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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→2024→General Aptitude→Verbal Ability

Q1

MCQ[1 Mark]

If '$\rightarrow$' denotes increasing order of intensity, then the meaning of the words [smile $\rightarrow$ giggle $\rightarrow$ laugh] is analogous to [disapprove $\rightarrow$ chide $\rightarrow$ ___]. Which one of the given options is appropriate to fill the blank?

(A)

reprove

(B)

praise

(C)

reprise

(D)

grieve

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q2

MCQ[1 Mark]

Find the odd one out in the set: {19, 37, 21, 17, 23, 29, 31, 11}

(A)

21

(B)

37

(C)

17

(D)

23

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q3

MCQ[1 Mark]

In the following series, identify the number that needs to be changed to form the Fibonacci series. 1, 1, 2, 3, 6, 8, 13, 21, ...

(A)

8

(B)

21

(C)

6

(D)

13

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q4

MCQ[1 Mark]

The real variables $x, y, z$, and the real constants $p, q, r$ satisfy $$\frac{x}{pq-r^{2}}=\frac{y}{qr-p^{2}}=\frac{z}{rp-q^{2}}$$\nGiven that the denominators are non-zero, the value of $px+qy+rz$ is

(A)

0

(B)

p+q+r

(C)

pqr

(D)

p^{2}+q^{2}+r^{2}

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q5

MCQ[1 Mark]

Take two long dice (rectangular parallelepiped), each having four rectangular faces labelled as 2, 3, 5, and 7. If thrown, the long dice cannot land on the square faces and has $1/4$ probability of landing on any of the four rectangular faces. The label on the top face of the dice is the score of the throw. If thrown together, what is the probability of getting the sum of the two long dice scores greater than 11?

(A)

3/8

(B)

1/8

(C)

1/16

(D)

3/16

Explanation

GATE→2024→General Aptitude→Verbal Ability

Q6

MCQ[2 Marks]

In the given text, the blanks are numbered (i)-(iv). Select the best match for all the blanks. \nProf. P **(i)** merely a man who narrated funny stories. **(ii)** in his blackest moments was he able to find humor. Prof. Q **(iii)** a man who hardly narrated funny stories. **(iv)** in his blackest moments he was capable of self-deprecating humor.

(A)

(i) was, (ii) Only

(B)

(i) wasn't, (ii) Even

(C)

(i) was, (ii) Even

(D)

(i) wasn't, (ii) Only

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q7

MCQ[2 Marks]

Sets A, B, C ... [Note: Official Key marked this as MTA (Marks To All)]

(A)

A

(B)

B

(C)

C

(D)

D

Explanation

GATE→2024→General Aptitude→Data Interpretation

Q8

MCQ[2 Marks]

The bar chart gives the batting averages of VK and RS for 11 calendar years from 2012 to 2022. Considering that 2015 and 2019 are world cup years, which one of the following options is true?

(A)

RS has a higher yearly batting average than that of VK in every world cup year.

(B)

VK has a higher yearly batting average than that of RS in every world cup year.

(C)

VK's yearly batting average is consistently higher than that of RS between the two world cup years (2016 to 2018).

(D)

RS's yearly batting average is consistently higher than that of VK in the last three years.

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q9

MCQ[2 Marks]

A planar rectangular paper has two V-shaped pieces attached as shown below. This piece of paper is folded to make the following closed three-dimensional object. The number of folds required to form the above object is

(A)

8

(B)

6

(C)

4

(D)

5

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q10

MCQ[2 Marks]

Four equilateral triangles are used to form a regular closed three-dimensional object by joining along the edges. The angle between any two faces is [Note: Official Key marked this as MTA (Marks To All)]

(A)

30^{\circ}

(B)

60^{\circ}

(C)

45^{\circ}

(D)

90^{\circ}

Explanation

Engineering Mathematics

9 Questions

GATE→2024→Engineering Mathematics→Numerical Methods

Q11

MCQ[1 Mark]

In order to numerically solve the ordinary differential equation $\frac{dy}{dt}=-y$ for $t>0$, with an initial condition $y(0)=1$, the following scheme is employed: $$\frac{y_{n+1}-y_{n}}{\Delta t}=-\frac{1}{2}(y_{n+1}+y_{n})$$\nHere, $\Delta t$ is the time step and $y_{n}=y(n\Delta t)$ for $n=0,1,2,...$ This numerical scheme will yield a solution with non-physical oscillations for $\Delta t>h$. The value of h is

(A)

1/2

(B)

1

(C)

3/2

(D)

2

Explanation

GATE→2024→Engineering Mathematics→Calculus

Q12

MCQ[1 Mark]

The value of the surface integral $$\oint_{S}z~dx~dy$$\nwhere S is the external surface of the sphere $x^{2}+y^{2}+z^{2}=R^{2}$ is

(A)

0

(B)

4\pi R^3

(C)

\frac{4\pi}{3}R^{3}

(D)

\pi R^3

Explanation

GATE→2024→Engineering Mathematics→Complex Variables

Q13

MCQ[1 Mark]

Let $f(z)$ be an analytic function, where $z=x+iy$. If the real part of $f(z)$ is $\cosh x \cos y$, and the imaginary part of $f(z)$ is zero for $y=0$ then $f(z)$ is

(A)

\cosh x \exp(-iy)

(B)

\cosh z \exp z

(C)

\cosh z \cos y

(D)

\cosh z

Explanation

GATE→2024→Engineering Mathematics→Linear Algebra

Q14

MCQ[1 Mark]

Consider the system of linear equations $x+2y+z=5$ $2x+ay+4z=12$ $2x+4y+6z=b$\nThe values of $a$ and $b$ such that there exists a non-trivial null space and the system admits infinite solutions are

(A)

a = 8, b = 14

(B)

a = 4, b = 12

(C)

a = 8, b = 12

(D)

a = 4, b = 14

Explanation

GATE→2024→Engineering Mathematics→Calculus

Q15

MCQ[1 Mark]

Let $f(.)$ be a twice differentiable function from $\mathbb{R}^{2}\rightarrow\mathbb{R}$. If $p,x_{0}\in\mathbb{R}^{2}$ where $||p||$ is sufficiently small, then $$f(x_{0}+p)=f(x_{0})+\nabla f(x_{0})^{T}p+\frac{1}{2}p^{T}\nabla^{2}f(\psi)p$$\nwhere $\psi\in\mathbb{R}^{2}$ is a point on the line segment joining $x_{0}$ and $x_{0}+p$. If $x_{0}$ is a strict local minimum of $f(x)$, then which one of the following statements is TRUE?

(A)

\nabla f(x_{0})^{T}p > 0 \text{ and } p^{T}\nabla^{2}f(\psi)p = 0

(B)

\nabla f(x_{0})^{T}p = 0 \text{ and } p^{T}\nabla^{2}f(\psi)p > 0

(C)

\nabla f(x_{0})^{T}p = 0 \text{ and } p^{T}\nabla^{2}f(\psi)p = 0

(D)

\nabla f(x_{0})^{T}p = 0 \text{ and } p^{T}\nabla^{2}f(\psi)p < 0

Explanation

GATE→2024→Engineering Mathematics→Linear Algebra

Q16

MCQ[2 Marks]

The matrix $$\begin{bmatrix} 1 & a \\ 8 & 3 \end{bmatrix}$$ (where $a>0$) has a negative eigenvalue if $a$ is greater than

(A)

3/8

(B)

1/8

(C)

1/4

(D)

1/5

Explanation

GATE→2024→Engineering Mathematics→Calculus

Q17

NAT[2 Marks]

If the value of the double integral $$\int_{x=3}^{4}\int_{y=1}^{2}\frac{dy~dx}{(x+y)^{2}}$$\nis $\log_{e}(a/24)$, then $a$ is ____ (answer in integer).

Explanation

GATE→2024→Engineering Mathematics→Differential Equations

Q18

NAT[2 Marks]

If $x(t)$ satisfies the differential equation $$t\frac{dx}{dt}+(t-x)=0$$\nsubject to the condition $x(1)=0$ then the value of $x(2)$ is ____ (rounded off to 2 decimal places).

Explanation

GATE→2024→Engineering Mathematics→Probability and Statistics

Q19

NAT[2 Marks]

Let X be a continuous random variable defined on $[0,1]$ such that its probability density function $f(x)=1$ for $0\le x\le 1$ and $0$ otherwise. Let $Y=\log_{e}(X+1)$. Then the expected value of Y is ____ (rounded off to 2 decimal places).

Explanation

Applied Mechanics and Design

15 Questions

GATE→2024→Applied Mechanics and Design→Machine Design

Q20

MCQ[1 Mark]

For a ball bearing, the fatigue life in millions of revolutions is given by $$L=\left(\frac{C}{P}\right)^{n}$$\nwhere $P$ is the constant applied load and $C$ is the basic dynamic load rating. Which one of the following statements is TRUE?

(A)

n = 3 assuming inner racing fixed and outer revolving

(B)

n = 1/3 assuming inner racing fixed and outer revolving

(C)

n = 3 assuming outer racing is fixed

(D)

n = 1/3 assuming outer racing is fixed

Explanation

GATE→2024→Applied Mechanics and Design→Theory of Machines

Q21

MCQ[1 Mark]

The change in kinetic energy $\Delta E$ of an engine is $300~J$, and minimum and maximum shaft speeds are $\omega_{min}=220~rad/s$ and $\omega_{max}=280~rad/s$, respectively. Assume that the torque-time function is purely harmonic. To achieve a coefficient of fluctuation of $0.05$, the moment of inertia (in $kg \cdot m^{2}$) of the flywheel to be mounted on the engine shaft is

(A)

0.15

(B)

0.31

(C)

0.24

(D)

0.053

Explanation

GATE→2024→Applied Mechanics and Design→Engineering Mechanics

Q22

MCQ[1 Mark]

A ram in the form of a rectangular body of size $l=9~m$ and $b=2~m$ is suspended by two parallel ropes of lengths $7~m$. Assume the center-of-mass of the body is at its geometric center and $g=9.81~m/s^{2}$. For striking the object P with a horizontal velocity of $5~m/s$, what is the angle $\theta$ with the vertical from which the ram should be released from rest?

(A)

67.1^{\circ}

(B)

40.2^{\circ}

(C)

35.1^{\circ}

(D)

79.5^{\circ}

Explanation

GATE→2024→Applied Mechanics and Design→Vibrations

Q23

MCQ[1 Mark]

A linear spring-mass-dashpot system with a mass of $2~kg$ is set in motion with viscous damping. If the natural frequency is $15~Hz$, and the amplitudes of two successive cycles measured are $7.75~mm$ and $7.20~mm$, the coefficient of viscous damping (in $N \cdot s/m$) is

(A)

4.41

(B)

7.51

(C)

2.52

(D)

6.11

Explanation

GATE→2024→Applied Mechanics and Design→Machine Design

Q24

MCQ[1 Mark]

Which one of the following failure theories is the most conservative design approach against fatigue failure?

(A)

Soderberg line

(B)

Modified Goodman line

(C)

Gerber line

(D)

Yield line

Explanation

GATE→2024→Applied Mechanics and Design→Engineering Mechanics

Q25

MCQ[1 Mark]

A rigid massless tetrahedron is placed such that vertex O is at the origin and the other three vertices A, B, and C lie on the coordinate axes as shown in the figure. The body is acted on by three point loads, of which one is acting at A along x-axis and another at point B along y-axis. For the body to be in equilibrium, the third point load acting at point O must be

(A)

along z-axis

(B)

in x-y plane but not along x or y axis

(C)

in y-z plane but not along y or z axis

(D)

in z-x plane but not along z or x axis

Explanation

GATE→2024→Applied Mechanics and Design→Engineering Mechanics

Q26

MSQ[2 Marks]

Which of the following beam(s) is/are statically indeterminate?

(A)

A

(B)

B

(C)

C

(D)

D

Explanation

GATE→2024→Applied Mechanics and Design→Theory of Machines

Q27

NAT[2 Marks]

The Levai type-A train illustrated in the figure has gears with module $m=8~mm/tooth$. Gears 2 and 3 have 19 and 24 teeth respectively. Gear 2 is fixed and internal gear 4 rotates at $20~rev/min$ counter-clockwise. The magnitude of angular velocity of the arm is ____ rev/min. (rounded off to 2 decimal places)

Explanation

GATE→2024→Applied Mechanics and Design→Engineering Mechanics

Q28

NAT[2 Marks]

A horizontal beam of length $1200~mm$ is pinned at the left end and is resting on a roller at the other end as shown in the figure. A linearly varying distributed load is applied on the beam. The magnitude of maximum bending moment acting on the beam is ____ N \cdot m (round off to 1 decimal place).

Explanation

GATE→2024→Applied Mechanics and Design→Theory of Machines

Q29

NAT[2 Marks]

At the instant when OP is vertical and AP is horizontal, the link OD is rotating counter clockwise at a constant rate $\omega=7~rad/s$. Pin P on link OD slides in the slot BC of link ABC which is hinged at A, and causes a clockwise rotation of the link ABC. The magnitude of angular velocity of link ABC for this instant is ____ rad/s (rounded off to 2 decimal places).

Explanation

GATE→2024→Applied Mechanics and Design→Vibrations

Q30

NAT[2 Marks]

A vibratory system consists of mass $m$, a vertical spring of stiffness $2k$ and a horizontal spring of stiffness $k$. The end A of the horizontal spring is given a horizontal motion $x_{A}=a \sin \omega t$. The other end of the spring is connected to an inextensible rope that passes over two massless pulleys as shown. Assume $m=10~kg$, $k=1.5~kN/m$ and neglect friction. The magnitude of critical driving frequency for which the oscillations of mass m tend to become excessively large is ____ rad/s (answer in integer).

Explanation

GATE→2024→Applied Mechanics and Design→Machine Design

Q31

NAT[2 Marks]

A solid massless cylindrical member of $50~mm$ diameter is rigidly attached at one end, and is subjected to an axial force $P=100~KN$ and a torque $T=600~N \cdot m$ at the other end as shown. Assume that the axis of the cylinder is normal to the support. Considering distortion energy theory with allowable yield stress as $300~MPa$, the factor of safety in the design is ____ (rounded off to 1 decimal place).

Explanation

GATE→2024→Applied Mechanics and Design→Machine Design

Q32

NAT[2 Marks]

The figure shows a thin cylindrical pressure vessel constructed by welding plates together along a line that makes an angle $\alpha=60^{\circ}$ with the horizontal. The closed vessel has a wall thickness of $10~mm$ and diameter of $2~m$. When subjected to an internal pressure of $200~kPa$, the magnitude of the normal stress acting on the weld is ____ MPa (rounded off to 1 decimal place).

Explanation

GATE→2024→Applied Mechanics and Design→Engineering Mechanics

Q33

NAT[2 Marks]

A three-hinge arch ABC in the form of a semi-circle is shown in the figure. The arch is in static equilibrium under vertical loads $P=100~kN$ and $Q=50~kN$. Neglect friction at all the hinges. The magnitude of the horizontal reaction at B is ____ kN (rounded off to 1 decimal place).

Explanation

GATE→2024→Applied Mechanics and Design→Machine Design

Q34

NAT[2 Marks]

A band brake shown in the figure has a coefficient of friction of $0.3$. The band can take a maximum force of $1.5~kN$. The maximum braking force ($F$) that can be safely applied is ____ N (rounded off to the nearest integer).

Explanation

Fluid Mechanics and Thermal Sciences

15 Questions

GATE→2024→Fluid Mechanics and Thermal Sciences→Fluid Mechanics

Q35

MCQ[1 Mark]

The velocity field of a two-dimensional, incompressible flow is given by $$\vec{V}=2~\sinh x\hat{i}+v(x,y)\hat{j}$$\nwhere $\hat{i}$ and $\hat{j}$ denote the unit vectors in $x$ and $y$ directions, respectively. If $v(x,0)=\cosh x$, then $v(0,-1)$ is

(A)

1

(B)

2

(C)

3

(D)

4

Explanation

GATE→2024→Fluid Mechanics and Thermal Sciences→Heat Transfer

Q36

MCQ[1 Mark]

A plane, solid slab of thickness L, shown in the figure, has thermal conductivity $k$ that varies with the spatial coordinate $x$ as $k=A+Bx$, where $A$ and $B$ are positive constants ($A>0, B>0$). The slab walls are maintained at fixed temperatures of $T(x=0)=0$ and $T(x=L)=T_{0}>0$. The slab has no internal heat sources. Considering one-dimensional heat transfer, which one of the following plots qualitatively depicts the steady-state temperature distribution within the slab?

(A)

A

(B)

B

(C)

C

(D)

D

Explanation

GATE→2024→Fluid Mechanics and Thermal Sciences→Heat Transfer

Q37

MCQ[1 Mark]

Consider incompressible laminar flow over a flat plate with freestream velocity of $u_{\infty}$. The Nusselt number corresponding to this flow velocity is $Nu_{1}$. If the freestream velocity is doubled, the Nusselt number changes to $Nu_{2}$. Choose the correct option for $Nu_{2}/Nu_{1}$.

(A)

\sqrt{2}

(B)

2

(C)

1.26

(D)

1

Explanation

GATE→2024→Fluid Mechanics and Thermal Sciences→Heat Transfer

Q38

MCQ[1 Mark]

Consider a hydrodynamically fully developed laminar flow through a circular pipe with the flow along the axis (i.e., $z$ direction). In the following statements, $T$ is the temperature of the fluid, $T_{w}$ is the wall temperature and $T_{m}$ is the bulk mean temperature of the fluid. Which one of the following statements is TRUE? [Note: Official Key marked this as MTA (Marks To All)]

(A)

For a thermally fully developed flow, \frac{\partial T}{\partial z} = 0 always

(B)

For constant wall temperature of duct, \frac{dT_m}{dz} = constant

(C)

Nusselt number varies linearly along z direction for thermally fully developed flow

(D)

For constant wall temperature (T_w > T_m), \frac{dT_m}{dz} increases exponentially with distance along z

Explanation

GATE→2024→Fluid Mechanics and Thermal Sciences→Thermodynamics

Q39

MCQ[1 Mark]

A furnace can supply heat steadily at $1200~K$ at a rate of $24000~kJ/min$. The maximum amount of power (in kW) that can be produced by using the heat supplied by this furnace in an environment at $300~K$ is

(A)

300

(B)

150

(C)

18000

(D)

0

Explanation

GATE→2024→Fluid Mechanics and Thermal Sciences→Thermodynamics

Q40

MCQ[1 Mark]

Which one of the following statements regarding a Rankine cycle is FALSE?

(A)

Superheating steam in boiler increases cycle efficiency

(B)

Pressure at turbine outlet depends on condenser temperature

(C)

Cycle efficiency increases as condenser pressure decreases

(D)

Cycle efficiency increases as boiler pressure decreases

Explanation

GATE→2024→Fluid Mechanics and Thermal Sciences→Fluid Mechanics

Q41

MCQ[2 Marks]

In the pipe network shown in the figure, all pipes have the same cross-section and can be assumed to have the same friction factor. The pipes connecting points W, N, and S with point J have an equal length L. The pipe connecting points J and E has a length 10L. The pressures at the ends N, E, and S are equal. The flow rate in the pipe connecting W and J is Q. Assume that the fluid flow is steady, incompressible, and the pressure losses at the pipe entrance and junction are negligible. Consider the following statements:\nI: The flow rate in pipe connecting J and E is Q/21.\nII: The pressure difference between J and N is equal to the pressure difference between J and E.\nWhich one of the following options is CORRECT?

(A)

Statement I is True and Statement II is False

(B)

Both I and II are True

(C)

Both I and II are False

(D)

Statement I is False and Statement II is True

Explanation

GATE→2024→Fluid Mechanics and Thermal Sciences→Fluid Mechanics

Q42

MSQ[2 Marks]

Steady, compressible flow of air takes place through an adiabatic converging-diverging nozzle, as shown in the figure. For a particular value of pressure difference across the nozzle, a stationary normal shock wave forms in the diverging section of the nozzle. If E and F denote the flow conditions just upstream and downstream of the normal shock, respectively, which of the following statement(s) is/are TRUE?

(A)

Static pressure at E is lower than static pressure at F

(B)

Density at E is lower than density at F

(C)

Mach number at E is lower than Mach number at F

(D)

Specific entropy at E is lower than specific entropy at F

Explanation

GATE→2024→Fluid Mechanics and Thermal Sciences→Applications (Power Engineering, I.C. Engines, Refrigeration, Turbomachinery)

Q43

NAT[2 Marks]

Consider an air-standard Brayton cycle with adiabatic compressor and turbine, and a regenerator, as shown in the figure. Air enters the compressor at $100~kPa$ and $300~K$ and exits the compressor at $600~kPa$ and $550~K$. The air exits the combustion chamber at $1250~K$ and exits the adiabatic turbine at $100~kPa$ and $800~K$. The exhaust air from the turbine is used to preheat the air in the regenerator. The exhaust air exits the regenerator (state 6) at $600~K$. There is no pressure drop across the regenerator and the combustion chamber. Also, there is no heat loss from the regenerator to the surroundings. The ratio of specific heats at constant pressure and volume is $c_{p}/c_{v}=1.4$. The thermal efficiency of the cycle is ____ % (answer in integer).

Explanation

GATE→2024→Fluid Mechanics and Thermal Sciences→Thermodynamics

Q44

NAT[2 Marks]

A piston-cylinder arrangement shown in the figure has a stop located $2~m$ above the base. The cylinder initially contains air at $140~kPa$ and $350^{\circ}C$ and the piston is resting in equilibrium at a position which is $1~m$ above the stops ($3~m$ total height). The system is now cooled to the ambient temperature of $25^{\circ}C$. Consider air to be an ideal gas with a value of gas constant $R=0.287~kJ/(kg \cdot K)$.\nThe absolute value of specific work done during the process is ____ kJ/kg (rounded off to 1 decimal place).

Explanation

GATE→2024→Fluid Mechanics and Thermal Sciences→Thermodynamics

Q45

NAT[2 Marks]

A heat pump (H.P.) is driven by the work output of a heat engine (H.E.) as shown in the figure. The heat engine extracts $150~kJ$ of heat from the source at $1000~K$. The heat pump absorbs heat from the ambient at $280~K$ and delivers heat to the room which is maintained at $300~K$. Considering the combined system to be ideal, the total amount of heat delivered to the room together by the heat engine and heat pump is ____ kJ (answer in integer).

Explanation

GATE→2024→Fluid Mechanics and Thermal Sciences→Heat Transfer

Q46

NAT[2 Marks]

Consider a slab of $20~mm$ thickness. There is a uniform heat generation of $\dot{q}=100~MW/m^{3}$ inside the slab. The left and right faces of the slab are maintained at $150^{\circ}C$ and $110^{\circ}C$, respectively. The plate has a constant thermal conductivity of $200~W/(m \cdot K)$. Considering a 1-D steady state heat conduction, the location of the maximum temperature from the left face will be at ____ mm (answer in integer).

Explanation

GATE→2024→Fluid Mechanics and Thermal Sciences→Heat Transfer

Q47

NAT[2 Marks]

A condenser is used as a heat exchanger in a large steam power plant in which steam is condensed to liquid water. The condenser is a shell and tube heat exchanger which consists of 1 shell and 20,000 tubes. Water flows through each of the tubes at a rate of $1~kg/s$ with an inlet temperature of $30^{\circ}C$. The steam in the condenser shell condenses at the rate of $430~kg/s$ at a temperature of $50^{\circ}C$. If the heat of vaporization is $2.326~MJ/kg$ and specific heat of water is $4~kJ/(kg \cdot K)$, the effectiveness of the heat exchanger is ____ (rounded off to 3 decimal places).

Explanation

GATE→2024→Fluid Mechanics and Thermal Sciences→Heat Transfer

Q48

NAT[2 Marks]

Consider a hemispherical furnace of diameter $D=6~m$ with a flat base. The dome of the furnace has an emissivity of $0.7$ and the flat base is a blackbody. The base and the dome are maintained at uniform temperature of $300~K$ and $1200~K$, respectively. Under steady state conditions, the rate of radiation heat transfer from the dome to the base is ____ kW (rounded off to 1 decimal place).\nUse Stefan-Boltzmann constant $=5.67\times 10^{-8}~W/(m^{2}K^{4})$

Explanation

GATE→2024→Fluid Mechanics and Thermal Sciences→Fluid Mechanics

Q49

NAT[2 Marks]

A liquid fills a horizontal capillary tube whose one end is dipped in a large pool of the liquid. Experiments show that the distance $L$ travelled by the liquid meniscus in time $t$ is given by $$L=k\gamma^{a}R^{b}\mu^{c}\sqrt{t}$$\nwhere $\gamma$ is the surface tension, $R$ is the inner radius of the capillary, and $\mu$ is the dynamic viscosity of the liquid. If $k$ is a dimensionless constant, then the value of $a$ is ____ (rounded off to 1 decimal place).

Explanation

Materials, Manufacturing and Industrial Engineering

16 Questions

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

Q50

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

Q51

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→Machining and Machine Tool Operations

Q52

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→Casting, Forming and Joining Processes

Q53

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

Q54

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→Computer Aided Manufacturing and Automation

Q55

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

Q56

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→Operations Research

Q57

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→Production Planning and Control

Q58

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

Q59

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→Machining and Machine Tool Operations

Q60

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→Casting, Forming and Joining Processes

Q61

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

Q62

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

Q63

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

Q64

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

Q65

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