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GATE Mechanical 2022 Set 1 | Question: 13
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The Clausius inequality holds good for
any process
any cycle
only reversible process
only reversible cycle
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GATE Mechanical 2022 Set 1 | Question: 1
The limit $p = \lim_{x\rightarrow \pi} \left ( \frac{x^{2} + \alpha x + 2 \pi^{2}}{x - \pi + 2 \sin x } \right )$ has a finite value for a real $\alpha$. The value of $\alpha$ and the corresponding limit $p$ are $\alpha = -3 \pi$ ,and $p= \pi$ $\alpha = -2 \pi$ ,and $p= 2\pi$ $\alpha = \pi$ ,and $p= \pi$ $\alpha = 2 \pi$ ,and $p=3 \pi$
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GATE Mechanical 2022 Set 1 | Question: 2
Solution of $\triangledown ^{2} T = 0$ in a square domain ($0 < x< 1$ and $0 < y< 1$) with boundary conditions: $T \left ( x,0 \right ) = x; T \left ( 0,y \right ) = y; T\left ( x,1 \right ) = 1 + x; T\left ( 1,y \right )= 1 +y$ ... $T \left ( x,y \right ) = -x + y$ $T \left ( x,y \right ) = x + xy + y$
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GATE Mechanical 2022 Set 1 | Question: 3
Given a function $\varphi =\frac{1}{2}\left (x ^{2} + y^{2} + z^{2} \right )$ in three-dimensional Cartesian space, the value of the surface integral $\oint_{s}\hat{n}\cdot \triangledown \varphi dS,$ where $S$ is the surface of a sphere of unit radius and $\hat{n}$ is the outward unit normal vector on $S$, is $4 \pi$ $3 \pi$ $\dfrac{4 \pi}{3}$ $0$
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GATE Mechanical 2022 Set 1 | Question: 4
The Fourier series expansion of $x^{3}$ in the interval $-1 \leq x < 1$ with periodic continuation has only sine terms only cosine terms both sine and cosine terms only sine terms and a non – zero constant
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GATE Mechanical 2022 Set 1 | Question: 5
If $A = \begin{bmatrix} 10 & 2k +5 \\ 3k - 3 & k +5 \end{bmatrix}$ is a symmetric matrix, the value of $k$ is __________________. $8$ $5$ $-0.4$ $\frac{1 + \sqrt{1561}}{12}$
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