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General Aptitude(10)Engineering Mathematics(9)Applied Mechanics and Design(15)Fluid Mechanics and Thermal Sciences(15)Materials, Manufacturing and Industrial Engineering(16)

General Aptitude

10 Questions

GATE→2025→General Aptitude→Verbal Ability

Q1

MCQ[1 Mark]

Fish : Shoal :: Lion : _____. Select the correct option to complete the analogy.

(A)

Pride

(B)

School

(C)

Forest

(D)

Series

Explanation

GATE→2025→General Aptitude→Verbal Ability

Q2

MCQ[1 Mark]

Identify the grammatically correct sentence:

(A)

It is I who am responsible for this fiasco.

(B)

It is myself who is responsible for this fiasco.

(C)

It is I who is responsible for this fiasco.

(D)

It is I who are responsible for this fiasco.

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q3

MCQ[1 Mark]

Two cars, P and Q, start from a point X in India at 10 AM. Car P travels North with a speed of $25~km/h$ and car Q travels East with a speed of $30~km/h$. Car P travels continuously but car Q stops for some time after travelling for one hour. If both the cars are at the same distance from X at 11:30 AM, for how long (in minutes) did car Q stop?

(A)

10

(B)

12

(C)

15

(D)

18

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q4

MCQ[1 Mark]

The ceiling function of a real number x, denoted by $ce(x)$, is defined as the smallest integer that is greater than or equal to x. Similarly, the floor function, denoted by $fl(x)$, is defined as the largest integer that is smaller than or equal to x. Which one of the following statements is NOT correct for all possible values of x?

(A)

ce(x) \ge x

(B)

fl(x) \le x

(C)

ce(x) \ge fl(x)

(D)

fl(x) < ce(x)

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q5

MCQ[1 Mark]

P and Q play chess frequently against each other. Of these matches, P has won 80% of the matches, drawn 15% of the matches and lost 5% of the matches. If they play 3 more matches, what is the probability of P winning exactly 2 of these 3 matches?

(A)

\frac{48}{125}

(B)

\frac{16}{125}

(C)

\frac{16}{25}

(D)

\frac{25}{48}

Explanation

GATE→2025→General Aptitude→Verbal Ability

Q6

MCQ[2 Marks]

Identify the option that has the most appropriate sequence such that a coherent paragraph is formed: \nP. At once, without thinking much, people rushed towards the city in hordes with the sole aim of grabbing as much gold as they could. \nQ. However, little did they realize about the impending hardships they would have to face on their way to the city: miles of mud, unfriendly forests, hungry beasts and inimical local lords all of which would reduce their chances of getting gold to almost zero. \nR. All of them thought that easily they could lay their hands on gold and become wealthy overnight. \nS. About a hundred years ago, the news that gold had been discovered in Kolar spread like wildfire and the whole State was in raptures.

(A)

P \rightarrow Q \rightarrow R \rightarrow S

(B)

Q \rightarrow S \rightarrow R \rightarrow P

(C)

S \rightarrow Q \rightarrow P \rightarrow R

(D)

S \rightarrow P \rightarrow R \rightarrow Q

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q7

MCQ[2 Marks]

If HIDE and CAGE are coded as 19-23-7-11 and 5-2-17-11 respectively, then what is the code for HIGH?

(A)

5-17-1-2

(B)

17-19-13-17

(C)

13-3-1-2

(D)

19-23-17-19

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q8

MCQ[2 Marks]

The given figure is reflected about the horizontal dashed line and then rotated clockwise by $90^{\circ}$ about an axis perpendicular to the plane of the figure. Which one of the following options correctly shows the resultant figure?\nNote: The figures shown are representative.

(A)

A

(B)

B

(C)

C

(D)

D

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q9

MCQ[2 Marks]

Which one of the following options has the correct sequence of objects arranged in the increasing number of mirror lines (lines of symmetry)?

(A)

Circle; Square; Equilateral triangle; Isosceles triangle

(B)

Isosceles triangle; Equilateral triangle; Square; Circle

(C)

Equilateral triangle; Isosceles triangle; Square; Circle

(D)

Isosceles triangle; Square; Equilateral triangle; Circle

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q10

MCQ[2 Marks]

A final year student appears for placement interview in two companies, S and T. Based on her interview performance, she estimates the probability of receiving job offers from companies S and T to be 0.8 and 0.6, respectively. Let $p$ be the probability that she receives job offers from both the companies. Select the most appropriate option.

(A)

0 \le p \le 0.2

(B)

0.4 \le p \le 0.6

(C)

0.2 \le p \le 0.4

(D)

0.6 \le p \le 1.0

Explanation

Engineering Mathematics

9 Questions

GATE→2025→Engineering Mathematics→Linear Algebra

Q11

MCQ[1 Mark]

Let A and B be real symmetric matrices of same size. Which one of the following options is correct?

(A)

A^{T} = A^{-1}

(B)

AB = BA

(C)

(AB)^{T} = B^{T}A^{T}

(D)

A = A^{-1}

Explanation

GATE→2025→Engineering Mathematics→Differential Equations

Q12

MCQ[1 Mark]

For the differential equation given below, which one of the following options is correct? $$\frac{\partial^{2}u}{\partial x^{2}}+\frac{\partial^{2}u}{\partial y^{2}}=0, \quad 0\le x\le 1, \quad 0\le y\le 1$$

(A)

u = e^{x+y} \text{ is a solution for all x and y}

(B)

u = e^{x} \sin y \text{ is a solution for all x and y}

(C)

u = \sin x \sin y \text{ is a solution for all x and y}

(D)

u = \cos x \cos y \text{ is a solution for all x and y}

Explanation

GATE→2025→Engineering Mathematics→Calculus

Q13

MCQ[1 Mark]

The divergence of the curl of a vector field is

(A)

the magnitude of this vector field

(B)

the argument of this vector field

(C)

the magnitude of the curl of this vector field

(D)

zero

Explanation

GATE→2025→Engineering Mathematics→Probability and Statistics

Q14

MCQ[1 Mark]

If two unbiased coins are tossed, then what is the probability of having at least one head?

(A)

0.25

(B)

0.5

(C)

0.6

(D)

0.75

Explanation

GATE→2025→Engineering Mathematics→Numerical Methods

Q15

NAT[1 Mark]

The values of a function $f(x)$ obtained for different values of $x$ are shown in the table below. | $x$ | 0 | 0.25 | 0.5 | 0.75 | 1.0 | | --- | --- | --- | --- | --- | --- | | $f(x)$ | 0.4 | 1.8 | 0.9 | 1.5 | 2.0 | \nUsing Simpson's one-third rule, $\int_{0}^{1.0} f(x) dx \approx$ _____ (rounded off to 2 decimal places).

Explanation

GATE→2025→Engineering Mathematics→Calculus

Q16

MCQ[2 Marks]

In the closed interval $[0, 3]$, the minimum value of the function $f$ given below is $$f(x)=2x^{3}-9x^{2}+12x$$

(A)

0

(B)

4

(C)

5

(D)

9

Explanation

GATE→2025→Engineering Mathematics→Complex Variables

Q17

NAT[2 Marks]

If C is the unit circle in the complex plane with its center at the origin, then the value of $n$ in the equation given below is ____ (rounded off to 1 decimal place). $$\oint_{c}\frac{z^{3}}{(z^{2}+4)(z^{2}-4)}dz=2~\pi~i~n$$

Explanation

GATE→2025→Engineering Mathematics→Calculus

Q18

NAT[2 Marks]

The directional derivative of the function $f$ given below at the point $(1,0)$ in the direction of $\frac{1}{2}(\hat{i}+\sqrt{3}\hat{j})$ is ____ (rounded off to 1 decimal place). $$f(x,y)=x^{2}+xy^{2}$$

Explanation

GATE→2025→Engineering Mathematics→Differential Equations

Q19

NAT[2 Marks]

Let $y$ be the solution of the differential equation with the initial conditions given below. If $y(x=2)=A~\ln 2$, then the value of $A$ is ____ (rounded off to 2 decimal places). $$x^{2}\frac{d^{2}y}{dx^{2}}+3x\frac{dy}{dx}+y=0, \quad y(x=1)=0, \quad \frac{dy}{dx}(x=1)=1$$

Explanation

Applied Mechanics and Design

15 Questions

GATE→2025→Applied Mechanics and Design→Mechanics of Materials

Q20

MCQ[1 Mark]

The yield stress of a metal in uniaxial tension is $200~MPa$. According to von Mises yield criterion, the yield stress (in MPa) of the metal in pure shear is closest to

(A)

115.5

(B)

100.0

(C)

66.7

(D)

141.4

Explanation

GATE→2025→Applied Mechanics and Design→Engineering Mechanics

Q21

MCQ[1 Mark]

A rigid circular disc of radius $r$ (in m) is rolling without slipping on a flat surface as shown in the figure below. The angular velocity of the disc is $\omega$ (in rad $s^{-1}$). The velocities (in m $s^{-1}$) at points O and A, respectively, are

(A)

r\omega\hat{i} \text{ and } 0\hat{i}

(B)

r\omega\hat{i} \text{ and } 0\hat{i}

(C)

r\omega\hat{i} \text{ and } r\omega\hat{i}

(D)

r\omega\hat{i} \text{ and } r\omega\hat{i}

Explanation

GATE→2025→Applied Mechanics and Design→Engineering Mechanics

Q22

MCQ[1 Mark]

A truss structure is loaded as shown in the figure below. Among the options given, which member in the truss is a zero-force member?

(A)

BD

(B)

BC

(C)

BA

(D)

AD

Explanation

GATE→2025→Applied Mechanics and Design→Mechanics of Materials

Q23

MCQ[1 Mark]

A metallic square plate is subjected to a uniform hydrostatic pressure (P). Choose the correct Mohr's circle representing the state of stress at any point in the plate from the options given below.\nFor the Mohr's circle, normal stress is positive towards right and shear stress is positive in the upward direction.

(A)

A

(B)

B

(C)

C

(D)

D

Explanation

GATE→2025→Applied Mechanics and Design→Theory of Machines

Q24

MCQ[1 Mark]

In the context of balancing of rotating and reciprocating masses, which one of the following options is true?

(A)

An unbalanced rigid rotor can be completely balanced using a single balancing mass

(B)

An unbalanced rigid rotor can be completely balanced using two balancing masses attached in two distinct planes

(C)

A single-cylinder internal combustion engine can be completely balanced using a single balancing mass

(D)

A single-cylinder internal combustion engine can be completely balanced using two balancing masses

Explanation

GATE→2025→Applied Mechanics and Design→Machine Design

Q25

MCQ[1 Mark]

A shaft carries a helical spur gear. Which one of the following bearings can NOT be used to support it?

(A)

Angular contact bearing

(B)

Double-row ball bearing

(C)

Straight roller bearing

(D)

Tapered roller bearing

Explanation

GATE→2025→Applied Mechanics and Design→Vibrations

Q26

NAT[1 Mark]

A block of mass $1~kg$ connected to a spring of stiffness $10~N~m^{-1}$ is operating in a viscous medium such that the damping ratio (or damping factor) is equal to the ratio of the damped frequency to the natural frequency. The magnitude of the damping ratio for this system is ____ (rounded off to 2 decimal places).

Explanation

GATE→2025→Applied Mechanics and Design→Vibrations

Q27

MCQ[2 Marks]

The system shown in the figure below consists of a cantilever beam (with flexural rigidity $EI$ and negligible mass), a spring (with spring constant $K$ and negligible mass) and a block of mass $m$. Assuming a lumped parameter model for the system, the fundamental natural frequency $(\omega_{n})$ of the system is

(A)

A

(B)

B

(C)

C

(D)

D

Explanation

GATE→2025→Applied Mechanics and Design→Machine Design

Q28

MCQ[2 Marks]

The endurance limit of a specific grade of steel is same as its yield strength. The ultimate strength of this grade of steel is twice of its yield strength. A component made of this steel is loaded in tension and unloaded periodically. It is required that the component does NOT fail for at least $10^{6}$ loading cycles, as per the Soderberg law. Considering a factor of safety of 2, the maximum applied tensile principal stress is

(A)

one-fourth of endurance limit

(B)

half of endurance limit

(C)

the endurance limit

(D)

twice the endurance limit

Explanation

GATE→2025→Applied Mechanics and Design→Mechanics of Materials

Q29

NAT[2 Marks]

The state of stress at a point is shown in the figure given below. Under plane stress assumption, the normal strain along the thickness direction $(\epsilon_{zz})$ is ____ (rounded off to 2 decimal places).\nUse the Young's Modulus $E=200~GPa$ and Poisson's ratio $\nu=0.27$.

Explanation

GATE→2025→Applied Mechanics and Design→Mechanics of Materials

Q30

NAT[2 Marks]

A simply supported beam of length $1~m$ is subjected to a uniformly distributed bending moment of $1~N~m$ per $m$ throughout the length as shown in the figure given below. The bending moment at the mid-point of the beam is ____ N m (rounded off to the nearest integer).

Explanation

GATE→2025→Applied Mechanics and Design→Mechanics of Materials

Q31

NAT[2 Marks]

An isotropic brittle material is tested in the universal testing machine. The stress-strain diagram for the material shows a bi-linear elastic behavior as shown in the figure given below. The strain energy density is ____ MJ $m^{-3}$ (rounded off to 2 decimal places).

Explanation

GATE→2025→Applied Mechanics and Design→Theory of Machines

Q32

NAT[2 Marks]

A pair of spur gears is required to maintain a velocity ratio of $1:2$. The module of the gears is $10~mm$ and the addendum is $10~mm$. If the operating pressure angle is $15^{\circ}$, the minimum number of teeth required on the pinion to ensure NO interference/undercutting is ____ (answer in integer).

Explanation

GATE→2025→Applied Mechanics and Design→Theory of Machines

Q33

NAT[2 Marks]

An offset slider-crank mechanism is shown in the figure below. The length of the stroke of the slider is ____ mm (rounded off to nearest integer).

Explanation

GATE→2025→Applied Mechanics and Design→Machine Design

Q34

NAT[2 Marks]

Two plates of thickness $10~mm$ each are to be joined by a transverse fillet weld on one side and the resulting structure is loaded as shown in the figure below. If the ultimate tensile strength of the weld material is $150~MPa$ and the factor of safety to be used is $3$, the minimum length of the weld required to ensure that the weld does NOT fail is ____ mm (rounded off to 2 decimal places).

Explanation

Fluid Mechanics and Thermal Sciences

15 Questions

GATE→2025→Fluid Mechanics and Thermal Sciences→Heat Transfer

Q35

MCQ[1 Mark]

Let a spherical block of ice at $-7^{\circ}C$ be exposed to atmospheric air at $30^{\circ}C$ with the gravitational direction as shown in the figure below. What will be the overall direction of air flow in this situation?

(A)

Upward

(B)

Downward

(C)

NO motion

(D)

Sideward

Explanation

GATE→2025→Fluid Mechanics and Thermal Sciences→Fluid Mechanics

Q36

MCQ[1 Mark]

Consider two identical tanks with a bottom hole of diameter $d$. One tank is filled with water and the other tank is filled with engine oil. The height of the fluid column $h$ is same in both the cases. The fluid exit velocity in the two tanks are $V_{1}$ and $V_{2}$. Neglecting all losses, which one of the following options is correct?

(A)

V_{2} > V_{1}

(B)

V_{2} = V_{1}

(C)

V_{2} < V_{1}

(D)

Insufficient data to definitively conclude relationship between V_1 and V_2

Explanation

GATE→2025→Fluid Mechanics and Thermal Sciences→Fluid Mechanics

Q37

MCQ[1 Mark]

In a laboratory experiment using a scaled down model to measure scour at a bridge pier, the Froude number is important. The ratio of the prototype length to the model length is $100$. If the velocity of the model is $1~m~s^{-1}$, the velocity (in $m~s^{-1}$) of the prototype is

(A)

0.1

(B)

1

(C)

10

(D)

100

Explanation

GATE→2025→Fluid Mechanics and Thermal Sciences→Thermodynamics

Q38

MCQ[1 Mark]

Air inside a rigid, thermally-insulated tank undergoes stirring as shown in the figure below. Which one of the following options is correct?

(A)

The enthalpy of the air increases while the entropy of the air remains constant

(B)

Both the enthalpy and the entropy of the air remain constant

(C)

Both the enthalpy and the entropy of the air increase

(D)

The enthalpy of the air decreases while the entropy of the air increases

Explanation

GATE→2025→Fluid Mechanics and Thermal Sciences→Applications (Power Engineering, I.C. Engines, Refrigeration, Turbomachinery)

Q39

MCQ[1 Mark]

In a psychrometric chart, one axis represents dry-bulb temperature. The axis, that is perpendicular to the dry-bulb temperature axis, represents

(A)

wet-bulb temperature

(B)

specific humidity

(C)

relative humidity

(D)

enthalpy

Explanation

GATE→2025→Fluid Mechanics and Thermal Sciences→Applications (Power Engineering, I.C. Engines, Refrigeration, Turbomachinery)

Q40

NAT[1 Mark]

The thermal efficiency of an ideal air-standard Otto cycle is $0.5$. The value of specific heat ratio of air is $1.4$. The compression ratio of the cycle is ____ (rounded off to 1 decimal place).

Explanation

GATE→2025→Fluid Mechanics and Thermal Sciences→Fluid Mechanics

Q41

MSQ[2 Marks]

For a fully-developed pipe flow, which of the following options is/are correct?

(A)

For the same maximum velocity, the average velocity is higher in the turbulent regime than that of the laminar regime

(B)

Compressibility effects are important if Mach number is less than 0.3

(C)

For laminar flow, the friction factor is independent of surface roughness

(D)

For laminar flow, friction factor decreases with decrease in Reynolds number

Explanation

GATE→2025→Fluid Mechanics and Thermal Sciences→Heat Transfer

Q42

NAT[2 Marks]

Consider a cylindrical furnace of $5~m$ diameter and $5~m$ length with bottom, top and curved surfaces maintained at uniform temperatures of $800~K$, $1500~K$ and $500~K$, respectively. The view factor between the bottom and top surfaces, $F_{12}$ is $0.2$. The magnitude of net radiation heat transfer rate between the bottom surface and the curved surface is ____ kW (rounded off to 1 decimal place).\nAll surfaces of the furnace can be assumed as black.\nThe Stefan-Boltzmann constant, $\sigma=5.67\times 10^{-8}~W~m^{-2}K^{-4}$.

Explanation

GATE→2025→Fluid Mechanics and Thermal Sciences→Fluid Mechanics

Q43

NAT[2 Marks]

A pitot tube connected to a U-tube mercury manometer measures the speed of air flowing in the wind tunnel as shown in the figure below. The density of air is $1.23~kg~m^{-3}$ while the density of water is $1000~kg~m^{-3}$. For the manometer reading of $h=30~mm$ of mercury, the speed of air in the wind tunnel is ____ $m~s^{-1}$ (rounded off to 1 decimal place).\nAssume: Specific gravity of mercury $=13.6$, Acceleration due to gravity $=10~m~s^{-2}$

Explanation

GATE→2025→Fluid Mechanics and Thermal Sciences→Fluid Mechanics

Q44

NAT[2 Marks]

Consider a velocity field $\vec{V}=3z\hat{i}+0\hat{j}+Cx\hat{k}$, where $C$ is a constant. If the flow is irrotational, the value of $C$ is ____ (rounded off to 1 decimal place).

Explanation

GATE→2025→Fluid Mechanics and Thermal Sciences→Heat Transfer

Q45

NAT[2 Marks]

Water enters a tube of diameter, $D=60~mm$ with mass flow rate of $0.01~kg~s^{-1}$ as shown in the figure below. The inlet mean temperature is $T_{m,i}=293~K$ and the uniform heat flux at the surface of the tube is $2000~W~m^{-2}$. For the exit mean temperature of $T_{m,o}=353~K$, the length of the tube, $L$ is ____ m (rounded off to 1 decimal place).\nUse the specific heat of water as $4181~J~kg^{-1}K^{-1}$.

Explanation

GATE→2025→Fluid Mechanics and Thermal Sciences→Applications (Power Engineering, I.C. Engines, Refrigeration, Turbomachinery)

Q46

NAT[2 Marks]

A thermal power plant is running with no reheat or regeneration. The specific enthalpy and specific entropy of steam at the turbine inlet are $3344~kJ~kg^{-1}$ and $6.5~kJ~kg^{-1}K^{-1}$ respectively. The turbine isentropic efficiency is $0.9$, and the mass flow rate of steam at the turbine inlet is $102~kg~s^{-1}$. The turbine power output is ____ MW (rounded off to 1 decimal place).

Explanation

GATE→2025→Fluid Mechanics and Thermal Sciences→Applications (Power Engineering, I.C. Engines, Refrigeration, Turbomachinery)

Q47

NAT[2 Marks]

Consider a Pelton wheel of $1~m$ diameter. The magnitude of relative velocity of water at the bucket inlet is same as the magnitude of relative velocity of water at the bucket exit. The absolute speed of water at the bucket inlet is $125.66~m~s^{-1}$. For maximum power output from the Pelton wheel, the rpm of the Pelton wheel is ____ (rounded off to 1 decimal place).

Explanation

GATE→2025→Fluid Mechanics and Thermal Sciences→Thermodynamics

Q48

NAT[2 Marks]

A thermodynamically closed system contains $1~kg$ of hydrogen. The system undergoes a reversible polytropic process with polytropic index $1.3$. The work output during the process is $400~kJ$. During the process, hydrogen behaves as an ideal gas with constant specific heats. The absolute value of heat transfer during the process is ____ kJ (rounded off to 1 decimal place).\nSpecific heat of hydrogen at constant pressure $= 14.56~kJ~kg^{-1}K^{-1}$\nSpecific heat of hydrogen at constant volume $= 10.4~kJ~kg^{-1}K^{-1}$

Explanation

GATE→2025→Fluid Mechanics and Thermal Sciences→Applications (Power Engineering, I.C. Engines, Refrigeration, Turbomachinery)

Q49

NAT[2 Marks]

A heat pump, operating in reversed Carnot cycle, maintains a steady air temperature of $300~K$ inside an auditorium. The heat pump receives heat from the ambient air. The ambient air temperature is $280~K$. Heat loss from the auditorium is $15~kW$. The power consumption of the heat pump is ____ kW (rounded off to 2 decimal places).

Explanation

Materials, Manufacturing and Industrial Engineering

16 Questions

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

Q50

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

Q51

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→Computer Aided Manufacturing and Automation

Q52

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

Q53

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→Metrology and Inspection

Q54

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

Q55

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

Q56

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→Production Planning and Control

Q57

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→Casting, Forming and Joining Processes

Q58

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

Q59

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→Additive Manufacturing

Q60

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

Q61

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

Q62

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

Q63

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

Q64

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

Q65

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