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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 1 | Question: 13
The Clausius inequality holds good for any process any cycle only reversible process only reversible cycle
The Clausius inequality holds good forany processany cycleonly reversible processonly reversible cycle
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GATE Mechanical 2022 Set 1 | Question: 12
Which one of the following is NOT a form of inventory? Raw materials Work-in-process materials Finished goods $\text{CNC}$ Milling Machines
Which one of the following is NOT a form of inventory?Raw materialsWork-in-process materialsFinished goods$\text{CNC}$ Milling Machines
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GATE2020-ME-2: 25
If a reversed Carnot cycle operates between the temperature limits of $27^\circ C$ and $-3^\circ C$, then the ratio of the COP of a refrigerator to that of a heat pump (COP of refrigerator / COP of heat pump) based on the cycle is __________ (round off to $2$ decimal places).
If a reversed Carnot cycle operates between the temperature limits of $27^\circ C$ and $-3^\circ C$, then the ratio of the COP of a refrigerator to that of a heat pump (C...
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GATE Mechanical 2021 Set 2 | Question: 12
Which of the following is responsible for eddy viscosity (or turbulent viscosity) in a turbulent boundary layer on a flat plate? Nikuradse stresses Reynolds stresses Boussinesq stresses Prandtl stresses
Which of the following is responsible for eddy viscosity (or turbulent viscosity) in a turbulent boundary layer on a flat plate?Nikuradse stressesReynolds stressesBoussin...
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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: 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 2022 Set 2 | Question: 38
If the sum and product of eigenvalues of a $2 \times 2$ real matrix $\begin{bmatrix} 3 & p\\ p & q \end{bmatrix}$ are $4$ and $-1$ respectively, then $\left | p \right |$ is ______________ (in integer).
If the sum and product of eigenvalues of a $2 \times 2$ real matrix $\begin{bmatrix} 3 & p\\ p & q \end{bmatrix}$ are $4$ and $-1$ respectively, then $\left | p \right |$...
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GATE Mechanical 2021 Set 2 | Question: 10
In forced convective heat transfer, Stanton number $\text{(St)}$, Nusselt number $\text{(Nu)}$, Reynolds number $\text{(Re)}$ and Prandtl number $\text{(Pr)}$ are related as $St=\frac{Nu}{Re\:Pr}$ $St=\frac{Nu\:Pr}{Re}$ $\text{St = Nu Pr Re}$ $St=\frac{Nu\:Re}{Pr}$
In forced convective heat transfer, Stanton number $\text{(St)}$, Nusselt number $\text{(Nu)}$, Reynolds number $\text{(Re)}$ and Prandtl number $\text{(Pr)}$ are related...
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GATE Mechanical 2022 Set 1 | Question: 17
Which of the following heat treatment processes is/are used for surface hardening of steels? Carburizing Cyaniding Annealing Carbonitriding
Which of the following heat treatment processes is/are used for surface hardening of steels?CarburizingCyanidingAnnealingCarbonitriding
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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: 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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