GATE PI 2012: Production and Industrial Engineering
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2012 PRODUCTION & INDUSTRIAL ENGG. – PI
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.
3. On the right half of the ORS, using ONLY a black ink ball point pen, (i) darken the bubble
corresponding to your test paper code and 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, please 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 ball point 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 ball point 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 unattempted, 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. Unattempted questions will result in zero mark and wrong answers will result in NEGATIVE marks.
For all 1 mark questions, ⅓ mark will be deducted for each wrong answer. For all 2 marks questions,
⅔ 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 paper itself. Blank pages are provided at the end of the
question paper 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 ball point pen.
Name
Registration Number PI
PI 1/16
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2012 PRODUCTION & INDUSTRIAL ENGG. – PI
Q. 1 – Q. 25 carry one mark each.
1 cos x
Q.1 lim is
x
x 0 2
(A) 1/4 (B) 1/2 (C) 1 (D) 2
Q.2 For the spherical surface x 2 y 2 z 2 1 , the unit outward normal vector at the point
1 1
( , , 0 ) is given by
2 2
1 ˆ 1 ˆ 1 ˆ 1 ˆ
(A) i j (B) i j
2 2 2 2
1 ˆ 1 ˆ 1 ˆ
(C) k̂ (D) i j k
3 3 3
Q.3 Consider the function f ( x) x in the interval 1 x 1 . At the point x = 0, f(x) is
(A) continuous and differentiable.
(B) non-continuous and differentiable.
(C) continuous and non-differentiable.
(D) neither continuous nor differentiable.
Q.4 At x = 0, the function f ( x) x3 1 has
(A) a maximum value (B) a minimum value
(C) a singularity (D) a point of inflection
Q.5 The area enclosed between the straight line y = x and the parabola y = x2 in the x-y plane is
(A) 1/6 (B) 1/4 (C) 1/3 (D) 1/2
Q.6 For a long slender column of uniform cross section, the ratio of critical buckling load for the case
with both ends clamped to the case with both ends hinged is
(A) 1 (B) 2 (C) 4 (D) 8
Q.7 A thin walled spherical shell is subjected to an internal pressure. If the radius of the shell is
increased by 1% and the thickness is reduced by 1%, with the internal pressure remaining the same,
the percentage change in the circumferential (hoop) stress is
(A) 0 (B) 1 (C) 1.08 (D) 2.02
Q.8 A cantilever beam of length L is subjected to a moment M at the free end. The moment of inertia of
the beam cross section about the neutral axis is I and the Young’s modulus is E. The magnitude of
the maximum deflection is
ML2 ML2 2ML2 4ML2
(A) (B) (C) (D)
2 EI EI EI EI
Q.9 A circular solid disc of uniform thickness 20 mm, radius 200 mm and mass 20 kg, is used as a
flywheel. If it rotates at 600 rpm, the kinetic energy of the flywheel, in Joules is
(A) 395 (B) 790
(C) 1580 (D) 3160
PI 2/16
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2012 PRODUCTION & INDUSTRIAL ENGG. – PI
Q.10 In the mechanism given below, if the angular velocity of the eccentric circular disc is 1 rad/s, the
angular velocity (rad/s) of the follower link for the instant shown in the figure is
Note: All dimensions are in mm.
25
45 5
(A) 0.05 (B) 0.1 (C) 5.0 (D) 10.0
Q.11 Steam enters an adiabatic turbine operating at steady state with an enthalpy of 3251.0 kJ/kg and
leaves as a saturated mixture at 15 kPa with quality (dryness fraction) 0.9. The enthalpies of the
saturated liquid and vapor at 15 kPa are hf = 225.94 kJ/kg and hg = 2598.3 kJ/kg respectively. The
mass flow rate of steam is 10 kg/s. Kinetic and potential energy changes are negligible. The power
output of the turbine in MW is
(A) 6.5 (B) 8.9 (C) 9.1 (D) 27.0
Q.12 An ideal gas of mass m and temperature T1 undergoes a reversible isothermal process from an
initial pressure P1 to final pressure P2. The heat loss during the process is Q. The entropy change S
of the gas is
P2 P1
(A) mR ln (B) mR ln
P1 P2
P2 Q
(C) mR ln (D) zero
P1 T1
Q.13 For an opaque surface, the absorptivity , transmissivity and reflectivity are related by
the equation:
(A) (B) 0 (C) 1 (D) 0
Q.14 Which one of the following configurations has the highest fin effectiveness?
(A) Thin, closely spaced fins (B) Thin, widely spaced fins
(C) Thick, widely spaced fins (D) Thick, closely spaced fins
Q.15 Oil flows through a 200 mm diameter horizontal cast iron pipe (friction factor, f = 0.0225) of
length 500 m. The volumetric flow rate is 0.2 m3/s. The head loss (in m) due to friction is (assume
g = 9.81 m/s2)
(A) 116.18 (B) 0.116 (C) 18.22 (D) 232.36
Q.16 A solid cylinder of diameter 100 mm and height 50 mm is forged between two frictionless flat dies
to a height of 25 mm. The percentage change in diameter is
(A) 0 (B) 2.07 (C) 20.7 (D) 41.4
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2012 PRODUCTION & INDUSTRIAL ENGG. – PI
0.040
0.010
Q.17 In an interchangeable assembly, shafts of size 25.000 mm mate with holes of size
0.030
0.020
25.000 mm. The maximum interference (in microns) in the assembly is
(A) 40 (B) 30 (C) 20 (D) 10
Q.18 A CNC vertical milling machine has to cut a straight slot of 10 mm width and 2 mm depth by a
cutter of 10 mm diameter between points (0, 0) and (100, 100) on the XY plane (dimensions in mm).
The feed rate used for milling is 50 mm/min. Milling time for the slot (in seconds) is
(A) 120 (B) 170 (C) 180 (D) 240
Q.19 Match the following metal forming processes with their associated stresses in the workpiece.
Metal forming process Type of stress
1. Coining P. Tensile
2. Wire Drawing Q. Shear
3. Blanking R. Tensile and compressive
4. Deep Drawing S. Compressive
(A) 1-S, 2-P, 3-Q, 4-R (B) 1-S, 2-P, 3-R, 4-Q
(C) 1-P, 2-Q, 3-S, 4-R (D) 1-P, 2-R, 3-Q, 4-S
Q.20 During normalizing process of steel, the specimen is heated
(A) between the upper and lower critical temperature and cooled in still air.
(B) above the upper critical temperature and cooled in furnace.
(C) above the upper critical temperature and cooled in still air.
(D) between the upper and lower critical temperature and cooled in furnace.
Q.21 In abrasive jet machining, as the distance between the nozzle tip and the work surface increases, the
material removal rate
(A) increases continuously.
(B) decreases continuously.
(C) decreases, becomes stable and then increases.
(D) increases, becomes stable and then decreases.
Q.22 Which one of the following is NOT a decision taken during the aggregate production planning
stage?
(A) Scheduling of machines (B) Amount of labour to be committed
(C) Rate at which production should happen (D) Inventory to be carried forward
Q.23 Which one of the following is NOT associated with the process of new product development?
(A) QFD (B) FEMA (C) KANBAN (D) DFMA
PI 4/16
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2012 PRODUCTION & INDUSTRIAL ENGG. – PI
Q.24 A process needs to be standardized for method and time. Which one of the following represents the
sequence of work study experiments?
(A) Time study followed by method study
(B) Only time study
(C) Time study and method study simultaneously
(D) Method study followed by time study
Q.25 Reduction in the variability of manufactured product characteristics will definitely result in
observations close to
(A) the upper control limit in X chart.
(B) the lower control limit in X chart.
(C) the lower control limit in R chart.
(D) the center line in R chart.
PI 5/16
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2012 PRODUCTION & INDUSTRIAL ENGG. – PI
Q. 26 - Q. 55 carry two marks each.
Q.26 x 2y z 4
2x y 2z 5
x y z 1
The system of algebraic equations given above has
(A) a unique solution of x = 1, y = 1 and z = 1.
(B) only the two solutions of (x = 1, y = 1, z = 1) and (x = 2, y = 1, z = 0).
(C) infinite number of solutions.
(D) no feasible solution.
5 3
Q.27 For the matrix A = , ONE of the normalized eigen vectors is given as
1 3
1 1 3 1
2 2
10 5
(A) (B) (C) (D)
3 1 1 2
2 2 10 5
d2y dy
Q.28 Consider the differential equation x 2
2
x 4 y 0 with the boundary conditions of
dx dx
y 0 0 and y 1 1 . The complete solution of the differential equation is
x x x
(A) x 2 (B) sin (C) e x sin (D) e x sin
2 2 2
1
Q.29 The inverse Laplace transform of the function F ( s) is given by
s( s 1)
(A) f (t ) sin t (B) f (t ) e t sin t
(C) f (t ) et (D) f (t ) 1 et
Q.30 A box contains 4 red balls and 6 black balls. Three balls are selected randomly from the box one
after another, without replacement. The probability that the selected set contains one red ball and
two black balls is
(A) 1/20 (B) 1/12 (C) 3/10 (D) 1/2
Q.31 The state of stress at a point under plane stress condition is
σxx = 40 MPa, σyy = 100 MPa and τxy = 40 MPa.
The radius of the Mohr’s circle representing the given state of stress in MPa is
(A) 40 (B) 50 (C) 60 (D) 100
PI 6/16
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2012 PRODUCTION & INDUSTRIAL ENGG. – PI
Q.32 A force of 400 N is applied to the brake drum of 0.5 m diameter in a band-brake system as shown in
the figure, where the wrapping angle is 180°. If the coefficient of friction between the drum and the
band is 0.25, the braking torque applied, in N.m is
400 N
(A) 100.6 (B) 54.4 (C) 22.1 (D) 15.7
Q.33 Water (Cp = 4.18 kJ/kg.K) at 80°C enters a counterflow heat exchanger with a mass flow rate of
0.5 kg/s. Air (Cp = 1 kJ/kg.K) enters at 30°C with a mass flow rate of 2.09 kg/s. If the effectiveness
of the heat exchanger is 0.8, the LMTD (in °C) is
(A) 40 (B) 20 (C) 10 (D) 5
Q.34 Consider two infinitely long thin concentric tubes of circular cross section as shown in the figure.
If D1 and D2 are the diameters of the inner and outer tubes respectively, then the view factor F22 is
given by
1
2
D2 D1 D1
(A) 1 (B) zero (C) (D) 1
D1 D2 D2
Q.35 A large tank with a nozzle attached contains three immiscible, inviscid fluids as shown. Assuming
that the changes in h1, h2 and h3 are negligible, the instantaneous discharge velocity is
h1 1
h2 2
h3 3
h h
(A) 2 gh3 1 1 1 2 2 (B) 2g h1 h2 h3
3 h3 3 h3
h 2 h2 3h3 h h 2 h3h1 3h1h2
(C) 2g 1 1 (D) 2g 1 2 3
1 2 3 1h1 2 h2 3h3
PI 7/16
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2012 PRODUCTION & INDUSTRIAL ENGG. – PI
Q.36 In a DC arc welding operation, the voltage-arc length characteristic was obtained as
Varc 20 5 l where the arc length l was varied between 5 mm and 7 mm. Here Varc denotes the
arc voltage in Volts. The arc current was varied from 400 A to 500 A. Assuming linear power
source characteristic, the open circuit voltage and the short circuit current for the welding
operation are
(A) 45 V, 450 A (B) 75 V, 750 A (C) 95 V, 950 A (D) 150 V, 1500 A
Q.37 In a single pass rolling process using 410 mm diameter steel rollers, a strip of width 140 mm and
thickness 8 mm undergoes 10 % reduction of thickness. The angle of bite in radians is
(A) 0.006 (B) 0.031 (C) 0.062 (D) 0.600
Q.38 A mould having dimensions 100 mm × 90 mm × 20 mm is filled with molten metal through a gate
as shown in the figure. For height h and cross-sectional area A, the mould filling time is t1. The
height is now quadrupled and the cross-sectional area is halved. The corresponding filling time is t2.
The ratio t2/t1 is
1
(A) (B) 1 (C) 2 (D) 2
2
Q.39 A thin square plate ABCD with side of unit length is kept in the X-Y plane as shown in the figure.
The plate is first rotated by 30° in the anti clockwise direction about the Z-axis with A fixed at the
origin. The plate is then rotated by 90° in the anti clockwise direction about the X-axis with A fixed
at the origin. The final co-ordinates of C are
Y
D C
A B X
Z
(A) (1.366, 0.366, 0.0) (B) (0.0, 1.366, 0.366)
(C) (1.366, 0.0, 0.366) (D) (0.366, 0.0, 1.366)
Q.40 A sine bar has a length of 250 mm. Each roller has a diameter of 20 mm. During taper angle
measurement of a component, the height from the surface plate to the centre of a roller is 100 mm.
The calculated taper angle (in degrees) is
(A) 21.1 (B) 22.8 (C) 23.6 (D) 68.9
PI 8/16
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2012 PRODUCTION & INDUSTRIAL ENGG. – PI
Q.41 Match the following plastic products with their most appropriate materials.
Products Materials
1. Gears P. Polymethylmethacrylate (PMMA)
2. Helmets Q. Polyamides (PA)
3. Lenses R. Polyethylene (PE)
4. Food packaging S. Acrylonitrile-butadiene-styrene (ABS)
(A) 1-Q, 2-R, 3-S, 4-P (B) 1-S, 2-P, 3-Q, 4-R
(C) 1-P, 2-Q, 3-R, 4-S (D) 1-Q, 2-S, 3-P, 4-R
Q.42 In a shaping process, the number of double strokes per minute is 30 and the quick return ratio is 0.6.
If the length of the stroke is 250 mm, the average cutting velocity in m/min is
(A) 3.0 (B) 4.5 (C) 7.5 (D) 12.0
Q.43 For a linear programming problem, the set of constraints x+y ≤ 2, 3x+5y ≥ 15, x ≥ 0 and y ≥ 0 leads
to
(A) an infeasible solution.
(B) a unique optimal solution.
(C) multiple but finite optimal solutions.
(D) infinite optimal solutions.
Q.44 A milk vendor incurs an overstocking cost of Rs. 2 per litre and a shortage cost of Rs. 0.5 per litre.
The demand is uniformly distributed between 1 litre and 6 litres. Using the Newsvendor Model, the
maximum quantity of milk in litre(s) the vendor should order is
(A) 2 (B) 6 (C) 1 (D) 3
Q.45 The specification limits for the weight of a product are 13.1 kg and 15 kg. If the process has a
variance of weight 0.05 kg2, then the process capability index is
(A) 6.3 (B) 1.9 (C) 1.4 (D) 8.6
Q.46 On an average, there are 30 customers in a queue. If the arrival rate of customers into the system is
16 customers per hour and on average 32 customers leave the system per hour, then the average
number of customers in the system is
(A) 16.5 (B) 30.5 (C) 32.0 (D) 46.0
Q.47 Data for four jobs that need to be processed on a single machine are given below.
Job P Q R S
Processing time (days) 12 9 21 10
Due date (days) 20 40 30 19
All the four jobs are available at time zero. If the jobs are scheduled using the Earliest Due Date
(EDD) algorithm, then the job with maximum tardiness is
(A) P (B) Q (C) R (D) S
PI 9/16
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2012 PRODUCTION & INDUSTRIAL ENGG. – PI
Common Data Questions
Common Data for Questions 48 and 49:
Two steel truss members, AC and BC, each having cross sectional area of 100 mm2, are subjected to a
horizontal force F as shown in figure. All the joints are hinged.
A
45º C
F
60º
B
Q.48 The maximum force F in kN that can be applied at C such that the axial stress in any of the truss
members DOES NOT exceed 100 MPa is
(A) 8.17 (B) 11.15 (C) 14.14 (D) 22.30
Q.49 If F = 1 kN, the magnitude of the vertical reaction force developed at the point B in kN is
(A) 0.63 (B) 0.32 (C) 1.26 (D) 1.46
Common Data for Questions 50 and 51:
Data for a plain milling operation are given below.
Length of workpiece 200 mm
Cutter diameter 100 mm
No. of teeth 4
Cutter speed 100 rpm
Feed 200 mm/min
Depth of cut 2 mm
Total clearance (entry 5 mm
and exit)
Q.50 Mean undeformed chip thickness (in microns) is
(A) 142 (B) 100 (C) 71 (D) 50
Q.51 Machining time for a single pass (in seconds) is
(A) 60 (B) 66 (C) 126 (D) 150
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2012 PRODUCTION & INDUSTRIAL ENGG. – PI
Linked Answer Questions
Statement for Linked Answer Questions 52 and 53:
In an EDM process using RC relaxation circuit, a 12 mm diameter through hole is made in a steel plate of
50 mm thickness using a graphite tool and kerosene as dielectric. Assume discharge time to be negligible.
Machining is carried out under the following conditions:
Resistance 40 Ω
Capacitance 20 μF
Supply voltage 220 V
Discharge voltage 110 V
Q.52 The time for one cycle, in milliseconds, is
(A) 0.55 (B) 0.32 (C) 0.89 (D) 0.24
Q.53 Average power input (in kW) is
(A) 0.373 (B) 0.137 (C) 0.218 (D) 0.500
Statement for Linked Answer Questions 54 and 55:
In a particular year, an organization earns cash revenues of Rs. 2,00,000. Total material and labour
expenses are Rs. 1,09,000. The depreciation claimed on the equipment is Rs. 25,000. The tax rate is 20%.
Q.54 The profit after tax (PAT) is
(A) Rs. 92,800 (B) Rs. 66,200 (C) Rs. 72,800 (D) Rs. 52,800
Q.55 The net cash flow is
(A) Rs. 97,800 (B) Rs. 77,800 (C) Rs. 66,000 (D) Rs. 72,800
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2012 PRODUCTION & INDUSTRIAL ENGG. – PI
General Aptitude (GA) Questions
Q. 56 – Q. 60 carry one mark each.
Q.56 Choose the most appropriate alternative from the options given below to complete the following
sentence:
Suresh’s dog is the one ––––––––– was hurt in the stampede.
(A) that (B) which (C) who (D) whom
Q.57 Choose the most appropriate alternative from the options given below to complete the following
sentence:
Despite several ––––––––– the mission succeeded in its attempt to resolve the conflict.
(A) attempts (B) setbacks (C) meetings (D) delegations
Q.58 Choose the grammatically INCORRECT sentence:
(A) They gave us the money back less the service charges of Three Hundred rupees.
(B) This country’s expenditure is not less than that of Bangladesh.
(C) The committee initially asked for a funding of Fifty Lakh rupees, but later settled for a lesser
sum.
(D) This country’s expenditure on educational reforms is very less.
Q.59 The cost function for a product in a firm is given by 5q2, where q is the amount of production. The
firm can sell the product at a market price of 50 per unit. The number of units to be produced by
the firm such that the profit is maximized is
(A) 5 (B) 10 (C) 15 (D) 25
Q.60 Which one of the following options is the closest in meaning to the word given below?
Mitigate
(A) Diminish (B) Divulge (C) Dedicate (D) Denote
Q. 61 - Q. 65 carry two marks each.
Q.61 Given the sequence of terms, AD CG FK JP, the next term is
(A) OV (B) OW (C) PV (D) PW
Q.62 A political party orders an arch for the entrance to the ground in which the annual convention is
being held. The profile of the arch follows the equation y = 2x – 0.1x2 where y is the height of the
arch in meters. The maximum possible height of the arch is
(A) 8 meters (B) 10 meters (C) 12 meters (D) 14 meters
PI 12/16
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2012 PRODUCTION & INDUSTRIAL ENGG. – PI
Q.63 Which of the following assertions are CORRECT?
P: Adding 7 to each entry in a list adds 7 to the mean of the list
Q: Adding 7 to each entry in a list adds 7 to the standard deviation of the list
R: Doubling each entry in a list doubles the mean of the list
S: Doubling each entry in a list leaves the standard deviation of the list unchanged
(A) P, Q (B) Q, R (C) P, R (D) R, S
Q.64 Wanted Temporary, Part-time persons for the post of Field Interviewer to conduct personal
interviews to collect and collate economic data. Requirements: High School-pass, must be
available for Day, Evening and Saturday work. Transportation paid, expenses reimbursed.
Which one of the following is the best inference from the above advertisement?
(A) Gender-discriminatory
(B) Xenophobic
(C) Not designed to make the post attractive
(D) Not gender-discriminatory
Q.65 An automobile plant contracted to buy shock absorbers from two suppliers X and Y. X supplies
60% and Y supplies 40% of the shock absorbers. All shock absorbers are subjected to a quality test.
The ones that pass the quality test are considered reliable. Of X’s shock absorbers, 96% are reliable.
Of Y’s shock absorbers, 72% are reliable.
The probability that a randomly chosen shock absorber, which is found to be reliable, is made by Y
is
(A) 0.288 (B) 0.334 (C) 0.667 (D) 0.720
END OF THE QUESTION PAPER
PI 13/16
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GATE 2012 ‐ Answer Key ‐ Paper : PI Paper Question no. Key Paper Question no. Key PI 1 B PI 41 D PI 2 A PI 42 D PI 3 C PI 43 A PI 4 D PI 44 A PI 5 A PI 45 C PI 6 C PI 46 B PI 7 D PI 47 C PI 8 A PI 48 B PI 9 B PI 49 A PI 10 B PI 50 C PI 11 B PI 51 B PI 12 B PI 52 A PI 13 C PI 53 C PI 14 A PI 54 D PI 15 A PI 55 B PI 16 D PI 56 Marks to All PI 17 C PI 57 B PI 18 B PI 58 D PI 19 A PI 59 A PI 20 C PI 60 A PI 21 D PI 61 A PI 22 A PI 62 B PI 23 Marks to All PI 63 C PI 24 D PI 64 D PI 25 C PI 65 B PI 26 C PI 27 B PI 28 A PI 29 D PI 30 D PI 31 B PI 32 B PI 33 C PI 34 D PI 35 A PI 36 C PI 37 C PI 38 B PI 39 D PI 40 A
Official key not published for this paper.
Page 1 of 14
Source: GATE. Question paper published by GATE.