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Type:ALLMCQNATMSQ

Engineering Materials(7)Casting, Forming and Joining Processes(17)Machining and Machine Tool Operations(12)Additive Manufacturing(3)Metrology and Inspection(6)Computer Aided Manufacturing and Automation(4)Production Planning and Control(8)Operations Research(12)

Engineering Materials

7 Questions

GATE→2026→Materials, Manufacturing and Industrial Engineering→Engineering Materials

Q1

NAT[2 Marks]

A metal has FCC crystal structure with $2.71~g/cm^{3}$ of density and $26.98~g/mol$ of atomic weight. Avogadro's number is $6.023 \times 10^{23}$. The atomic radius of the metal is ____ nm (rounded off to 2 decimal places).

Explanation

GATE→2025→Materials, Manufacturing and Industrial Engineering→Engineering Materials

Q2

MCQ[1 Mark]

Among the following surface hardening processes, steel is heated to the lowest temperature in

(A)

carburizing

(B)

cyaniding

(C)

nitriding

(D)

carbonitriding

Explanation

GATE→2024→Materials, Manufacturing and Industrial Engineering→Engineering Materials

Q3

MCQ[1 Mark]

The phases present in pearlite are

(A)

austenite and ferrite

(B)

cementite and austenite

(C)

ferrite and cementite

(D)

martensite and ferrite

Explanation

GATE→2023→Materials, Manufacturing and Industrial Engineering→Engineering Materials

Q4

NAT[2 Marks]

The atomic radius of a hypothetical face-centered cubic (FCC) metal is $(\sqrt{2}/10)~nm$. The atomic weight of the metal is $24.092~g/mol$. Taking Avogadro's number to be $6.023\times 10^{23}~atoms/mol$, the density of the metal is ____ $kg/m^{3}$. (Answer in integer)

Explanation

GATE→2023→Materials, Manufacturing and Industrial Engineering→Engineering Materials

Q5

NAT[2 Marks]

A steel sample with $1.5~wt.\%$ carbon (no other alloying elements present) is slowly cooled from $1100^{\circ}C$ to just below the eutectoid temperature $(723^{\circ}C)$. A part of the iron-cementite phase diagram is shown in the figure. The ratio of the pro-eutectoid cementite content to total cementite content in the microstructure that develops just below the eutectoid temperature is ____ (Rounded off to two decimal places)

Explanation

GATE→2022→Materials, Manufacturing and Industrial Engineering→Engineering Materials

Q6

MSQ[1 Mark]

Which of the following heat treatment processes is/are used for surface hardening of steels? (A) Carburizing (B) Cyaniding (C) Annealing (D) Carbonitriding

(A)

Carburizing

(B)

Cyaniding

(C)

Annealing

(D)

Carbonitriding

Explanation

GATE→2022→Materials, Manufacturing and Industrial Engineering→Engineering Materials

Q7

NAT[2 Marks]

A 1 mm thick cylindrical tube, 100 mm in diameter, is orthogonally turned such that the entire wall thickness of the tube is cut in a single pass. The axial feed of the tool is 1 m/minute and the specific cutting energy (u) of the tube material is 6 J mmଷ ⁄ . Neglect contribution of feed force towards power. The power required to carry out this operation is _________ kW (round off to one decimal place).

Explanation

Casting, Forming and Joining Processes

17 Questions

GATE→2026→Materials, Manufacturing and Industrial Engineering→Casting, Forming and Joining Processes

Q8

MCQ[1 Mark]

In relation to metal casting defects, match the following: | Description | Defect | | --- | --- | | P: Shallow blow found on a flat casting surface | I: Dross | | Q: Lighter impurities appearing on the top surface of a casting | II: Scab | | R: A rough, thin layer of metal, protruding above the casting surface, on top of a thin layer of sand | III: Scar | \nOptions:

(A)

P-II, Q-III, R-I

(B)

P-II, Q-I, R-III

(C)

P-III, Q-I, R-II

(D)

P-III, Q-II, R-I

Explanation

GATE→2026→Materials, Manufacturing and Industrial Engineering→Casting, Forming and Joining Processes

Q9

NAT[2 Marks]

In a deep drawing operation of a rectangular sheet metal, $30\%$ stretching in length results in $15\%$ reduction in thickness. Assuming volume constancy, the normal anisotropy of the sheet metal is ____ (rounded off to 2 decimal places).

Explanation

GATE→2025→Materials, Manufacturing and Industrial Engineering→Casting, Forming and Joining Processes

Q10

MCQ[1 Mark]

The welding process commonly used for fabricating tailor-welded blanks of dissimilar thickness for automotive applications is

(A)

gas welding

(B)

laser welding

(C)

arc welding

(D)

friction welding

Explanation

GATE→2025→Materials, Manufacturing and Industrial Engineering→Casting, Forming and Joining Processes

Q11

NAT[1 Mark]

During a welding operation, thermal power of $2500~W$ is incident normally on a metallic surface. As shown in the figure below (figure is NOT to scale), the heated area is circular. Out of the incident power, $85\%$ of the power is absorbed within a circle of radius $5~mm$ while $65\%$ is absorbed within an inner concentric circle of radius $3~mm$. The power density in the shaded area is ____ $W~mm^{-2}$ (rounded off to 2 decimal places).

Explanation

GATE→2025→Materials, Manufacturing and Industrial Engineering→Casting, Forming and Joining Processes

Q12

NAT[1 Mark]

A liquid metal is poured in a mold cavity of size $200~mm \times 200~mm \times 200~mm$. The cooling is uniform in all directions with NO additional compensation for shrinkage. Considering the volumetric shrinkage during solidification and solid contraction as $7\%$ and $8\%$ respectively, the length of the cube edge after cooling down to the room temperature is ____ mm (rounded off to 1 decimal place).

Explanation

GATE→2025→Materials, Manufacturing and Industrial Engineering→Casting, Forming and Joining Processes

Q13

MCQ[2 Marks]

Match the mold elements in the casting process with the most suitable function: | Mold element | Function | | --- | --- | | P: Blind riser | I: Casting with internal cavity | | Q: Chill | II: Molten metal reservoir | | R: Skim bob | III: Nucleating agent | | S: Core | IV: Assisting in faster heat removal from melt | | T: Insulating sleeve | V: Removal of impurities | | U: Inoculant | VI: Increasing the solidification time |

(A)

P-II, Q-IV, R-V, S-I, T-VI, U-III

(B)

P-II, Q-V, R-VI, S-I, T-III, U-IV

(C)

P-V, Q-I, R-VI, S-3, T-II, U-IV

(D)

P-II, Q-IV, R-I, S-V, T-VI, U-III

Explanation

GATE→2025→Materials, Manufacturing and Industrial Engineering→Casting, Forming and Joining Processes

Q14

MCQ[2 Marks]

Wire drawing operation is performed on a perfectly plastic metal without any strain hardening. Assuming no friction and no redundant work, the maximum possible percentage reduction in area in a single pass is closest to

(A)

51.2

(B)

63.2

(C)

75.0

(D)

93.2

Explanation

GATE→2025→Materials, Manufacturing and Industrial Engineering→Casting, Forming and Joining Processes

Q15

MCQ[2 Marks]

A plate of $30~mm$ thickness is fed through a rolling mill with two powered rolls. Each roll has a diameter of $500~mm$. The plate thickness is to be reduced to $27~mm$ in a single pass. Assume no change in width. The process feasibility and the maximum draft (in mm) can be represented, respectively, as\nUse the coefficient of friction as $0.12$

(A)

feasible and 3.6

(B)

NOT feasible and 2.6

(C)

feasible and 3.0

(D)

NOT feasible and 6.0

Explanation

GATE→2025→Materials, Manufacturing and Industrial Engineering→Casting, Forming and Joining Processes

Q16

NAT[2 Marks]

Two metal parts (a cylinder and a cube) of same volume are cast under identical conditions. The diameter of the cylinder is equal to its height. The ratio of the solidification time of the cube to that of the cylinder is ____ (rounded off to 2 decimal places).\nAssume that solidification time follows Chvorinov's rule with an exponent of 2.

Explanation

GATE→2024→Materials, Manufacturing and Industrial Engineering→Casting, Forming and Joining Processes

Q17

MCQ[1 Mark]

The 'Earing' phenomenon in metal forming is associated with

(A)

deep drawing

(B)

rolling

(C)

extrusion

(D)

forging

Explanation

GATE→2024→Materials, Manufacturing and Industrial Engineering→Casting, Forming and Joining Processes

Q18

MCQ[1 Mark]

The allowance provided to a pattern for easy withdrawal from a sand mold is

(A)

finishing allowance

(B)

shrinkage allowance

(C)

distortion allowance

(D)

shake allowance

Explanation

GATE→2024→Materials, Manufacturing and Industrial Engineering→Casting, Forming and Joining Processes

Q19

MCQ[1 Mark]

The most suitable electrode material used for joining low alloy steels using Gas Metal Arc Welding (GMAW) process is

(A)

copper

(B)

low alloy steel

(C)

mild steel

(D)

tungsten

Explanation

GATE→2024→Materials, Manufacturing and Industrial Engineering→Casting, Forming and Joining Processes

Q20

NAT[2 Marks]

Aluminium is casted in a cube-shaped mold having dimensions as $20~mm \times 20~mm \times 20~mm$. Another mold of the same mold material is used to cast a sphere of aluminium having a diameter of $20~mm$. The pouring temperature for both cases is the same. The ratio of the solidification times of the cube-shaped mold to the spherical mold is ____ (answer in integer).

Explanation

GATE→2024→Materials, Manufacturing and Industrial Engineering→Casting, Forming and Joining Processes

Q21

NAT[2 Marks]

A blanking operation is performed on C20 steel sheet to obtain a circular disc having a diameter of $20~mm$ and a thickness of $2~mm$. An allowance of $0.04$ is provided. The punch size used for the operation is ____ mm (rounded off to 2 decimal places).

Explanation

GATE→2024→Materials, Manufacturing and Industrial Engineering→Casting, Forming and Joining Processes

Q22

NAT[2 Marks]

In an arc welding process, the voltage and current are $30~V$ and $200~A$, respectively. The cross-sectional area of the joint is $20~mm^{2}$ and the welding speed is $5~mm/s$. The heat required to melt the material is $200~J/s$. The percentage of heat lost to the surrounding during the welding process is ____ (rounded off to 2 decimal places). [Note: Official Key marked this as MTA (Marks To All)]

Explanation

GATE→2023→Materials, Manufacturing and Industrial Engineering→Casting, Forming and Joining Processes

Q23

MSQ[1 Mark]

Two surfaces P and Q are to be joined together. In which of the given joining operation(s), there is no melting of the two surfaces P and Q for creating the joint?

(A)

Arc welding

(B)

Brazing

(C)

Adhesive bonding

(D)

Spot welding

Explanation

GATE→2023→Materials, Manufacturing and Industrial Engineering→Casting, Forming and Joining Processes

Q24

MSQ[1 Mark]

In a metal casting process to manufacture parts, both patterns and moulds provide shape by dictating where the material should or should not go. Which of the option(s) given correctly describe(s) the mould and the pattern?

(A)

Mould walls indicate boundaries within which molten part material is allowed, while pattern walls indicate boundaries of regions where mould material is not allowed

(B)

Moulds can be used to make patterns

(C)

Pattern walls indicate boundaries within which molten part material is allowed...

(D)

Patterns can be used to make moulds

Explanation

Machining and Machine Tool Operations

12 Questions

GATE→2026→Materials, Manufacturing and Industrial Engineering→Machining and Machine Tool Operations

Q25

MCQ[1 Mark]

A work piece is to be firmly held in a fixture. It is to be machined by using a plain slab milling cutter as shown in the figure below. Which one of the following options is the most suitable value of height H of the fixture in mm?

(A)

200

(B)

210

(C)

150

(D)

70

Explanation

GATE→2026→Materials, Manufacturing and Industrial Engineering→Machining and Machine Tool Operations

Q26

NAT[2 Marks]

During orthogonal turning by using a single point cutting tool, feed rate is $0.24~mm/rev$. The uncut chip thickness is $0.23~mm$. The shear angle, tangential force component, and radial force component are $20^{\circ}$, $800~N$, and $150~N$, respectively. The value of shear force is ____ N (rounded off to 2 decimal places).

Explanation

GATE→2026→Materials, Manufacturing and Industrial Engineering→Machining and Machine Tool Operations

Q27

NAT[2 Marks]

A drill bit during its lifetime can produce 150 through holes in a plate at a drill-speed of $200~RPM$. If the drill-speed increases to $300~RPM$, then it can produce 60 through holes in the same plate before the drill bit fails. Assume all other parameters remain constant. The value of the exponent in Taylor's tool life equation is ____ (rounded off to 2 decimal places).

Explanation

GATE→2025→Materials, Manufacturing and Industrial Engineering→Machining and Machine Tool Operations

Q28

MCQ[1 Mark]

Ceramics and glass are machined by

(A)

electric discharge machining

(B)

ultrasonic machining

(C)

electrochemical machining

(D)

transferred arc plasma machining

Explanation

GATE→2025→Materials, Manufacturing and Industrial Engineering→Machining and Machine Tool Operations

Q29

NAT[2 Marks]

Cylindrical workpieces of diameter $60~mm$ and length $400~mm$ are machined on a lathe at a cutting speed of $25~m~min^{-1}$ and a feed of $0.2~mm~rev^{-1}$. The Taylor's tool life parameters $C$ and $n$ for this setup are $75$ and $0.25$, respectively. The tool changing time is $3~minutes$. With a labor and overhead cost of $5 per minute, the tool changing cost per piece is ____ (rounded off to 2 decimal places).

Explanation

GATE→2024→Materials, Manufacturing and Industrial Engineering→Machining and Machine Tool Operations

Q30

MCQ[1 Mark]

The grinding wheel used to provide the best surface finish is

(A)

A36L5V

(B)

A80L5V

(C)

A36S5V

(D)

A80S5V

Explanation

GATE→2024→Materials, Manufacturing and Industrial Engineering→Machining and Machine Tool Operations

Q31

NAT[2 Marks]

A cutting tool provides a tool life of $60~minutes$ while machining with the cutting speed of $60~m/min$. When the same tool is used for machining the same material, it provides a tool life of $10~minutes$ for a cutting speed of $100~m/min$. If the cutting speed is changed to $80~m/min$ for the same tool and work material combination, the tool life computed using Taylor's tool life model is ____ minutes (rounded off to 2 decimal places).

Explanation

GATE→2024→Materials, Manufacturing and Industrial Engineering→Machining and Machine Tool Operations

Q32

NAT[2 Marks]

A flat surface of a C60 steel having dimensions of $100~mm$ (length) $\times 200~mm$ (width) is produced by a HSS slab mill cutter. The 8-toothed cutter has $100~mm$ diameter and $200~mm$ width. The feed per tooth is $0.1~mm$, cutting velocity is $20~m/min$ and depth of cut is $2~mm$. The machining time required to remove the entire stock is ____ minutes (rounded off to 2 decimal places).

Explanation

GATE→2023→Materials, Manufacturing and Industrial Engineering→Machining and Machine Tool Operations

Q33

MCQ[2 Marks]

In an ideal orthogonal cutting experiment (see figure), the cutting speed V is $1~m/s$, the rake angle of the tool $\alpha=5^{\circ}$ and the shear angle, $\phi$, is known to be $45^{\circ}$. Applying the ideal orthogonal cutting model, consider two shear planes PQ and RS close to each other. As they approach the thin shear zone (shown as a thick line in the figure), plane RS gets sheared with respect to PQ (point R1 shears to R2, and S1 shears to S2). Assuming that the perpendicular distance between PQ and RS is $\delta=25~\mu m$, what is the value of shear strain rate (in $s^{-1}$) that the material undergoes at the shear zone?

(A)

1.84 \times 10^4

(B)

5.20 \times 10^4

(C)

0.71 \times 10^4

(D)

1.30 \times 10^4

Explanation

GATE→2022→Materials, Manufacturing and Industrial Engineering→Machining and Machine Tool Operations

Q34

MCQ[1 Mark]

Which one of the following is NOT a form of inventory? (A) Raw materials (B) Work-in-process materials (C) Finished goods (D) CNC Milling Machines

(A)

Raw materials

(B)

Work-in-process materials

(C)

Finished goods

(D)

CNC Milling Machines

Explanation

GATE→2022→Materials, Manufacturing and Industrial Engineering→Machining and Machine Tool Operations

Q35

MSQ[1 Mark]

Which of the following additive manufacturing technique(s) can use a wire as a feedstock material? (A) Stereolithography (B) Fused deposition modeling (C) Selective laser sintering (D) Directed energy deposition processes

(A)

Stereolithography

(B)

Fused deposition modeling

(C)

Selective laser sintering

(D)

Directed energy deposition processes

Explanation

GATE→2022→Materials, Manufacturing and Industrial Engineering→Machining and Machine Tool Operations

Q36

NAT[1 Mark]

Electrochemical machining operations are performed with tungsten as the tool, and copper and aluminum as two different workpiece materials. Properties of copper and aluminum are given in the table below. Material Atomic mass (amu) Valency Density (g/cm3) Copper 63 2 9 Aluminum 27 3 2.7 Ignore overpotentials, and assume that current efficiency is 100% for both the workpiece materials. Under identical conditions, if the material removal rate (MRR) of copper is 100 mg/s, the MRR of aluminum will be ________________ mg/s (round-off to two decimal places). 𝑟 G A 𝑅 𝑔

Explanation

Additive Manufacturing

3 Questions

GATE→2026→Materials, Manufacturing and Industrial Engineering→Additive Manufacturing

Q37

MCQ[1 Mark]

Which one of the following options is NOT an error associated with STereoLithography (STL) file in additive manufacturing?

(A)

Staircase effect

(B)

Missing facet

(C)

Non-manifold topology conditions

(D)

Degenerate facets

Explanation

GATE→2025→Materials, Manufacturing and Industrial Engineering→Additive Manufacturing

Q38

MCQ[2 Marks]

In relation to additive manufacturing, match the following: | Process | Layer creation technique | Material | | --- | --- | --- | | P: Stereolithography | 1: Injection of powder stream | I: Paper | | Q: Fused deposition modeling | 2: Extrusion of melted polymer | II: Epoxy | | R: Laminated object manufacturing | 3: Liquid layer curing | III: Titanium | | S: Laser-engineered net shaping | 4: Sheet material deposition | IV: Acrylonitrile butadiene styrene (ABS) |

(A)

P-3-III, Q-1-IV, R-4-I, S-2-II

(B)

P-3-II, Q-2-IV, R-4-I, S-1-III

(C)

P-4-III, Q-2-IV, R-1-II, S-3-I

(D)

P-3-II, Q-2-IV, R-1-I, S-4-III

Explanation

GATE→2023→Materials, Manufacturing and Industrial Engineering→Additive Manufacturing

Q39

NAT[2 Marks]

A solid part (see figure) of polymer material is to be fabricated by additive manufacturing (AM) in square-shaped layers starting from the bottom of the part working upwards. The nozzle diameter of the AM machine is $a/10~mm$ and the nozzle follows a linear serpentine path parallel to the sides of the square layers with a feed rate of $a/5~mm/min$.\nIgnore any tool path motions other than those involved in adding material, and any other delays between layers or the serpentine scan lines.\nThe time taken to fabricate this part is ____ minutes. (Answer in integer) [Note: Official Key marked this as MTA (Marks To All)]

Explanation

Metrology and Inspection

6 Questions

GATE→2026→Materials, Manufacturing and Industrial Engineering→Metrology and Inspection

Q40

MCQ[1 Mark]

A two-dimensional surface profile is obtained over a sampling length by using a contact type stylus profilometer as shown in the figure below. A line AA parallel to the general lay of the trace is considered. The true heights from AA to the peaks and valleys $(in~\mu m)$ in the trace are also shown in the figure. The ten-point height average in $\mu m$ is

(A)

6.7

(B)

5.99

(C)

3.09

(D)

2.90

Explanation

GATE→2025→Materials, Manufacturing and Industrial Engineering→Metrology and Inspection

Q41

MCQ[1 Mark]

When assembled, the hole $30_{-0.000}^{+0.030}~mm$ and shaft $30_{-0.020}^{+0.020}$ [Wait, source shows $30_{-0.020}$] mm will result in

(A)

loose fit

(B)

interference fit

(C)

transition fit

(D)

clearance fit

Explanation

GATE→2023→Materials, Manufacturing and Industrial Engineering→Metrology and Inspection

Q42

MCQ[1 Mark]

A cuboidal part has to be accurately positioned first, arresting six degrees of freedom and then clamped in a fixture, to be used for machining. Locating pins in the form of cylinders with hemi-spherical tips are to be placed on the fixture for positioning. Four different configurations of locating pins are proposed as shown. Which one of the options given is correct?

(A)

Configuration P1 arrests 6 degrees of freedom, while Configurations P2 and P4 are over-constrained and Configuration P3 is under-constrained.

(B)

Configuration P2 arrests 6 degrees of freedom, while Configurations P1 and P3 are over-constrained and Configuration P4 is under-constrained.

(C)

Configuration P3 arrests 6 degrees of freedom, while Configurations P2 and P4 are over-constrained and Configuration P1 is under-constrained.

(D)

Configuration P4 arrests 6 degrees of freedom, while Configurations P1 and P3 are over-constrained and Configuration P2 is under-constrained.

Explanation

GATE→2023→Materials, Manufacturing and Industrial Engineering→Metrology and Inspection

Q43

NAT[2 Marks]

A part, produced in high volumes, is dimensioned as shown. The machining process making this part is known to be statistically in control based on sampling data. The sampling data shows that D1 follows a normal distribution with a mean of $20~mm$ and a standard deviation of $0.3~mm$, while D2 follows a normal distribution with a mean of $35~mm$ and a standard deviation of $0.4~mm$. An inspection of dimension C is carried out in a sufficiently large number of parts. To be considered under six-sigma process control, the upper limit of dimension C should be ____ mm. (Rounded off to one decimal place)

Explanation

GATE→2023→Materials, Manufacturing and Industrial Engineering→Metrology and Inspection

Q44

NAT[2 Marks]

A coordinate measuring machine (CMM) is used to determine the distance between Surface SP and Surface SQ of an approximately cuboidal shaped part. Surface SP is declared as the datum as per the engineering drawing used for manufacturing this part. The CMM is used to measure four points P1, P2, P3, P4 on Surface SP, and four points Q1, Q2, Q3, Q4 on Surface SQ as shown. A regression procedure is used to fit the necessary planes. The distance between the two fitted planes is ____ mm. (Answer in integer)

Explanation

GATE→2022→Materials, Manufacturing and Industrial Engineering→Metrology and Inspection

Q45

NAT[1 Mark]

A rigid uniform annular disc is pivoted on a knife edge A in a uniform gravitational field as shown, such that it can execute small amplitude simple harmonic motion in the plane of the figure without slip at the pivot point. The inner radius 𝑟 and outer radius 𝑅 are such that 𝑟ଶ= 𝑅ଶ/2, and the acceleration due to gravity is 𝑔. If the time period of small amplitude simple harmonic motion is given by 𝑇= 𝛽𝜋ඥ𝑅/𝑔, where 𝜋 is the ratio of circumference to diameter of a circle, then 𝛽= ________ (round off to 2 decimal places).

Explanation

Computer Aided Manufacturing and Automation

4 Questions

GATE→2026→Materials, Manufacturing and Industrial Engineering→Computer Aided Manufacturing and Automation

Q46

MCQ[2 Marks]

Consider the Euler variables of polyhedral objects namely, P1, P2, P3, and P4 given in the table below. | Polyhedral objects | Faces (F) | Edges (E) | Vertices (V) | Faces' inner loops (L) | Bodies (B) | Genus (G) | | --- | --- | --- | --- | --- | --- | --- | | P1 | 6 | 12 | 8 | 0 | 1 | 0 | | P2 | 5 | 8 | 5 | 0 | 1 | 0 | | P3 | 8 | 12 | 6 | 0 | 1 | 2 | | P4 | 10 | 24 | 16 | 0 | 1 | 0 | \nWhich one of the following options is NOT a topologically valid closed polyhedral object as per Euler's law?

(A)

P3

(B)

P1

(C)

P4

(D)

P2

Explanation

GATE→2025→Materials, Manufacturing and Industrial Engineering→Computer Aided Manufacturing and Automation

Q47

MCQ[1 Mark]

In computer aided design (CAD), solid models can be constructed using

(A)

boundary representation (B-rep)

(B)

Bezier curves

(C)

B-splines

(D)

nonuniform rational B-splines (NURBS)

Explanation

GATE→2024→Materials, Manufacturing and Industrial Engineering→Computer Aided Manufacturing and Automation

Q48

MCQ[1 Mark]

The preparatory functions in Computer Numerical Controlled (CNC) machine programming are denoted by the alphabet

(A)

G

(B)

M

(C)

P

(D)

O

Explanation

GATE→2023→Materials, Manufacturing and Industrial Engineering→Computer Aided Manufacturing and Automation

Q49

MCQ[2 Marks]

A CNC machine has one of its linear positioning axes as shown in the figure, consisting of a motor rotating a lead screw, which in turn moves a nut horizontally on which a table is mounted. The motor moves in discrete rotational steps of 50 steps per revolution. The pitch of the screw is 5 mm and the total horizontal traverse length of the table is 100 mm. What is the total number of controllable locations at which the table can be positioned on this axis?

(A)

5000

(B)

2

(C)

1000

(D)

200

Explanation

Production Planning and Control

8 Questions

GATE→2026→Materials, Manufacturing and Industrial Engineering→Production Planning and Control

Q50

MCQ[2 Marks]

Four jobs are on order in a factory. As on day 20 of the production calendar, corresponding due date and work remaining to complete these jobs (in days) are given in the table below. | Job | Due date | Work remaining (in days) | | --- | --- | --- | | M | 26 | 5 | | N | 24 | 10 | | O | 28 | 10 | | P | 31 | 5 | \nWhich job(s) has/have critical ratio less than unity?

(A)

Job N and Job O

(B)

Job M and Job N

(C)

Job P

(D)

Job O and Job P

Explanation

GATE→2026→Materials, Manufacturing and Industrial Engineering→Production Planning and Control

Q51

NAT[2 Marks]

The actual demand for castings in a factory is 500 units and 635 units for the months of January 2026 and February 2026, respectively. The forecasted demand for January 2026 is 250 units and smoothing constant is $0.7$. Using the exponential smoothing method, the forecast of the demand for castings in March 2026 is ____ units (in integer).

Explanation

GATE→2026→Materials, Manufacturing and Industrial Engineering→Production Planning and Control

Q52

NAT[2 Marks]

The inventory holding cost of an item is $0.50 per unit per month and the ordering cost per order is$550. A stockist needs to supply 10000 units of the item per year to the customers. Assume demand is fixed and shortage cost is infinite. Using classical economic order quantity (EOQ) model, the optimal lot size is ____ units per order (rounded off to nearest integer).

Explanation

GATE→2025→Materials, Manufacturing and Industrial Engineering→Production Planning and Control

Q53

MCQ[2 Marks]

Considering the actual demand and the forecast for a product given in the table below, the mean forecast error and the mean absolute deviation, respectively, are | Period | Actual demand | Forecast | | --- | --- | --- | | 1 | 425 | 427 | | 2 | 421 | 423 | | 3 | 416 | 420 | | 4 | 418 | 422 | | 5 | 415 | 416 | | 6 | 420 | 422 | | 7 | 430 | 415 | | 8 | 418 | 430 | | 9 | 427 | 418 | | 10 | 426 | 419 |

(A)

0.8 and 42.0

(B)

0.8 and 4.2

(C)

8.0 and 42.0

(D)

8.0 and 4.2

Explanation

GATE→2025→Materials, Manufacturing and Industrial Engineering→Production Planning and Control

Q54

NAT[2 Marks]

A company uses $3000$ units of a part annually. The units are priced as given in the table below. It costs $150$ to place an order. Carrying costs are $40$ percent of the purchase price per unit on an annual basis. The minimum total annual cost is ____ (rounded off to 1 decimal place). | Unit price | Order quantity | | --- | --- | | 9.0 | 1 to 499 | | 8.5 | 500 to 999 | | 8.0 | 1000 or more |

Explanation

GATE→2024→Materials, Manufacturing and Industrial Engineering→Production Planning and Control

Q55

MCQ[1 Mark]

A set of jobs U, V, W, X, Y, Z arrive at time $t=0$ to a production line consisting of two workstations in series. Each job must be processed by both workstations in sequence (i.e., the first followed by the second). The process times (in minutes) for each job on each workstation in the production line are given below. | Job | U | V | W | X | Y | Z | | --- | --- | --- | --- | --- | --- | --- | | Workstation 1 | 5 | 7 | 3 | 4 | 6 | 8 | | Workstation 2 | 4 | 6 | 6 | 8 | 5 | 7 | \nThe sequence in which the jobs must be processed by the production line if the total makespan of production is to be minimized is [Note: Official Key marked this as MTA (Marks To All)]

(A)

W-X-Z-V-Y-U

(B)

W-X-V-Z-Y-U

(C)

W-U-Z-V-Y-X

(D)

U-Y-V-Z-X-W

Explanation

GATE→2024→Materials, Manufacturing and Industrial Engineering→Production Planning and Control

Q56

MCQ[2 Marks]

A company orders gears in conditions identical to those considered in the economic order quantity (EOQ) model in inventory control. The annual demand is $8000$ gears, the cost per order is $300$ rupees, and the holding cost is $12$ rupees per month per gear. The company uses an order size that is $25\%$ more than the optimal order quantity determined by the EOQ model. The percentage change in the total cost of ordering and holding inventory from that associated with the optimal order quantity is

(A)

2.5

(B)

5

(C)

0

(D)

12.5

Explanation

GATE→2023→Materials, Manufacturing and Industrial Engineering→Production Planning and Control

Q57

MCQ[1 Mark]

With reference to the Economic Order Quantity (EOQ) model, which one of the options given is correct?

(A)

Curve P1: Total cost, Curve P2: Holding cost, Curve P3: Setup cost, and Curve P4: Production cost.

(B)

Curve P1: Holding cost, Curve P2: Setup cost, Curve P3: Production cost, and Curve P4: Total cost.

(C)

Curve P1: Production cost, Curve P2: Holding cost, Curve P3: Total cost, and Curve P4: Setup cost.

(D)

Curve P1: Total cost, Curve P2: Production cost, Curve P3: Holding cost, and Curve P4: Setup cost.

Explanation

Operations Research

12 Questions

GATE→2026→Materials, Manufacturing and Industrial Engineering→Operations Research

Q58

MCQ[2 Marks]

An objective function Z of primal variables ($x_{1}$ and $x_{2}$) is described below:\nMinimize $Z=0.07~x_{1}+0.05~x_{2}$\nsubject to $0.1~x_{1}\ge0.4$ $0.1~x_{2}\ge0.6$ $0.1~x_{1}+0.2~x_{2}\ge2.0$ $0.2~x_{1}+0.1~x_{2}\ge1.8$ $x_{1},x_{2}\ge0$ $W$ is the objective function of the dual of $Z$. $k_{1}, k_{2}, k_{3},$ and $k_{4}$ represent the corresponding dual variables. Which one of the following options represents the correct form of $W$?

(A)

A

(B)

B

(C)

C

(D)

D

Explanation

GATE→2026→Materials, Manufacturing and Industrial Engineering→Operations Research

Q59

NAT[2 Marks]

The activities of a PERT network and their corresponding activity time estimates (in weeks) i.e., optimistic ($t_{o}$), most likely ($t_{m}$), and pessimistic ($t_{p}$) are given in the table below. | Activity | $t_{o}$ | $t_{m}$ | $t_{p}$ | | --- | --- | --- | --- | | 1-2 | 2 | 4 | 12 | | 1-3 | 2 | 4 | 6 | | 1-4 | 3 | 4 | 11 | | 2-5 | 3 | 6 | 9 | | 3-4 | 2 | 5 | 14 | | 3-5 | 3 | 3 | 3 | | 4-5 | 3 | 6 | 15 | | 5-6 | 2 | 5 | 8 | \nThe expected project length is ____ weeks (in integer).

Explanation

GATE→2025→Materials, Manufacturing and Industrial Engineering→Operations Research

Q60

NAT[2 Marks]

A project involves eight activities with the precedence relationship and duration as shown in the table below. The slack for the activity D is ____ hours (answer in integer). | Activity | Immediate predecessor | Duration (hours) | | --- | --- | --- | | A | - | 4 | | B | A | 8 | | C | A | 5 | | D | B | 2 | | E | B | 7 | | F | C | 6 | | G | D | 3 | | H | E, F, G | 9 |

Explanation

GATE→2024→Materials, Manufacturing and Industrial Engineering→Operations Research

Q61

MCQ[1 Mark]

A queueing system has one single server workstation that admits an infinitely long queue. The rate of arrival of jobs to the queueing system follows the Poisson distribution with a mean of 5 jobs/hour. The service time of the server is exponentially distributed with a mean of 6 minutes. In steady state operation of the queueing system, the probability that the server is not busy at any point in time is

(A)

0.20

(B)

0.17

(C)

0.50

(D)

0.83

Explanation

GATE→2024→Materials, Manufacturing and Industrial Engineering→Operations Research

Q62

MCQ[2 Marks]

At the current basic feasible solution (bfs) $v_{0}$, the simplex method yields the following form of a linear programming problem in standard form. $z=-x_{1}-2x_{2}$ $x_{3}=2+2x_{1}-x_{2}$ $x_{4}=7+x_{1}-2x_{2}$ $x_{5}=3-x_{1}$ $x_{1}, x_{2}, x_{3}, x_{4}, x_{5}\ge0$\nis written as a function of the non-basic variables. If the simplex method moves to the adjacent bfs $v_{1}$ that best improves the objective function, which of the following represents the objective function at $v_{1}$, assuming that the objective function is written in the same manner as above?

(A)

z = -4 - 5x_1 + 2x_3

(B)

z = -3 + x_5 - 2x_2

(C)

z = -4 - 5x_1 + 2x_4

(D)

z = -6 - 5x_1 + 2x_3

Explanation

GATE→2024→Materials, Manufacturing and Industrial Engineering→Operations Research

Q63

NAT[2 Marks]

In a supplier-retailer supply chain, the demand of each retailer, the capacity of each supplier, and the unit cost in rupees of material supply from each supplier to each retailer are tabulated below. The supply chain manager wishes to minimize the total cost of transportation across the supply chain. | | Retailer I | Retailer II | Retailer III | Retailer IV | Capacity | | --- | --- | --- | --- | --- | --- | | Supplier A | 11 | 16 | 19 | 13 | 300 | | Supplier B | 5 | 10 | 7 | 8 | 300 | | Supplier C | 12 | 14 | 17 | 11 | 300 | | Supplier D | 8 | 15 | 11 | 9 | 300 | | Demand | 300 | 300 | 300 | 300 | | \nThe optimal cost of satisfying the total demand from all retailers is ____ rupees (answer in integer).

Explanation

GATE→2023→Materials, Manufacturing and Industrial Engineering→Operations Research

Q64

MCQ[1 Mark]

Which one of the options given represents the feasible region of the linear programming model:\nMaximize $45X_{1}+60X_{2}$ $X_{1}\le 45$ $X_{2}\le 50$ $10X_{1}+10X_{2}\ge 600$ $25X_{1}+5X_{2}\le 750$

(A)

Region P

(B)

Region Q

(C)

Region R

(D)

Region S

Explanation

GATE→2022→Materials, Manufacturing and Industrial Engineering→Operations Research

Q65

MCQ[1 Mark]

- 35 Carry ONE mark each.

Explanation

GATE→2022→Materials, Manufacturing and Industrial Engineering→Operations Research

Q66

MCQ[1 Mark]

Solution of ∇ଶ𝑇= 0 in a square domain (0 < 𝑥< 1 and 0 < 𝑦< 1) with boundary conditions: 𝑇(𝑥, 0) = 𝑥; 𝑇(0, 𝑦) = 𝑦; 𝑇(𝑥, 1) = 1 + 𝑥; 𝑇(1, 𝑦) = 1 + 𝑦 is (A) 𝑇(𝑥, 𝑦) = 𝑥−𝑥𝑦+ 𝑦 (B) 𝑇(𝑥, 𝑦) = 𝑥+ 𝑦 (C) 𝑇(𝑥, 𝑦) = −𝑥+ 𝑦 (D) 𝑇(𝑥, 𝑦) = 𝑥+ 𝑥𝑦+ 𝑦

(A)

𝑇(𝑥, 𝑦) = 𝑥−𝑥𝑦+ 𝑦

(B)

𝑇(𝑥, 𝑦) = 𝑥+ 𝑦

(C)

𝑇(𝑥, 𝑦) = −𝑥+ 𝑦

(D)

𝑇(𝑥, 𝑦) = 𝑥+ 𝑥𝑦+ 𝑦

Explanation

GATE→2022→Materials, Manufacturing and Industrial Engineering→Operations Research

Q67

MCQ[1 Mark]

In a linear programming problem, if a resource is not fully utilized, the shadow price of that resource is (A) positive (B) negative (C) zero (D) infinity

(A)

positive

(B)

negative

(C)

zero

(D)

infinity

Explanation

GATE→2022→Materials, Manufacturing and Industrial Engineering→Operations Research

Q68

MCQ[2 Marks]

Activities A to K are required to complete a project. The time estimates and the immediate predecessors of these activities are given in the table. If the project is to be completed in the minimum possible time, the latest finish time for the activity G is ____________ hours. Activity Time (hours) Immediate predecessors A 2 ─ B 3 ─ C 2 ─ D 4 A E 5 B F 4 B G 3 C H 10 D, E I 5 F J 8 G K 3 H, I, J (A) 5 (B) 10 (C) 8 (D) 9

(A)

5

(B)

10

(C)

8

(D)

9

Explanation

GATE→2022→Materials, Manufacturing and Industrial Engineering→Operations Research

Q69

NAT[2 Marks]

An assignment problem is solved to minimize the total processing time of four jobs (1, 2, 3 and 4) on four different machines such that each job is processed exactly by one machine and each machine processes exactly one job. The minimum total processing time is found to be 500 minutes. Due to a change in design, the processing time of Job 4 on each machine has increased by 20 minutes. The revised minimum total processing time will be _____________ minutes (in integer).

Explanation