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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 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...
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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 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 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 | 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 | 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: 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: 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}$$...
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GATE Mechanical 2024 | Question: 2
​​The value of the surface integral $\oiint_{S} z d x d y$ where $S$ is the external surface of the sphere $x^{2}+y^{2}+z^{2}=R^{2}$ is $0$ $4 \pi R^{3}$ $\frac{4 \pi}{3} R^{3}$ $\pi R^{3}$
​​The value of the surface integral$\oiint_{S} z d x d y$ where $S$ is the external surface of the sphere $x^{2}+y^{2}+z^{2}=R^{2}$ is$0$$4 \pi R^{3}$$\frac{4 \pi}{3}...
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GATE Mechanical 2024 | 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: 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: 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: 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: 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: 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: 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: 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}$$\mathrm{A} 60 ...
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GATE Mechanical 2024 | Question: 21
​​​​The allowance provided to a pattern for easy withdrawal from a sand mold is finishing allowance shrinkage allowance distortion allowance shake allowance
​​​​The allowance provided to a pattern for easy withdrawal from a sand mold isfinishing allowanceshrinkage allowancedistortion allowanceshake allowance
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GATE Mechanical 2024 | Question: 22
​​​​The most suitable electrode material used for joining low alloy steels using Gas Metal Arc Welding $\text{(GMAW)}$ process is copper cadmium low alloy steel tungsten
​​​​The most suitable electrode material used for joining low alloy steels using Gas Metal Arc Welding $\text{(GMAW)}$ process iscoppercadmiumlow alloy steeltungs...
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GATE Mechanical 2024 | Question: 23
​​​The preparatory functions in Computer Numerical Controlled $\text{(CNC)}$ machine programing are denoted by the alphabet $\mathrm{G}$ $\mathrm{M}$ $\mathrm{P}$ $\mathrm{O}$
​​​The preparatory functions in Computer Numerical Controlled $\text{(CNC)}$ machine programing are denoted by the alphabet$\mathrm{G}$$\mathrm{M}$$\mathrm{P}$$\mat...
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