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GATE Mechanical 2023 | Question: 33
A cylindrical rod of length $h$ and diameter $d$ is placed inside a cubic enclosure of side length $L. S$ denotes the inner surface of the cube. The view-factor $F_{S-S}$ is $0$ $1$ $\frac{\left(\pi d h+\pi d^2 / 2\right)}{6 L^2}$ $1-\frac{\left(\pi d h+\pi d^2 / 2\right)}{6 L^2}$
A cylindrical rod of length $h$ and diameter $d$ is placed inside a cubic enclosure of side length $L. S$ denotes the inner surface of the cube. The view-factor $F_{S-S}$...
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GATE Mechanical 2023 | Question: 39
Consider the second-order linear ordinary differential equation $ x^2 \frac{d^2 y}{d x^2}+x \frac{d y}{d x}-y=0, \quad x \geq 1 $ with the initial conditions $ y(x=1)=6,\left.\quad \frac{d y}{d x}\right|_{x=1}=2 . $ The value of $y$ at $x=2$ equals __________. (Answer in integer)
Consider the second-order linear ordinary differential equation$$x^2 \frac{d^2 y}{d x^2}+x \frac{d y}{d x}-y=0, \quad x \geq 1$$with the initial conditions$$y(x=1)=6,\lef...
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GATE Mechanical 2022 Set 2 | GA Question: 6
Fish belonging to species $\text{S}$ in the deep sea have skins that are extremely black (ultra-black skin). This helps them not only to avoid predators but also sneakily attack their prey. However, having this extra layer of black ... $\text{S}$ but advantageous only to their predators
Fish belonging to species $\text{S}$ in the deep sea have skins that are extremely black (ultra-black skin). This helps them not only to avoid predators but also sneakily...
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GATE Mechanical 2022 Set 1 | GA Question: 6
Humans are naturally compassionate and honest. In a study using strategically placed wallets that appear "lost", it was found that wallets with money are more likely to be returned than wallets without money. Similarly, wallets ... are more likely to be returned than wallets that are really lost Money is always more important than keys
Humans are naturally compassionate and honest. In a study using strategically placed wallets that appear "lost", it was found that wallets with money are more likely to b...
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GATE Mechanical 2021 Set 2 | GA Question: 9
Consider a square sheet of side $1$ unit. The sheet is first folded along the main diagonal. This is followed by a fold along its line of symmetry. The resulting folded shape is again folded along its line of symmetry. The area of each face of the final folded shape, ... units, equal to _________ $\frac{1}{4}$ $\frac{1}{8}$ $\frac{1}{16}$ $\frac{1}{32}$
Consider a square sheet of side $1$ unit. The sheet is first folded along the main diagonal. This is followed by a fold along its line of symmetry. The resulting folded s...
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GATE Mechanical 2022 Set 2 | Question: 28
A linear elastic structure under plane stress condition is subjected to two sets of loading, $\text{I}$ and $\text{II}$. The resulting states of stress at a point corresponding to these two loadings are as shown in the figure below. If these two sets of loading are applied ... $\sigma /2$ $\sigma \left ( 1-1/\sqrt{2} \right )$
A linear elastic structure under plane stress condition is subjected to two sets of loading, $\text{I}$ and $\text{II}$. The resulting states of stress at a point corresp...
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GATE Mechanical 2022 Set 1 | GA Question: 7
A rhombus is formed by joining the midpoints of the sides of a unit square. What is the diameter of the largest circle that can be inscribed within the rhombus? $\dfrac{1}{\sqrt{2}}$ $\dfrac{1}{2\sqrt{2}}$ $\sqrt{2}$ $2 \sqrt{2}$
A rhombus is formed by joining the midpoints of the sides of a unit square.What is the diameter of the largest circle that can be inscribed within the rhombus?$\dfrac{1}{...
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GATE Mechanical 2022 Set 1 | GA Question: 10
In a $12$-hour clock that runs correctly, how many times do the second, minute, and hour hands of the clock coincide, in a $12$-hour duration from $3$ PM in a day to $3$ AM the next day? $11$ $12$ $144$ $2$
In a $12$-hour clock that runs correctly, how many times do the second, minute, and hour hands of the clock coincide, in a $12$-hour duration from $3$ PM in a day to $3$ ...
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GATE Mechanical 2022 Set 1 | GA Question: 5
A block with a trapezoidal cross-section is placed over a block with rectangular cross section as shown above. Which one of the following is the correct drawing of the view of the $\text{3D}$ object as viewed in the direction indicated by an arrow in the above figure?
A block with a trapezoidal cross-section is placed over a block with rectangular cross section as shown above.Which one of the following is the correct drawing of the vie...
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GATE Mechanical 2022 Set 1 | GA Question: 3
A person travelled $80$ $\text{km}$ in $6$ hours. If the person travelled the first part with a uniform speed of $10$ $\text{kmph}$ and the remaining part with a uniform speed of $18$ $\text{kmph}$. What percentage of the total distance is travelled at a uniform speed of $10$ $\text{kmph}$? $28.25$ $37.25$ $43.75$ $50.00$
A person travelled $80$ $\text{km}$ in $6$ hours. If the person travelled the first part with a uniform speed of $10$ $\text{kmph}$ and the remaining part with a uniform ...
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GATE Mechanical 2022 Set 2 | GA Question: 4
A person was born on the fifth Monday of February in a particular year. Which one of the following statements is correct based on the above information? The $2^{\text{nd}}$ February of that year is a Tuesday There will be five Sundays in the ... year The $1^{\text{st}}$ February of that year is a Sunday All Mondays of February in that year have even dates
A person was born on the fifth Monday of February in a particular year.Which one of the following statements is correct based on the above information?The $2^{\text{nd}}$...
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GATE Mechanical 2022 Set 2 | GA Question: 9
Four cities $\text{P, Q, R}$ and $\text{S}$ are connected through one-way routes as shown in the figure. The travel time between any two connected cities is one hour. The boxes beside each city name describe the starting time of first train of the ... required? $6$ hours $30$ minutes $3$ hours $45$ minutes $4$ hours $30$ minutes $5$ hours $15$ minutes
Four cities $\text{P, Q, R}$ and $\text{S}$ are connected through one-way routes as shown in the figure. The travel time between any two connected cities is one hour. The...
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GATE Mechanical 2022 Set 1 | GA Question: 2
The average of the monthly salaries of $\text{M, N}$ and $\text{S}$ is ₹$4000$. The average of the monthly salaries of $\text{N, S}$ and $\text{P}$ is ₹$5000$. The monthly salary of $\text{P}$ is ₹$6000$. What is the monthly salary of $\text{M}$ as a percentage of the monthly salary of $\text{P}?$ $50\%$ $75\%$ $100\%$ $125\%$
The average of the monthly salaries of $\text{M, N}$ and $\text{S}$ is ₹$4000$. The average of the monthly salaries of $\text{N, S}$ and $\text{P}$ is ₹$5000$. The mo...
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GATE Mechanical 2022 Set 2 | GA Question: 10
Equal sized circular regions are shaded in a square sheet of paper of $1$ cm side length. Two cases, case $\text{M}$ and case $\text{N}$, are considered as shown in the figures below. In the case $\text{M}$ ... of case $\text{M}$ to that of case $\text{N}$? $2 : 3$ $1 : 1$ $3 : 2$ $2 : 1$
Equal sized circular regions are shaded in a square sheet of paper of $1$ cm side length. Two cases, case $\text{M}$ and case $\text{N}$, are considered as shown in the f...
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GATE Mechanical 2022 Set 1 | GA Question: 9
Given below are three conclusions drawn based on the following three statements. Statement $1$ : All teachers are professors. Statement $2$ : No professor is a male. Statement $3$ : Some males are engineers. Conclusion $\text{I}$: No ... $\text{III}$ are correct Only conclusion $\text{I}$ and conclusion $\text{III}$ are correct
​​​​​​Given below are three conclusions drawn based on the following three statements.Statement $1$ : All teachers are professors.Statement $2$ : No professor...
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GATE Mechanical 2022 Set 1 | GA Question: 8
An equilateral triangle, a square and a circle have equal areas. What is the ratio of the perimeters of the equilateral triangle to square to circle? $3\sqrt{3} : 2 : \sqrt{\pi}$ $\sqrt{\left ( 3 \sqrt{3} \right )} : 2 : \sqrt{\pi}$ $\sqrt{\left ( 3 \sqrt{3} \right )} : 4 : 2\sqrt{\pi}$ $\sqrt{\left ( 3 \sqrt{3} \right )} : 2 : 2\sqrt{\pi}$
An equilateral triangle, a square and a circle have equal areas.What is the ratio of the perimeters of the equilateral triangle to square to circle?$3\sqrt{3} : 2 : \sqrt...
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GATE2020-ME-2: 5
An attempt is made to pull a roller of weight $W$ over a curb (step) by applying a horizontal force $F$ as shown in the figure. The coefficient of static friction between the roller and the ground (including the edge of the step) is $\mu$ Identify the correct free body diagram (FBD) of the roller when the roller is just about to climb over the step.
An attempt is made to pull a roller of weight $W$ over a curb (step) by applying a horizontal force $F$ as shown in the figure. The coefficient of static friction between...
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GATE Mechanical 2022 Set 1 | GA Question: 1
After playing __________ hours of tennis, I am feeling __________________ tired to walk back. too/too too/two two/ two two/too
After playing __________ hours of tennis, I am feeling __________________ tired to walk back.too/tootoo/twotwo/ twotwo/too
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GATE Mechanical 2022 Set 2 | GA Question: 8
Consider the following for non-zero positive integers, $p$ and $q$. $f\left ( p, q \right ) = \frac{p\times p\times p\times \cdots\: \cdots\: \cdots \times p \:= \:p^{q}}{q\:{terms}}; f\left ( p, 1 \right )=p$ ... $g\left ( 2,1 \right ) \neq f\left ( 2,1 \right )$ $f\left ( 3,2 \right )> g\left ( 3,2 \right )$
Consider the following for non-zero positive integers, $p$ and $q$.$f\left ( p, q \right ) = \frac{p\times p\times p\times \cdots\: \cdots\: \cdots \times p \:= \:p^{q}}{...
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GATE Mechanical 2022 Set 2 | GA Question: 5
Which one of the groups given below can be assembled to get the shape that is shown above using each piece only once without overlapping with each other? (rotation and translation operations may be used).
Which one of the groups given below can be assembled to get the shape that is shown above using each piece only once without overlapping with each other? (rotation and tr...
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GATE Mechanical 2022 Set 1 | GA Question: 4
Four girls $\text{P, Q, R and S}$ are studying languages in a University. $\text{P}$ is learning French and Dutch. $\text{Q}$ is learning Chinese and Japanese. $\text{R}$ is learning Spanish and French. $\text{S}$ is learning Dutch and Japanese ... , which girl is learning the most difficult pair of languages? $\text{P}$ $\text{Q}$ $\text{R}$ $\text{S}$
Four girls $\text{P, Q, R and S}$ are studying languages in a University. $\text{P}$ is learning French and Dutch. $\text{Q}$ is learning Chinese and Japanese. $\text{R}$...
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GATE Mechanical 2022 Set 2 | GA Question: 7
For the past $m$ days, the average daily production at a company was $100$ units per day. If today’s production of $180$ units changes the average to $110$ units per day, What is the value of $m$? $18$ $10$ $7$ $5$
For the past $m$ days, the average daily production at a company was $100$ units per day.If today’s production of $180$ units changes the average to $110$ units per day...
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GATE Mechanical 2022 Set 2 | GA Question: 3
If $f\left ( x \right ) = 2 \:\ln \left ( \sqrt{e^{x}} \right )$, what is the area bounded by $f\left ( x \right )$ for the interval $\left [ 0,2 \right ]$ on the $x$ – axis? $\frac{1}{2}$ $1$ $2$ $4$
If $f\left ( x \right ) = 2 \:\ln \left ( \sqrt{e^{x}} \right )$, what is the area bounded by $f\left ( x \right )$ for the interval $\left [ 0,2 \right ]$ on the $x$ –...
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GATE Mechanical 2022 Set 2 | GA Question: 2
Which one of the following is a representation (not to scale and in bold) of all values of $x$ satisfying the inequality $2 - 5x \leq - \dfrac{6x - 5}{3}$ on the real number line? A. B. C. D.
Which one of the following is a representation (not to scale and in bold) of all values of $x$ satisfying the inequality $2 - 5x \leq - \dfrac{6x - 5}{3}$ on the real num...
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GATE Mechanical 2022 Set 2 | GA Question: 1
Writing too many things on the ___________ while teaching could make the students get _____________. bored / board board / bored board / board bored / bored
Writing too many things on the ___________ while teaching could make the students get _____________.bored / boardboard / boredboard / boardbored / bored
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GATE Mechanical 2022 Set 2 | Question: 12
Which one of the following $\text{CANNOT}$ impart linear motion in a $\text{CNC}$ machine? Linear motor Ball screw Lead screw Chain and sprocket
Which one of the following $\text{CANNOT}$ impart linear motion in a $\text{CNC}$ machine?Linear motorBall screwLead screwChain and sprocket
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