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GATE Mechanical 2022 Set 2 | Question: 14
Consider a steady flow through a horizontal divergent channel, as shown in the figure, with supersonic flow at the inlet. The direction of flow is from left to right. Pressure at location $B$ is observed to be higher than that at an ... flow rate is constant, velocity at $B$ is lower than velocity at $A$ Normal shock Viscous effect Boundary layer separation
Consider a steady flow through a horizontal divergent channel, as shown in the figure, with supersonic flow at the inlet. The direction of flow is from left to right.Pres...
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GATE2019 ME-1: 4
The lengths of a large stock of titanium rods follow a normal distribution with a mean $(\mu)$ of $440$ mm and a standard deviation $(\sigma)$ of $1$ mm.What is the percentage of rods whose lengths lie between $438$ mm and $441$ mm? $81.85 \%$ $68.4 \%$ $99.75 \%$ $86.64 \%$
The lengths of a large stock of titanium rods follow a normal distribution with a mean $(\mu)$ of $440$ mm and a standard deviation $(\sigma)$ of $1$ mm.What is the perce...
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GATE Mechanical 2021 Set 2 | Question: 52
The wheels and axle system lying on a rough surface is shown in the figure. Each wheel has diameter $\text{0.8 m}$ and mass $\text{1 kg}$. Assume that the mass of the wheel is concentrated at rim and neglect the mass of the spokes. The ... of the wheel axle system in horizontal direction is ______ $\text{m/s}^{2} (\textit{round off to one decimal place}$).
The wheels and axle system lying on a rough surface is shown in the figure.Each wheel has diameter $\text{0.8 m}$ and mass $\text{1 kg}$. Assume that the mass of the whe...
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GATE Mechanical 2022 Set 2 | Question: 17
Consider sand casting of a cube of edge length $a$. A cylindrical riser is placed at the top of the casting. Assume solidification time, $t_{s} \:\alpha\: V/A$, where $V$ is the volume and $A$ is the total surface area dissipating heat. If the top of the ... /radii of riser is/are acceptable? $\dfrac{a}{3}$ $\dfrac{a}{2}$ $\dfrac{a}{4}$ $\dfrac{a}{6}$
Consider sand casting of a cube of edge length $a$. A cylindrical riser is placed at the top of the casting. Assume solidification time, $t_{s} \:\alpha\: V/A$, where $V$...
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GATE Mechanical 2021 Set 1 | Question: 54
A machine part in the form of cantilever beam is subjected to fluctuating load as shown in the figure The load varies from $\text{800 N}$ to $\text{1600 N}$. The modified endurance. yield and ultimate strengths of the ... factor of safety of the beam using modified Goodman criterion is ____________________ ($\textit{round off to one decimal place}$).
A machine part in the form of cantilever beam is subjected to fluctuating load as shown in the figure The load varies from $\text{800 N}$ to $\text{1600 N}$. The modified...
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Feb 22, 2021
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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 2021 Set 1 | Question: 55
A cantilever beam of rectangular cross-section is welded to a support by means of two filled welds as shown in figure. A vertical load of $\text{2 kN}$ acts at free end of the beam. Considering that the allowable shear stress in weld ... minimum size (leg) of the weld required is _____________________ $\text{mm} (\textit{round off to one decimal place}$).
A cantilever beam of rectangular cross-section is welded to a support by means of two filled welds as shown in figure. A vertical load of $\text{2 kN}$ acts at free end o...
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Feb 22, 2021
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GATE Mechanical 2023 | Question: 38
The smallest perimeter that a rectangle with area of $4$ square units can have is __________ units. (Answer in integer)
The smallest perimeter that a rectangle with area of $4$ square units can have is __________ units. (Answer in integer)
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GATE Mechanical 2021 Set 1 | Question: 50
Two smooth identical spheres each of radius $\text{125 mm}$ and weight $\text{100 N}$ rest in a horizontal channel having vertical walls. The distance between vertical walls of the channel is $\text{400 mm}$. The reaction at the point of contact between two spheres is ___________________ $\text{N} (\textit{round off to one decimal place}$).
Two smooth identical spheres each of radius $\text{125 mm}$ and weight $\text{100 N}$ rest in a horizontal channel having vertical walls. The distance between vertical wa...
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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
The correct sequence of machining operations to be performed to finish a large diameter through hole isdrilling, boring, reamingboring, drilling, reamingdrilling, reaming...
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GATE Mechanical 2021 Set 1 | Question: 20
Robot $\text{Ltd}$ ... fulfillment probability for the lead time period is _____________ units ($\textit{round off to two decimal places}$).
Robot $\text{Ltd}$. wishes to maintain enough safety stock during the lead time period between starting a new production run and its completion such that the probability ...
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GATE Mechanical 2022 Set 2 | Question: 22
An electric car manufacturer underestimated the January sales of car by $20$ units, while the actual sales was $120$ units. If the manufacturer uses exponential smoothing method with a smoothing constant of $\alpha = 0.2$, then the sales forecast for the month of February of the same year is ____________ units (in integer).
An electric car manufacturer underestimated the January sales of car by $20$ units, while the actual sales was $120$ units. If the manufacturer uses exponential smoothing...
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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 2023 | Question: 23
The value of $k$ that makes the complex-valued function $ f(z)=e^{-k x}(\cos 2 y-i \sin 2 y) $ analytic, where $z=x+i y$, is __________. (Answer in integer)
The value of $k$ that makes the complex-valued function$$f(z)=e^{-k x}(\cos 2 y-i \sin 2 y)$$analytic, where $z=x+i y$, is __________. (Answer in integer)
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GATE Mechanical 2023 | Question: 8
The $\text{S-N}$ curve from a fatigue test for steel is shown. Which one of the options gives the endurance limit? $S_{u t}$ $S_2$ $S_3$ $S_4$
The $\text{S-N}$ curve from a fatigue test for steel is shown. Which one of the options gives the endurance limit? $S_{u t}$$S_2$$S_3$$S_4$
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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: 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 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 2023 | Question: 30
The figure shows a thin-walled open-top cylindrical vessel of radius $r$ and wall thickness $t$. The vessel is held along the brim and contains a constant-density liquid to height $h$ from the base. Neglect atmospheric pressure, the weight ... magnitudes of axial wall stress $\left(\sigma_1\right)$ and circumferential wall stress $\left(\sigma_2\right)$ on $y$?
The figure shows a thin-walled open-top cylindrical vessel of radius $r$ and wall thickness $t$. The vessel is held along the brim and contains a constant-density liquid ...
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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}$).
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}$. T...
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Feb 22, 2021
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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 2021 Set 2 | Question: 31
A plane frame $\text{PQR}$ (fixed at $\text{P}$ and free at $\text{R}$) is shown in the figure. Both members ($\text{PQ}$ and $\text{QR}$) have length, $\text{L}$, and flexural rigidity, $\text{EI}$. Neglecting the effect of axial stress and transverse shear, the ... , is $\frac{5FL^{3}}{3EI}$ $\frac{4FL^{3}}{3EI}$ $\frac{2FL^{3}}{3EI}$ $\frac{FL^{3}}{3EI}$
A plane frame $\text{PQR}$ (fixed at $\text{P}$ and free at $\text{R}$) is shown in the figure. Both members ($\text{PQ}$ and $\text{QR}$) have length, $\text{L}$, and fl...
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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 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 2023 | Question: 22
A linear transformation maps a point $(x, y)$ in the plane to the point $(\hat{x}, \hat{y})$ according to the rule $\hat{x}=3 y, \quad \hat{y}=2 x .$ Then, the disc $x^2+y^2 \leq 1$ gets transformed to a region with an area equal to ________. (Rounded off to two decimals) Use $\pi=3.14$
A linear transformation maps a point $(x, y)$ in the plane to the point $(\hat{x}, \hat{y})$ according to the rule$$\hat{x}=3 y, \quad \hat{y}=2 x .$$Then, the disc $x^2+...
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May 21, 2023
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GATE Mechanical 2024 | GA Question: 2
Find the odd one out in the set: $\{19,37,21,17,23,29,31,11\}$ $21$ $29$ $37$ $23$
Find the odd one out in the set: $\{19,37,21,17,23,29,31,11\}$$21$$29$$37$$23$
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GATE Mechanical 2021 Set 1 | Question: 43
An uninsulated cylindrical wire of radius $\text{1.0 mm}$ produces electric heating at the rate of $\text{5.0 W/m}$. The temperature of the surface of the wire is $75\;^{\circ}C$ when placed in air at $25\;^{\circ}C$. When the wire is ... Wire. The thermal conductivity of $\text{PVC}$ is ______ $\text{W/m.K}$ ($\textit{round off to two decimal places}$).
An uninsulated cylindrical wire of radius $\text{1.0 mm}$ produces electric heating at the rate of $\text{5.0 W/m}$. The temperature of the surface of the wire is $75\;^{...
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Feb 22, 2021
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GATE Mechanical 2023 | Question: 29
A beam of length $L$ is loaded in the $x y-$ plane by a uniformly distributed load, and by a concentrated tip load parallel to the $z$-axis, as shown in the figure. The resulting bending moment distributions about the $y$ ... Which one of the options given depicts qualitatively $\text{CORRECT}$ variations of $M_y$ and $M_z$ along the length of the beam?
A beam of length $L$ is loaded in the $x y-$ plane by a uniformly distributed load, and by a concentrated tip load parallel to the $z$-axis, as shown in the figure. The r...
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May 21, 2023
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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 2023 | Question: 44
A coordinate measuring machine (CMM) is used to determine the distance between Surface $\text{SP}$ and Surface $\text{SQ}$ of an approximately cuboidal shaped part. Surface $\text{SP}$ is declared as the datum as per the engineering ... to fit the necessary planes. The distance between the two fitted planes is ____________ $\mathrm{mm}$. (Answer in integer)
A coordinate measuring machine (CMM) is used to determine the distance between Surface $\text{SP}$ and Surface $\text{SQ}$ of an approximately cuboidal shaped part. Surfa...
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GATE Mechanical 2021 Set 1 | Question: 52
The Whitworth quick return mechanism is shown in the figure with link lengths as follows: $\text{OP = 300 mm, OA = 150 mm, AR = 160 mm, RS = 450 mm}$. The quick return ratio for the mechanism is ____________________ ($\textit{round off to one decimal place}$).
The Whitworth quick return mechanism is shown in the figure with link lengths as follows: $\text{OP = 300 mm, OA = 150 mm, AR = 160 mm, RS = 450 mm}$.The quick return rat...
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Feb 22, 2021
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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 2021 Set 2 | Question: 42
A $\text{76.2 mm}$ gauge block is used under one end of a $\text{254 mm}$ sine bar with roll diameter of $\text{25.4 mm}$. The height of gauge blocks required at the other end of the sine bar to measure an angle of $30^{\circ}$ is ______ $\text{mm} (\textit{round off to two decimal places}$).
A $\text{76.2 mm}$ gauge block is used under one end of a $\text{254 mm}$ sine bar with roll diameter of $\text{25.4 mm}$. The height of gauge blocks required at the othe...
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GATE Mechanical 2023 | Question: 53
Consider a unidirectional fluid flow with the velocity field given by $ V(x, y, z, t)=u(x, t) \hat{\imath} $ where $u(0, t)=1$. If the spatially homogeneous density field varies with time $t$ as $ \rho(t)=1+0.2 e^{-t} $ the value of $u(2,1)$ is ______________. (Rounded off to two decimal places) Assume all quantities to be dimensionless.
Consider a unidirectional fluid flow with the velocity field given by$$V(x, y, z, t)=u(x, t) \hat{\imath}$$where $u(0, t)=1$. If the spatially homogeneous density field v...
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GATE Mechanical 2023 | Question: 54
The figure shows two fluids held by a hinged gate. The atmospheric pressure is $P_a=100 \mathrm{kPa}$. The moment per unit width about the base of the hinge is ____________ $\mathrm{kNm} / \mathrm{m}$. (Rounded off to one decimal place) Take the acceleration due to gravity to be $\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^2$.
The figure shows two fluids held by a hinged gate. The atmospheric pressure is $P_a=100 \mathrm{kPa}$. The moment per unit width about the base of the hinge is __________...
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May 21, 2023
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GATE Mechanical 2021 Set 1 | Question: 30
Consider a two degree of freedom system as shown in the figure, where $\text{PQ}$ is a rigid uniform rod of length, $\text{b}$ and mass, $\text{m}$. Assume that the spring deflects only horizontally and force $\text{F}$ is applied horizontally at $\text{Q}$. For ...
Consider a two degree of freedom system as shown in the figure, where $\text{PQ}$ is a rigid uniform rod of length, $\text{b}$ and mass, $\text{m}$.Assume that the spring...
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Feb 22, 2021
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GATE Mechanical 2022 Set 1 | Question: 36
The system of linear equations in real $\left ( x,y \right )$ given by $\left ( x \: y \right )\begin{bmatrix} 2 &5 - 2 \alpha \\ \alpha & 1 \end{bmatrix} = \left ( 0\:0 \right )$ involves a real parameter $\alpha$ and has infinitely many non-trivial solutions for special ... $\alpha$? $x = 2, y = -2$ $x = -1, y = 4$ $x = 1, y = 1$ $x = 4, y = -2$
The system of linear equations in real $\left ( x,y \right )$ given by $$\left ( x \: y \right )\begin{bmatrix} 2 &5 - 2 \alpha \\ \alpha & 1 \end{bmatrix} = \left ( 0\:0...
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Feb 15, 2022
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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
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 representsdirect sh...
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Feb 22, 2021
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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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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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