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GATE Mechanical 2021 Set 1 | Question: 36
A true centrifugal casting operation needs to be performed horizontally to make copper tube sections with outer diameter of $\text{250 mm}$ and inner diameter of $\text{230 mm}$ ... the tube, the rotational speed required is _________ $\text{rpm}$ ($\textit{round off to the nearest integer}$).
A true centrifugal casting operation needs to be performed horizontally to make copper tube sections with outer diameter of $\text{250 mm}$ and inner diameter of $\text{2...
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Feb 22, 2021
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GATE Mechanical 2021 Set 1 | Question: 10
Consider the surface roughness profile as shown in the figure The center line average roughness ($R_{a}$, in $\mu m$) of the measured length $\text{(L)}$ is $0$ $1$ $2$ $4$
Consider the surface roughness profile as shown in the figureThe center line average roughness ($R_{a}$, in $\mu m$) of the measured length $\text{(L)}$ is$0$$1$$2$$4$
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Feb 22, 2021
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GATE Mechanical 2021 Set 1 | Question: 53
A short shoe drum (radius $\text{260 mm}$) brake is shown in the figure. A force of $\text{1 kN}$ is applied to the lever. The coefficient of friction is $0.4$. The magnitude of the torque applied by the brake is ____________________ $\text{N.m}(\textit{round off to one decimal place}$).
A short shoe drum (radius $\text{260 mm}$) brake is shown in the figure. A force of $\text{1 kN}$ is applied to the lever. The coefficient of friction is $0.4$.The magnit...
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Feb 22, 2021
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GATE Mechanical 2021 Set 1 | Question: 25
Consider a single degree of freedom system comprising a mass $\text{M}$, supported on a spring and a dashpot as shown in the figure. If the amplitude of the free vibration response reduces from $\text{8 mm}$ to $\text{1.5 mm}$ in $3$ cycles, the damping ratio of the system is ______________ ($\textit{round off to three decimal places}$).
Consider a single degree of freedom system comprising a mass $\text{M}$, supported on a spring and a dashpot as shown in the figure.If the amplitude of the free vibration...
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Feb 22, 2021
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GATE Mechanical 2021 Set 1 | Question: 51
An overhanging beam $\text{PQR}$ is subjected to uniformly distributed load $\text{20 kN/m}$ as shown in the figure. The maximum bending stree developed in the beam is ___________________ $\text{MPa} (\textit{round off to one decimal place}$).
An overhanging beam $\text{PQR}$ is subjected to uniformly distributed load $\text{20 kN/m}$ as shown in the figure.The maximum bending stree developed in the beam is ___...
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GATE Mechanical 2021 Set 1 | Question: 22
Consider fully developed, steady state incompressible laminar flow of a viscous fluid between two large parallel horizontal plates. The bottom plate is fixed and the top plate moves with a constant velocity of $\text{U= 4 m/s}$. Separation between the ... average shear stress in the fluid is _____ $\text{Pa}$ ($\textit{round off to the nearest integer}$).
Consider fully developed, steady state incompressible laminar flow of a viscous fluid between two large parallel horizontal plates. The bottom plate is fixed and the top ...
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GATE Mechanical 2021 Set 1 | Question: 18
A prismatic bar $\text{PQRST}$ is subjected to axial loads as shown in the figure. The segments having maximum and minimum axial stresses, respectively, are $\text{QR}$ and $\text{PQ}$ $\text{ST}$ and $\text{PQ}$ $\text{QR}$ and $\text{RS}$ $\text{ST}$ and $\text{RS}$
A prismatic bar $\text{PQRST}$ is subjected to axial loads as shown in the figure. The segments having maximum and minimum axial stresses, respectively, are$\text{QR}$ an...
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GATE Mechanical 2021 Set 1 | Question: 6
The loading and unloading response of a metal is shown in the figure. The elastic and plastic strains corresponding to $\text{200 MPa}$, respectively, are $0.01$ and $0.01$ $0.02$ and $0.01$ $0.01$ and $0.02$ $0.02$ and $0.02$
The loading and unloading response of a metal is shown in the figure. The elastic and plastic strains corresponding to $\text{200 MPa}$, respectively, are$0.01$ and $0.01...
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GATE Mechanical 2021 Set 1 | Question: 26
Consider a vector $\text{p}$ in $2$-dimensional space. Let its direction (counter-clockwise angle with the positive $\text{x}$-axis) be $\theta$. Let $\text{p}$ be an eigenvector of a $2\times2$ matrix $\text{A}$ ... ${p}'=\theta ,\left \| {p}' \right \|= \left \| p \right \|/\lambda$
Consider a vector $\text{p}$ in $2$-dimensional space. Let its direction (counter-clockwise angle with the positive $\text{x}$-axis) be $\theta$. Let $\text{p}$ be an ei...
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Linear Algebra
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linear-algebra
eigen-values
eigen-vectors
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GATE Mechanical 2021 Set 1 | Question: 40
A $\text{200 mm}$ wide plate having a thickness of $\text{20 mm}$ is fed through a rolling mill with two rolls. The radius of each roll is $\text{300 mm}$. The plate thickness is to be reduced to $\text{18 mm}$ in one pass ... to permit the rolling operation then the roll force will be _________ $\text{kN}$ ($\textit{round off to the nearest integer}$).
A $\text{200 mm}$ wide plate having a thickness of $\text{20 mm}$ is fed through a rolling mill with two rolls. The radius of each roll is $\text{300 mm}$. The plate thic...
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GATE Mechanical 2021 Set 1 | Question: 32
A tappet valve mechanism in an $\text{IC}$ engine comprises a rocker arm $\text{ABC}$ that is hinged at $\text{B}$ as shown in the figure. The rocker is assumed rigid and it oscillates about the hinge $\text{B}$. The mass moment of inertia of ... at a speed of ____________ $\text{rpm} (\textit{round off to the nearest integer}$). $496$ $4739$ $790$ $2369$
A tappet valve mechanism in an $\text{IC}$ engine comprises a rocker arm $\text{ABC}$ that is hinged at $\text{B}$ as shown in the figure. The rocker is assumed rigid and...
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GATE Mechanical 2021 Set 1 | Question: 23
A rigid insulated tank is initially evacuated. It is connected through a valve to a supply line that carries air at a constant pressure and temperature of $\text{250 kPa}$ and $\text{400 K}$ respectively. Now the valve is opened and air is ... Final temperature of the air inside the tank is _______ $\text{K}$ ($\textit{round off to one decimal place}$).
A rigid insulated tank is initially evacuated. It is connected through a valve to a supply line that carries air at a constant pressure and temperature of $\text{250 kPa}...
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GATE Mechanical 2021 Set 1 | Question: 1
If $y(x)$ satisfies the differential equation $(\sin x) \dfrac{\mathrm{d}y }{\mathrm{d} x} + y \cos x = 1,$ subject to the condition $y(\pi/2) = \pi/2,$ then $y(\pi/6)$ is $0$ $\frac{\pi}{6}$ $\frac{\pi}{3}$ $\frac{\pi}{2}$
If $y(x)$ satisfies the differential equation $(\sin x) \dfrac{\mathrm{d}y }{\mathrm{d} x} + y \cos x = 1,$subject to the condition $y(\pi/2) = \pi/2,$ then $y(\pi/6)$ is...
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Feb 22, 2021
Differential Equations
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GATE Mechanical 2021 Set 1 | Question: 14
An infinitely long pin fin, attached to an isothermal hot surface, transfers heat at a steady rate $\dot{Q}_{1}$ to the ambient air. If the thermal conductivity of the fin material is doubled, while keeping everything else constant, the rate of steady-state heat transfer from the fin ... $\sqrt{2}$ $2$ $\frac{1}{\sqrt{2}}$ $\frac{1}{2}$
An infinitely long pin fin, attached to an isothermal hot surface, transfers heat at a steady rate $\dot{Q}_{1}$ to the ambient air. If the thermal conductivity of the fi...
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GATE Mechanical 2021 Set 1 | Question: 35
Activities $\text{A, B, C}$ and $\text{D}$ form the critical path for a project with a $\text{PERT}$ network. The means and variances of the activity duration for each activity are given below. All activity durations follow the Gaussian (normal) ... $\text{Note}$: Probability is a number between $0$ and $1$).
Activities $\text{A, B, C}$ and $\text{D}$ form the critical path for a project with a $\text{PERT}$ network. The means and variances of the activity duration for each ac...
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GATE Mechanical 2021 Set 1 | Question: 21
A pressure measurement device fitted on the surface of a submarine, located at a depth $\text{H}$ below the surface of an ocean, reads an absolute pressure of $\text{4.2 MPa}$. The density of sea water is $\text{1050 kg/m$^{3}$ ... $}$ The depth $\text{H}$ is _____________ $\text{m}$ ($\textit{round off to the nearest integer}$).
A pressure measurement device fitted on the surface of a submarine, located at a depth $\text{H}$ below the surface of an ocean, reads an absolute pressure of $\text{4.2 ...
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GATE Mechanical 2021 Set 1 | Question: 41
The $\text{XY}$ table of a $\text{NC}$ machine tool is to move from $P(1,1)$ to $Q(51,1)$; all coordinates are in $\text{mm}$. The pitch of the $\text{NC}$ drive leadscrew is $\text{1 mm}$. If the backlash between the leadscrew and the ... of the table on moving from $\text{P}$ to $\text{Q}$ is ______ $\text{mm}$ ($\textit{round off to two decimal places}$)
The $\text{XY}$ table of a $\text{NC}$ machine tool is to move from $P(1,1)$ to $Q(51,1)$; all coordinates are in $\text{mm}$. The pitch of the $\text{NC}$ drive leadscre...
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GATE Mechanical 2021 Set 1 | Question: 27
Let $\text{C}$ represent the unit circle centered at origin in the complex plane, and complex variable, $z=x+iy$. The value of the contour integral $\oint _{C}\dfrac{\cosh \:3z}{2z}\:dz$ (where integration is taken counter clockwise) is $0$ $2$ $\pi i$ $2 \pi i$
Let $\text{C}$ represent the unit circle centered at origin in the complex plane, and complex variable, $z=x+iy$. The value of the contour integral $\oint _{C}\dfrac{\cos...
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Feb 22, 2021
Calculus
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calculus
complex-variables
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GATE Mechanical 2021 Set 1 | Question: 13
A hot steel spherical ball is suddenly dipped into a low temperature oil bath. Which of the following dimensionless parameters are required to determine instantaneous center temperature of the ball using a Heisler chart? Biot number and Fourier number Reynolds number and Prandtl number Biot number and Froude number Nusselt number and Grashoff number
A hot steel spherical ball is suddenly dipped into a low temperature oil bath.Which of the following dimensionless parameters are required to determine instantaneous cent...
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GATE Mechanical 2021 Set 1 | Question: 4
The ordinary differential equation $\dfrac{dy}{dt}=-\pi y$ subject to an initial condition $y\left ( 0 \right )=1$ ... ___________________. $0< h< \frac{2}{\pi }$ $0< h< 1$ $0< h< \frac{\pi }{2}$ for all $h> 0$
The ordinary differential equation $\dfrac{dy}{dt}=-\pi y$ subject to an initial condition $y\left ( 0 \right )=1$ is solved numerically using the following scheme:$$\fra...
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Differential Equations
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GATE Mechanical 2021 Set 1 | Question: 33
Customers arrive at a shop according to the Poisson distribution with a mean of $10$ customers/hour. The manager notes that no customer arrives tor the first $3$ minutes after the shop opens. The probability that a customer arrives within the next $3$ minutes is $0.39$ $0.86$ $0.50$ $0.61$
Customers arrive at a shop according to the Poisson distribution with a mean of $10$ customers/hour. The manager notes that no customer arrives tor the first $3$ minutes ...
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Feb 22, 2021
Probability and Statistics
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probability
poisson-distribution
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GATE Mechanical 2021 Set 1 | Question: 11
In which of the following pairs of cycles, both cycles have at least one isothermal process? Diesel cycle and Otto cycle Carnot cycle and Stirling cycle Brayton cycle and Rankine cycle Bell-Coleman cycle and Vapour compression refrigeration cycle
In which of the following pairs of cycles, both cycles have at least one isothermal process?Diesel cycle and Otto cycleCarnot cycle and Stirling cycleBrayton cycle and Ra...
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GATE Mechanical 2021 Set 1 | Question: 28
A set of jobs $\text{A, B, C, D, E, F, G, H}$ arrive at time $t= 0$ for processing on turning and grinding machines. Each job needs to be processed in sequence first on the turning machine and second on the grinding machine, and the grinding must occur immediately after turning. The ... $\text{G-E-D-F-H-C-A-B}$ $\text{B-G-C-H-F-D-E-A}$
A set of jobs $\text{A, B, C, D, E, F, G, H}$ arrive at time $t= 0$ for processing on turning and grinding machines. Each job needs to be processed in sequence first on ...
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GATE Mechanical 2021 Set 1 | Question: 34
Let $f\left ( x \right )=x^{2}-2x+2$ be a continuous function defined on $x \in \left [ 1,3 \right ]$. The point $x$ at which the tangent of $f\left ( x \right )$ becomes parallel to the straight line joining $f\left ( 1 \right )$ and $f\left ( 3 \right )$ is $0$ $1$ $2$ $3$
Let $f\left ( x \right )=x^{2}-2x+2$ be a continuous function defined on $x \in \left [ 1,3 \right ]$. The point $x$ at which the tangent of $f\left ( x \right )$ becomes...
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Feb 22, 2021
Calculus
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GATE Mechanical 2021 Set 1 | Question: 39
In a grinding operation of a metal, specific energy consumption is $15 \text{ J/mm}^{3}$. If a grinding wheel with a diameter of $\text{200 mm}$ is rotating at $\text{3000 rpm}$ to obtain a material removal rate of $6000\text{ mm$^{3}$/min}$, then the tangential force on the wheel is _______ $\text{N}$ ($\textit{round off to two decimal places}$).
In a grinding operation of a metal, specific energy consumption is $15 \text{ J/mm}^{3}$. If a grinding wheel with a diameter of $\text{200 mm}$ is rotating at $\text{300...
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GATE Mechanical 2021 Set 1 | Question: 31
A right solid circular cone standing on its base on a horizontal surface is of height $\text{H}$ and base radius $\text{R}$. The cone is made of a material with specific weight $\text{w}$ and elastic modulus $\text{E}$. The vertical deflection at the mid-height ... $\frac{\text{wH}^{2}}{6E}$ $\frac{\text{wRH}}{8E}$ $\frac{\text{wRH}}{6E}$
A right solid circular cone standing on its base on a horizontal surface is of height $\text{H}$ and base radius $\text{R}$. The cone is made of a mater...
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GATE Mechanical 2021 Set 1 | Question: 37
The resistance spot welding of two $\text{1.55 mm}$ thick metal sheets is performed using welding current of $\text{10000 A}$ for $\text{0.25 s}$. The contact resistance at the interface of the metal sheets is $0.0001\; \Omega$ . The ... $\%$ ($\textit{round off to one decimal place}$).
The resistance spot welding of two $\text{1.55 mm}$ thick metal sheets is performed using welding current of $\text{10000 A}$ for $\text{0.25 s}$. The contact resistance ...
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GATE Mechanical 2021 Set 1 | Question: 16
Consider a reciprocating engine with crank radius $\text{R}$ and connecting rod of length $\text{L}$ ... $\frac{L}{2}$ rotating at twice the engine speed
Consider a reciprocating engine with crank radius $\text{R}$ and connecting rod of length $\text{L}$. The secondary unbalance force for this case is equivalent to primary...
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GATE Mechanical 2021 Set 1 | Question: 12
Superheated steam at $\text{1500 kPa}$, has a specific volume of $2.75$ $\text{m$^{3}$/kmol}$ and compressibility factor $\text{(Z)}$ of $0.95$. The temperature of steam is _______________ $^{\circ}C$ ($\textit{rounded off to the nearest integer}$). $522$ $471$ $249$ $198$
Superheated steam at $\text{1500 kPa}$, has a specific volume of $2.75$ $\text{m$^{3}$/kmol}$ and compressibility factor $\text{(Z)}$ of $0.95$. The temperature of steam ...
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GATE Mechanical 2021 Set 1 | Question: 45
Consider a steam power plant operating on an ideal reheat Rankine cycle. The work input to the pump is $\text{20 kJ/kg}$. The work output from the high pressure turbine is $\text{750 kJ/kg}$. The work output from the low pressure turbine is ... of steam at the exit of the low pressure turbine is ______ $\%$ ($\textit{round off to the nearest integer}$).
Consider a steam power plant operating on an ideal reheat Rankine cycle. The work input to the pump is $\text{20 kJ/kg}$. The work output from the high pressure turbine i...
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GATE Mechanical 2021 Set 1 | Question: 17
A cantilever beam of length, $\text{L}$, and flexural rigidity, $\text{EI}$, is subjected to an end moment, $\text{M}$, as shown in the figure. The deflection of the beam at $x=\frac{L}{2}$ is $\frac{ML^{2}}{2EI}$ $\frac{ML^{2}}{4EI}$ $\frac{ML^{2}}{8EI}$ $\frac{ML^{2}}{16EI}$
A cantilever beam of length, $\text{L}$, and flexural rigidity, $\text{EI}$, is subjected to an end moment, $\text{M}$, as shown in the figure. The deflection of the beam...
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GATE Mechanical 2021 Set 1 | Question: 15
The relative humidity of ambient air at $\text{300 K}$ is $50\%$ with a partial pressure of water vapour equal to $p_{v}$. The saturation pressure of water at $\text{300 K}$ is $p_{sat}$. The correct relation for the air-water mixture is $p_{v}=0.5\:p_{sat}$ $p_{v}=p_{sat}$ $p_{v}=0.622\:p_{sat}$ $p_{v}=2\:p_{sat}$
The relative humidity of ambient air at $\text{300 K}$ is $50\%$ with a partial pressure of water vapour equal to $p_{v}$. The saturation pressure of...
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GATE Mechanical 2021 Set 1 | Question: 44
A solid sphere of radius $\text{10 mm}$ is placed at the centroid of a hollow cubical enclosure of side length $\text{30 mm}$. The outer surface of the sphere is denoted by $1$ and the inner surface of the cube is denoted by $2$. The view factor $F_{22}$ for radiation heat transfer is ______ ($\textit{rounded off to two decimal places}$).
A solid sphere of radius $\text{10 mm}$ is placed at the centroid of a hollow cubical enclosure of side length $\text{30 mm}$. The outer surface of the sphere is denoted ...
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GATE Mechanical 2021 Set 1 | Question: 42
Consider a single machine workstation to which jobs arrive according to a Poisson distribution with a mean arrival rate of $12$ jobs/hour. The process time of the workstation is exponentially distributed with a mean of $4$ minutes. The expected ... at the workstation at any given point of time is _______ ($\textit{round off to the nearest integer}$).
Consider a single machine workstation to which jobs arrive according to a Poisson distribution with a mean arrival rate of $12$ jobs/hour. The process time of the worksta...
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GATE Mechanical 2021 Set 1 | Question: 47
A cylindrical jet of water (density = $1000 \text{ kg/m}^{3}$ ... jet, then the velocity of the incoming jet is ___________________ $\text{m/s} (\textit{round off to one decimal place}$).
A cylindrical jet of water (density = $1000 \text{ kg/m}^{3}$) impinges at the center of a flat, circular plate and spreads radially outwards, as shown in the figure. The...
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GATE Mechanical 2021 Set 1 | Question: 48
A single jet Pelton wheel operates at $\text{300 rpm}$. The mean diameter of the wheel is $\text{2 m}$. Operating head and dimensions of jet are such that water comes out of the jet with a velocity of $\text{40 m/s}$ and flow rate ... all losses, the power developed by the Pelton wheel is _______ $\text{MW}$ ($\textit{round off to two decimal places}$).
A single jet Pelton wheel operates at $\text{300 rpm}$. The mean diameter of the wheel is $\text{2 m}$. Operating head and dimensions of jet are such that water comes out...
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GATE Mechanical 2021 Set 1 | Question: 46
In the vicinity of the triple point, the equation of liquid-vapour boundary in the $\text{P-T}$ phase diagram for ammonia is $ \ln p=24.38-3063/T$, where $\text{P}$ is pressure (in $\text{Pa}$) and $\text{T}$ is temperature (in ... $\text{K}$ ($\textit{round off to one decimal place}$).
In the vicinity of the triple point, the equation of liquid-vapour boundary in the $\text{P-T}$ phase diagram for ammonia is $ \ln p=24.38-3063/T$, where $\text{P}$ is pr...
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GATE Mechanical 2021 Set 1 | Question: 29
The fundamental thermodynamic relation for a rubber band is given by $dU=TdS+\tau dL$, where $\text{T}$ is the absolute temperature, $\text{S}$ is the entropy, $\tau$ is the tension in the rubber band, and $\text{L}$ is the length of the rubber band. ... $T=\left ( \frac{\partial U}{\partial S} \right )_{\tau}$
The fundamental thermodynamic relation for a rubber band is given by $dU=TdS+\tau dL$, where $\text{T}$ is the absolute temperature, $\text{S}$ is the entropy, $\tau$ is ...
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GATE Mechanical 2021 Set 1 | Question: 38
An orthogonal cutting operation is performed using a single point cutting tool with a rake angle of $12^{\circ}$ on a lathe. During turning, the cutting force and the friction force are $\text{1000 N}$ and $\text{600 N}$, respectively. If the ... $\text{N}$ ($\textit{round off to two decimal places}$).
An orthogonal cutting operation is performed using a single point cutting tool with a rake angle of $12^{\circ}$ on a lathe. During turning, the cutting force and the fri...
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GATE Mechanical 2019 Set 1 | GA Question: 6
Under a certain legal system, prisoners are allowed to make one statement. If their statements turns out to be true then they are hanged. If the statements turns to be false then they are shot. One prisoner made a statement and the judge ... could be that statement? I did not commit the crime I committed the crime I will be shot You committed the crime
Under a certain legal system, prisoners are allowed to make one statement. If their statements turns out to be true then they are hanged. If the statements turns to be fa...
Arjun
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Arjun
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Feb 9, 2019
Verbal Aptitude
gateme-2019-set1
verbal-aptitude
verbal-reasoning
passage-reading
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