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GATE Mechanical 2021 Set 2 | Question: 9
The allowance provided in between a hole and a shaft is calculated from the difference between lower limit of the shaft and the upper limit of the hole upper limit of the shaft and the upper limit of the hole upper limit of the shaft and the lower limit of the hole lower limit of the shaft and the lower limit of the hole
The allowance provided in between a hole and a shaft is calculated from the difference betweenlower limit of the shaft and the upper limit of the holeupper limit of the s...
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Mar 1, 2021
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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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Feb 22, 2021
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GATE Mechanical 2022 Set 2 | Question: 46
The best size wire is fitted in a groove of a metric screw such that the wire touches the flanks of the thread on the pitch line as shown in the figure. The pitch $(p)$ and included angle of the thread are $4$ $\text{mm}$ and $60^{\circ}$, respectively. The diameter of the best size wire is _______________ $\text{mm}$ (round off to $2$ decimal places).
The best size wire is fitted in a groove of a metric screw such that the wire touches the flanks of the thread on the pitch line as shown in the figure. The pitch $(p)$ a...
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GATE Mechanical 2022 Set 1 | Question: 47
Two mild steel plates of similar thickness, in butt-joint configuration, are welded by gas tungsten arc welding process using the following welding parameters. ... $\text{mm/s}$ (round off to one decimal place).
Two mild steel plates of similar thickness, in butt-joint configuration, are welded by gas tungsten arc welding process using the following welding parameters.$$\begin{ar...
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GATE Mechanical 2021 Set 2 | Question: 40
In a pure orthogonal turning by a zero rake angle single point carbide cutting tool, the shear force has been computed to be $\text{400 N}$. The cutting velocity, $V_{c}=100$ $\text{m/min}$, depth of cut, $\text{t= 2.0 mm}$ ... , the shear strength, $\tau_{s}$, of the material will be ______ $\text{MPa} (\textit{round off to two decimal places}$).
In a pure orthogonal turning by a zero rake angle single point carbide cutting tool, the shear force has been computed to be $\text{400 N}$. The cutting velocity, $V_{c}=...
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Mar 1, 2021
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GATE Mechanical 2021 Set 2 | Question: 51
A block of negligible mass rests on a surface that is inclined at $30^{\circ}$ to the horizontal plane as shown in the figure. When a vertical force of $\text{900 N}$ and a horizontal force of $\text{750 N}$ are applied, ... to slide. The coefficient of static friction between the block and surface is _______ ($\textit{round off to two decimal places}$).
A block of negligible mass rests on a surface that is inclined at $30^{\circ}$ to the horizontal plane as shown in the figure. When a vertical force of $\text{900 N}$ and...
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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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Feb 22, 2021
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GATE2020-ME-2: 42
A mould cavity of $1200 \: cm^3$ volume has to be filled through a sprue of $10$ cm length feeding a horizontal runner. Cross-sectional area at the base of the sprue is $2 \: cm^2$ ... frictional losses due to molten metal flow, the time taken to fill the mould cavity is ________ seconds (round off to $2$ decimal places)
A mould cavity of $1200 \: cm^3$ volume has to be filled through a sprue of $10$ cm length feeding a horizontal runner. Cross-sectional area at the base of the sprue is $...
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Sep 18, 2020
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GATE2020-ME-2: 46
A point $ P'$ on a CNC controlled $XY$-stage is moved to another point $ Q'$ using the coordinate system shown in the figure below and rapid positioning command $(G00)$ A pair of stepping motors with maximum speed of $800$ rpm, controlling both the $X$ ... The time needed to position the point $ P'$ to the point $ Q'$ is _________ minutes (round off to $2$ decimal places).
A point $‘P’$ on a CNC controlled $XY$-stage is moved to another point $‘Q’$ using the coordinate system shown in the figure below and rapid positioning command $...
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GATE Mechanical 2024 | Question: 31
Which of the following beam(s) is/are statically indeterminate?
Which of the following beam(s) is/are statically indeterminate?
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GATE Mechanical 2022 Set 2 | Question: 54
Saturated vapor at $200\: ^{\circ}C$ condenses to saturated liquid at the rate of $150$ $\text{kg/s}$ on the shell side of a heat exchanger (enthalpy of condensation $h_{fg} = 2400$ $\text{kJ/kg}$ ... heat exchanger is $0.9$, then the mass flow rate of the fluid in the tube side is ____________ $\text{kg/s}$ (in integer).
Saturated vapor at $200\: ^{\circ}C$ condenses to saturated liquid at the rate of $150$ $\text{kg/s}$ on the shell side of a heat exchanger (enthalpy of condensation $h_{...
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GATE Mechanical 2021 Set 2 | Question: 29
A factory produces $m (i= 1,2,\cdots, m)$ products, each of which requires processing on $n(j = 1,2,\cdots, n)$ workstations. Let $a_{ij}$ be the amount of processing time that one unit of the $i^{th}$ product requires on the $j^{th}$ workstation. Let the revenue ... $I_{it}=I_{i,t-1}+S_{it}-X_{it}\:\forall \:i,t$
A factory produces $m (i= 1,2,\cdots, m)$ products, each of which requires processing on $n(j = 1,2,\cdots, n)$ workstations. Let $a_{ij}$ be the amount of processing ti...
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Mar 1, 2021
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GATE Mechanical 2021 Set 2 | Question: 44
A shell and tube heat exchanger is used as a steam condenser. Coolant water enters the tube at $300 \text{ K}$ at a rate of $100 \text{ kg/s}$ ... temperature of the coolant water coming out of the condenser is __________________ $\text{K} (\textit{round off to the nearest integer}$).
A shell and tube heat exchanger is used as a steam condenser. Coolant water enters the tube at $300 \text{ K}$ at a rate of $100 \text{ kg/s}$. The overall heat transfer ...
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Mar 1, 2021
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GATE Mechanical 2024 | Question: 17
A rigid massless tetrahedron is placed such that vertex $\mathrm{O}$ is at the origin and the other three vertices $\text{A, B}$, and $\text{C}$ lie on the coordinate axes as shown in the figure. The body is acted on by three point loads, of which one is ... $y-z$ plane but not along $y$ or $z$ axis in $z-x$ plane but not along $z$ or $x$ axis
A rigid massless tetrahedron is placed such that vertex $\mathrm{O}$ is at the origin and the other three vertices $\text{A, B}$, and $\text{C}$ lie on the co...
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Feb 16
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GATE Mechanical 2022 Set 1 | Question: 55
During open-heart surgery, a patient's blood is cooled down to $25^{\circ}C$ from $37^{\circ}C$ using a concentric tube counter-flow heat exchanger. Water enters the heat exchanger at $4^{\circ}C$ ... $2$ decimal places).
During open-heart surgery, a patient's blood is cooled down to $25^{\circ}C$ from $37^{\circ}C$ using a concentric tube counter-flow heat exchanger. Water enters the heat...
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Feb 15, 2022
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GATE Mechanical 2021 Set 2 | Question: 33
A machine of mass $\text{100 kg}$ is subjected to an external harmonic force with a frequency of $\text{40 rad/s}$. The designer decides to mount the machine on an isolator to reduce the force transmitted to the foundation. The isolator can be considered as a combination ... the force transmitted to the foundation. $1-3-4-2$ $1-3-2-4$ $4-3-1-2$ $3-1-2-4$
A machine of mass $\text{100 kg}$ is subjected to an external harmonic force with a frequency of $\text{40 rad/s}$. The designer decides to mount the machine on an isolat...
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Mar 1, 2021
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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 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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Feb 22, 2021
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GATE Mechanical 2024 | Question: 20
The grinding wheel used to provide the best surface finish is $\mathrm{A} 36 \mathrm{~L} 5 \mathrm{~V}$ $\mathrm{A} 54 \mathrm{~L} 5 \mathrm{~V}$ $\mathrm{A} 60 \mathrm{~L} 5 \mathrm{~V}$ $\mathrm{A} 80 \mathrm{~L} 5 \mathrm{~V}$
The grinding wheel used to provide the best surface finish is$\mathrm{A} 36 \mathrm{~L} 5 \mathrm{~V}$$\mathrm{A} 54 \mathrm{~L} 5 \mathrm{~V}$$\mathrm{A} 60 ...
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GATE Mechanical 2022 Set 2 | Question: 48
A cylindrical billet of $100$ $\text{mm}$ diameter and $100$ $\text{mm}$ length is extruded by a direct extrusion process to produce a bar of $L$-section. The cross sectional dimensions of this $L$-section bar are shown in the ... $\text{kN}$ (round off to one decimal place).
A cylindrical billet of $100$ $\text{mm}$ diameter and $100$ $\text{mm}$ length is extruded by a direct extrusion process to produce a bar of $L$-section. The cross secti...
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Feb 15, 2022
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GATE Mechanical 2021 Set 2 | Question: 37
A cast product of a particular material has dimensions $75\: \text{mm} \times 125\: \text{mm} \times 20 \:\text{mm}$. The total solidification time for the cast product is found to be $2.0$ minutes as calculated using Chvorinov's ... = $\text{50 mm}$, the total solidification time will be ______ minutes ($\textit{round off to two decimal places}$).
A cast product of a particular material has dimensions $75\: \text{mm} \times 125\: \text{mm} \times 20 \:\text{mm}$. The total solidification time for the cast product i...
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Mar 1, 2021
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GATE2020-ME-2: 41
A steel spur pinion has a module $(m)$ of $1.25$ mm, $20$ teeth and $20^\circ$ pressure angle. The pinion rotates at $1200$ rpm and transmits power to a $60$ teeth gear. The face width $(F)$ is $50$ mm, Lewis form factor $Y=0.322$ and a ... round off to one decimal place). Lewis formula: $\sigma = \dfrac{K_vW^t}{FmY}$, where $W^t$ is the tangential load acting on the pinion.
A steel spur pinion has a module $(m)$ of $1.25$ mm, $20$ teeth and $20^\circ$ pressure angle. The pinion rotates at $1200$ rpm and transmits power to a $60$ teeth gear. ...
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Sep 18, 2020
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GATE Mechanical 2024 | Question: 15
A linear spring-mass-dashpot system with a mass of $2 \mathrm{~kg}$ is set in motion with viscous damping. If the natural frequency is $15 \mathrm{~Hz}$, and the amplitudes of two successive cycles measured are $7.75 \mathrm{~mm}$ and $7.20 \mathrm{~mm}$, the coefficient of viscous damping (in $\text{N.s/m}$) is $4.41$ $7.51$ $2.52$ $6.11$
A linear spring-mass-dashpot system with a mass of $2 \mathrm{~kg}$ is set in motion with viscous damping. If the natural frequency is $15 \mathrm{~Hz}$, and ...
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Feb 16
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GATE Mechanical 2024 | Question: 37
A heat pump $\text{(H.P.)}$ is driven by the work output of a heat engine $\text{(H.E.)}$ as shown in the figure. The heat engine extracts $150 \mathrm{~kJ}$ of heat from the source at $1000 \mathrm{~K}$. The heat pump ... , the total amount of heat delivered to the room together by the heat engine and heat pump is ___________ $\mathrm{kJ}$ (answer in integer).
A heat pump $\text{(H.P.)}$ is driven by the work output of a heat engine $\text{(H.E.)}$ as shown in the figure. The heat engine extracts $150 \mathrm{~kJ}$ of heat from...
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Feb 16
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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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Feb 22, 2021
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GATE2020-ME-2: 15
In the space above the mercury column in a barometer tube, the gauge pressure of the vapour is positive, but more than one atmosphere negative zero positive, but less than one atmosphere
In the space above the mercury column in a barometer tube, the gauge pressure of the vapour ispositive, but more than one atmospherenegativezeropositive, but less than on...
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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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Feb 22, 2021
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GATE Mechanical 2022 Set 2 | Question: 42
In the configuration of the planar four-bar mechanism at a certain instant as shown in the figure, the angular velocity of the $2$ $\text{cm}$ long link is $w_{2} = 5$ $\text{rad/s}$. Given the dimensions as shown, the magnitude of the angular ... of the $4$ $\text{cm}$ long link is given by ______________ $\text{rad/s}$ (round off to $2$ decimal places).
In the configuration of the planar four-bar mechanism at a certain instant as shown in the figure, the angular velocity of the $2$ $\text{cm}$ long link is $w_{2} = 5$ $...
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GATE Mechanical 2022 Set 2 | Question: 51
At steady state, $500$ $\text{kg/s}$ of steam enters a turbine with specific enthalpy equal to $3500$ $\text{kJ/kg}$ and specific entropy equal to $6.5$ ${kJ \cdot kg^{-1} \cdot K^{-1}}$. It expands reversibly in the turbine to the ... $\text{MW}$ (in integer).
At steady state, $500$ $\text{kg/s}$ of steam enters a turbine with specific enthalpy equal to $3500$ $\text{kJ/kg}$ and specific entropy equal to $6.5$ ${kJ \cdot kg^{-1...
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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 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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Feb 22, 2021
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GATE Mechanical 2024 | Question: 51
Aluminium is casted in a cube-shaped mold having dimensions as $20 \mathrm{~mm} \times 20 \mathrm{~mm} \times 20 \mathrm{~mm}$ ... is the same. The ratio of the solidification times of the cube-shaped mold to the spherical mold is __________ (answer in integer).
Aluminium is casted in a cube-shaped mold having dimensions as $20 \mathrm{~mm} \times 20 \mathrm{~mm} \times 20 \mathrm{~mm}$. Another mold of the same mold material is ...
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GATE Mechanical 2022 Set 1 | Question: 46
A $4$ $\text{mm}$ thick aluminum sheet of width $w = 100$ $\text{mm}$ is rolled in a two-roll mill of roll diameter $200$ $\text{mm}$ ... $\bar{\sigma}$ is average flow stress, $L$ is roll-workpiece contact length, and $\bar{h}$ is the average sheet thickness.
A $4$ $\text{mm}$ thick aluminum sheet of width $w = 100$ $\text{mm}$ is rolled in a two-roll mill of roll diameter $200$ $\text{mm}$ each. The workpiece is lubricated wi...
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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 2024 | Question: 52
A blanking operation is performed on $\text{C}20$ steel sheet to obtain a circular disc having a diameter of $20 \mathrm{~mm}$ and a thickness of $2 \mathrm{~mm}$. An allowance of $0.04$ is provided. The punch size used for the operation is _________ $\mathrm{mm}$ (rounded off to $2$ decimal places).
A blanking operation is performed on $\text{C}20$ steel sheet to obtain a circular disc having a diameter of $20 \mathrm{~mm}$ and a thickness of $2 \mathrm{~mm}$. An all...
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GATE Mechanical 2022 Set 2 | Question: 49
A project consists of five activities $\text{(A, B, C, D and E)}$. The duration of each activity follows beta distribution. The three time estimates (in weeks) of each activity and immediate predecessor$(s)$ are listed in the table. The expected time of the project completion is ... Pessimistic time A 4 5 6 None B 1 3 5 A C 1 2 3 A D 2 4 6 C E 3 4 5 B, D
A project consists of five activities $\text{(A, B, C, D and E)}$. The duration of each activity follows beta distribution. The three time estimates (in weeks) of each ac...
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GATE Mechanical 2024 | Question: 5
Let $f(.)$ be a twice differentiable function from $\mathbb{R}^2 \rightarrow \mathbb{R}$. If $\boldsymbol{p}, x_0 \in \mathbb{R}^2$ where $\|p\|$ is sufficiently small (here $|| . ||$ ... $\boldsymbol{p}^{T} \nabla^{2} f(\boldsymbol{\psi}) \boldsymbol{p}<0$
Let $f(.)$ be a twice differentiable function from $\mathbb{R}^2 \rightarrow \mathbb{R}$. If $\boldsymbol{p}, x_0 \in \mathbb{R}^2$ where $\|p\|$ is sufficiently...
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GATE Mechanical 2024 | Question: 11
Which one of the following statements regarding a Rankine cycle is FALSE? Superheating the steam in the boiler increases the cycle efficiency. The pressure at the turbine outlet depends on the condenser temperature. Cycle efficiency increases as condenser pressure decreases. Cycle efficiency increases as boiler pressure decreases.
Which one of the following statements regarding a Rankine cycle is FALSE?Superheating the steam in the boiler increases the cycle efficiency.The pressure at t...
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GATE Mechanical 2024 | Question: 14
A ram in the form of a rectangular body of size $l=9 \mathrm{~m}$ and $b=2 \mathrm{~m}$ is suspended by two parallel ropes of lengths $7 \mathrm{~m}$ ... from which the ram should be released from rest? $67.1^{\circ}$ $40.2^{\circ}$ $35.1^{\circ}$ $79.5^{\circ}$
A ram in the form of a rectangular body of size $l=9 \mathrm{~m}$ and $b=2 \mathrm{~m}$ is suspended by two parallel ropes of lengths $7 \mathrm{~m}$. Assume ...
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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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