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GATE Mechanical 2022 Set 2 | Question: 11
Match the additive manufacturing technique in Column $\text{I}$ with its corresponding input material in Column $\text{II}$. Additive manufacturing technique (Column $\text{I}$) Input material (Column $\text{II}$) $P$ Fused deposition modelling $1$ Photo sensitive liquid resin $Q$ Laminated object ... $P -2, Q -3, R -1$ $P -4, Q -1, R -4$
Match the additive manufacturing technique in Column $\text{I}$ with its corresponding input material in Column $\text{II}$. Additive manufacturing technique (Column $\t...
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Feb 24, 2022
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GATE Mechanical 2022 Set 2 | Question: 10
A shaft of diameter $25_{-0.07}^{-0.04}$ $\text{mm}$ is assembled in a hole of diameter $25_{-0.00}^{+0.02}$ $\text{mm}$. Match the allowance and limit parameter in Column $\text{I}$ with its corresponding quantitative value in Column $\text{II}$ for this shaft-hole assembly. Allowance ... $P -1, Q -3, R -2$ $P -1, Q -3 R -4$ $P -3, Q -1, R -2$
A shaft of diameter $25_{-0.07}^{-0.04}$ $\text{mm}$ is assembled in a hole of diameter $25_{-0.00}^{+0.02}$ $\text{mm}$. Match the allowance and limit parameter in Colum...
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Feb 24, 2022
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GATE Mechanical 2022 Set 2 | Question: 9
Fluidity of a molten alloy during sand casting depends on its solidification range. The phase diagram of a hypothetical binary alloy of components $A$ and $B$ is shown in the figure with its eutectic composition and temperature. All the lines in this phase diagram, ... the solidification range is $400^{\circ}C$ $250^{\circ}C$ $800^{\circ}C$ $150^{\circ}C$
Fluidity of a molten alloy during sand casting depends on its solidification range. The phase diagram of a hypothetical binary alloy of components $A$ and $B$ is shown in...
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GATE Mechanical 2022 Set 2 | Question: 7
A massive uniform rigid circular disc is mounted on a frictionless bearing at the end $E$ of a massive uniform rigid shaft $\text{AE}$ which is suspended horizontally in a uniform gravitational field by two identical light inextensible strings ... about the positive $y$-axis direction rotate slowly (compared to $\omega$) about the negative $y$-axis direction
A massive uniform rigid circular disc is mounted on a frictionless bearing at the end $E$ of a massive uniform rigid shaft $\text{AE}$ which is suspended horizontally in ...
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Feb 24, 2022
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GATE Mechanical 2022 Set 2 | Question: 2
Consider a cube of unit edge length and sides parallel to co-ordinate axes, with its centroid at the point $(1, 2, 3)$. The surface integral $\int _{A} \vec{F}.d\vec{A}$ of a vector field $\vec{F} = 3x\hat{i} + 5y\hat{j} + 6z\hat{k}$ over the entire surface $A$ of the cube is _____________. $14$ $27$ $28$ $31$
Consider a cube of unit edge length and sides parallel to co-ordinate axes, with its centroid at the point $(1, 2, 3)$. The surface integral $\int _{A} \vec{F}.d\vec{A}$ ...
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GATE Mechanical 2022 Set 2 | GA Question: 8
Consider the following for non-zero positive integers, $p$ and $q$. $f\left ( p, q \right ) = \frac{p\times p\times p\times \cdots\: \cdots\: \cdots \times p \:= \:p^{q}}{q\:{terms}}; f\left ( p, 1 \right )=p$ ... $g\left ( 2,1 \right ) \neq f\left ( 2,1 \right )$ $f\left ( 3,2 \right )> g\left ( 3,2 \right )$
Consider the following for non-zero positive integers, $p$ and $q$.$f\left ( p, q \right ) = \frac{p\times p\times p\times \cdots\: \cdots\: \cdots \times p \:= \:p^{q}}{...
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Feb 24, 2022
Quantitative Aptitude
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GATE Mechanical 2022 Set 2 | GA Question: 7
For the past $m$ days, the average daily production at a company was $100$ units per day. If today’s production of $180$ units changes the average to $110$ units per day, What is the value of $m$? $18$ $10$ $7$ $5$
For the past $m$ days, the average daily production at a company was $100$ units per day.If today’s production of $180$ units changes the average to $110$ units per day...
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GATE Mechanical 2022 Set 2 | GA Question: 4
A person was born on the fifth Monday of February in a particular year. Which one of the following statements is correct based on the above information? The $2^{\text{nd}}$ February of that year is a Tuesday There will be five Sundays in the ... year The $1^{\text{st}}$ February of that year is a Sunday All Mondays of February in that year have even dates
A person was born on the fifth Monday of February in a particular year.Which one of the following statements is correct based on the above information?The $2^{\text{nd}}$...
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Feb 24, 2022
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GATE Mechanical 2022 Set 2 | GA Question: 3
If $f\left ( x \right ) = 2 \:\ln \left ( \sqrt{e^{x}} \right )$, what is the area bounded by $f\left ( x \right )$ for the interval $\left [ 0,2 \right ]$ on the $x$ – axis? $\frac{1}{2}$ $1$ $2$ $4$
If $f\left ( x \right ) = 2 \:\ln \left ( \sqrt{e^{x}} \right )$, what is the area bounded by $f\left ( x \right )$ for the interval $\left [ 0,2 \right ]$ on the $x$ –...
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GATE Mechanical 2022 Set 2 | GA Question: 1
Writing too many things on the ___________ while teaching could make the students get _____________. bored / board board / bored board / board bored / bored
Writing too many things on the ___________ while teaching could make the students get _____________.bored / boardboard / boredboard / boardbored / bored
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GATE Mechanical 2022 Set 2 | Question: 3
Consider the definite integral $\int_{1}^{2} \left ( 4x^{2} + 2x + 6 \right )dx.$ Let $I_{e}$ be the exact value of the integral. If the same integral is estimated using Simpson's rule with $10$ equal subintervals, the value is $I_{S}$. The percentage error is defined ... $e$ is $2.5$ $3.5$ $1.2$ $0$
Consider the definite integral$$\int_{1}^{2} \left ( 4x^{2} + 2x + 6 \right )dx.$$Let $I_{e}$ be the exact value of the integral. If the same integral is estimated using ...
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GATE Mechanical 2022 Set 2 | Question: 4
Given $\int_{-\infty }^{\infty } e^{-x^{2}} dx = \sqrt{\pi }.$ If $a$ and $b$ are positive integers, the value of $\int_{-\infty }^{\infty } e^{-a\left ( x+b \right )^{2}} dx$ is _______________. $\sqrt{\pi a}$ $\sqrt{\frac{\pi }{a}}$ $b\sqrt{\pi a}$ $b\sqrt{\frac{\pi }{a}}$
Given $\int_{-\infty }^{\infty } e^{-x^{2}} dx = \sqrt{\pi }.$If $a$ and $b$ are positive integers, the value of $\int_{-\infty }^{\infty } e^{-a\left ( x+b \right )^{2}}...
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GATE Mechanical 2022 Set 2 | Question: 5
A polynomial $\varphi \left ( s \right ) = a_{n}s^{n} + a_{n-1}s^{n-1} + \cdots + a_{1}s+a_{0}$ of degree $n>3$ with constant real coefficients $a_{n}, a_{n-1}, \:\dots a_{0}$ has triple roots at $s = -\sigma$. Which one of the following ... $\frac{d^{3}\varphi \left ( s \right )}{ds^{3}} = 0$ at $s = -\sigma$
A polynomial $\varphi \left ( s \right ) = a_{n}s^{n} + a_{n-1}s^{n-1} + \cdots + a_{1}s+a_{0}$ of degree $n>3$ with constant real coefficients $a_{n}, a_{n-1}, \:\dots a...
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GATE Mechanical 2022 Set 2 | Question: 6
Which one of the following is the definition of ultimate tensile strength $\text{(UTS)}$ obtained from a stress-strain test on a metal specimen? Stress value where the stress-strain curve transitions from elastic ... -sectional area The maximum load attained divided by the corresponding instantaneous cross-sectional area Stress where the specimen fractures
Which one of the following is the definition of ultimate tensile strength $\text{(UTS)}$ obtained from a stress-strain test on a metal specimen?Stress value where the str...
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GATE Mechanical 2022 Set 2 | Question: 8
A structural member under loading has a uniform state of plane stress which is usual notations is given by $\sigma _{x} = 3P, \sigma _{y} = -2P$ and $\tau_{xy} = \sqrt{2}P$, where $P>0$. The yield strength of the material is $350$ ... maximum distortion energy theory) is $70$ $\text{MPa}$ $90$ $\text{MPa}$ $120$ $\text{MPa}$ $75$ $\text{MPa}$
A structural member under loading has a uniform state of plane stress which is usual notations is given by $\sigma _{x} = 3P, \sigma _{y} = -2P$ and $\tau_{xy} = \sqrt{2}...
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GATE Mechanical 2022 Set 2 | Question: 12
Which one of the following $\text{CANNOT}$ impart linear motion in a $\text{CNC}$ machine? Linear motor Ball screw Lead screw Chain and sprocket
Which one of the following $\text{CANNOT}$ impart linear motion in a $\text{CNC}$ machine?Linear motorBall screwLead screwChain and sprocket
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GATE Mechanical 2022 Set 2 | Question: 13
Which one of the following is an intensive property of a thermodynamic system? Mass Density Energy Volume
Which one of the following is an intensive property of a thermodynamic system?MassDensityEnergyVolume
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GATE Mechanical 2022 Set 2 | Question: 15
Which of the following non-dimensional terms is an estimate of Nusselt number? Ratio of internal thermal resistance of a solid to the boundary layer thermal resistance Ratio of the rate at which internal energy is ... to the rate of conduction heat transfer Non-dimensional temperature gradient Non-dimensional velocity gradient multiplied by Prandtl number
Which of the following non-dimensional terms is an estimate of Nusselt number?Ratio of internal thermal resistance of a solid to the boundary layer thermal resistanceRati...
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GATE Mechanical 2022 Set 2 | Question: 20
A rope with two mass-less platforms at its two ends passes over a fixed pulley as shown in the figure. Discs with narrow slots and having equal weight of $20\: N$ each can be placed on the platforms. The number of discs placed ... $\text{(ii)}$ of the figure) required to prevent downward motion of the left side platform is _____________________(in integer).
A rope with two mass-less platforms at its two ends passes over a fixed pulley as shown in the figure. Discs with narrow slots and having equal weight of $20\: N$ each ca...
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GATE Mechanical 2022 Set 1 | Question: 32
Activities $A$ to $K$ are required to complete a project. The time estimates and the immediate predecessors of these activities are given in the table. If the project is to be completed in the minimum possible time, the latest finish time for the activity $G$ is _______________ ... $5$ $10$ $8$ $9$
Activities $A$ to $K$ are required to complete a project. The time estimates and the immediate predecessors of these activities are given in the table. If the project is ...
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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 $...
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GATE Mechanical 2022 Set 1 | Question: 33
A solid spherical bead of lead (uniform density= $11000 \; kg/m^{3}$) of diameter $d = 0.1\; mm$ sinks with a constant velocity $V$ in a large stagnant pool of a liquid (dynamic viscosity = $1.1 \times 10^{-3}\; kg \cdot m^{-1} \cdot s^{-1}$). The ... $V$ is ____________ $m/s$. $\frac{1}{24}$ $\frac{1}{6}$ $\frac{1}{18}$ $\frac{1}{12}$
A solid spherical bead of lead (uniform density= $11000 \; kg/m^{3}$) of diameter $d = 0.1\; mm$ sinks with a constant velocity $V$ in a large stagnant pool of a liquid (...
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GATE Mechanical 2022 Set 1 | Question: 34
Consider steady, one-dimensional compressible flow or a gas in a pipe or diameter $1\; m$. At one location in the pipe, the density and velocity are $1\; kg/m^{3}$ and $100\; m/s$, respectively. At a downstream location in the pipe, the ... the gas on the pipe between these two locations is ________________$N$. $350 \pi^{2}$ $750 \pi$ $1000 \pi$ $3000$
Consider steady, one-dimensional compressible flow or a gas in a pipe or diameter $1\; m$. At one location in the pipe, the density and velocity are $1\; kg/m^{3}$ and $1...
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GATE Mechanical 2022 Set 1 | Question: 51
In a steam power plant based on Rankine cycle, steam is initially expanded in a high-pressure turbine. The steam is then reheated in a reheater and finally expanded in a low-pressure turbine. The expansion work in the high-pressure turbine is ... $\text{kJ/kg}$ (round off to $2$ decimal places)
In a steam power plant based on Rankine cycle, steam is initially expanded in a high-pressure turbine. The steam is then reheated in a reheater and finally expanded in a ...
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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: 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: 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: 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: 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 | 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}{...
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Quantitative Aptitude
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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...
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Quantitative Aptitude
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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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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. $\text{R}$...
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Analytical Aptitude
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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 ...
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Quantitative Aptitude
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quantitative-aptitude
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