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GATE Mechanical 2022 Set 1 | GA Question: 2
The average of the monthly salaries of $\text{M, N}$ and $\text{S}$ is ₹$4000$. The average of the monthly salaries of $\text{N, S}$ and $\text{P}$ is ₹$5000$. The monthly salary of $\text{P}$ is ₹$6000$. What is the monthly salary of $\text{M}$ as a percentage of the monthly salary of $\text{P}?$ $50\%$ $75\%$ $100\%$ $125\%$
The average of the monthly salaries of $\text{M, N}$ and $\text{S}$ is ₹$4000$. The average of the monthly salaries of $\text{N, S}$ and $\text{P}$ is ₹$5000$. The mo...
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Quantitative Aptitude
gateme-2022-set1
quantitative-aptitude
average
percentage
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GATE Mechanical 2022 Set 1 | GA Question: 3
A person travelled $80$ $\text{km}$ in $6$ hours. If the person travelled the first part with a uniform speed of $10$ $\text{kmph}$ and the remaining part with a uniform speed of $18$ $\text{kmph}$. What percentage of the total distance is travelled at a uniform speed of $10$ $\text{kmph}$? $28.25$ $37.25$ $43.75$ $50.00$
A person travelled $80$ $\text{km}$ in $6$ hours. If the person travelled the first part with a uniform speed of $10$ $\text{kmph}$ and the remaining part with a uniform ...
Arjun
28.5k
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Arjun
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Quantitative Aptitude
gateme-2022-set1
quantitative-aptitude
speed-time-distance
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GATE Mechanical 2022 Set 1 | GA Question: 4
Four girls $\text{P, Q, R and S}$ are studying languages in a University. $\text{P}$ is learning French and Dutch. $\text{Q}$ is learning Chinese and Japanese. $\text{R}$ is learning Spanish and French. $\text{S}$ is learning Dutch and Japanese ... , which girl is learning the most difficult pair of languages? $\text{P}$ $\text{Q}$ $\text{R}$ $\text{S}$
Four girls $\text{P, Q, R and S}$ are studying languages in a University. $\text{P}$ is learning French and Dutch. $\text{Q}$ is learning Chinese and Japanese. $\text{R}$...
Arjun
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Arjun
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Analytical Aptitude
gateme-2022-set1
analytical-aptitude
logical-reasoning
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GATE Mechanical 2022 Set 1 | GA Question: 5
A block with a trapezoidal cross-section is placed over a block with rectangular cross section as shown above. Which one of the following is the correct drawing of the view of the $\text{3D}$ object as viewed in the direction indicated by an arrow in the above figure?
A block with a trapezoidal cross-section is placed over a block with rectangular cross section as shown above.Which one of the following is the correct drawing of the vie...
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Spatial Aptitude
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patterns-in-two-dimensions
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GATE Mechanical 2022 Set 1 | GA Question: 6
Humans are naturally compassionate and honest. In a study using strategically placed wallets that appear "lost", it was found that wallets with money are more likely to be returned than wallets without money. Similarly, wallets ... are more likely to be returned than wallets that are really lost Money is always more important than keys
Humans are naturally compassionate and honest. In a study using strategically placed wallets that appear "lost", it was found that wallets with money are more likely to b...
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Verbal Aptitude
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verbal-aptitude
passage-reading
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GATE Mechanical 2022 Set 1 | GA Question: 7
A rhombus is formed by joining the midpoints of the sides of a unit square. What is the diameter of the largest circle that can be inscribed within the rhombus? $\dfrac{1}{\sqrt{2}}$ $\dfrac{1}{2\sqrt{2}}$ $\sqrt{2}$ $2 \sqrt{2}$
A rhombus is formed by joining the midpoints of the sides of a unit square.What is the diameter of the largest circle that can be inscribed within the rhombus?$\dfrac{1}{...
Arjun
28.5k
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Arjun
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Quantitative Aptitude
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quantitative-aptitude
geometry
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GATE Mechanical 2022 Set 1 | GA Question: 8
An equilateral triangle, a square and a circle have equal areas. What is the ratio of the perimeters of the equilateral triangle to square to circle? $3\sqrt{3} : 2 : \sqrt{\pi}$ $\sqrt{\left ( 3 \sqrt{3} \right )} : 2 : \sqrt{\pi}$ $\sqrt{\left ( 3 \sqrt{3} \right )} : 4 : 2\sqrt{\pi}$ $\sqrt{\left ( 3 \sqrt{3} \right )} : 2 : 2\sqrt{\pi}$
An equilateral triangle, a square and a circle have equal areas.What is the ratio of the perimeters of the equilateral triangle to square to circle?$3\sqrt{3} : 2 : \sqrt...
Arjun
28.5k
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Quantitative Aptitude
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quantitative-aptitude
geometry
triangles
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GATE Mechanical 2022 Set 1 | GA Question: 9
Given below are three conclusions drawn based on the following three statements. Statement $1$ : All teachers are professors. Statement $2$ : No professor is a male. Statement $3$ : Some males are engineers. Conclusion $\text{I}$: No ... $\text{III}$ are correct Only conclusion $\text{I}$ and conclusion $\text{III}$ are correct
Given below are three conclusions drawn based on the following three statements.Statement $1$ : All teachers are professors.Statement $2$ : No professor...
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Analytical Aptitude
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GATE Mechanical 2022 Set 1 | GA Question: 10
In a $12$-hour clock that runs correctly, how many times do the second, minute, and hour hands of the clock coincide, in a $12$-hour duration from $3$ PM in a day to $3$ AM the next day? $11$ $12$ $144$ $2$
In a $12$-hour clock that runs correctly, how many times do the second, minute, and hour hands of the clock coincide, in a $12$-hour duration from $3$ PM in a day to $3$ ...
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Quantitative Aptitude
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clock-time
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GATE Mechanical 2022 Set 1 | Question: 1
The limit $p = \lim_{x\rightarrow \pi} \left ( \frac{x^{2} + \alpha x + 2 \pi^{2}}{x - \pi + 2 \sin x } \right )$ has a finite value for a real $\alpha$. The value of $\alpha$ and the corresponding limit $p$ are $\alpha = -3 \pi$ ,and $p= \pi$ $\alpha = -2 \pi$ ,and $p= 2\pi$ $\alpha = \pi$ ,and $p= \pi$ $\alpha = 2 \pi$ ,and $p=3 \pi$
The limit $$p = \lim_{x\rightarrow \pi} \left ( \frac{x^{2} + \alpha x + 2 \pi^{2}}{x - \pi + 2 \sin x } \right )$$ has a finite value for a real $\alph...
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GATE Mechanical 2022 Set 1 | Question: 2
Solution of $\triangledown ^{2} T = 0$ in a square domain ($0 < x< 1$ and $0 < y< 1$) with boundary conditions: $T \left ( x,0 \right ) = x; T \left ( 0,y \right ) = y; T\left ( x,1 \right ) = 1 + x; T\left ( 1,y \right )= 1 +y$ ... $T \left ( x,y \right ) = -x + y$ $T \left ( x,y \right ) = x + xy + y$
Solution of $\triangledown ^{2} T = 0$ in a square domain ($0 < x< 1$ and $0 < y< 1$) with boundary conditions: $T \left ( x,0 \right ) = x; T \left ( 0,y \right ) = y; T...
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GATE Mechanical 2022 Set 1 | Question: 3
Given a function $\varphi =\frac{1}{2}\left (x ^{2} + y^{2} + z^{2} \right )$ in three-dimensional Cartesian space, the value of the surface integral $\oint_{s}\hat{n}\cdot \triangledown \varphi dS,$ where $S$ is the surface of a sphere of unit radius and $\hat{n}$ is the outward unit normal vector on $S$, is $4 \pi$ $3 \pi$ $\dfrac{4 \pi}{3}$ $0$
Given a function $\varphi =\frac{1}{2}\left (x ^{2} + y^{2} + z^{2} \right )$ in three-dimensional Cartesian space, the value of the surface integral $$\oint_{s}\hat{n}\...
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GATE Mechanical 2022 Set 1 | Question: 4
The Fourier series expansion of $x^{3}$ in the interval $-1 \leq x < 1$ with periodic continuation has only sine terms only cosine terms both sine and cosine terms only sine terms and a non – zero constant
The Fourier series expansion of $x^{3}$ in the interval $-1 \leq x < 1$ with periodic continuation hasonly sine termsonly cosine termsboth sine and cosine termsonly sine ...
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GATE Mechanical 2022 Set 1 | Question: 5
If $A = \begin{bmatrix} 10 & 2k +5 \\ 3k - 3 & k +5 \end{bmatrix}$ is a symmetric matrix, the value of $k$ is __________________. $8$ $5$ $-0.4$ $\frac{1 + \sqrt{1561}}{12}$
If $A = \begin{bmatrix} 10 & 2k +5 \\ 3k - 3 & k +5 \end{bmatrix}$ is a symmetric matrix, the value of $k$ is __________________.$8$$5$$-0.4$$\frac{1 + \sqrt{1561}}{12}$...
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GATE Mechanical 2022 Set 1 | Question: 6
A uniform light slender beam $\text{AB}$ of section modulus $\text{EI}$ is pinned by a frictionless joint $A$ to the ground and supported by a light inextensible cable $\text{CB}$ to hang a weight $W$ as shown. If the maximum value of $W$ ... $\beta$ is $0.0924\:m^{-2}$ $0.0713\:m^{-2}$ $0.1261\:m^{-2}$ $0.1417\:m^{-2}$
A uniform light slender beam $\text{AB}$ of section modulus $\text{EI}$ is pinned by a frictionless joint $A$ to the ground and supported by a light inextensible cable $\...
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GATE Mechanical 2022 Set 1 | Question: 7
The figure shows a schematic of a simple Watt governor mechanism with the spindle $O_{1}O_{2}$ rotating at an angular velocity $\omega$ about a vertical axis. The balls at $P$ and $S$ have equal mass. Assume that there is no friction anywhere and all ... If $\omega$ is doubled, the value of $h$ will be _________________ $\text{mm}$. $50$ $100$ $150$ $200$
The figure shows a schematic of a simple Watt governor mechanism with the spindle $O_{1}O_{2}$ rotating at an angular velocity $\omega$ about a vertical axis. The balls a...
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GATE Mechanical 2022 Set 1 | Question: 8
A square threaded screw is used to lift a load $W$ by applying a force $F$. Efficiency of square threaded screw is expressed as The ratio of work done by $W$ per revolution to work done by $F$ per revolution $\frac{W}{F}$ $\frac{F}{W}$ The ratio of work done by $F$ per revolution to work done by $W$ per revolution
A square threaded screw is used to lift a load $W$ by applying a force $F$. Efficiency of square threaded screw is expressed asThe ratio of work done by $W$ per revolutio...
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GATE Mechanical 2022 Set 1 | Question: 9
A $\text{CNC}$ worktable is driven in a linear direction by a lead screw connected directly to a stepper motor. The pitch of the lead screw is $5$ $\text{mm}$. The stepper motor completes one full revolution upon receiving $600$ ... stepper motor is $20$ $\text{kHz}$ $10$ $\text{kHz}$ $3$ $\text{kHz}$ $15$ $\text{kHz}$
A $\text{CNC}$ worktable is driven in a linear direction by a lead screw connected directly to a stepper motor. The pitch of the lead screw is $5$ $\text{mm}$. The steppe...
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GATE Mechanical 2022 Set 1 | Question: 10
The type of fit between a mating shaft of diameter $25.0 ^{+0.010}_{- 0.010}$ $\text{mm}$ and a hole of diameter $25.015 ^{+0.015}_{- 0.015}$ $\text{mm}$ is __________________. Clearance Transition Interference Linear
The type of fit between a mating shaft of diameter $25.0 ^{+0.010}_{- 0.010}$ $\text{mm}$ and a hole of diameter $25.015 ^{+0.015}_{- 0.015}$ $\text{mm}$ is ____________...
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GATE Mechanical 2022 Set 1 | Question: 11
In a linear programming problem, if a resource is not fully utilized, the shadow price of that resource is positive negative zero infinity
In a linear programming problem, if a resource is not fully utilized, the shadow price of that resource ispositivenegativezeroinfinity
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GATE Mechanical 2022 Set 1 | Question: 12
Which one of the following is NOT a form of inventory? Raw materials Work-in-process materials Finished goods $\text{CNC}$ Milling Machines
Which one of the following is NOT a form of inventory?Raw materialsWork-in-process materialsFinished goods$\text{CNC}$ Milling Machines
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GATE Mechanical 2022 Set 1 | Question: 13
The Clausius inequality holds good for any process any cycle only reversible process only reversible cycle
The Clausius inequality holds good forany processany cycleonly reversible processonly reversible cycle
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GATE Mechanical 2022 Set 1 | Question: 14
A tiny temperature probe is fully immersed in a flowing fluid and is moving with zero relative velocity with respect to the fluid. The velocity field in the fluid is $\vec{V} = \left ( 2x\right ) \hat{i} + \left ( y + 3t \right )\hat{j}$, and the temperature field ... by the probe at $\left ( x = 1, y = 1, t = 1 \right )$ is _____________. $4$ $0$ $18$ $14$
A tiny temperature probe is fully immersed in a flowing fluid and is moving with zero relative velocity with respect to the fluid. The velocity field in the fluid is $\ve...
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GATE Mechanical 2022 Set 1 | Question: 15
In the following two-dimensional momentum equation for natural convection over a surface immersed in a quiescent fluid at temperature $T_{\infty}$ ($g$ is the gravitational acceleration, $\beta$ is the volumetric thermal expansion ... viscous force. Ratio of buoyancy force to viscous force. Viscous force per unit mass. Buoyancy force per unit mass.
In the following two-dimensional momentum equation for natural convection over a surface immersed in a quiescent fluid at temperature $T_{\infty}$ ($g$ ...
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GATE Mechanical 2022 Set 1 | Question: 16
Assuming the material considered in each statement is homogeneous, isotropic, linear elastic, and the deformations are in the elastic range, which one or more of the following statement(s) is/are TRUE? A body subjected to hydrostatic pressure ... a beam has zero shear force, then the corresponding portion of the elastic curve of the beam is always straight.
Assuming the material considered in each statement is homogeneous, isotropic, linear elastic, and the deformations are in the elastic range, which one or more of the foll...
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GATE Mechanical 2022 Set 1 | Question: 17
Which of the following heat treatment processes is/are used for surface hardening of steels? Carburizing Cyaniding Annealing Carbonitriding
Which of the following heat treatment processes is/are used for surface hardening of steels?CarburizingCyanidingAnnealingCarbonitriding
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GATE Mechanical 2022 Set 1 | Question: 18
Which of the following additive manufacturing technique(s) can use a wire as a feedstock material? Stereolithography Fused deposition modeling Selective laser sintering Directed energy deposition processes
Which of the following additive manufacturing technique(s) can use a wire as a feedstock material?StereolithographyFused deposition modelingSelective laser sinteringDirec...
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GATE Mechanical 2022 Set 1 | Question: 19
Which of the following methods can improve the fatigue strength of a circular mild steel $\text{(MS)}$ shaft? Enhancing surface finish Shot peening of the shaft Increasing relative humidity Reducing relative humidity
Which of the following methods can improve the fatigue strength of a circular mild steel $\text{(MS)}$ shaft?Enhancing surface finishShot peening of the shaftIncreasing r...
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GATE Mechanical 2022 Set 1 | Question: 20
The figure shows a purely convergent nozzle with a steady, inviscid compressible flow of an ideal gas with constant thermophysical properties operating under choked condition. The exit plane shown in the figure is located within the nozzle. If the ... through the nozzle will increase. Mach number at the exit plane of the nozzle will become more than unity.
The figure shows a purely convergent nozzle with a steady, inviscid compressible flow of an ideal gas with constant thermophysical properties operating under choked condi...
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GATE Mechanical 2022 Set 1 | Question: 21
The plane of the figure represents a horizontal plane. A thin rigid rod at rest is pivoted without friction about a fixed vertical axis passing through $O$. Its mass moment of inertia is equal to $0.1\; kg.cm^{2}$ about $O$. A ... and sticks to it. Immediately after the impact, the angular velocity of the rod is ______________ $\text{rad/s}$ (in integer).
The plane of the figure represents a horizontal plane. A thin rigid rod at rest is pivoted without friction about a fixed vertical axis passing through $O$. Its mass mome...
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GATE Mechanical 2022 Set 1 | Question: 22
A rigid uniform annular disc is pivoted on a knife edge $A$ in a uniform gravitational field as shown, such that it can execute small amplitude simple harmonic motion in the plane of the figure without slip at the pivot point. The inner ... of circumference to diameter of a circle, then $\beta = $ ____________________ (round off to $2$ decimal places).
A rigid uniform annular disc is pivoted on a knife edge $A$ in a uniform gravitational field as shown, such that it can execute small amplitude simple harmonic motion in ...
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GATE Mechanical 2022 Set 1 | Question: 23
Electrochemical machining operations are performed with tungsten as the tool, and copper and aluminum as two different workpiece materials. Properties of copper and aluminum are given in the table below. ... $\text{MRR}$ of aluminum will be _______________________ $\text{mg/s}$ (round-off to two decimal places)
Electrochemical machining operations are performed with tungsten as the tool, and copper and aluminum as two different workpiece materials. Properties of copper and alumi...
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GATE Mechanical 2022 Set 1 | Question: 24
A polytropic process is carried out from an initial pressure of $110$ $\text{kPa}$ and volume of $5\; m^{3}$ to a final volume of $2.5\; m^{3}$. The polytropic index is given by $n = 1.2$. The absolute value of the work done during the process is ______________ $\text{kJ}$ (round off to $2$ decimal places).
A polytropic process is carried out from an initial pressure of $110$ $\text{kPa}$ and volume of $5\; m^{3}$ to a final volume of $2.5\; m^{3}$. The polytropic index is g...
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GATE Mechanical 2022 Set 1 | Question: 25
A flat plate made of cast iron is exposed to a solar flux of $600\; W/m^{2}$ at an ambient temperature of $25^{\circ}C$. Assume that the entire solar flux is absorbed by the plate. Cast iron has a low ... the aforementioned conditions, the radiation equilibrium temperature of the plate is _____________$^{\circ}C$ (round off to the nearest integer).
A flat plate made of cast iron is exposed to a solar flux of $600\; W/m^{2}$ at an ambient temperature of $25^{\circ}C$. Assume that the entire solar flux is absorbed by ...
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GATE Mechanical 2022 Set 1 | Question: 26
The value of the integral $\oint \left ( \frac{6z}{2z^{4} - 3z^{3} + 7z^{2} - 3z + 5 } \right )dz$ evaluated over a counter-clockwise circular contour in the complex plane enclosing only the pole $z = i$, where $i$ is the imaginary unit, is $\left ( -1 + i \right )\pi$ $\left ( 1 + i \right )\pi$ $2\left ( 1 - i \right )\pi$ $\left ( 2 + i \right )\pi$
The value of the integral $$\oint \left ( \frac{6z}{2z^{4} - 3z^{3} + 7z^{2} - 3z + 5 } \right )dz$$ evaluated over a counter-clockwise circular contour in the complex pl...
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GATE Mechanical 2022 Set 1 | Question: 27
An $L$-shaped elastic member $\text{ABC}$ with slender arms $\text{AB}$ and $\text{BC}$ of uniform cross-section is clamped at end $A$ and connected to a pin at end $C$. The pin remains in continuous contact with and is constrained to move in a smooth ... $\frac{5P}{8}$, and upwards $\frac{P}{4}$, and downwards $\frac{3P}{4}$, and upwards
An $L$-shaped elastic member $\text{ABC}$ with slender arms $\text{AB}$ and $\text{BC}$ of uniform cross-section is clamped at end $A$ and connected to a pin at end $C$. ...
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GATE Mechanical 2022 Set 1 | Question: 28
A planar four-bar linkage mechanism with $3$ revolute kinematic pairs and $1$ prismatic kinematic pair is shown in the figure, where $AB \perp CE$ and $FD \perp CE$. The $T$-shaped link $\text{CDEF}$ is constructed such that the ... $\text{AG and CDEF}$ on the border of Grashof and non-Grashof chains with uncertain configuration(s)
A planar four-bar linkage mechanism with $3$ revolute kinematic pairs and $1$ prismatic kinematic pair is shown in the figure, where $AB \perp CE$ and $FD \perp CE$. The ...
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GATE Mechanical 2022 Set 1 | Question: 29
Consider a forced single degree-of-freedom system governed by $\ddot{\chi }\left ( t \right ) + 2 \zeta \omega _{n}\dot{\chi }\left ( t \right ) +\omega _{n}^{2}\chi(t)= \omega _{n}^{2} \cos \left ( \omega t \right )$, where $\zeta$ and $\omega_{n}$ ... $\omega _{d} < \omega _{n} = \omega _{p}$ $\omega _{d} < \omega _{n} < \omega _{p}$
Consider a forced single degree-of-freedom system governed by $\ddot{\chi }\left ( t \right ) + 2 \zeta \omega _{n}\dot{\chi }\left ( t \right ) +\omega _{n}^{2}\chi(t)= ...
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GATE Mechanical 2022 Set 1 | Question: 30
A bracket is attached to a vertical column by means of two identical rivets $U$ and $V$ separated by a distance of $2a = 100\; mm$, as shown in the figure. The permissible shear stress of the rivet material is $50$ $\text{MPa}$. If a ... cross-sectional area of each of the rivets to avoid failure is ________________$mm^2$. $800$ $25$ $100\sqrt{7}$ $200$
A bracket is attached to a vertical column by means of two identical rivets $U$ and $V$ separated by a distance of $2a = 100\; mm$, as shown in the figure. The permissibl...
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GATE Mechanical 2022 Set 1 | Question: 31
In $Fe-Fe_{3}C$ phase diagram, the eutectoid composition is $0.8$ weight $\%$ of carbon at $725^{\circ}C$. The maximum solubility of carbon in $\alpha$-ferrite phase is $0.025$ weight $\%$ of carbon. A steel sample, having no other ... of pro-eutectoid $\alpha$-ferrite in the above steel sample at room temperature is $0.387$ $0.864$ $0.475$ $0.775$
In $Fe-Fe_{3}C$ phase diagram, the eutectoid composition is $0.8$ weight $\%$ of carbon at $725^{\circ}C$. The maximum solubility of carbon in $\alpha$-ferrite phase is $...
Arjun
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Arjun
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Feb 15, 2022
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