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42
GATE ECE 2022 | Question: 22
A simple closed path $C$ in the complex plane is shown in the figure. If $\oint_{c} \frac{2^{z}}{z^{2} – 1}dz = – i \pi A,$ where $i = \sqrt{-1},$ then the value of $A$ is _________ (rounded off to two decimal places).
A simple closed path $C$ in the complex plane is shown in the figure. If$$\oint_{c} \frac{2^{z}}{z^{2} – 1}dz = – i \pi A,$$where $i = \sqrt{-1},$ then the value of $...
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43
GATE ECE 2022 | Question: 23
Let $x_{1} (t) = e^{-t}u(t)$ and $x_{2}(t) = u(t) – u(t – 2),$ where $u(\cdot)$ denotes the unit step function. If $y(t)$ denotes the convolution of $x_{1}(t)$ and $x_{2}(t),$ then $\displaystyle \lim_{t \rightarrow \infty} y(t) =$ ______________ (rounded off to one decimal place).
Let $x_{1} (t) = e^{-t}u(t)$ and $x_{2}(t) = u(t) – u(t – 2),$ where $u(\cdot)$ denotes the unit step function.If $y(t)$ denotes the convolution of $x_{1}(t)$ and $x...
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45
GATE ECE 2022 | Question: 25
A symbol stream contains alternate $\text{QPSK}$ and $\text{16-QAM}$ symbols. If symbols from this stream are transmitted at the rate of $1$ mega-symbols per second, the raw (uncoded) data rate is ____________ mega-bits per second (rounded off to one decimal place).
A symbol stream contains alternate $\text{QPSK}$ and $\text{16-QAM}$ symbols. If symbols from this stream are transmitted at the rate of $1$ mega-symbols per second, the ...
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46
GATE ECE 2022 | Question: 26
The function $f(x) = 8 \log_{e} x – x^{2} + 3$ attains its minimum over the interval $[1, e]$ at $x = $____________. (Here $\log_{e}x$ is the natural logarithm of $x$.) $2$ $1$ $e$ $\frac{1+e}{2}$
The function $f(x) = 8 \log_{e} x – x^{2} + 3$ attains its minimum over the interval $[1, e]$ at $x = $____________.(Here $\log_{e}x$ is the natural logarithm of $x$.)$...
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48
GATE ECE 2022 | Question: 28
For the circuit shown, the locus of the impedance $Z (j \omega)$ is plotted as $\omega$ increases from zero to infinity. The values of $R_{1}$ and $R_{2}$ are: $R_{1} = 2 \; \text{k} \Omega, R_{2} = 3 \; \text{k} \Omega$ ... $R_{1} = 2 \; \text{k} \Omega, R_{2} = 5 \; \text{k} \Omega$
For the circuit shown, the locus of the impedance $Z (j \omega)$ is plotted as $\omega$ increases from zero to infinity. The values of $R_{1}$ and $R_{2}$ are:$R_{1} = 2 ...
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51
GATE ECE 2022 | Question: 31
For the following circuit with an ideal $\text{OPAMP},$ the difference between the maximum and the minimum values of the capacitor voltage $(V_{c})$ is ____________. $15 \; \text{V}$ $27 \; \text{V}$ $13 \; \text{V}$ $14 \; \text{V}$
For the following circuit with an ideal $\text{OPAMP},$ the difference between the maximum and the minimum values of the capacitor voltage $(V_{c})$ is ____________.$15 \...
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55
GATE ECE 2022 | Question: 35
Consider the following series: $ \sum_{n=1}^{\infty} \frac{n^{d}}{c^{n}}$ For which of the following combinations of $c, d$ values does this series converge? $ c= 1, d = – 1$ $ c= 2, d = 1$ $ c= 0.5, d = – 10$ $ c= 1, d = – 2$
Consider the following series:$$ \sum_{n=1}^{\infty} \frac{n^{d}}{c^{n}}$$For which of the following combinations of $c, d$ values does this series converge?$ c= 1, d = �...
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63
GATE ECE 2022 | Question: 43
The value of the integral $ \iint_{D} 3(x^{2} + y^{2})dxdy,$ where $D$ is the shaded triangular region shown in the diagram, is ___________ (rounded off to the nearest integer).
The value of the integral$$ \iint_{D} 3(x^{2} + y^{2})dxdy,$$where $D$ is the shaded triangular region shown in the diagram, is ___________ (rounded off to the nearest in...
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67
GATE ECE 2022 | Question: 47
A circuit and the characteristics of the diode $\text{(D)}$ in it are shown. The ratio of the minimum to the maximum small signal voltage gain $\frac{\partial V_{\text{out}}}{\partial V_{\text{in}}}$ is ____________ (rounded off to two decimal places).
A circuit and the characteristics of the diode $\text{(D)}$ in it are shown. The ratio of the minimum to the maximum small signal voltage gain $\frac{\partial V_{\text{ou...
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68
GATE ECE 2022 | Question: 48
Consider the circuit shown with an ideal $\text{OPAMP}.$ The output voltage $V_{0}$ is ____________ $V$ (rounded off to two decimal places).
Consider the circuit shown with an ideal $\text{OPAMP}.$ The output voltage $V_{0}$ is ____________ $V$ (rounded off to two decimal places).
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70
GATE ECE 2022 | Question: 50
The block diagram of a closed-loop control system is shown in the figure. $R(s), Y(s),$ and $D(s)$ are the Laplace transforms of the time-domain signals $r(t), y(t),$ and $d(t),$ ... $e (\infty),$ due to a unit step disturbance $d(t),$ is __________ (rounded off to two decimal places).
The block diagram of a closed-loop control system is shown in the figure. $R(s), Y(s),$ and $D(s)$ are the Laplace transforms of the time-domain signals $r(t), y(t),$ and...
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76
GATE ECE 2021 | GA Question: 1
The current population of a city is $11,02,500$ . If it has been increasing at the rate of $5\%$ per annum, what was its population $2$ years ago? $9,92,500$ $9,95,006$ $10,00,000$ $12,51,506$
The current population of a city is $11,02,500$ . If it has been increasing at the rate of $5\%$ per annum, what was its population $2$ years ago?$9,92,500$$9,95,006$$10,...
1 votes
2 answers
77
GATE ECE 2021 | GA Question: 2
$p$ and $q$ are positive integers and $\dfrac{p}{q}+\dfrac{q}{p}=3,$ then, $\dfrac{p^{2}}{q^{2}}+\dfrac{q^{2}}{p^{2}}=$ $3$ $7$ $9$ $11$
$p$ and $q$ are positive integers and $\dfrac{p}{q}+\dfrac{q}{p}=3,$ then, $\dfrac{p^{2}}{q^{2}}+\dfrac{q^{2}}{p^{2}}=$$3$$7$$9$$11$
1 votes
1 answer
78
GATE ECE 2021 | GA Question: 3
The least number of squares that must be added so that the line $P-Q$ becomes the line of symmetry is ____________ $4$ $3$ $6$ $7$
The least number of squares that must be added so that the line $P-Q$ becomes the line of symmetry is ____________$4$$3$$6$$7$
2 votes
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79
GATE ECE 2021 | GA Question: 4
$\textit{Nostalgia}$ is to $\textit{anticipation}$ as ____________ is to _____________ Which one of the following options maintains a similar logical relation in the above sentence? Present, past Future, past Past, future Future, present
$\textit{Nostalgia}$ is to $\textit{anticipation}$ as ____________ is to _____________Which one of the following options maintains a similar logical relation in the above...
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