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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
The Fourier series expansion of $x^{3}$ in the interval $-1 \leq x < 1$ with periodic continuation hasonly sine termsonly cosine termsboth sine and cosine termsonly sine ...
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GATE Mechanical 2022 Set 1 | Question: 37
Let a random variable $X$ follow Poisson distribution such that $\text{Prob (X = 1) = Prob (X = 2)}$. The value of $\text{Prob (X = 3)}$ is ______________ (round off to $2$ decimal places).
Let a random variable $X$ follow Poisson distribution such that $$\text{Prob (X = 1) = Prob (X = 2)}$$. The value of $\text{Prob (X = 3)}$ is ______________ (round off t...
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GATE Mechanical 2022 Set 2 | Question: 32
A manufacturing unit produces two products $P1$ and $P2$. For each piece of $P1$ and $P2$, the table below provides quantities of materials $\text{M1, M2}$ and $M3$ ... $5000$ $4000$ $3000$ $6000$
A manufacturing unit produces two products $P1$ and $P2$. For each piece of $P1$ and $P2$, the table below provides quantities of materials $\text{M1, M2}$ and $M3$ requi...
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GATE Mechanical 2022 Set 1 | Question: 38
Consider two vectors: $\vec{a} = 5 i + 7j + 2k$$\vec{b} = 3 i - j + 6k$ Magnitude of the component of $\vec{a}$ orthogonal to $\vec{b}$ in the plane containing the vectors $\vec{a}$ and $\vec{b}$ is _____________ (round off to $2$ decimal places).
Consider two vectors: $$\vec{a} = 5 i + 7j + 2k$$$$\vec{b} = 3 i - j + 6k$$Magnitude of the component of $\vec{a}$ orthogonal to $\vec{b}$ in the plane containing the vec...
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GATE Mechanical 2022 Set 1 | Question: 19
Which of the following methods can improve the fatigue strength of a circular mild steel $\text{(MS)}$ shaft? Enhancing surface finish Shot peening of the shaft Increasing relative humidity Reducing relative humidity
Which of the following methods can improve the fatigue strength of a circular mild steel $\text{(MS)}$ shaft?Enhancing surface finishShot peening of the shaftIncreasing r...
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GATE Mechanical 2022 Set 2 | Question: 30
A spring mass damper system (mass $m$, stiffness $k$, and damping coefficient $c$) excited by a force $F(t) = B \sin w t$, where $B$, $w$ and $t$ are the amplitude, frequency and time, respectively, is shown in the figure. Four different responses of ...
A spring mass damper system (mass $m$, stiffness $k$, and damping coefficient $c$) excited by a force $F(t) = B \sin w t$, where $B$, $w$ and $t$ are the amplitude, frequ...
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GATE Mechanical 2022 Set 2 | Question: 26
For the exact differential equation, $\frac{du}{dx}= \frac{-xu^{2}}{2+x^{2}u},$ which one of the following is the solution? $u^{2} + 2x^{2} =$ constant $xu^{2} + u =$ constant $\frac{1}{2}x^{2}u^{2} + 2u =$ constant $\frac{1}{2}ux^{2} + 2x =$ constant
For the exact differential equation,$$\frac{du}{dx}= \frac{-xu^{2}}{2+x^{2}u},$$which one of the following is the solution?$u^{2} + 2x^{2} =$ constant$xu^{2} + u =$ const...
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GATE Mechanical 2022 Set 1 | Question: 11
In a linear programming problem, if a resource is not fully utilized, the shadow price of that resource is positive negative zero infinity
In a linear programming problem, if a resource is not fully utilized, the shadow price of that resource ispositivenegativezeroinfinity
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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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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 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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