GATE 2023 Question Paper PI Production & Industrial Engineering

The Graduate Aptitude Test in Engineering

GATE 2023
Question Paper
GATE is an entrance examination conducted in India that
primarily tests the comprehensive understanding of
undergraduate subjects in engineering and sciences for
admission into technical postgraduate programs.

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General Aptitude (GA)
Q.1 – Q.5 Carry ONE mark Each

Q.1 “You are delaying the completion of the task. Send _______ contributions at the
earliest.”

(A) you are

(B) your

(C) you’re

(D) yore

Q.2 References : ______ : : Guidelines : Implement

(By word meaning)

(A) Sight

(B) Site

(C) Cite

(D) Plagiarise

Page 1 of 32

Q.3 In the given figure, PQRS is a parallelogram with PS = 7 cm, PT = 4 cm and
PV = 5 cm. What is the length of RS in cm? (The diagram is representative.)

7
P S

5 90°
4
90° V
Q T R

(A) 20
7

(B) 28
5

(C) 9
2

(D) 35
4

Page 2 of 32

Q.4 In 2022, June Huh was awarded the Fields medal, which is the highest prize in
Mathematics.

When he was younger, he was also a poet. He did not win any medals in the
International Mathematics Olympiads. He dropped out of college.

Based only on the above information, which one of the following statements can be
logically inferred with certainty?

(A) Every Fields medalist has won a medal in an International Mathematics Olympiad.

(B) Everyone who has dropped out of college has won the Fields medal.

(C) All Fields medalists are part-time poets.

(D) Some Fields medalists have dropped out of college.

Page 3 of 32

Q.5 A line of symmetry is defined as a line that divides a figure into two parts in a way
such that each part is a mirror image of the other part about that line.

The given figure consists of 16 unit squares arranged as shown. In addition to the
three black squares, what is the minimum number of squares that must be coloured
black, such that both PQ and MN form lines of symmetry? (The figure is
representative)

P N

M
Q

(A) 3

(B) 4

(C) 5

(D) 6

Page 4 of 32

Q.6 – Q.10 Carry TWO marks Each

Q.6 Human beings are one among many creatures that inhabit an imagined world. In
this imagined world, some creatures are cruel. If in this imagined world, it is given
that the statement “Some human beings are not cruel creatures” is FALSE, then
which of the following set of statement(s) can be logically inferred with certainty?

(i) All human beings are cruel creatures.
(ii) Some human beings are cruel creatures.
(iii) Some creatures that are cruel are human beings.
(iv) No human beings are cruel creatures.

(A) only (i)

(B) only (iii) and (iv)

(C) only (i) and (ii)

(D) (i), (ii) and (iii)

Q.7 To construct a wall, sand and cement are mixed in the ratio of 3:1. The cost of sand
and that of cement are in the ratio of 1:2.

If the total cost of sand and cement to construct the wall is 1000 rupees, then what
is the cost (in rupees) of cement used?

(A) 400

(B) 600

(C) 800

(D) 200

Page 5 of 32

The World Bank has declared that it does not plan to offer new financing to Sri
Q.8 Lanka, which is battling its worst economic crisis in decades, until the country has
an adequate macroeconomic policy framework in place. In a statement, the World
Bank said Sri Lanka needed to adopt structural reforms that focus on economic
stabilisation and tackle the root causes of its crisis. The latter has starved it of
foreign exchange and led to shortages of food, fuel, and medicines. The bank is
repurposing resources under existing loans to help alleviate shortages of essential
items such as medicine, cooking gas, fertiliser, meals for children, and cash for
vulnerable households.

Based only on the above passage, which one of the following statements can be
inferred with certainty?

(A) According to the World Bank, the root cause of Sri Lanka’s economic crisis is that
it does not have enough foreign exchange.

(B) The World Bank has stated that it will advise the Sri Lankan government about how
to tackle the root causes of its economic crisis.

(C) According to the World Bank, Sri Lanka does not yet have an adequate
macroeconomic policy framework.

(D) The World Bank has stated that it will provide Sri Lanka with additional funds for
essentials such as food, fuel, and medicines.

Q.9 The coefficient of 𝑥 4 in the polynomial (𝑥 − 1)3 (𝑥 − 2)3 is equal to _______.

(A) 33

(B) ̶ 3

(C) 30

(D) 21

Page 6 of 32

Q.10 Which one of the following shapes can be used to tile (completely cover by
repeating) a flat plane, extending to infinity in all directions, without leaving any
empty spaces in between them? The copies of the shape used to tile are identical
and are not allowed to overlap.

(A) circle

(B) regular octagon

(C) regular pentagon

(D) rhombus

Page 7 of 32

Q.11 – Q.35 Carry ONE mark Each

Q.11 Given matrices

1 −1 4 𝐵11 𝐵12 𝐵13
𝐴 = [3 2 −1] and 𝐵 = [𝐵21 𝐵22 𝐵23 ] ;
2 1 −1 𝐵31 𝐵32 𝐵33

B is skew-symmetric matrix of A. B13 is

(A) −3

(B) −2

(C) 2

(D) 3

Q.12 The non-linear differential equation from the following options is

(A) 𝑑 2 𝑦 𝑑𝑦
+ + 10𝑦 = 0
𝑑𝑥 2 𝑑𝑥

(B) 𝑑2𝑦 𝑑𝑦 2
+ ( ) + 10𝑦 = 0
𝑑𝑥 2 𝑑𝑥

(C) 𝑑 2 𝑦 𝑑𝑦
+ + 10𝑥 = 0
𝑑𝑥 2 𝑑𝑥

(D) 𝑑 2 𝑦 𝑑𝑦
+ + 10𝑥𝑦 = 0
𝑑𝑥 2 𝑑𝑥

Page 8 of 32

Q.13 The power series expansion of a function is given as

1
ln(1 + 𝑥) = 1 + 𝑏𝑥 + 𝑐𝑥 2 + ⋯
𝑥
for 0 < 𝑥 ≤ 1.

The values of constants b and c, respectively, are

(A) 1 1
− and
2 3

(B) 1 1
and −
2 3

(C) 1
− 1 and
2

(D) 1
1 and −
2

Page 9 of 32

Q.14 Three unbiased coins are tossed. Provided that at least two outcomes are tails, the
probability of having all three outcomes as tails is

(A) 1
8

(B) 1
4

(C) 1
3

(D) 1
2

Q.15 Two plane parallel surfaces exchange heat by thermal radiation. A radiation shield
is placed in between at equal distance from the two surfaces to reduce heat transfer.
All surfaces are black with infinite length and width. The ratio of heat transfer rate
between surfaces with and without radiation shield is

(A) 1
2

(B) 1
4

(C) 1
6

(D) 1
8

Page 10 of 32

Q.16 As per the ANSI marking system, a grinding wheel with alumina as abrasive is
designated as

51 A 36 K 5 V 23

Here, K indicates that

(A) abrasive used in the wheel is aluminum oxide

(B) hardness of the wheel is medium

(C) bonding material of the wheel is shellac

(D) structure of the wheel is dense

Q.17 The combination of Directrix and Generatrix in a machining operation is shown in
figure. The surface produced is

Generatrix

Directrix

(A) cylindrical

(B) planar

(C) helical

(D) parabolic

Page 11 of 32

Q.18 In NC machine, the function of interpolator is to

(A) compute and maintain the tool feed rate

(B) compute and maintain the velocity of the slide

(C) generate warning signal based on the error

(D) generate reference signals prescribing the shape of the produced part

Q.19 Vacuum in the machining zone is an essential requirement for

(A) Electric Discharge Machining

(B) Chemical Machining

(C) Electro Chemical Machining

(D) Electron Beam Machining

Page 12 of 32

Q.20 The qualitative method of forecasting amongst the given options is

(A) Linear Regression

(B) Weighted Moving Average

(C) Delphi

(D) Exponential Smoothing

Q.21 Transformation matrix to translate a point P from (10, 15) to (15, 25) is

(A) 1 0 5
[0 1 10]
0 0 1

(B) 1 0 10
[0 1 5]
0 0 1

(C) 5 0 0
[0 10 0]
0 0 1

(D) 10 0 0
[ 0 5 0]
0 0 1

Page 13 of 32

Q.22 A copper rod of 200 mm diameter and 400 mm length is extruded to the final
diameter of 100 mm. The extrusion ratio is

(A) 1

(B) 2

(C) 4

(D) 8

Q.23 A symbol for surface texture parameters is shown in figure. The difference between
maximum and minimum values of surface roughness ( Ra ) is

(A) 0.499 µm

(B) 0.508 µm

(C) 0.762 µm

(D) 1.524 µm

Page 14 of 32

Q.24 A thin cylinder has length L, diameter d, and thickness 𝑡. It is made of a material
with modulus of elasticity E and Poisson’s ratio 𝜇. When the cylinder is subjected
to an internal pressure P, the change in length is

(A) 𝑃𝑑𝐿 1
( − 𝜇)
2𝑡𝐸 2

(B) 𝑃𝑑𝐿
(2 − 𝜇)
2𝑡𝐸

(C) 𝑃𝑑𝐿
(1 − 2𝜇)
2𝑡𝐸

(D) 𝑃𝑑𝐿 1
( − 𝜇)
4𝑡𝐸 2

Q.25 Creep of mild steel at elevated temperature involves

(A) elastic deformation under constant load

(B) elastic deformation under dynamic load

(C) plastic deformation under constant load

(D) plastic deformation under dynamic load

Page 15 of 32

Q.26 Number of minimum control points required to generate a quadratic B-Spline
curve is

(A) 2

(B) 4

(C) 8

(D) 16

Q.27 The Euler’s method is used to solve

𝑑𝑦
= 𝑥 3 𝑦 − 4, 𝑦 (0) = 1
𝑑𝑥

The step size is 0.1. The approximate value of 𝑦 (0.1) is _____ (round off to 2
decimal places).

Q.28 A solid circular disk of 0.025 m thickness is used as flywheel. The density of the
disk material is 7800 kg/m3 and the mass moment of inertia of the disk about its
center is 4.36 kg-m2. The radius, in m, of the disk is _____(round off to 2 decimal
places).

Q.29 The standard time for completing a job on a machine is 10 minutes. Number of
machines available is 5, each machine is available for 300 hours/month, and average

machine utilization is 80 %. The maximum number of jobs that can be produced in
a month is _____ (in integer).

Page 16 of 32

Q.30 Travel details of two persons P and Q travelling from city X to city Y are given as

Monetary worth of functions Ticket cost,
Person Mode of travel (travel time and comfort), in Rupees
in Rupees
P Aircraft 8000 4000

Q Train 2000 2000

The positive difference in value of travel between the two modes
is _____ (in integer).

Q.31 A wooden cubical block of side 0.1 m has specific gravity (SG) of 0.75. It is held
submerged in a pool of oil and water by a massless rigid wire as shown in figure.
The density of water is 1000 kg/m3 and acceleration due to gravity is 9.8 m/s2.
The tension, in N, in the wire is _____ (round off to 2 decimal places).

Q.32 Under steady state conditions, superheated steam enters the turbine with enthalpy,
h1 = 3200 kJ/kg and wet steam leaves the turbine at pressure 𝑝2 = 0.1 bar. The heat
loss is 100 kJ/kg and work output is 1000 kJ/kg. Kinetic and potential energies for
inflow and outflow are neglected. At pressure 0.1 bar, the enthalpy of saturated

liquid is 200 kJ/kg and the enthalpy of vaporization is 2400 kJ/kg. The dryness
fraction of the steam at the exit of the turbine is _____ (round off to 2 decimal
places).

Page 17 of 32

Q.33 The total number of nonconformities is 420 from 30 samples. The size of each
sample is 100. The lower control limit for the control chart for number of
nonconformities is _____ (round off to 2 decimal places).

Q.34 Two metal sheets are joined using resistance spot welding. A welding current of
4500 A is applied for 0.2 s. The effective contact resistance at the sheet interface is
400 × 10−6 Ω. The thermal efficiency of the welding process is 50 %. The amount
of heat, in J, used for producing a spot weld is _____(in integer).

Q.35 A metal rod of diameter 14 mm is subjected to a tensile test. After the test, its
cross-sectional diameter at the fractured end is 12 mm. The ductility, in % ,
is _____ (round off to 2 decimal places).

Page 18 of 32

Q.36 – Q.65 Carry TWO marks Each

Q.36 Given, 𝑧 (𝑥, 𝑦) = 𝑒 𝑥−2𝑦 , where 𝑥(𝑡) = 𝑒 𝑡 and 𝑦(𝑡) = 𝑒 −𝑡 . All the variables are

𝑑𝑧
real. The total differential is
𝑑𝑡

(A) −𝑧(𝑥 + 2𝑦)

(B) −𝑧(𝑥 − 2𝑦)

(C) 𝑧(𝑥 + 2𝑦)

(D) 𝑧(𝑥 − 2𝑦)

Q.37 Two cards are drawn one after the other from a regular deck of 52 playing cards
without replacement. The probability that the drawn cards are of different suits is

(A) 39
51

(B) 13
52

(C) 2
52

2

(D)
51

Page 19 of 32

Q.38 Match the machine elements with their functions.

Machine element Function

P Collet 1 Indexing

Q Dividing head 2 Thread cutting

R Lead screw 3 Holding the tool in place

.

(A) P – 3, Q – 2, R – 1

(B) P – 3, Q – 1, R – 2

(C) P – 2, Q – 1, R – 3

(D) P – 1, Q – 3, R – 2

Page 20 of 32

Q.39 A massless beam is fixed at one end and supported on a roller at other end. A point
force P is applied at the midpoint of the beam as shown in figure. The reaction at
the roller support is

(A) 5𝑃
16

(B) 2𝑃
3

(C) 4𝑃
9

(D) 9𝑃
25

Page 21 of 32

Q.40 Six jobs (1, 2, 3, 4, 5, 6) undergo drilling, followed by reaming operation. The time
required for each operation is given as

Job Drilling Reaming
(min) (min)
1 30 45
2 30 15
3 60 40
4 20 25
5 35 28
6 45 70

The sequence of processing the jobs, using the Johnson’s rule, is

(A) 4–1–6–3–5–2

(B) 4–6–1–5–3–2

(C) 2–1–6–3–5–4

(D) 2–1–3–6–5–4

Page 22 of 32

Q.41 Match the engineering materials at room temperature with the given crystal
structures.

Engineering material Crystal structure

P Si 1 FCC

Q Fe 2 HCP

R Al 3 Diamond Cubic

S Zn 4 BCC

(A) P – 3, Q – 4, R – 1, S – 2

(B) P – 2, Q – 1, R – 4, S – 3

(C) P – 2, Q – 4, R – 1, S – 3

(D) P – 3, Q – 1, R – 4, S – 2

Page 23 of 32

Q.42 Match the recording techniques used in method study with the most appropriate
application areas.

Recording technique Application area

P Outline process chart 1 Factory layout – movement of
workers

Q String diagram 2 Gang work

R Multiple activity chart 3 Complete manufacturing sequence of
a product

S Two-handed process 4 Manual assembly of nuts and bolts
chart

(A) P – 3, Q – 4, R – 2, S – 1

(B) P – 3, Q – 1, R – 2, S – 4

(C) P – 2, Q – 4, R – 3, S – 1

(D) P – 2, Q – 1, R – 3, S – 4

Page 24 of 32

Q.43 Match the products to be manufactured with the given metal working processes.

Product Process

P Beverage can 1 Forging

Q Seamless pipe 2 Skew Rolling

R Connecting rod 3 Extrusion

S Steel balls for bearing 4 Deep Drawing

(A) P – 3, Q – 4, R – 1, S – 2

(B) P – 2, Q – 4, R – 1, S – 3

(C) P – 4, Q – 3, R – 2, S – 1

(D) P – 4, Q – 3, R – 1, S – 2

Page 25 of 32

Q.44 The dual of a LPP is

𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑒 𝑤 = 4𝑤1 + 6𝑤2 + 5𝑤3 − 𝑤4

subject to,
𝑤1
1 0 1 0 𝑤2 3
[ ] [𝑤 ] ≥ [ ]
0 0 1 −1 3 −2
𝑤4

and 𝑤𝑖 ≥ 0 for 𝑖 = 1, 2, 3, 4

The objective function of the primal is

(A) 𝑀𝑎𝑥𝑖𝑚𝑖𝑧𝑒 𝑧 = −3𝑥1 + 2𝑥2

(B) 𝑀𝑎𝑥𝑖𝑚𝑖𝑧𝑒 𝑧 = 𝑥1 + 𝑥3

(C) 𝑀𝑎𝑥𝑖𝑚𝑖𝑧𝑒 𝑧 = 𝑥3 − 𝑥4

(D) 𝑀𝑎𝑥𝑖𝑚𝑖𝑧𝑒 𝑧 = 3𝑥1 − 2𝑥2

Page 26 of 32

Q.45 There are four locations (P, Q, R, S) and four factors to be considered for setting up
a facility. The scores (on a scale of 0 to 10, with 10 being the maximum) for the
given locations and the weight assigned to each factor are given as

Factor Weight P Q R S

Availability of raw material 0.4 6 8 5 4

Availability of skilled labor 0.3 7 4 10 6

Infrastructure 0.2 8 3 10 8

Proximity to market 0.1 10 8 7 5

The best location for setting up the facility is

(A) P

(B) Q

(C) R

(D) S

Page 27 of 32

Q.46 As per the Fe-C phase diagram, the microstructure of plain carbon steel with
0.4 wt.% carbon at room temperature contains

(A) proeutectoid ferrite and pearlite

(B) proeutectoid cementite and pearlite

(C) ferrite and austenite

(D) austenite and cementite

Q.47 The most appropriate process for manufacturing of plastic chair is

(A) injection molding

(B) extrusion

(C) calendering

(D) blow molding

Q.48 The following equation is solved using Newton-Raphson method

𝑥 5 − 15 = 0

with initial value 𝑥0 = 1.0.

The value of first approximation 𝑥1 is _____(round off to 2 decimal places).

Page 28 of 32

Q.49 4 2 2
For the matrix [ ] , eigenvalue corresponding to the eigenvector [ ]
3 3 −3
is _____(in integer).

Q.50 The work sampling study, with 100 observations, revealed 25 % idle time of a
worker. The number of observations required for ±10 % accuracy and 95.45 %
confidence level is _____ (in integer).

Q.51 The information of two products P and Q is given as

Annual Ordering cost Holding cost
Product
demand per order per unit per year
(units) (Rupees) (Rupees)

P 2500 60 30

Q 3600 80 40

Economic Order Quantity of product P
The value of is _____ (round off to 2
Economic Order Quantity of product Q

decimal places).

Q.52 A system shown in figure has seven components with reliabilities RA = 0.96,
RB = 0.92, RC = 0.94, RD = 0.89, RE = 0.95, RF = 0.88, and RG = 0.90.
The reliability of the system is _____ (round off to 2 decimal places).

Page 29 of 32

Q.53 Details of activities of a project are given as

Activity A B C D E F G H I J

Time (days) 8 10 8 7 16 15 18 14 9 4

Predecessors - - - A A B, D C C F, G E, I, H

The time required, in days, to complete the project along the critical path
is _____ (in integer).

Q.54 A system has 10 essential components. Each component has an exponential
time-to-failure distribution with constant failure rate of 0.04 per 4000 hours.
The mean-time-to-failure, in hours, of the system is _____ (in integer).

Q.55 A CNC water jet cutting machine is used to cut a straight slot between the
points (2, 1) and (10, 10) on the XY plane (dimensions are in mm). If the feed rate
is 1.5 mm/s, the time, in s, required to machine the slot following the shortest path,
is _____ (round off to 2 decimal places).

Q.56 In an orthogonal cutting with a tool of rake angle 0°, the value of the cutting force
is two times of the thrust force. The coefficient of friction is _____ (round off to 1
decimal place).

Q.57 The solidification of a cubical casting of side 100 mm takes place with volumetric
solidification shrinkage and solid contraction of 10 % each. The shape of the casting

is retained on cooling to room temperature. The side of the cubical cast, in mm, at
room temperature is _____ (round off to 2 decimal places).

Page 30 of 32

Q.58 A straight turning operation is carried out at the feed rate of 100 mm/min using a
single point cutting tool with signature 8 – 8 – 5 – 5 – 7 – 25 – 0 (ASA).
The spindle speed is 1600 rpm. The roughness, in μm, of the machined surface in
terms of peak-to-valley height is _____ (round off to 2 decimal places).

Q.59 An arc welding operation is performed at 25 V and 200 A at welding speed of
2 mm/s. The heat used for melting is 80 % of the total heat generated. The unit
melting energy of the metal to be joined is 10 J/mm3. The volume of the weld metal
produced per unit time, in mm3/s, is _____ (in integer).

Q.60 Water flows through a pipe of diameter 0.02 m. The Reynolds number of the flow
is 1000. The pipe is heated from outside with a uniform heat flux. The flow and heat
transfer in the pipe are steady and fully developed. The thermal conductivity of
water is 0.66 W/(m-K). The convective heat transfer coefficient, in W/(m2-K),
is _____ (round off to 2 decimal places).

Q.61 In an ideal air-standard Brayton cycle, air enters the compressor at 100 kPa and
300 K. Thermal efficiency of the cycle is 50 %. The heat added to air is
1000 kJ/kg. Air has constant specific heat 𝑐𝑝 = 1.0 kJ/(kg-K) and 𝛾 = 1.4.
Air temperature, in K, at the turbine inlet is ______ (round off to 2 decimal places).

Q.62 A key of width and height of 6 mm each is used to fix a gear on a shaft of 20 mm
diameter. The shaft is used to transmit 10 kW power at 600 rpm to the gear.
Permissible shear stress in the key is 80 N/mm2, while compressive stress in the key
is neglected. The minimum length of the key, in mm, is _____ (round off to 2
decimal places).

Page 31 of 32

Q.63 A cylindrical casting has 10 cm diameter and a mass of 12.56 kg. The material
density is 7.85 × 10−3 kg/cm3. The value of exponent ‘n’ is 2 and solidification
time is 12 min. The Chvorinov’s constant, in min/cm2, is ______ (round off to 2
decimal places).

Q.64 A pair of spur gears is designed to transmit 20 kW power at a pitch line velocity of
10 m/s. Diameter of the driving gear is 0.5 m. The tangential force, in N, between
the driver and the driven gear is _____(in integer).

Q.65 Two products, P and Q , are sold in the ratio of 10:1. The fixed cost is Rs. 1,40,000.
The selling price of P is Rs. 10/unit and Q is Rs. 40/unit. The variable costs of P and
Q are Rs. 5/unit and Rs. 20/unit, respectively. The break-even point in terms of
revenue, in Rs., is _____(in integer).

END OF QUESTION PAPER

Page 32 of 32
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