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GATE Mechanical 2021 Set 1 | Question: 16
Consider a reciprocating engine with crank radius $\text{R}$ and connecting rod of length $\text{L}$ ... $\frac{L}{2}$ rotating at twice the engine speed

Consider a reciprocating engine with crank radius $\text{R}$ and connecting rod of length $\text{L}$. The secondary unbalance force for this case is equivalent to primary...

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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: 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 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: 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 2021 Set 2 | Question: 53
A cantilever beam with a uniform flexural rigidity ($\text{EI} = 200 \times 10^{6} \text{N.m}^{2}$ ) is loaded with a concentrated force at its free end. The area of the bending moment diagram corresponding to the full length of the ... magnitude of the slope of the beam at its free end is ______ micro radian ($\textit{round off to the nearest integer}$).

A cantilever beam with a uniform flexural rigidity ($\text{EI} = 200 \times 10^{6} \text{N.m}^{2}$ ) is loaded with a concentrated force at its free end. The area of the ...

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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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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: 12
For a ball bearing, the fatigue life in millions of revolutions is given by $L=\left(\frac{C}{P}\right)^{n}$, where $\text{P}$ is the constant applied load and $\text{C}$ is the basic dynamic load rating. Which one of the ... outer racing is fixed and inner racing is revolving $n=1 / 3$, assuming that the outer racing is fixed and inner racing is revolving

For a ball bearing, the fatigue life in millions of revolutions is given by $L=\left(\frac{C}{P}\right)^{n}$, where $\text{P}$ is the constant applied load and $...

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GATE Mechanical 2021 Set 1 | Question: 45
Consider a steam power plant operating on an ideal reheat Rankine cycle. The work input to the pump is $\text{20 kJ/kg}$. The work output from the high pressure turbine is $\text{750 kJ/kg}$. The work output from the low pressure turbine is ... of steam at the exit of the low pressure turbine is ______ $\%$ ($\textit{round off to the nearest integer}$).

Consider a steam power plant operating on an ideal reheat Rankine cycle. The work input to the pump is $\text{20 kJ/kg}$. The work output from the high pressure turbine i...

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GATE2020-ME-2: 43
A cylindrical bar with $200$ mm diameter is being turned with a tool having geometry $0 ^\circ - 9 ^\circ -7^ \circ - 8^ \circ - 15^ \circ - 30^ \circ - 0.05$ inch (coordinate system, ASA) resulting in a cutting force $F_{c1}$. If the tool geometry is ... .e. $\displaystyle \bigg( \frac{F_{c2} - F_{c1}}{F_{c1}} \bigg) \times 100$, is ________ (round off to one decimal place)

A cylindrical bar with $200$ mm diameter is being turned with a tool having geometry $0 ^\circ – 9 ^\circ -7^ \circ – 8^ \circ – 15^ \circ – 30^ \circ – 0.05$ i...

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GATE Mechanical 2024 | Question: 8
Consider incompressible laminar flow over a flat plate with freestream velocity of $u_{\infty}$. The Nusselt number corresponding to this flow velocity is $N u_{1}$. If the freestream velocity is doubled, the Nusselt number changes to $\mathrm{Nu}_{2}$. Choose the correct option for $N u_{2} / N u_{1}$. $\sqrt{2}$ $2$ $1.26$ $1$

Consider incompressible laminar flow over a flat plate with freestream velocity of $u_{\infty}$. The Nusselt number corresponding to this flow velocity is ...

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GATE Mechanical 2022 Set 2 | Question: 31
Parts $P1 - P7$ are machined first on a milling machine and then polished at a separate machine. Using the information in the following table, the minimum total completion time required tor carrying out both the operations for all $7$ ... $31$ $33$ $30$ $32$

Parts $P1 – P7$ are machined first on a milling machine and then polished at a separate machine. Using the information in the following table, the minimum total complet...

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GATE Mechanical 2022 Set 2 | Question: 45
ln an orthogonal machining operation, the cutting and thrust forces are equal in magnitude. The uncut chip thickness is $0.5$ $\text{mm}$ and the shear angle is $15^{\circ}$. The orthogonal rake angle of the tool is $0^{\circ}$ and ... strength is $500$ $\text{MPa}$. The cutting force is ___________________ $\text{N}$ (round off to the nearest integer).

ln an orthogonal machining operation, the cutting and thrust forces are equal in magnitude. The uncut chip thickness is $0.5$ $\text{mm}$ and the shear angle is $15^{\cir...

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GATE Mechanical 2024 | Question: 25
A queueing system has one single server workstation that admits an infinitely long queue. The rate of arrival of jobs to the queueing system follows the Poisson distribution with a mean of $5$ jobs/hour. The service time of the server is exponentially distributed ... probability that the server is not busy at any point in time is $0.20$ $0.17$ $0.50$ $0.83$

A queueing system has one single server workstation that admits an infinitely long queue. The rate of arrival of jobs to the queueing system follows the Po...

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GATE Mechanical 2021 Set 1 | Question: 17
A cantilever beam of length, $\text{L}$, and flexural rigidity, $\text{EI}$, is subjected to an end moment, $\text{M}$, as shown in the figure. The deflection of the beam at $x=\frac{L}{2}$ is $\frac{ML^{2}}{2EI}$ $\frac{ML^{2}}{4EI}$ $\frac{ML^{2}}{8EI}$ $\frac{ML^{2}}{16EI}$

A cantilever beam of length, $\text{L}$, and flexural rigidity, $\text{EI}$, is subjected to an end moment, $\text{M}$, as shown in the figure. The deflection of the beam...

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GATE Mechanical 2024 | Question: 4
Consider the system of linear equations \[ \begin{array}{c} x+2 y+z=5 \\ 2 x+a y+4 z=12 \\ 2 x+4 y+6 z=b \end{array} \] The values of $a$ and $b$ such that there exists a non-trivial null space and the system admits infinite solutions are $a=8, b=14$ $a=4, b=12$ $a=8, b=12$ $a=4, b=14$

Consider the system of linear equations\[\begin{array}{c}x+2 y+z=5 \\2 x+a y+4 z=12 \\2 x+4 y+6 z=b\end{array}\]The values of $a$ and $b$ such that there e...

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GATE Mechanical 2024 | Question: 43
A horizontal beam of length $1200 \mathrm{~mm}$ is pinned at the left end and is resting on a roller at the other end as shown in the figure. A linearly varying distributed load is applied on the beam. The magnitude of maximum bending moment acting on the beam is ________ $\text{N.m}$. (round off to $1$ decimal place)

A horizontal beam of length $1200 \mathrm{~mm}$ is pinned at the left end and is resting on a roller at the other end as shown in the figure. A linearly varying distribut...

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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 2021 Set 2 | Question: 47
Consider the open feed water heater $\text{(FWH)}$ shown in the figure given below: Specific enthalpy of steam at location $2$ is $\text{2624 kJ/kg}$, specific enthalpy of water at location $5$ is $\text{226.7 kJ/kg}$ and specific enthalpy ... then the mass flow rate of steam at location $2$ will be ________ $\text{kg/s}$ (round off to one decimal place).

Consider the open feed water heater $\text{(FWH)}$ shown in the figure given below:Specific enthalpy of steam at location $2$ is $\text{2624 kJ/kg}$, specific enthalpy of...

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GATE Mechanical 2024 | Question: 28
A company orders gears in conditions identical to those considered in the economic order quantity $\text{(EOQ)}$ model in inventory control. The annual demand is $8000$ gears, the cost per order is $300$ rupees, and the holding cost is $12$ ... cost of ordering and holding inventory from that associated with the optimal order quantity is $2.5$ $5$ $0$ $12.5$

A company orders gears in conditions identical to those considered in the economic order quantity $\text{(EOQ)}$ model in inventory control. The annual demand...

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GATE Mechanical 2021 Set 1 | Question: 15
The relative humidity of ambient air at $\text{300 K}$ is $50\%$ with a partial pressure of water vapour equal to $p_{v}$. The saturation pressure of water at $\text{300 K}$ is $p_{sat}$. The correct relation for the air-water mixture is $p_{v}=0.5\:p_{sat}$ $p_{v}=p_{sat}$ $p_{v}=0.622\:p_{sat}$ $p_{v}=2\:p_{sat}$

The relative humidity of ambient air at $\text{300 K}$ is $50\%$ with a partial pressure of water vapour equal to $p_{v}$. The saturation pressure of...

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GATE Mechanical 2024 | Question: 41
A liquid fills a horizontal capillary tube whose one end is dipped in a large pool of the liquid. Experiments show that the distance $L$ travelled by the liquid meniscus inside the capillary in time $t$ is given by \[ L=k \gamma^{a} R^{b} \ ... of the liquid. If $k$ is a dimensionless constant, then the exponent $a$ is ________ (rounded off to $1$ decimal place).

A liquid fills a horizontal capillary tube whose one end is dipped in a large pool of the liquid. Experiments show that the distance $L$ travelled by the liquid meniscus ...

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GATE Mechanical 2021 Set 2 | Question: 41
The thickness, width and length of a metal slab are $\text{50 mm}$, $\text{250 mm}$ and $\text{3600 mm}$, respectively. A rolling operation on this slab reduces the thickness by $10\%$ and increases the width by $3\%$. The length of the rolled slab is ________ $\text{mm} \:(\textit{round off to one decimal place}$).

The thickness, width and length of a metal slab are $\text{50 mm}$, $\text{250 mm}$ and $\text{3600 mm}$, respectively. A rolling operation on this slab reduces the thick...

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GATE Mechanical 2021 Set 1 | Question: 44
A solid sphere of radius $\text{10 mm}$ is placed at the centroid of a hollow cubical enclosure of side length $\text{30 mm}$. The outer surface of the sphere is denoted by $1$ and the inner surface of the cube is denoted by $2$. The view factor $F_{22}$ for radiation heat transfer is ______ ($\textit{rounded off to two decimal places}$).

A solid sphere of radius $\text{10 mm}$ is placed at the centroid of a hollow cubical enclosure of side length $\text{30 mm}$. The outer surface of the sphere is denoted ...

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GATE Mechanical 2024 | Question: 50
A cutting tool provides a tool life of $60$ minutes while machining with the cutting speed of $60 \mathrm{~m} / \mathrm{min}$. When the same tool is used for machining the same material, it provides a tool life of $10$ ... material combination, the tool life computed using Taylor's tool life model is ________ minutes (rounded off to $2$ decimal places).

A cutting tool provides a tool life of $60$ minutes while machining with the cutting speed of $60 \mathrm{~m} / \mathrm{min}$. When the same tool is used for machining th...

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GATE Mechanical 2024 | Question: 16
Which one of the following failure theories is the most conservative design approach against fatigue failure? Soderberg line Modified Goodman line Gerber line Yield line

Which one of the following failure theories is the most conservative design approach against fatigue failure?Soderberg lineModified Goodman lineGerber lineYie...

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GATE Mechanical 2024 | Question: 19
The "Earing" phenomenon in metal forming is associated with deep drawing rolling extrusion forging

The "Earing" phenomenon in metal forming is associated withdeep drawingrollingextrusionforging

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GATE Mechanical 2024 | Question: 21
The allowance provided to a pattern for easy withdrawal from a sand mold is finishing allowance shrinkage allowance distortion allowance shake allowance

The allowance provided to a pattern for easy withdrawal from a sand mold isfinishing allowanceshrinkage allowancedistortion allowanceshake allowance

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GATE Mechanical 2021 Set 2 | Question: 54
The torque provided by an engine is given by $T(\theta) =12000+ 2500 \sin(2 \theta) \text{N.m}$, where $\theta$ is the angle turned by the crank from inner dead center. The mean speed of the engine is $\text{200 rpm}$ and it ... minimum mass moment of inertia of the flywheel should be _______ $\text{kg.m}^{2} (\textit{round off to the nearest integer}$).

The torque provided by an engine is given by $T(\theta) =12000+ 2500 \sin(2 \theta) \text{N.m}$, where $\theta$ is the angle turned by the crank from inner dead center. T...

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GATE Mechanical 2024 | Question: 36
A piston-cylinder arrangement shown in the figure has a stop located $2 \mathrm{~m}$ above the base. The cylinder initially contains air at $140 \mathrm{kPa}$ and $350^{\circ} \mathrm{C}$ and the piston is resting in equilibrium at a ... of specific work done during the process is ___________ $\mathrm{kJ} / \mathrm{kg}$ (rounded off to $1$ decimal place)

A piston-cylinder arrangement shown in the figure has a stop located $2 \mathrm{~m}$ above the base. The cylinder initially contains air at $140 \mathrm{kPa}$ and $350^{\...

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GATE Mechanical 2021 Set 1 | Question: 42
Consider a single machine workstation to which jobs arrive according to a Poisson distribution with a mean arrival rate of $12$ jobs/hour. The process time of the workstation is exponentially distributed with a mean of $4$ minutes. The expected ... at the workstation at any given point of time is _______ ($\textit{round off to the nearest integer}$).

Consider a single machine workstation to which jobs arrive according to a Poisson distribution with a mean arrival rate of $12$ jobs/hour. The process time of the worksta...

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GATE Mechanical 2024 | Question: 6
The velocity field of a two-dimensional, incompressible flow is given by \[ \vec{V}=2 \sinh x \hat{\imath}+v(x, y) \hat{\jmath} \] where $\hat{\imath}$ and $\hat{\jmath}$ denote the unit vectors in $x$ and $y$ directions, respectively. If $v(x, 0)=\cosh x$, then $v(0,-1)$ is $1$ $2$ $3$ $4$

The velocity field of a two-dimensional, incompressible flow is given by\[\vec{V}=2 \sinh x \hat{\imath}+v(x, y) \hat{\jmath}\]where $\hat{\imath}$ and $\hat{...

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GATE Mechanical 2024 | Question: 33
If $x(t)$ satisfies the differential equation \[ t \frac{d x}{d t}+(t-x)=0 \] subject to the condition $x(1)=0$, then the value of $x(2)$ is __________ (rounded off to 2 decimal places).

If $x(t)$ satisfies the differential equation\[t \frac{d x}{d t}+(t-x)=0\]subject to the condition $x(1)=0$, then the value of $x(2)$ is __________ (rounded off to 2 deci...

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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 2021 Set 1 | Question: 47
A cylindrical jet of water (density = $1000 \text{ kg/m}^{3}$ ... jet, then the velocity of the incoming jet is ___________________ $\text{m/s} (\textit{round off to one decimal place}$).

A cylindrical jet of water (density = $1000 \text{ kg/m}^{3}$) impinges at the center of a flat, circular plate and spreads radially outwards, as shown in the figure. The...

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GATE Mechanical 2024 | Question: 32
If the value of the double integral \[ \int_{x=3}^{4} \int_{y=1}^{2} \frac{d y d x}{(x+y)^{2}} \] is $\log _{e}(a / 24)$, then $a$ is __________ (answer in integer).

If the value of the double integral\[\int_{x=3}^{4} \int_{y=1}^{2} \frac{d y d x}{(x+y)^{2}}\]is $\log _{e}(a / 24)$, then $a$ is __________ (answer in integer).

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GATE Mechanical 2021 Set 1 | Question: 48
A single jet Pelton wheel operates at $\text{300 rpm}$. The mean diameter of the wheel is $\text{2 m}$. Operating head and dimensions of jet are such that water comes out of the jet with a velocity of $\text{40 m/s}$ and flow rate ... all losses, the power developed by the Pelton wheel is _______ $\text{MW}$ ($\textit{round off to two decimal places}$).

A single jet Pelton wheel operates at $\text{300 rpm}$. The mean diameter of the wheel is $\text{2 m}$. Operating head and dimensions of jet are such that water comes out...

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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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