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GATE Mechanical 2024 | GA Question: 2
Find the odd one out in the set: $\{19,37,21,17,23,29,31,11\}$ $21$ $29$ $37$ $23$

Find the odd one out in the set: $\{19,37,21,17,23,29,31,11\}$$21$$29$$37$$23$

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GATE Mechanical 2024 | GA Question: 1
If ' $\rightarrow$ ' denotes increasing order of intensity, then the meaning of the words [smile $\rightarrow$ giggle $\rightarrow$ laugh] is analogous to [disapprove $\rightarrow$ _________$\rightarrow$ chide] Which one of the given options is appropriate to fill the blank? reprove praise reprise grieve

If ' $\rightarrow$ ' denotes increasing order of intensity, then the meaning of the words [smile $\rightarrow$ giggle $\rightarrow$ laugh] is analogous to [disappro...

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GATE Mechanical 2024 | GA Question: 7
How many combinations of non-null sets $\text{A, B, C}$ are possible from the subsets of $\{2,3,5\}$ satisfying the conditions: (i) $\mathrm{A}$ is a subset of $\mathrm{B}$, and (ii) $\mathrm{B}$ is a subset of $\mathrm{C}$ ? $28$ $27$ $18$ $19$

How many combinations of non-null sets $\text{A, B, C}$ are possible from the subsets of $\{2,3,5\}$ satisfying the conditions: (i) $\mathrm{A}$ is a subset of $\mathrm{B...

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GATE Mechanical 2024 | GA Question: 10
Four equilateral triangles are used to form a regular closed three-dimensional object by joining along the edges. The angle between any two faces is $30^{\circ}$ $60^{\circ}$ $45^{\circ}$ $90^{\circ}$

Four equilateral triangles are used to form a regular closed three-dimensional object by joining along the edges. The angle between any two faces is$30^{\circ}$$...

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GATE Mechanical 2024 | GA Question: 9
A planar rectangular paper has two $\text{V}$-shaped pieces attached as shown below. This piece of paper is folded to make the following closed three-dimensional object. The number of folds required to form the above object is $9$ $7$ $11$ $8$

A planar rectangular paper has two $\text{V}$-shaped pieces attached as shown below.This piece of paper is folded to make the following closed three-dimensional object.Th...

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GATE Mechanical 2024 | GA Question: 6
In the given text, the blanks are numbered $\text{(i)-(iv)}$. Select the best match for all the blanks. Prof. $\text{P}$ (i) merely a man who narrated funny stories. (ii) in his blackest moments he was capable of self-deprecating humor. Prof. $\text{Q}$ ... (iv) Only (i) was (ii) Even (iii) wasn't (iv) Only (i) wasn't (ii) Only (iii) was (iv) Even

In the given text, the blanks are numbered $\text{(i)-(iv)}$. Select the best match for all the blanks.Prof. $\text{P}$ (i) merely a man who narrated funny stories. (...

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GATE Mechanical 2024 | Question: 2
The value of the surface integral $\oiint_{S} z d x d y$ where $S$ is the external surface of the sphere $x^{2}+y^{2}+z^{2}=R^{2}$ is $0$ $4 \pi R^{3}$ $\frac{4 \pi}{3} R^{3}$ $\pi R^{3}$

The value of the surface integral$\oiint_{S} z d x d y$ where $S$ is the external surface of the sphere $x^{2}+y^{2}+z^{2}=R^{2}$ is$0$$4 \pi R^{3}$$\frac{4 \pi}{3}...

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GATE Mechanical 2024 | GA Question: 5
Take two long dice (rectangular parallelepiped), each having four rectangular faces labelled as $2,3,5$, and $7$. If thrown, the long dice cannot land on the square faces and has $1 / 4$ probability of landing on any of the four rectangular faces. The label on the top ... the sum of the two long dice scores greater than $11$? $3 / 8$ $1 / 8$ $1 / 16$ $3 / 16$

Take two long dice (rectangular parallelepiped), each having four rectangular faces labelled as $2,3,5$, and $7$. If thrown, the long dice cannot land on the square faces...

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GATE Mechanical 2024 | GA Question: 8
The bar chart gives the batting averages of $\mathrm{VK}$ and $\mathrm{RS}$ for $11$ calendar years from $2012$ to $2022$. Considering that $2015$ and $2019$ ... cup years. $\mathrm{RS's}$ yearly batting average is consistently higher than that of $\mathrm{VK}$ in the last three years.

The bar chart gives the batting averages of $\mathrm{VK}$ and $\mathrm{RS}$ for $11$ calendar years from $2012$ to $2022$. Considering that $2015$ and $2019$ are world cu...

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GATE Mechanical 2024 | Question: 22
The most suitable electrode material used for joining low alloy steels using Gas Metal Arc Welding $\text{(GMAW)}$ process is copper cadmium low alloy steel tungsten

The most suitable electrode material used for joining low alloy steels using Gas Metal Arc Welding $\text{(GMAW)}$ process iscoppercadmiumlow alloy steeltungs...

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GATE Mechanical 2024 | Question: 27
In the pipe network shown in the figure, all pipes have the same cross-section and can be assumed to have the same friction factor. The pipes connecting points $W, N$, and $S$ with point $J$ have an equal length $L$. The pipe connecting points $J$ ... $\text{I}$ and $\text{II}$ are True Both $\text{I}$ and $\text{II}$ are False

In the pipe network shown in the figure, all pipes have the same cross-section and can be assumed to have the same friction factor. The pipes connecting po...

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GATE Mechanical 2024 | GA Question: 3
In the following series, identify the number that needs to be changed to form the Fibonacci series. $1,1,2,3,6,8,13,21, \ldots$ $8$ $21$ $6$ $13$

In the following series, identify the number that needs to be changed to form the Fibonacci series.$1,1,2,3,6,8,13,21, \ldots$$8$$21$$6$$13$

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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 2024 | Question: 53
In an arc welding process, the voltage and current are $30 \mathrm{~V}$ and $200 \mathrm{~A}$, respectively. The cross-sectional area of the joint is $20 \mathrm{~mm}^{2}$ ... $2$ decimal places).

In an arc welding process, the voltage and current are $30 \mathrm{~V}$ and $200 \mathrm{~A}$, respectively. The cross-sectional area of the joint is $20 \mathrm{~mm}^{2}...

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GATE Mechanical 2024 | Question: 55
In a supplier-retailer supply chain, the demand of each retailer, the capacity of each supplier, and the unit cost in rupees of material supply from each supplier to each retailer are tabulated below. The supply chain manager wishes to ... \end{array} The optimal cost of satisfying the total demand from all retailers is __________ rupees (answer in integer).

In a supplier-retailer supply chain, the demand of each retailer, the capacity of each supplier, and the unit cost in rupees of material supply from each supplier to each...

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GATE Mechanical 2024 | Question: 24
A set of jobs $\text{U, V, W, X, Y, Z}$ arrive at time $t=0$ to a production line consisting of two workstations in series. Each job must be processed by both workstations in sequence (i.e., the first followed by the second). The process times (in minutes) for each job on each ... $\text{W-X-V-Z-Y-U}$ $\text{W-U-Z-V-Y-X}$ $\text{U-Y-V-Z-X-W}$

A set of jobs $\text{U, V, W, X, Y, Z}$ arrive at time $t=0$ to a production line consisting of two workstations in series. Each job must be processed by b...

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GATE Mechanical 2024 | Question: 3
Let $f(z)$ be an analytic function, where $z=x+i y$. If the real part of $f(z)$ is $\cosh x \cos y$, and the imaginary part of $f(z)$ is zero for $y=0$, then $f(z)$ is $\cosh x \exp (-i y)$ $\cosh z \exp z$ $\cosh z \cos y$ $\cosh z$

Let $f(z)$ be an analytic function, where $z=x+i y$. If the real part of $f(z)$ is $\cosh x \cos y$, and the imaginary part of $f(z)$ is zero for $y=0$, th...

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GATE Mechanical 2024 | Question: 7
A plane, solid slab of thickness $L$, shown in the figure, has thermal conductivity $k$ that varies with the spatial coordinate $x$ as $k=A+B x$, where $A$ and $B$ ... . Considering one-dimensional heat transfer, which one of the following plots qualitatively depicts the steady-state temperature distribution within the slab?

A plane, solid slab of thickness $L$, shown in the figure, has thermal conductivity $k$ that varies with the spatial coordinate $x$ as $k=A+B x$, where $A$ an...

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GATE Mechanical 2024 | Question: 30
Steady, compressible flow of air takes place through an adiabatic convergingdiverging nozzle, as shown in the figure. For a particular value of pressure difference across the nozzle, a stationary normal shock wave forms in the diverging section of the nozzle. If ... at $\text{F}$ Specific entropy at $\text{E}$ is lower than the specific entropy at $\text{F}$

Steady, compressible flow of air takes place through an adiabatic convergingdiverging nozzle, as shown in the figure. For a particular value of pressure differen...

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GATE Mechanical 2024 | Question: 9
Consider a hydrodynamically fully developed laminar flow through a circular pipe with the flow along the axis (i.e., $z$ direction). In the following statements, $T$ is the temperature of the fluid, $T_{w}$ is the wall temperature and $T_{m}$ is the ... $\frac{d T_{m}}{d z}$ increases exponentially with distance along $z$ direction.

Consider a hydrodynamically fully developed laminar flow through a circular pipe with the flow along the axis (i.e., $z$ direction). In the following statements, $T$ i...

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GATE Mechanical 2024 | Question: 26
The matrix $\left[\begin{array}{ll}1 & a \\ 8 & 3\end{array}\right]$ (where $a>0$ ) has a negative eigenvalue if $a$ is greater than $\frac{3}{8}$ $\frac{1}{8}$ $\frac{1}{4}$ $\frac{1}{5}$

The matrix $\left[\begin{array}{ll}1 & a \\ 8 & 3\end{array}\right]$ (where $a>0$ ) has a negative eigenvalue if $a$ is greater than$\frac{3}{8}$$\frac{1}{8}$...

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GATE Mechanical 2024 | Question: 1
In order to numerically solve the ordinary differential equation $\frac{d y}{d t}=-y$ for $t>0$, with an initial condition $y(0)=1$, the following scheme is employed \[ \frac{y_{n+1}-y_{n}}{\Delta t}=-\frac{1}{2}\left(y_{n+1}+y_{n}\right) ... solution with non-physical oscillations for $\Delta t>h$. The value of $h$ is $\frac{1}{2}$ $1$ $\frac{3}{2}$ $2$

In order to numerically solve the ordinary differential equation $\frac{d y}{d t}=-y$ for $t>0$, with an initial condition $y(0)=1$, the following scheme is empl...

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GATE Mechanical 2024 | Question: 23
The preparatory functions in Computer Numerical Controlled $\text{(CNC)}$ machine programing are denoted by the alphabet $\mathrm{G}$ $\mathrm{M}$ $\mathrm{P}$ $\mathrm{O}$

The preparatory functions in Computer Numerical Controlled $\text{(CNC)}$ machine programing are denoted by the alphabet$\mathrm{G}$$\mathrm{M}$$\mathrm{P}$$\mat...

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GATE Mechanical 2024 | GA Question: 4
The real variables $x, y, z$, and the real constants $p, q, r$ satisfy \[ \frac{x}{p q-r^{2}}=\frac{y}{q r-p^{2}}=\frac{z}{r p-q^{2}} \] Given that the denominators are non-zero, the value of $p x+q y+r z$ is $0$ $1$ $p q r$ $p^{2}+q^{2}+r^{2}$

The real variables $x, y, z$, and the real constants $p, q, r$ satisfy\[\frac{x}{p q-r^{2}}=\frac{y}{q r-p^{2}}=\frac{z}{r p-q^{2}}\]Given that the denominators are...

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GATE Mechanical 2024 | Question: 10
A furnace can supply heat steadily at $1200 \mathrm{~K}$ at a rate of $24000 \mathrm{~kJ} / \mathrm{min}$. The maximum amount of power (in $\mathrm{kW}$ ) that can be produced by using the heat supplied by this furnace in an environment at $300 \mathrm{~K}$ is $300$ $150$ $18000$ $0$

A furnace can supply heat steadily at $1200 \mathrm{~K}$ at a rate of $24000 \mathrm{~kJ} / \mathrm{min}$. The maximum amount of power (in $\mathrm{kW}$ ) tha...

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GATE Mechanical 2024 | Question: 18
The phases present in pearlite are austenite and ferrite cementite and austenite ferrite and cementite martensite and ferrite

The phases present in pearlite areaustenite and ferritecementite and austeniteferrite and cementitemartensite and ferrite

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GATE Mechanical 2024 | Question: 31
Which of the following beam(s) is/are statically indeterminate?

Which of the following beam(s) is/are statically indeterminate?

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GATE Mechanical 2024 | Question: 15
A linear spring-mass-dashpot system with a mass of $2 \mathrm{~kg}$ is set in motion with viscous damping. If the natural frequency is $15 \mathrm{~Hz}$, and the amplitudes of two successive cycles measured are $7.75 \mathrm{~mm}$ and $7.20 \mathrm{~mm}$, the coefficient of viscous damping (in $\text{N.s/m}$) is $4.41$ $7.51$ $2.52$ $6.11$

A linear spring-mass-dashpot system with a mass of $2 \mathrm{~kg}$ is set in motion with viscous damping. If the natural frequency is $15 \mathrm{~Hz}$, and ...

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GATE Mechanical 2024 | Question: 17
A rigid massless tetrahedron is placed such that vertex $\mathrm{O}$ is at the origin and the other three vertices $\text{A, B}$, and $\text{C}$ lie on the coordinate axes as shown in the figure. The body is acted on by three point loads, of which one is ... $y-z$ plane but not along $y$ or $z$ axis in $z-x$ plane but not along $z$ or $x$ axis

A rigid massless tetrahedron is placed such that vertex $\mathrm{O}$ is at the origin and the other three vertices $\text{A, B}$, and $\text{C}$ lie on the co...

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GATE Mechanical 2024 | Question: 29
At the current basic feasible solution $\text{(bfs)}$ $v_{0}\left(v_{0} \in \mathbb{R}^{5}\right)$, the simplex method yields the following form of a linear programming problem in standard form. \[ \begin{array}{ll} \text { minimize } & z=-x_{1}-2 x_{2} \\ \text { s.t. } ... $z=-3+x_{5}-2 x_{2}$ $z=-4-5 x_{1}+2 x_{4}$ $z=-6-5 x_{1}+2 x_{3}$

At the current basic feasible solution $\text{(bfs)}$ $v_{0}\left(v_{0} \in \mathbb{R}^{5}\right)$, the simplex method yields the following form of a linear p...

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GATE Mechanical 2024 | Question: 52
A blanking operation is performed on $\text{C}20$ steel sheet to obtain a circular disc having a diameter of $20 \mathrm{~mm}$ and a thickness of $2 \mathrm{~mm}$. An allowance of $0.04$ is provided. The punch size used for the operation is _________ $\mathrm{mm}$ (rounded off to $2$ decimal places).

A blanking operation is performed on $\text{C}20$ steel sheet to obtain a circular disc having a diameter of $20 \mathrm{~mm}$ and a thickness of $2 \mathrm{~mm}$. An all...

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GATE Mechanical 2024 | Question: 13
The change in kinetic energy $\Delta E$ of an engine is $300 \mathrm{~J}$, and minimum and maximum shaft speeds are $\omega_{\min }=220 \mathrm{rad} / \mathrm{s}$ and $\omega_{\max }=280 \mathrm{rad} / \mathrm{s}$, respectively. Assume that the ... $0.113$ $0.096$ $0.071$ $0.053$

The change in kinetic energy $\Delta E$ of an engine is $300 \mathrm{~J}$, and minimum and maximum shaft speeds are $\omega_{\min }=220 \mathrm{rad} / \mathrm...

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GATE Mechanical 2024 | Question: 20
The grinding wheel used to provide the best surface finish is $\mathrm{A} 36 \mathrm{~L} 5 \mathrm{~V}$ $\mathrm{A} 54 \mathrm{~L} 5 \mathrm{~V}$ $\mathrm{A} 60 \mathrm{~L} 5 \mathrm{~V}$ $\mathrm{A} 80 \mathrm{~L} 5 \mathrm{~V}$

The grinding wheel used to provide the best surface finish is$\mathrm{A} 36 \mathrm{~L} 5 \mathrm{~V}$$\mathrm{A} 54 \mathrm{~L} 5 \mathrm{~V}$$\mathrm{A} 60 ...

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GATE Mechanical 2024 | Question: 37
A heat pump $\text{(H.P.)}$ is driven by the work output of a heat engine $\text{(H.E.)}$ as shown in the figure. The heat engine extracts $150 \mathrm{~kJ}$ of heat from the source at $1000 \mathrm{~K}$. The heat pump ... , the total amount of heat delivered to the room together by the heat engine and heat pump is ___________ $\mathrm{kJ}$ (answer in integer).

A heat pump $\text{(H.P.)}$ is driven by the work output of a heat engine $\text{(H.E.)}$ as shown in the figure. The heat engine extracts $150 \mathrm{~kJ}$ of heat from...

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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 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 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: 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 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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