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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 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 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 2024 | Question: 42
The Levai type-$\text{A}$ train illustrated in the figure has gears with module $m=8 \mathrm{~mm} /$ tooth. Gears $2$ and $3$ have $19$ and $24$ teeth respectively. Gear $2$ is fixed and internal gear $4$ ... $\text{rev/min}$. (rounded off to $2$ decimal places)
The Levai type-$\text{A}$ train illustrated in the figure has gears with module $m=8 \mathrm{~mm} /$ tooth. Gears $2$ and $3$ have $19$ and $24$ teeth respectively. Gear ...
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GATE Mechanical 2024 | Question: 49
A band brake shown in the figure has a coefficient of friction of $0.3$. The band can take a maximum force of $1.5 \mathrm{kN}$. The maximum braking force $\text{(F)}$ that can be safely applied is ___________ $\mathrm{N}$ (rounded off to the nearest integer).
A band brake shown in the figure has a coefficient of friction of $0.3$. The band can take a maximum force of $1.5 \mathrm{kN}$. The maximum braking force $\text{(F)}$ th...
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transfer function for second order system
A second order real system has the following properties.The damping ratio is 0.5 and undamped natural frequency is 10rad/sec, the steady state value at zero is 1.02.the transfer function for the system is?
A second order real system has the following properties.The damping ratio is 0.5 and undamped natural frequency is 10rad/sec, the steady state value at zero is 1.02.the t...
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GATE Mechanical 2023 | GA Question: 9
How many pairs of sets $\text{(S, T)}$ are possible among the subsets of $\{1,2,3,4,5,6\}$ that satisfy the condition that $\mathrm{S}$ is a subset of $\mathrm{T}?$ $729$ $728$ $665$ $664$
How many pairs of sets $\text{(S, T)}$ are possible among the subsets of $\{1,2,3,4,5,6\}$ that satisfy the condition that $\mathrm{S}$ is a subset of $\mathrm{T}?$ $729$...
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GATE Mechanical 2023 | Question: 6
The effective stiffness of a cantilever beam of length $L$ and flexural rigidity $E I$ subjected to a transverse tip load $\mathrm{W}$ is $\frac{3 E I}{L^{3}}$ $\frac{2 E I}{L^{3}}$ $\frac{L^{3}}{2 E I}$ $\frac{L^{3}}{3 E I}$
The effective stiffness of a cantilever beam of length $L$ and flexural rigidity $E I$ subjected to a transverse tip load $\mathrm{W}$ is$\frac{3 E I}{L^{3}}$$\frac{2 E I...
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GATE Mechanical 2023 | Question: 8
The $\text{S-N}$ curve from a fatigue test for steel is shown. Which one of the options gives the endurance limit? $S_{u t}$ $S_2$ $S_3$ $S_4$
The $\text{S-N}$ curve from a fatigue test for steel is shown. Which one of the options gives the endurance limit? $S_{u t}$$S_2$$S_3$$S_4$
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GATE Mechanical 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 2023 | Question: 42
A steel sample with $1.5 \; \mathrm{wt}. \%$ carbon (no other alloying elements present) is slowly cooled from $1100^{\circ} \mathrm{C}$ ... the total cementite content in the microstructure that develops just below the eutectoid temperature is ___________. (Rounded off to two decimal places)
A steel sample with $1.5 \; \mathrm{wt}. \%$ carbon (no other alloying elements present) is slowly cooled from $1100^{\circ} \mathrm{C}$ to just below the eutectoid tempe...
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GATE Mechanical 2023 | Question: 1
A machine produces a defective component with a probability of $0.015$. The number of defective components in a packed box containing $200$ components produced by the machine follows a Poisson distribution. The mean and the variance of the distribution are $3$ ... $\sqrt{3}$, respectively $0.015$ and $0.015$, respectively $3$ and $9$, respectively
A machine produces a defective component with a probability of $0.015$. The number of defective components in a packed box containing $200$ components produced by the mac...
1 answers
2 votes
GATE Mechanical 2023 | GA Question: 3
A certain country has $504$ universities and $25951$ colleges. These are categorised into Grades I, II, and III as shown in the given pie charts. What is the percentage, correct to one decimal place, of higher education institutions (colleges and universities) that fall into Grade III? $22.7$ $23.7$ $15.0$ $66.8$
A certain country has $504$ universities and $25951$ colleges. These are categorised into Grades I, II, and III as shown in the given pie charts.What is the percentage, c...
1 answers
2 votes
GATE Mechanical 2023 | GA Question: 4
The minute-hand and second-hand of a clock cross each other ___________ times between $09:15:00$ AM and $09:45:00$ AM on a day. $30$ $15$ $29$ $31$
The minute-hand and second-hand of a clock cross each other ___________ times between $09:15:00$ AM and $09:45:00$ AM on a day.$30$$15$$29$$31$
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GATE Mechanical 2023 | GA Question: 10
An opaque pyramid (shown below), with a square base and isosceles faces, is suspended in the path of a parallel beam of light, such that its shadow is cast on a screen oriented perpendicular to the direction of the light beam. The pyramid can be reoriented in any ... $\mathbf{S}$ is NOT possible? $\mathbf{P}$ $\mathbf{Q}$ $\mathbf{R}$ $\mathbf{S}$
An opaque pyramid (shown below), with a square base and isosceles faces, is suspended in the path of a parallel beam of light, such that its shadow is cast on a screen or...
2 answers
2 votes
GATE Mechanical 2023 | GA Question: 5
The symbols $\bigcirc, \ast , \bigtriangleup$, and $\square$ are to be filled, one in each box, as shown below. The rules for filling in the four symbols are as follows. Every row and every column must contain each of the four symbols. ... will occupy the box marked with '?' in the partially filled figure? $\bigcirc$ $\ast$ $\bigtriangleup$ $\square$
The symbols $\bigcirc, \ast , \bigtriangleup$, and $\square$ are to be filled, one in each box, as shown below.The rules for filling in the four symbols are as follows.Ev...
1 answers
3 votes
GATE Mechanical 2023 | GA Question: 1
He did not manage to fix the car himself, so he ________ in the garage. got it fixed getting it fixed gets fixed got fixed
He did not manage to fix the car himself, so he ________ in the garage.got it fixedgetting it fixedgets fixedgot fixed
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2 votes
GATE Mechanical 2023 | GA Question: 6
In a recently held parent-teacher meeting, the teachers had very few complaints about Ravi. After all, Ravi was a hardworking and kind student. Incidentally, almost all of Ravi's friends at school were hardworking and kind too. But the ... and kind. None of Ravi's friends are interested in sports. Some of Ravi's friends are hardworking and kind.
In a recently held parent-teacher meeting, the teachers had very few complaints about Ravi. After all, Ravi was a hardworking and kind student. Incidentally, almost all o...
1 answers
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GATE Mechanical 2023 | GA Question: 2
Planting : Seed: : Raising: _________ (By word meaning) Child Temperature Height Lift
Planting : Seed: : Raising: _________(By word meaning)ChildTemperatureHeightLift
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