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GATE Mechanical 2022 Set 1 | Question: 37
Let a random variable $X$ follow Poisson distribution such that $\text{Prob (X = 1) = Prob (X = 2)}$. The value of $\text{Prob (X = 3)}$ is ______________ (round off to $2$ decimal places).
Let a random variable $X$ follow Poisson distribution such that $$\text{Prob (X = 1) = Prob (X = 2)}$$. The value of $\text{Prob (X = 3)}$ is ______________ (round off t...
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GATE Mechanical 2022 Set 1 | Question: 38
Consider two vectors: $\vec{a} = 5 i + 7j + 2k$$\vec{b} = 3 i - j + 6k$ Magnitude of the component of $\vec{a}$ orthogonal to $\vec{b}$ in the plane containing the vectors $\vec{a}$ and $\vec{b}$ is _____________ (round off to $2$ decimal places).
Consider two vectors: $$\vec{a} = 5 i + 7j + 2k$$$$\vec{b} = 3 i - j + 6k$$Magnitude of the component of $\vec{a}$ orthogonal to $\vec{b}$ in the plane containing the vec...
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GATE Mechanical 2022 Set 1 | Question: 39
A structure, along with the loads applied on it, is shown in the figure. Self-weight of all the members is negligible and all the pin joints are friction-less. $AE$ is a single member that contains pin $C$. Likewise, $BE$ is a ... and $FH$ are overlapping rigid members. The magnitude of the force carried by member $CI$ is ______________ $kN$ (in integer).
A structure, along with the loads applied on it, is shown in the figure. Self-weight of all the members is negligible and all the pin joints are friction-less. $AE$ is a ...
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GATE Mechanical 2022 Set 1 | Question: 40
Two rigid massless rods $PR$ and $RQ$ are joined at frictionless pin-joint $R$ and are resting on ground at $P$ and $Q$, respectively, as shown in the figure. A vertical force $F$ acts on the pin $R$ ... friction at $Q$ to that at $P\left(\mu_{Q}/\mu_{P}\right)$ is ___________________ (round off to two decimal places).
Two rigid massless rods $PR$ and $RQ$ are joined at frictionless pin-joint $R$ and are resting on ground at $P$ and $Q$, respectively, as shown in the figure. A vertical ...
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GATE Mechanical 2022 Set 1 | Question: 41
A cylindrical disc of $\text{mass m = 1 kg}$ and $\text{radius r = 0.15 m}$ was spinning at $\omega =5\; rad/s$ when it was placed on a flat horizontal surface and released (refer to the figure). Gravity $g$ acts ... of the center of the disc, when it starts rolling without slipping, will be __________________$m/s$ (round off to $2$ decimal places).
A cylindrical disc of $\text{mass m = 1 kg}$ and $\text{radius r = 0.15 m}$ was spinning at $\omega =5\; rad/s$ when it was placed on a flat horizontal surface and releas...
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GATE Mechanical 2022 Set 1 | Question: 42
A thin-walled cylindrical pressure vessel has mean wall thickness of $t$ and nominal radius of $r$. The Poisson's ratio of the wall material is $1/3$. When it was subjected to some internal pressure, its nominal perimeter in the cylindrical portion increased ... $\%$ (round off to $3$ decimal places).
A thin-walled cylindrical pressure vessel has mean wall thickness of $t$ and nominal radius of $r$. The Poisson's ratio of the wall material is $1/3$. When it was subject...
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GATE Mechanical 2022 Set 1 | Question: 43
A schematic of an epicyclic gear train is shown in the figure. The sun $\text{(gear 1)}$ and planet $\text{(gear 2)}$ are external, and the ring gear $\text{(gear 3)}$ is internal. Gear $1$, gear $3$ and arm $OP$ are ... $\text{(ccw)}$, the magnitude of angular velocity of arm $OP$ is _____________________ $\text{rpm}$ (in integer)
A schematic of an epicyclic gear train is shown in the figure. The sun $\text{(gear 1)}$ and planet $\text{(gear 2)}$ are external, and the ring gear $\text{(gear 3)}$ is...
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GATE Mechanical 2022 Set 1 | Question: 44
Under orthogonal cutting condition, a turning operation is carried out on a metallic workpiece at a cutting speed of $4\; m/s$. The orthogonal rake angle of the cutting tool is $5^{\circ}$ ... condition is $1000$ $\text{MPa}$, then the cutting force is _________________ $N$ (round off to one decimal place).
Under orthogonal cutting condition, a turning operation is carried out on a metallic workpiece at a cutting speed of $4\; m/s$. The orthogonal rake angle of the cutting t...
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GATE Mechanical 2022 Set 1 | Question: 45
A $1$ $\text{mm}$ thick cylindrical tube, $100$ $\text{mm}$ in diameter, is orthogonally turned such that the entire wall thickness of the tube is cut in a single pass. The axial feed of the tool is $1$ ... of feed force towards power. The power required to carry out this operation is _______________ $kW$ (round off to one decimal place).
A $1$ $\text{mm}$ thick cylindrical tube, $100$ $\text{mm}$ in diameter, is orthogonally turned such that the entire wall thickness of the tube is cut in a single pass. T...
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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 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 2022 Set 1 | Question: 48
An assignment problem is solved to minimize the total processing time of four jobs ($1,2,3$ and $4$) on four different machines such that each job is processed exactly by one machine and each machine processes exactly one ... machine has increased by $20$ minutes. The revised minimum total processing time will be ___________________ minutes (in integer).
An assignment problem is solved to minimize the total processing time of four jobs ($1,2,3$ and $4$) on four different machines such that each job is processed exactly by...
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GATE Mechanical 2022 Set 1 | Question: 49
The product structure diagram shows the number of different components required at each level to produce one unit of the final product $P$. If there are $50$ units of on-hand inventory of component $A$, the number of additional units of component $A$ needed to produce 10 units of product $P$ is ______________ (in integer).
The product structure diagram shows the number of different components required at each level to produce one unit of the final product $P$. If there are $50$ units of on-...
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GATE Mechanical 2022 Set 1 | Question: 50
Consider a one-dimensional steady heat conduction process through a solid slab of thickness $0.1\: m$. The higher temperature side $A$ has a surface temperature of $80^{\circ}C$, and the heat transfer rate per unit area to low temperature side ... per unit area during the heat transfer process is _______________ $W/m^{2}.K$ (round off to $2$ decimal places)
Consider a one-dimensional steady heat conduction process through a solid slab of thickness $0.1\: m$. The higher temperature side $A$ has a surface temperature of $80^{\...
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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: 52
An engine running on an air standard Otto cycle has a displacement volume $250\: cm^{3}$ and a clearance volume $35.7\: cm^{3}$. The pressure and temperature at the beginning of the compression process are $100$ ... constant during the cycle. The maximum pressure in the cycle is _______________ $\text{kPa}$ (round off to the nearest integer)
An engine running on an air standard Otto cycle has a displacement volume $250\: cm^{3}$ and a clearance volume $35.7\: cm^{3}$. The pressure and temperature at the begin...
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GATE Mechanical 2022 Set 1 | Question: 53
A steady two-dimensional flow field is specified by the stream function $\psi = kx^{3}y,$ where $x$ and $y$ are in meter and the constant $k = 1 \:m^{-2}\:s^{-1}$. The magnitude of acceleration at a point $(x, y) = (1\;m, 1\;m)$ is _______________ $m/s^{2}$ (round off to $2$ decimal places).
A steady two-dimensional flow field is specified by the stream function $$\psi = kx^{3}y,$$ where $x$ and $y$ are in meter and the constant $k = 1 \:m^{-2}\:s^{-1}$. The ...
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GATE Mechanical 2022 Set 1 | Question: 54
Consider a solid slab (thermal conductivity, $k = 10\; W \cdot m^{-1}\cdot K^{-1})$ with thickness $0.2\; m$ and of infinite extent in the other two directions as shown in the figure. Surface $2$, at $300 K$, is exposed ... $T_{1}$ of Surface $1$ of the slab, under steady-state conditions, is ______________ $K$ (round off to the nearest integer).
Consider a solid slab (thermal conductivity, $k = 10\; W \cdot m^{-1}\cdot K^{-1})$ with thickness $0.2\; m$ and of infinite extent in the other two directions as shown i...
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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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GATE Mechanical 2021 Set 2 | Question: 4
The Cast Iron which possesses all the carbon in the combined form as cementite is known as Grey Cast Iron Spheroidal Cast Iron Malleable Cast Iron White Cast Iron
The Cast Iron which possesses all the carbon in the combined form as cementite is known asGrey Cast IronSpheroidal Cast IronMalleable Cast IronWhite Cast Iron
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GATE Mechanical 2021 Set 2 | Question: 5
The size distribution of the powder particles used in Powder Metallurgy process can be determined by Laser scattering Laser reflection Laser absorption Laser penetration
The size distribution of the powder particles used in Powder Metallurgy process can be determined byLaser scatteringLaser reflectionLaser absorptionLaser penetration
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GATE Mechanical 2021 Set 2 | Question: 6
In a $\text{CNC}$ machine tool, the function of an interpolator is to generate signal for the lubrication pump during machining error signal for tool radius compensation during machining $\text{NC}$ code from the part drawing during post processing reference signal prescribing the shape of the part to be machined
In a $\text{CNC}$ machine tool, the function of an interpolator is to generatesignal for the lubrication pump during machiningerror signal for tool radius compensation du...
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GATE Mechanical 2021 Set 2 | Question: 7
The machining process that involves ablation is Abrasive Jet Machining Chemical Machining Electrochemical Machining Laser Beam Machining
The machining process that involves ablation isAbrasive Jet MachiningChemical MachiningElectrochemical MachiningLaser Beam Machining
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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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GATE Mechanical 2021 Set 2 | Question: 10
In forced convective heat transfer, Stanton number $\text{(St)}$, Nusselt number $\text{(Nu)}$, Reynolds number $\text{(Re)}$ and Prandtl number $\text{(Pr)}$ are related as $St=\frac{Nu}{Re\:Pr}$ $St=\frac{Nu\:Pr}{Re}$ $\text{St = Nu Pr Re}$ $St=\frac{Nu\:Re}{Pr}$
In forced convective heat transfer, Stanton number $\text{(St)}$, Nusselt number $\text{(Nu)}$, Reynolds number $\text{(Re)}$ and Prandtl number $\text{(Pr)}$ are related...
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GATE Mechanical 2021 Set 2 | Question: 12
Which of the following is responsible for eddy viscosity (or turbulent viscosity) in a turbulent boundary layer on a flat plate? Nikuradse stresses Reynolds stresses Boussinesq stresses Prandtl stresses
Which of the following is responsible for eddy viscosity (or turbulent viscosity) in a turbulent boundary layer on a flat plate?Nikuradse stressesReynolds stressesBoussin...
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GATE Mechanical 2021 Set 2 | Question: 14
A plane truss $\text{PQRS}$ ($\text{PQ=RS}$, and $\angle PQR=90^{\circ}$) is shown in the figure. The forces in the members $\text{PR}$ and $\text{RS}$, respectively, are _____________________ $F\sqrt{2}$ (tensile) and $\text{F}$ (tensile ... (compressive) $\text{F}$ (compressive) and $F\sqrt{2}$ (compressive) $\text{F}$ (tensile) and $F\sqrt{2}$ (tensile)
A plane truss $\text{PQRS}$ ($\text{PQ=RS}$, and $\angle PQR=90^{\circ}$) is shown in the figure.The forces in the members $\text{PR}$ and $\text{RS}$, respectively, are ...
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GATE Mechanical 2021 Set 2 | Question: 15
Consider the mechanism shown in the figure. There is rolling contact without slip between the disc and ground. Select the correct statement about instantaneous centers in the mechanism. Only points $\text{P, Q}$, and $\text{S}$ are instantaneous centers of ... mechanism All points $\text{P, Q, R, S, T}$ and $\text{U}$ are instantaneous centers of mechanism
Consider the mechanism shown in the figure. There is rolling contact without slip between the disc and ground.Select the correct statement about instantaneous centers in ...
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GATE Mechanical 2021 Set 2 | Question: 16
The controlling force curves $\text{P, Q,}$ and $\text{R}$ for a spring controlled governor are shown in the figure, where $r_{1}$ and $r_{2}$ are any two radii of rotation. The characteristics shown by the curves are $\text{P}$ ... $\text{R}$ - Unstable $\text{P}$ - Stable; $\text{Q}$ - Unstable; $\text{R}$ - Isochronous
The controlling force curves $\text{P, Q,}$ and $\text{R}$ for a spring controlled governor are shown in the figure, where $r_{1}$ and $r_{2}$ are any two radii of rotati...
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GATE Mechanical 2021 Set 2 | Question: 17
The von Mises stress at a point in a body subjected to forces is proportional to the square root of the total strain energy per unit volume plastic strain energy per unit volume dilatational strain energy per unit volume distortional strain energy per unit volume
The von Mises stress at a point in a body subjected to forces is proportional to the square root of thetotal strain energy per unit volumeplastic strain energy per unit v...
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GATE Mechanical 2021 Set 2 | Question: 20
Consider adiabatic flow of air through a duct. At a given point in the duct, velocity of air is $\text{300 m/s}$, temperature is $\text{330 K}$ and pressure is $\text{180 kPa}$. Assume that the air behaves as a perfect gas with constant ... $\text{K} (\textit{round off to two decimal places}$).
Consider adiabatic flow of air through a duct. At a given point in the duct, velocity of air is $\text{300 m/s}$, temperature is $\text{330 K}$ and pressure is $\text{180...
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GATE Mechanical 2021 Set 2 | Question: 21
Consider an ideal vapour compression refrigeration cycle working on $\text{R-134a}$ refrigerant. The $\text{COP}$ of the cycle is $10$ and the refrigeration capacity is $\text{150 kJ/kg}$. The heat rejected by the refrigerant in the condenser is __________ $\text{kJ/kg} (\textit{round off to the nearest integer}$).
Consider an ideal vapour compression refrigeration cycle working on $\text{R-134a}$ refrigerant. The $\text{COP}$ of the cycle is $10$ and the refrigeration capacity is $...
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GATE Mechanical 2021 Set 2 | Question: 22
A rigid tank of volume $50 \text{ m}^{3}$ contains a pure substance as a saturated liquid vapour mixture at $\text{400 kPa}$. Of the total mass of the mixture, $20\%$ mass is liquid and $80\%$ ... $\text{kg } (\textit{round off to the nearest integer}$).
A rigid tank of volume $50 \text{ m}^{3}$ contains a pure substance as a saturated liquid vapour mixture at $\text{400 kPa}$. Of the total mass of the mixture, $20\%$ mas...
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GATE Mechanical 2021 Set 2 | Question: 23
An object is moving with a Mach number of $0.6$ in an ideal gas environment, which is at a temperature of $\text{350 K}$. The gas constant is $\text{320 J/kg.K}$ and ratio of specific heats is $1.3$. The speed of object is _________ $\text{m/s} (\textit{round off to the nearest integer}$).
An object is moving with a Mach number of $0.6$ in an ideal gas environment, which is at a temperature of $\text{350 K}$. The gas constant is $\text{320 J/kg.K}$ and rati...
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GATE Mechanical 2021 Set 2 | Question: 24
A column with one end fixed and one end free has a critical buckling load of $\text{100 N}$. For the same column, if the free end is replaced with a pinned end then the critical buckling load will be _______ $\text{N}\; (\textit{round off to the nearest integer}$).
A column with one end fixed and one end free has a critical buckling load of $\text{100 N}$. For the same column, if the free end is replaced with a pinned end then the c...
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GATE Mechanical 2021 Set 2 | Question: 25
A steel cubic block of side $\text{200 mm}$ is subjected to hydrostatic pressure of $\text{250 N/mm}^{2}$. The elastic modulus is $2 \times 10^{5}\:\text{N/mm}^{2}$ and Poisson ratio is $0.3$ for steel. The side of the block is reduced by _________ $\text{mm}\: (\textit{round off to two decimal places}$).
A steel cubic block of side $\text{200 mm}$ is subjected to hydrostatic pressure of $\text{250 N/mm}^{2}$. The elastic modulus is $2 \times 10^{5}\:\text{N/mm}^{2}$ and P...
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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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GATE Mechanical 2021 Set 2 | Question: 30
Ambient pressure, temperature, and relative humidity at a location are $\text{101 kPa}$, $\text{300 K}$, and $60\%$, respectively. The saturation pressure of the water at $\text{300 K}$ is $\text{3.6 kPa}$. The specific humidity of ambient air is ____________________ $\text{g/kg}$ of dry air. $21.4$ $35.1$ $21.9$ $13.6$
Ambient pressure, temperature, and relative humidity at a location are $\text{101 kPa}$, $\text{300 K}$, and $60\%$, respectively. The saturation pressure of the water at...
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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 2021 Set 2 | Question: 32
A power transmission mechanism consists of a belt drive and a gear train as shown in the figure. Diameters of pulleys of belt drive and number of teeth $\text{(T)}$ on the gears $2$ to $7$ are indicated in the figure. The speed and ... $\text{255.68 rpm}$; anticlockwise $\text{575.28 rpm}$; clockwise $\text{575.28 rpm}$; anticlockwise
A power transmission mechanism consists of a belt drive and a gear train as shown in the figure.Diameters of pulleys of belt drive and number of teeth $\text{(T)}$ on the...
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