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GATE Mechanical 2021 Set 1 | GA Question: 10
Five persons $\text{P, Q, R, S and T}$ are sitting in a row not necessarily in the same order. $Q$ and $R$ are separated by one person, and $S$ should not be seated adjacent to $Q.$ The number of distinct seating arrangements possible is: $4$ $8$ $10$ $16$
answer selected
in
Quantitative Aptitude
Apr 14, 2021
gateme-2021-set1
numerical-ability
permutation-and-combination
seating-arrangements
1
answer
GATE Mechanical 2020 Set 2 | GA Question: 9
An engineer measures THREE quantities, $X, Y$ and $Z$ in an experiment. She finds that they follow a relationship that is represented in the figure below$: ($the product of $X$ and $Y$ linearly varies with $Z)$ Then, which of the following statements is ... fixed $Y$; $X$ is proportional to $Z$ For fixed $X$; $Z$ is proportional to $Y$ $XY/Z$ is constant
answer selected
in
Quantitative Aptitude
Apr 5, 2021
gateme-2020-set2
numerical-ability
ratio-proportion
1
answer
GATE Mechanical 2021 Set 1 | GA Question: 1
Consider the following sentences: After his surgery, Raja hardly could walk. After his surgery, Raja could barely walk. After his surgery, Raja barely could walk. After his surgery, Raja could hardly walk. Which of the above sentences are grammatically $\text{CORRECT}$ ... $\text{(i) and (iii)}$ $\text{(iii) and (iv)}$ $\text{(ii) and (iv)}$
asked
in
Verbal Aptitude
Feb 22, 2021
gateme-2021-set1
verbal-ability
english-grammar
1
answer
GATE Mechanical 2021 Set 1 | GA Question: 2
Ms. $X$ came out of a building through its front door to find her shadow due to the morning sun failing to her right side with the building to her back. From this, it can be inferred that building is facing _________ North East West South
asked
in
Analytical Aptitude
Feb 22, 2021
gateme-2021-set1
analytical-aptitude
direction-sense
1
answer
GATE Mechanical 2021 Set 1 | GA Question: 3
In the above figure, $\textsf{O}$ is the center of the circle and, $\textsf{M}$ and $\textsf{N}$ lie on the circle. The area of the right triangle $\textsf{MON}$ is $50\;\text{cm}^{2}$. What is the area of the circle in $\text{cm}^{2}?$ $2\pi$ $50\pi$ $75\pi$ $100\pi$
asked
in
Quantitative Aptitude
Feb 22, 2021
gateme-2021-set1
numerical-ability
geometry
triangles
circle
area
1
answer
GATE Mechanical 2021 Set 1 | GA Question: 4
If $\left\{\begin{matrix} “ \oplus” \; \text{means}\; “-” \\ “ \otimes” \; \text{means}\; “\div” \\ “ \triangle” \; \text{means}\; “+” \\ “ \triangledown” \; \text{means}\; “\times” \end{matrix}\right.$ then, the value of the expression $\triangle 2 \oplus 3 \triangle \left((4 \otimes 2) \triangledown 4) \right) = $ $-1$ $-0.5$ $6$ $7$
asked
in
Analytical Aptitude
Feb 22, 2021
gateme-2021-set1
analytical-aptitude
logical-reasoning
1
answer
GATE Mechanical 2021 Set 1 | GA Question: 5
The increased consumption of leafy vegetables in the recent months is a clear indication that the people in the state have begun to lead a healthy lifestyle Which of the following can be logically inferred from the information ... leafy vegetables The people in the state have increased awareness of healthy hazards causing by consumption of junk foods
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in
Verbal Aptitude
Feb 22, 2021
gateme-2021-set1
verbal-ability
verbal-reasoning
statements-follow
1
answer
GATE Mechanical 2021 Set 1 | GA Question: 6
Oxpeckers and rhinos manifest a symbiotic relationship in the wild. The oxpeckers warn the rhinos about approaching poachers, thus possibly saving the lives of the rhinos. Oxpeckers also feed on the parasitic ticks found on rhinos. In the ... source, rhinos may be saved from the poachers Oxpeckers save the lives of poachers, rhinos save their own lives
asked
in
Verbal Aptitude
Feb 22, 2021
gateme-2021-set1
verbal-ability
easy
verbal-reasoning
passage-reading
1
answer
GATE Mechanical 2021 Set 1 | GA Question: 7
A jigsaw puzzle has $2$ pieces. One of the pieces is shown above. Which one of the given options for the missing piece when assembled will form a rectangle? The piece can be moved, rotated or flipped to assemble with the above piece.
asked
in
Spatial Aptitude
Feb 22, 2021
gateme-2021-set1
spatial-aptitude
assembling-pieces
1
answer
GATE Mechanical 2021 Set 1 | GA Question: 8
The number of hens, ducks and goats in farm $P$ are $65,91$ and $169,$ respectively. The total number of hens, ducks and goats in a nearby farm $Q$ is $416.$ The ratio of hens : ducks : goats in farm $Q$ is $5:14:13.$ All the hens, ducks and goats ... $P$ is ________ $5:7:13$ $5:14:13$ $10:21:26$ $21:10:26$
asked
in
Quantitative Aptitude
Feb 22, 2021
gateme-2021-set1
numerical-ability
ratio-proportion
1
answer
GATE Mechanical 2021 Set 1 | GA Question: 9
... number of management degree holders among the executives in companies $\textsf{C2}$ and $\textsf{C5}$ together is ________. $225$ $600$ $1900$ $2500$
asked
in
Quantitative Aptitude
Feb 22, 2021
gateme-2021-set1
numerical-ability
data-interpretation
pie-chart
0
answers
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 $0$ $\frac{\pi}{6}$ $\frac{\pi}{3}$ $\frac{\pi}{2}$
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in
Differential Equations
Feb 22, 2021
gateme-2021-set1
differential-equations
0
answers
GATE Mechanical 2021 Set 1 | Question: 2
The value of $\displaystyle{} \lim_{x \rightarrow 0} \left( \frac{1 – \cos x}{x^{2}}\right)$ is $\frac{1}{4}$ $\frac{1}{3}$ $\frac{1}{2}$ $1$
asked
in
Calculus
Feb 22, 2021
gateme-2021-set1
calculus
limits
0
answers
GATE Mechanical 2021 Set 1 | Question: 3
The Dirac-delta function $\left ( \delta \left ( t-t_{0} \right ) \right )$ for $\text{t}$, $t_{0} \in \mathbb{R}$ ... $0$ $\infty$ $e^{sa}$ $e^{-sa}$
asked
in
Differential Equations
Feb 22, 2021
gateme-2021-set1
differential-equations
laplace-transforms
0
answers
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 $h> 0$
asked
in
Differential Equations
Feb 22, 2021
gateme-2021-set1
differential-equations
0
answers
GATE Mechanical 2021 Set 1 | Question: 5
Consider a binomial random variable $\text{X}$. If $X_{1},X_{2},\dots ,X_{n}$ are independent and identically distributed samples from the distribution of $\text{X}$ with sum $Y=\sum_{i=1}^{n}X_{i}$, then the distribution of $\text{Y}$ as $n\rightarrow \infty$ can be approximated as Exponential Bernoulli Binomial Normal
asked
in
Probability and Statistics
Feb 22, 2021
gateme-2021-set1
probability-and-statistics
probability
random-variables
normal-distribution
0
answers
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 $0.02$
asked
in
Others
Feb 22, 2021
gateme-2021-set1
0
answers
GATE Mechanical 2021 Set 1 | Question: 7
In a machining operation, if a cutting tool traces the workpiece such that the directrix is perpendicular to the plane of the generatrix as shown in figure, the surface generated is plane cylindrical spherical a surface of revolution
asked
in
Others
Feb 22, 2021
gateme-2021-set1
0
answers
GATE Mechanical 2021 Set 1 | Question: 8
The correct sequence of machining operations to be performed to finish a large diameter through hole is drilling, boring, reaming boring, drilling, reaming drilling, reaming, boring boring, reaming, drilling
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in
Others
Feb 22, 2021
gateme-2021-set1
0
answers
GATE Mechanical 2021 Set 1 | Question: 9
In modern $\text{CNC}$ machine tools, the backlash has been eliminated by preloaded ballscrews rack and pinion ratchet and pinion slider crank mechanism
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in
Others
Feb 22, 2021
gateme-2021-set1
0
answers
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 $0$ $1$ $2$ $4$
asked
in
Others
Feb 22, 2021
gateme-2021-set1
0
answers
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
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in
Others
Feb 22, 2021
gateme-2021-set1
0
answers
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 _______________ $^{\circ}C$ ($\textit{rounded off to the nearest integer}$). $522$ $471$ $249$ $198$
asked
in
Others
Feb 22, 2021
gateme-2021-set1
0
answers
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
asked
in
Others
Feb 22, 2021
gateme-2021-set1
0
answers
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 ... $\sqrt{2}$ $2$ $\frac{1}{\sqrt{2}}$ $\frac{1}{2}$
asked
in
Others
Feb 22, 2021
gateme-2021-set1
0
answers
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 $p_{v}=0.5\:p_{sat}$ $p_{v}=p_{sat}$ $p_{v}=0.622\:p_{sat}$ $p_{v}=2\:p_{sat}$
asked
in
Others
Feb 22, 2021
gateme-2021-set1
0
answers
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
asked
in
Others
Feb 22, 2021
gateme-2021-set1
0
answers
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 $\frac{ML^{2}}{2EI}$ $\frac{ML^{2}}{4EI}$ $\frac{ML^{2}}{8EI}$ $\frac{ML^{2}}{16EI}$
asked
in
Others
Feb 22, 2021
gateme-2021-set1
0
answers
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 $\text{RS}$
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in
Others
Feb 22, 2021
gateme-2021-set1
0
answers
GATE Mechanical 2021 Set 1 | Question: 19
Shear stress distribution on the cross-section of the coil wire in a helical compression spring is shown in the figure. This shear stress distribution represents direct shear stress in the coil wire cross-section torsional shear stress ... and torsional shear stress along with the effect of stress concentration at inside edge of the coil wire cross-section
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in
Others
Feb 22, 2021
gateme-2021-set1
0
answers
GATE Mechanical 2021 Set 1 | Question: 20
Robot $\text{Ltd}$ ... fulfillment probability for the lead time period is _____________ units ($\textit{round off to two decimal places}$).
asked
in
Others
Feb 22, 2021
gateme-2021-set1
numerical-answers
0
answers
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 _____________ $\text{m}$ ($\textit{round off to the nearest integer}$).
asked
in
Others
Feb 22, 2021
gateme-2021-set1
numerical-answers
0
answers
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 _____ $\text{Pa}$ ($\textit{round off to the nearest integer}$).
asked
in
Others
Feb 22, 2021
gateme-2021-set1
numerical-answers
0
answers
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 _______ $\text{K}$ ($\textit{round off to one decimal place}$).
asked
in
Others
Feb 22, 2021
gateme-2021-set1
numerical-answers
0
answers
GATE Mechanical 2021 Set 1 | Question: 24
The figure shows an arrangement of a heavy propeller shaft in a ship. The combined polar mass moment of inertia of the propeller and the shaft is $\text{100 kg.m}^{2}$. The propeller rotates at $\omega =12$ $\text{rad/s}$. The ... moment generated on the shaft due to the motion described is ________ $\text{N.m}(\textit{round off to the nearest integer}$).
asked
in
Others
Feb 22, 2021
gateme-2021-set1
numerical-answers
0
answers
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 ______________ ($\textit{round off to three decimal places}$).
asked
in
Others
Feb 22, 2021
gateme-2021-set1
numerical-answers
0
answers
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 $\text{A}$ ... ${p}'=\theta ,\left \| {p}' \right \|= \left \| p \right \|/\lambda$
asked
in
Linear Algebra
Feb 22, 2021
gateme-2021-set1
linear-algebra
eigen-values
eigen-vectors
0
answers
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 $0$ $2$ $\pi i$ $2 \pi i$
asked
in
Calculus
Feb 22, 2021
gateme-2021-set1
calculus
complex-variables
0
answers
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 ... $\text{G-E-D-F-H-C-A-B}$ $\text{B-G-C-H-F-D-E-A}$
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in
Others
Feb 22, 2021
gateme-2021-set1
0
answers
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. ... $T=\left ( \frac{\partial U}{\partial S} \right )_{\tau}$
asked
in
Others
Feb 22, 2021
gateme-2021-set1
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