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Recent questions tagged gateme-2022-set1
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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 $0.387$ $0.864$ $0.475$ $0.775$
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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 _______________ ... $5$ $10$ $8$ $9$
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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 ____________ $m/s$. $\frac{1}{24}$ $\frac{1}{6}$ $\frac{1}{18}$ $\frac{1}{12}$
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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 ________________$N$. $350 \pi^{2}$ $750 \pi$ $1000 \pi$ $3000$
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GATE Mechanical 2022 Set 1 | Question: 35
Consider a rod of uniform thermal conductivity whose one end $(x = 0)$ is insulated and the other end $(x =L)$ is exposed to flow of air at temperature $T_{\infty}$ with convective heat transfer coefficient $h$. The cylindrical surface of the rod is insulated so that the heat ...
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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 ... $\alpha$? $x = 2, y = -2$ $x = -1, y = 4$ $x = 1, y = 1$ $x = 4, y = -2$
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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).
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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).
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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).
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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).
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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).
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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 by ... $\%$ (round off to $3$ decimal places).
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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)
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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).
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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).
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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.
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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).
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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).
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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).
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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)
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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)
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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)
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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).
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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).
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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 $4^{\circ}C$ and leaves at $18^{\circ}C$. ... $2$ decimal places).
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