1 min. Assuming that customer arrivals form a 
Poisson process and service times are exponentially distributed, the average waiting time in queue 
in min is 
(A) 3 (B) 4 (C) 5 (D) 6 
 
Q.4 Circular blanks of 10 mm diameter are punched from an aluminum sheet of 2 mm thickness. The 
shear strength of aluminum is 80 MPa. The minimum punching force required in kN  is 
(A) 2.57 (B) 3.29 (C) 5.03 (D) 6.33 
 
Q.5 A metric thread of pitch 2 mm and thread angle 60° is inspected for its pitch diameter using 3-wire 
method. The diameter of the best size wire in mm is 
(A) 0.866 (B) 1.000 (C) 1.154 (D) 2.000 
 
Q.6 Match the CORRECT pairs. 
 
Processes Characteristics / Applications 
P. Friction Welding 1. Non-consumable electrode 
Q. Gas Metal Arc Welding 2. Joining of thick plates 
R. Tungsten Inert Gas Welding 3. Consumable electrode wire 
S. Electroslag Welding 4. Joining of cylindrical dissimilar materials 
 
(A) P-4, Q-3, R-1, S-2 (B) P-4, Q-2, R-3, S-1 
(C) P-2, Q-3, R-4, S-1 (D) P-2, Q-4, R-1, S-3 
 
Q.7 In a rolling process, the state of stress of the material undergoing deformation is 
(A) pure compression (B) pure shear 
(C) compression and shear (D) tension and shear 
 
Q.8 Consider one-dimensional steady state heat conduction along x-axis (0 = x = L), through a plane 
wall; with the boundary surfaces (x=0 and x=L) maintained at temperatures of 0°C and 100°C. 
Heat is generated uniformly throughout the wall. Choose the CORRECT statement. 
(A) The direction of heat transfer will be from the surface at 100°C  to the surface at 0°C. 
(B) The maximum temperature inside the wall must be greater than 100°C. 
(C) The temperature distribution is linear within the wall. 
(D) The temperature distribution is symmetric about the mid-plane of the wall. 
Page 3


2013                                                                                                                           Question Booklet Code                                                                           
 
PI-A 
 
1/16
PI : PRODUCTION AND INDUSTRIAL ENGINEERING 
 
Duration: Three Hours                                                                                                                          Maximum Marks: 100 
Read the following instructions carefully. 
 
1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator. 
2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal 
and read the instructions printed on the ORS carefully. If you find that either 
a. The Question Booklet Code printed at the right hand top corner of this page does not match with 
the Question Booklet Code at the right hand top corner of the ORS or 
b. The Question Paper Code preceding the Registration number on the ORS is not PI,  
            then exchange the booklet immediately with a new sealed Question Booklet.  
3. On the right hand side of the ORS, using ONLY a black ink ballpoint pen, (i) darken the appropriate 
bubble under each digit of your registration number and (ii) write your registration number, your name 
and name of the examination centre and put your signature at the specified location. 
4. This Question Booklet contains 16 pages including blank pages for rough work. After you are 
permitted to open the seal, check all pages and report discrepancies, if any, to the invigilator.  
5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each 
question has only one correct answer. Questions must be answered on the left hand side of the ORS 
by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ballpoint pen 
against the question number. For each question darken the bubble of the correct answer. More 
than one answer bubbled against a question will be treated as an incorrect response. 
6. Since bubbles darkened by the black ink ballpoint pen cannot be erased, candidates should darken the 
bubbles in the ORS very carefully. 
7. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks 
questions include two pairs of common data questions and two pairs of linked answer questions. The 
answer to the second question of the linked answer questions depends on the answer to the first 
question of the pair. If the first question in the linked pair is wrongly answered or is not attempted, 
then the answer to the second question in the pair will not be evaluated. 
8. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks. 
Questions Q.56 – Q.60 carry 1 mark each, and questions Q.61 – Q.65 carry 2 marks each. 
9. Questions not attempted will result in zero mark and wrong answers will result in NEGATIVE 
marks.  For all 1 mark questions, ? mark will be deducted for each wrong answer. For all 2 marks 
questions, ? mark will be deducted for each wrong answer.  However, in the case of the linked 
answer question pair, there will be negative marks only for wrong answer to the first question and no 
negative marks for wrong answer to the second question.  
10. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall. 
11. Rough work can be done on the Question Booklet itself. Blank pages are provided at the end of the 
Question Booklet for rough work. 
12. Before the start of the examination, write your name and registration number in the space provided 
below using a black ink ballpoint pen. 
 
 
Name 
 
 
Registration Number 
PI 
       
 
 
A 
2013                                                                                                                            PRODUCTION & INDUSTRIAL ENGG - PI                                                                                                   
 
PI- A 2/16
Q.1  to Q.25 carry one mark each. 
Q.1 The fixed cost and the variable cost of production of a product are Rs. 20000 and Rs. 50 per unit, 
respectively. The demand for the item is 500 units. To break even, the unit price of the items in  
Rs. should be 
(A) 50 (B) 75 (C) 90 (D) 100 
 
Q.2 Therbligs refer to the 
(A) basic types of fixtures used in machining. 
(B) fundamental motions used in manual work. 
(C) basic types of waste in manufacturing process. 
(D) fundamental types of material handling systems. 
 
Q.3 Customers arrive at a ticket counter at a rate of 50 per hr and tickets are issued in the order of their 
arrival. The average time taken for issuing a ticket is 1 min. Assuming that customer arrivals form a 
Poisson process and service times are exponentially distributed, the average waiting time in queue 
in min is 
(A) 3 (B) 4 (C) 5 (D) 6 
 
Q.4 Circular blanks of 10 mm diameter are punched from an aluminum sheet of 2 mm thickness. The 
shear strength of aluminum is 80 MPa. The minimum punching force required in kN  is 
(A) 2.57 (B) 3.29 (C) 5.03 (D) 6.33 
 
Q.5 A metric thread of pitch 2 mm and thread angle 60° is inspected for its pitch diameter using 3-wire 
method. The diameter of the best size wire in mm is 
(A) 0.866 (B) 1.000 (C) 1.154 (D) 2.000 
 
Q.6 Match the CORRECT pairs. 
 
Processes Characteristics / Applications 
P. Friction Welding 1. Non-consumable electrode 
Q. Gas Metal Arc Welding 2. Joining of thick plates 
R. Tungsten Inert Gas Welding 3. Consumable electrode wire 
S. Electroslag Welding 4. Joining of cylindrical dissimilar materials 
 
(A) P-4, Q-3, R-1, S-2 (B) P-4, Q-2, R-3, S-1 
(C) P-2, Q-3, R-4, S-1 (D) P-2, Q-4, R-1, S-3 
 
Q.7 In a rolling process, the state of stress of the material undergoing deformation is 
(A) pure compression (B) pure shear 
(C) compression and shear (D) tension and shear 
 
Q.8 Consider one-dimensional steady state heat conduction along x-axis (0 = x = L), through a plane 
wall; with the boundary surfaces (x=0 and x=L) maintained at temperatures of 0°C and 100°C. 
Heat is generated uniformly throughout the wall. Choose the CORRECT statement. 
(A) The direction of heat transfer will be from the surface at 100°C  to the surface at 0°C. 
(B) The maximum temperature inside the wall must be greater than 100°C. 
(C) The temperature distribution is linear within the wall. 
(D) The temperature distribution is symmetric about the mid-plane of the wall. 
2013                                                                                                                            PRODUCTION & INDUSTRIAL ENGG - PI                                                                                                   
 
PI- A 3/16
Q.9 A cylinder contains 5 m
3
 of an ideal gas at a pressure of 1 bar. This gas is compressed in a 
reversible isothermal process till its pressure increases to 5 bar. The work in kJ required for this 
process is 
(A) 804.7 (B) 953.2 (C) 981.7 (D) 1012.2 
 
Q.10 A planar closed kinematic chain is formed with rigid links PQ = 2.0 m,  QR = 3.0 m,  RS = 2.5 m   
and  SP = 2.7 m with all revolute joints. The link to be fixed to obtain a double rocker (rocker-
rocker) mechanism is 
(A)  PQ (B) QR (C) RS (D) SP 
 
Q.11 Let  X  be a normal random variable with mean 1 and variance 4. The probability  P{X<0}  is 
(A)  0.5 (B) greater than zero and less than 0.5 
(C)  greater than 0.5  and less than 1.0 (D) 1.0 
 
Q.12 Choose the CORRECT set of functions, which are linearly dependent. 
(A) x sin , 
2
sin x and 
2
cos x 
(B)
  
cos x , x sin and x tan 
(C)
 
cos 2x , 
2
sin x and 
2
cos x  
(D)  cos 2x , x sin and x cos 
 
Q.13 The eigenvalues of a symmetric matrix are all 
(A)  complex with non-zero positive imaginary part 
(B)  complex with non-zero negative imaginary part 
(C)  real 
(D)  pure imaginary 
 
Q.14 
The partial differential equation 
2
2
x
u
x
u
u
t
u
?
?
=
?
?
+
?
?
 is a 
 
(A)  linear equation of order 2 (B) non-linear equation of order 1 
(C)  linear equation of order 1 (D) non-linear equation of order 2 
 
Q.15 Match the CORRECT pairs. 
 
Numerical Integration Scheme Order of Fitting Polynomial 
P. Simpson’s 3/8 Rule 1. First 
Q. Trapezoidal Rule 2. Second 
R. Simpson’s 1/3 Rule 3. Third 
 
(A)  P-2, Q-1, R-3 (B) P-3, Q-2, R-1 (C) P-1, Q-2, R-3 (D) P-3, Q-1, R-2 
 
Page 4


2013                                                                                                                           Question Booklet Code                                                                           
 
PI-A 
 
1/16
PI : PRODUCTION AND INDUSTRIAL ENGINEERING 
 
Duration: Three Hours                                                                                                                          Maximum Marks: 100 
Read the following instructions carefully. 
 
1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator. 
2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal 
and read the instructions printed on the ORS carefully. If you find that either 
a. The Question Booklet Code printed at the right hand top corner of this page does not match with 
the Question Booklet Code at the right hand top corner of the ORS or 
b. The Question Paper Code preceding the Registration number on the ORS is not PI,  
            then exchange the booklet immediately with a new sealed Question Booklet.  
3. On the right hand side of the ORS, using ONLY a black ink ballpoint pen, (i) darken the appropriate 
bubble under each digit of your registration number and (ii) write your registration number, your name 
and name of the examination centre and put your signature at the specified location. 
4. This Question Booklet contains 16 pages including blank pages for rough work. After you are 
permitted to open the seal, check all pages and report discrepancies, if any, to the invigilator.  
5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each 
question has only one correct answer. Questions must be answered on the left hand side of the ORS 
by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ballpoint pen 
against the question number. For each question darken the bubble of the correct answer. More 
than one answer bubbled against a question will be treated as an incorrect response. 
6. Since bubbles darkened by the black ink ballpoint pen cannot be erased, candidates should darken the 
bubbles in the ORS very carefully. 
7. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks 
questions include two pairs of common data questions and two pairs of linked answer questions. The 
answer to the second question of the linked answer questions depends on the answer to the first 
question of the pair. If the first question in the linked pair is wrongly answered or is not attempted, 
then the answer to the second question in the pair will not be evaluated. 
8. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks. 
Questions Q.56 – Q.60 carry 1 mark each, and questions Q.61 – Q.65 carry 2 marks each. 
9. Questions not attempted will result in zero mark and wrong answers will result in NEGATIVE 
marks.  For all 1 mark questions, ? mark will be deducted for each wrong answer. For all 2 marks 
questions, ? mark will be deducted for each wrong answer.  However, in the case of the linked 
answer question pair, there will be negative marks only for wrong answer to the first question and no 
negative marks for wrong answer to the second question.  
10. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall. 
11. Rough work can be done on the Question Booklet itself. Blank pages are provided at the end of the 
Question Booklet for rough work. 
12. Before the start of the examination, write your name and registration number in the space provided 
below using a black ink ballpoint pen. 
 
 
Name 
 
 
Registration Number 
PI 
       
 
 
A 
2013                                                                                                                            PRODUCTION & INDUSTRIAL ENGG - PI                                                                                                   
 
PI- A 2/16
Q.1  to Q.25 carry one mark each. 
Q.1 The fixed cost and the variable cost of production of a product are Rs. 20000 and Rs. 50 per unit, 
respectively. The demand for the item is 500 units. To break even, the unit price of the items in  
Rs. should be 
(A) 50 (B) 75 (C) 90 (D) 100 
 
Q.2 Therbligs refer to the 
(A) basic types of fixtures used in machining. 
(B) fundamental motions used in manual work. 
(C) basic types of waste in manufacturing process. 
(D) fundamental types of material handling systems. 
 
Q.3 Customers arrive at a ticket counter at a rate of 50 per hr and tickets are issued in the order of their 
arrival. The average time taken for issuing a ticket is 1 min. Assuming that customer arrivals form a 
Poisson process and service times are exponentially distributed, the average waiting time in queue 
in min is 
(A) 3 (B) 4 (C) 5 (D) 6 
 
Q.4 Circular blanks of 10 mm diameter are punched from an aluminum sheet of 2 mm thickness. The 
shear strength of aluminum is 80 MPa. The minimum punching force required in kN  is 
(A) 2.57 (B) 3.29 (C) 5.03 (D) 6.33 
 
Q.5 A metric thread of pitch 2 mm and thread angle 60° is inspected for its pitch diameter using 3-wire 
method. The diameter of the best size wire in mm is 
(A) 0.866 (B) 1.000 (C) 1.154 (D) 2.000 
 
Q.6 Match the CORRECT pairs. 
 
Processes Characteristics / Applications 
P. Friction Welding 1. Non-consumable electrode 
Q. Gas Metal Arc Welding 2. Joining of thick plates 
R. Tungsten Inert Gas Welding 3. Consumable electrode wire 
S. Electroslag Welding 4. Joining of cylindrical dissimilar materials 
 
(A) P-4, Q-3, R-1, S-2 (B) P-4, Q-2, R-3, S-1 
(C) P-2, Q-3, R-4, S-1 (D) P-2, Q-4, R-1, S-3 
 
Q.7 In a rolling process, the state of stress of the material undergoing deformation is 
(A) pure compression (B) pure shear 
(C) compression and shear (D) tension and shear 
 
Q.8 Consider one-dimensional steady state heat conduction along x-axis (0 = x = L), through a plane 
wall; with the boundary surfaces (x=0 and x=L) maintained at temperatures of 0°C and 100°C. 
Heat is generated uniformly throughout the wall. Choose the CORRECT statement. 
(A) The direction of heat transfer will be from the surface at 100°C  to the surface at 0°C. 
(B) The maximum temperature inside the wall must be greater than 100°C. 
(C) The temperature distribution is linear within the wall. 
(D) The temperature distribution is symmetric about the mid-plane of the wall. 
2013                                                                                                                            PRODUCTION & INDUSTRIAL ENGG - PI                                                                                                   
 
PI- A 3/16
Q.9 A cylinder contains 5 m
3
 of an ideal gas at a pressure of 1 bar. This gas is compressed in a 
reversible isothermal process till its pressure increases to 5 bar. The work in kJ required for this 
process is 
(A) 804.7 (B) 953.2 (C) 981.7 (D) 1012.2 
 
Q.10 A planar closed kinematic chain is formed with rigid links PQ = 2.0 m,  QR = 3.0 m,  RS = 2.5 m   
and  SP = 2.7 m with all revolute joints. The link to be fixed to obtain a double rocker (rocker-
rocker) mechanism is 
(A)  PQ (B) QR (C) RS (D) SP 
 
Q.11 Let  X  be a normal random variable with mean 1 and variance 4. The probability  P{X<0}  is 
(A)  0.5 (B) greater than zero and less than 0.5 
(C)  greater than 0.5  and less than 1.0 (D) 1.0 
 
Q.12 Choose the CORRECT set of functions, which are linearly dependent. 
(A) x sin , 
2
sin x and 
2
cos x 
(B)
  
cos x , x sin and x tan 
(C)
 
cos 2x , 
2
sin x and 
2
cos x  
(D)  cos 2x , x sin and x cos 
 
Q.13 The eigenvalues of a symmetric matrix are all 
(A)  complex with non-zero positive imaginary part 
(B)  complex with non-zero negative imaginary part 
(C)  real 
(D)  pure imaginary 
 
Q.14 
The partial differential equation 
2
2
x
u
x
u
u
t
u
?
?
=
?
?
+
?
?
 is a 
 
(A)  linear equation of order 2 (B) non-linear equation of order 1 
(C)  linear equation of order 1 (D) non-linear equation of order 2 
 
Q.15 Match the CORRECT pairs. 
 
Numerical Integration Scheme Order of Fitting Polynomial 
P. Simpson’s 3/8 Rule 1. First 
Q. Trapezoidal Rule 2. Second 
R. Simpson’s 1/3 Rule 3. Third 
 
(A)  P-2, Q-1, R-3 (B) P-3, Q-2, R-1 (C) P-1, Q-2, R-3 (D) P-3, Q-1, R-2 
 
2013                                                                                                                            PRODUCTION & INDUSTRIAL ENGG - PI                                                                                                   
 
PI- A 4/16
Q.16 A rod of length L having uniform cross-sectional area A is subjected to a tensile force P as shown in 
the figure below. If the Young’s modulus of the material varies linearly from 
1
E to 
2
E along the 
length of the rod, the normal stress developed at the section-SS is 
 
 
 
 
 
 
 
 
 
 
 
(A) 
A
P
 (B)
 
 
( )
( )
2 1
2 1
E E A
E E P
+
- (C) 
1
2
AE
PE
 (D) 
2
1
AE
PE
 
 
Q.17 For steady, fully developed flow inside a straight pipe of diameter D, neglecting gravity effects, the 
pressure drop p ? over a length L and the wall shear stress 
w
t are related by 
(A) 
L
D p
w
4
?
= t 
(B) 
2
2
4L
D p
w
?
= t 
(C) 
L
D p
w
2
?
= t (D) 
D
L p
w
?
=
4
t 
 
Q.18 For a ductile material, toughness is a measure of 
(A) resistance to scratching (B) ability to absorb energy upto fracture 
(C) ability to absorb energy till elastic limit (D) resistance to indentation 
 
Q.19 A cube shaped casting solidifies in 5 min. The solidification time in min for a cube of the same 
material, which is 8 times heavier than the original casting, will be 
(A) 10 (B) 20 (C) 24 (D) 40 
 
Q.20 A steel bar 200 mm in diameter is turned at a feed of 0.25 mm/rev with a depth of cut of 4 mm. The 
rotational speed of the workpiece is 160 rpm. The material removal rate in mm
3
/s is 
(A) 160 (B) 167.6 (C) 1600 (D) 1675.5 
 
Q.21 In the 3-2-1 principle of fixture design, 3 refers to the number of 
(A) clamps required 
(B)  locators on the primary datum face 
(C) degrees of freedom of the workpiece 
(D) operations carried out on the primary datum face 
 
Q.22 In simple exponential smoothing forecasting, to give higher weightage to recent demand 
information, the smoothing constant must be close to 
(A)  - 1 (B) zero (C) 0.5 (D) 1 
 
S 
P P 
S 
L 
L/2 
E
1
 E
2
 
Page 5


2013                                                                                                                           Question Booklet Code                                                                           
 
PI-A 
 
1/16
PI : PRODUCTION AND INDUSTRIAL ENGINEERING 
 
Duration: Three Hours                                                                                                                          Maximum Marks: 100 
Read the following instructions carefully. 
 
1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator. 
2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal 
and read the instructions printed on the ORS carefully. If you find that either 
a. The Question Booklet Code printed at the right hand top corner of this page does not match with 
the Question Booklet Code at the right hand top corner of the ORS or 
b. The Question Paper Code preceding the Registration number on the ORS is not PI,  
            then exchange the booklet immediately with a new sealed Question Booklet.  
3. On the right hand side of the ORS, using ONLY a black ink ballpoint pen, (i) darken the appropriate 
bubble under each digit of your registration number and (ii) write your registration number, your name 
and name of the examination centre and put your signature at the specified location. 
4. This Question Booklet contains 16 pages including blank pages for rough work. After you are 
permitted to open the seal, check all pages and report discrepancies, if any, to the invigilator.  
5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each 
question has only one correct answer. Questions must be answered on the left hand side of the ORS 
by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ballpoint pen 
against the question number. For each question darken the bubble of the correct answer. More 
than one answer bubbled against a question will be treated as an incorrect response. 
6. Since bubbles darkened by the black ink ballpoint pen cannot be erased, candidates should darken the 
bubbles in the ORS very carefully. 
7. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks 
questions include two pairs of common data questions and two pairs of linked answer questions. The 
answer to the second question of the linked answer questions depends on the answer to the first 
question of the pair. If the first question in the linked pair is wrongly answered or is not attempted, 
then the answer to the second question in the pair will not be evaluated. 
8. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks. 
Questions Q.56 – Q.60 carry 1 mark each, and questions Q.61 – Q.65 carry 2 marks each. 
9. Questions not attempted will result in zero mark and wrong answers will result in NEGATIVE 
marks.  For all 1 mark questions, ? mark will be deducted for each wrong answer. For all 2 marks 
questions, ? mark will be deducted for each wrong answer.  However, in the case of the linked 
answer question pair, there will be negative marks only for wrong answer to the first question and no 
negative marks for wrong answer to the second question.  
10. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall. 
11. Rough work can be done on the Question Booklet itself. Blank pages are provided at the end of the 
Question Booklet for rough work. 
12. Before the start of the examination, write your name and registration number in the space provided 
below using a black ink ballpoint pen. 
 
 
Name 
 
 
Registration Number 
PI 
       
 
 
A 
2013                                                                                                                            PRODUCTION & INDUSTRIAL ENGG - PI                                                                                                   
 
PI- A 2/16
Q.1  to Q.25 carry one mark each. 
Q.1 The fixed cost and the variable cost of production of a product are Rs. 20000 and Rs. 50 per unit, 
respectively. The demand for the item is 500 units. To break even, the unit price of the items in  
Rs. should be 
(A) 50 (B) 75 (C) 90 (D) 100 
 
Q.2 Therbligs refer to the 
(A) basic types of fixtures used in machining. 
(B) fundamental motions used in manual work. 
(C) basic types of waste in manufacturing process. 
(D) fundamental types of material handling systems. 
 
Q.3 Customers arrive at a ticket counter at a rate of 50 per hr and tickets are issued in the order of their 
arrival. The average time taken for issuing a ticket is 1 min. Assuming that customer arrivals form a 
Poisson process and service times are exponentially distributed, the average waiting time in queue 
in min is 
(A) 3 (B) 4 (C) 5 (D) 6 
 
Q.4 Circular blanks of 10 mm diameter are punched from an aluminum sheet of 2 mm thickness. The 
shear strength of aluminum is 80 MPa. The minimum punching force required in kN  is 
(A) 2.57 (B) 3.29 (C) 5.03 (D) 6.33 
 
Q.5 A metric thread of pitch 2 mm and thread angle 60° is inspected for its pitch diameter using 3-wire 
method. The diameter of the best size wire in mm is 
(A) 0.866 (B) 1.000 (C) 1.154 (D) 2.000 
 
Q.6 Match the CORRECT pairs. 
 
Processes Characteristics / Applications 
P. Friction Welding 1. Non-consumable electrode 
Q. Gas Metal Arc Welding 2. Joining of thick plates 
R. Tungsten Inert Gas Welding 3. Consumable electrode wire 
S. Electroslag Welding 4. Joining of cylindrical dissimilar materials 
 
(A) P-4, Q-3, R-1, S-2 (B) P-4, Q-2, R-3, S-1 
(C) P-2, Q-3, R-4, S-1 (D) P-2, Q-4, R-1, S-3 
 
Q.7 In a rolling process, the state of stress of the material undergoing deformation is 
(A) pure compression (B) pure shear 
(C) compression and shear (D) tension and shear 
 
Q.8 Consider one-dimensional steady state heat conduction along x-axis (0 = x = L), through a plane 
wall; with the boundary surfaces (x=0 and x=L) maintained at temperatures of 0°C and 100°C. 
Heat is generated uniformly throughout the wall. Choose the CORRECT statement. 
(A) The direction of heat transfer will be from the surface at 100°C  to the surface at 0°C. 
(B) The maximum temperature inside the wall must be greater than 100°C. 
(C) The temperature distribution is linear within the wall. 
(D) The temperature distribution is symmetric about the mid-plane of the wall. 
2013                                                                                                                            PRODUCTION & INDUSTRIAL ENGG - PI                                                                                                   
 
PI- A 3/16
Q.9 A cylinder contains 5 m
3
 of an ideal gas at a pressure of 1 bar. This gas is compressed in a 
reversible isothermal process till its pressure increases to 5 bar. The work in kJ required for this 
process is 
(A) 804.7 (B) 953.2 (C) 981.7 (D) 1012.2 
 
Q.10 A planar closed kinematic chain is formed with rigid links PQ = 2.0 m,  QR = 3.0 m,  RS = 2.5 m   
and  SP = 2.7 m with all revolute joints. The link to be fixed to obtain a double rocker (rocker-
rocker) mechanism is 
(A)  PQ (B) QR (C) RS (D) SP 
 
Q.11 Let  X  be a normal random variable with mean 1 and variance 4. The probability  P{X<0}  is 
(A)  0.5 (B) greater than zero and less than 0.5 
(C)  greater than 0.5  and less than 1.0 (D) 1.0 
 
Q.12 Choose the CORRECT set of functions, which are linearly dependent. 
(A) x sin , 
2
sin x and 
2
cos x 
(B)
  
cos x , x sin and x tan 
(C)
 
cos 2x , 
2
sin x and 
2
cos x  
(D)  cos 2x , x sin and x cos 
 
Q.13 The eigenvalues of a symmetric matrix are all 
(A)  complex with non-zero positive imaginary part 
(B)  complex with non-zero negative imaginary part 
(C)  real 
(D)  pure imaginary 
 
Q.14 
The partial differential equation 
2
2
x
u
x
u
u
t
u
?
?
=
?
?
+
?
?
 is a 
 
(A)  linear equation of order 2 (B) non-linear equation of order 1 
(C)  linear equation of order 1 (D) non-linear equation of order 2 
 
Q.15 Match the CORRECT pairs. 
 
Numerical Integration Scheme Order of Fitting Polynomial 
P. Simpson’s 3/8 Rule 1. First 
Q. Trapezoidal Rule 2. Second 
R. Simpson’s 1/3 Rule 3. Third 
 
(A)  P-2, Q-1, R-3 (B) P-3, Q-2, R-1 (C) P-1, Q-2, R-3 (D) P-3, Q-1, R-2 
 
2013                                                                                                                            PRODUCTION & INDUSTRIAL ENGG - PI                                                                                                   
 
PI- A 4/16
Q.16 A rod of length L having uniform cross-sectional area A is subjected to a tensile force P as shown in 
the figure below. If the Young’s modulus of the material varies linearly from 
1
E to 
2
E along the 
length of the rod, the normal stress developed at the section-SS is 
 
 
 
 
 
 
 
 
 
 
 
(A) 
A
P
 (B)
 
 
( )
( )
2 1
2 1
E E A
E E P
+
- (C) 
1
2
AE
PE
 (D) 
2
1
AE
PE
 
 
Q.17 For steady, fully developed flow inside a straight pipe of diameter D, neglecting gravity effects, the 
pressure drop p ? over a length L and the wall shear stress 
w
t are related by 
(A) 
L
D p
w
4
?
= t 
(B) 
2
2
4L
D p
w
?
= t 
(C) 
L
D p
w
2
?
= t (D) 
D
L p
w
?
=
4
t 
 
Q.18 For a ductile material, toughness is a measure of 
(A) resistance to scratching (B) ability to absorb energy upto fracture 
(C) ability to absorb energy till elastic limit (D) resistance to indentation 
 
Q.19 A cube shaped casting solidifies in 5 min. The solidification time in min for a cube of the same 
material, which is 8 times heavier than the original casting, will be 
(A) 10 (B) 20 (C) 24 (D) 40 
 
Q.20 A steel bar 200 mm in diameter is turned at a feed of 0.25 mm/rev with a depth of cut of 4 mm. The 
rotational speed of the workpiece is 160 rpm. The material removal rate in mm
3
/s is 
(A) 160 (B) 167.6 (C) 1600 (D) 1675.5 
 
Q.21 In the 3-2-1 principle of fixture design, 3 refers to the number of 
(A) clamps required 
(B)  locators on the primary datum face 
(C) degrees of freedom of the workpiece 
(D) operations carried out on the primary datum face 
 
Q.22 In simple exponential smoothing forecasting, to give higher weightage to recent demand 
information, the smoothing constant must be close to 
(A)  - 1 (B) zero (C) 0.5 (D) 1 
 
S 
P P 
S 
L 
L/2 
E
1
 E
2
 
2013                                                                                                                            PRODUCTION & INDUSTRIAL ENGG - PI                                                                                                   
 
PI- A 5/16
Q.23 A company manufactures 1000 toys every day. On an average, 10% of the toys are defective and 
40% of the defective toys can be reworked into defect-free ones. The average number of defect-free 
toys manufactured daily is 
(A) 900 (B) 920 (C) 940 (D) 960 
 
Q.24 The type of control chart used to monitor the amount of dispersion in a sample is 
(A) c-chart (B) p-chart (C) x -chart (D) R-chart 
 
Q.25 Which one of the following is modeled based on adaptation capabilities of biological systems? 
(A) Relational database (B) Fuzzy system 
(C) Simulated annealing algorithm (D) Genetic algorithm