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81
GATE IN 2023 | Question: 16
The opamp in the circuit shown is ideal, except that it has an input bias current of $1 ~ \mathrm{nA}$ and an input offset voltage of $10 ~ \mu \mathrm{V}$. The resulting worst-case output voltage will be $\pm$______________$\mu \mathrm{V}$ (rounded off to the nearest integer).
The opamp in the circuit shown is ideal, except that it has an input bias current of $1 ~ \mathrm{nA}$ and an input offset voltage of $10 ~ \mu \mathrm{V}$. The resulting...
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82
GATE IN 2023 | Question: 17
The force per unit length between two infinitely long parallel conductors, with a gap of $2 \mathrm{~cm} $ between them is $10~ \mu \mathrm{N} / \mathrm{m}.$ When the gap is doubled, the force per unit length will be____________$\mu \mathrm{N} / \mathrm{m}$ (rounded off to one decimal place).
The force per unit length between two infinitely long parallel conductors, with a gap of $2 \mathrm{~cm} $ between them is $10~ \mu \mathrm{N} / \mathrm{m}.$ When the gap...
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83
GATE IN 2023 | Question: 18
Consider the discrete-time signal $x[n]=u[-n+5]-u[n+3],$ where $u[n]=\left\{\begin{array}{l}1 ; n \geq 0 \\ 0 ; n<0\end{array}\right . $ The smallest $n$ for which $x[n]=0$ is___________.
Consider the discrete-time signal $x[n]=u[-n+5]-u[n+3],$ where $u[n]=\left\{\begin{array}{l}1 ; n \geq 0 \\ 0 ; n<0\end{array}\right . $ The smallest $n$ for which $x[n]=...
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84
GATE IN 2023 | Question: 19
Let $y(t)=x(4 t),$ where $x(t)$ is a continuous-time periodic signal with fundamental period of $100 \mathrm{~s}.$ The fundamental period of $ y(t)$ is___________$s$ (rounded off to the nearest integer).
Let $y(t)=x(4 t),$ where $x(t)$ is a continuous-time periodic signal with fundamental period of $100 \mathrm{~s}.$ The fundamental period of $ y(t)$ is___________$s$ (rou...
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85
GATE IN 2023 | Question: 20
When the bridge given below is balanced, the current through the resistor $\mathrm{R}_{\mathrm{a}}$ is____________ $\mathrm{mA}$ (rounded off to two decimal places).
When the bridge given below is balanced, the current through the resistor $\mathrm{R}_{\mathrm{a}}$ is____________ $\mathrm{mA}$ (rounded off to two decimal places).
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86
GATE IN 2023 | Question: 21
In the circuit given, the Thevenin equivalent resistance $\mathrm{R}_{\mathrm{th}}$ across the terminals '$\mathrm{a}$' and ' $\mathrm{b}$' is____________$\Omega$ (rounded off to one decimal place).
In the circuit given, the Thevenin equivalent resistance $\mathrm{R}_{\mathrm{th}}$ across the terminals '$\mathrm{a}$' and ' $\mathrm{b}$' is____________$\Omega$ (rounde...
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87
GATE IN 2023 | Question: 22
$X$ is a discrete random variable which takes values $0,1$ and $2.$ The probabilities are $P(X=0)=0.25$ and $P(X=1)=0.5$. With $E[ .]$ denoting the expectation operator, the value of $E[X]-E\left[X^{2}\right]$ is_____________(rounded off to one decimal place).
$X$ is a discrete random variable which takes values $0,1$ and $2.$ The probabilities are $P(X=0)=0.25$ and $P(X=1)=0.5$. With $E[ .]$ denoting the expectation operator, ...
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88
GATE IN 2023 | Question: 23
The diode in the circuit is ideal. The current source $\mathrm{i}_{\mathrm{s}}(t)=\pi \sin (3000 \pi \mathrm{t}) \mathrm{~mA}.$ The magnitude of the average current flowing through the resistor $\mathrm{R}$ is______________$\mathrm{mA}$ (rounded off to two decimal places).
The diode in the circuit is ideal. The current source $\mathrm{i}_{\mathrm{s}}(t)=\pi \sin (3000 \pi \mathrm{t}) \mathrm{~mA}.$ The magnitude of the average current flowi...
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94
GATE IN 2023 | Question: 29
Let $f(z)=j \frac{1-z}{1+z}$, where $z$ denotes a complex number and $j$ denotes $\sqrt{-1}$. The inverse function $f^{-1}(z)$ maps the real axis to the___________. unit circle with centre at the origin unit circle with centre not at the origin imaginary axis real axis
Let $f(z)=j \frac{1-z}{1+z}$, where $z$ denotes a complex number and $j$ denotes $\sqrt{-1}$. The inverse function $f^{-1}(z)$ maps the real axis to the___________.unit c...
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95
GATE IN 2023 | Question: 30
The simplified form of the Boolean function $\mathrm{F}(W, X, Y, Z)=\Sigma(4,5,10,11,12,13$, $14,15)$ with the minimum number of terms and smallest number of literals in each term is $W X+\bar{W} X \bar{Y}+W \bar{X} Y$ $W X+W Y+X \bar{Y}$ $X \bar{Y}+W Y$ $\bar{X} Y+\bar{W} \bar{Y}$
The simplified form of the Boolean function $\mathrm{F}(W, X, Y, Z)=\Sigma(4,5,10,11,12,13$, $14,15)$ with the minimum number of terms and smallest number of literals in ...
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98
GATE IN 2023 | Question: 33
The magnitude and phase plots shown in the figure match with the transfer-function______________. $\frac{10000}{s^2+2 s+10000} $ $ \frac{10000}{s^2+2 s+10000} e^{-0.05 s}$ $\frac{10000}{s^2+2 s+10000} e^{-0.5 \times 10^{-12} s} $ $\frac{100}{s^2+2 s+100}$
The magnitude and phase plots shown in the figure match with the transfer-function______________.$\frac{10000}{s^2+2 s+10000} $$ \frac{10000}{s^2+2 s+10000} e^{-0.05 s}$$...
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99
GATE IN 2023 | Question: 34
A continuous real-valued signal $x(t)$ has finite positive energy and $x(t)=0, \forall \; t<0.$ From the list given below, select ALL the signals whose continuous-time Fourier transform is purely imaginary. $x(t)+x(-t)$ $x(t)-x(-t)$ $j(x(t)+x(-t))$ $j(x(t)-x(-t))$
A continuous real-valued signal $x(t)$ has finite positive energy and $x(t)=0, \forall \; t<0.$ From the list given below, select ALL the signals whose continuous-time Fo...
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101
GATE IN 2023 | Question: 36
In the circuit shown, $\omega=100 \pi \mathrm{rad} / \mathrm{s}, \mathrm{R}_1=\mathrm{R}_2=2.2 \Omega$ and $\mathrm{L}=7 \mathrm{mH}$. The capacitance $C$ for which $Y_{\text {in }}$ is purely real is__________________$\mathrm{mF}$ (rounded off to two decimal places).
In the circuit shown, $\omega=100 \pi \mathrm{rad} / \mathrm{s}, \mathrm{R}_1=\mathrm{R}_2=2.2 \Omega$ and $\mathrm{L}=7 \mathrm{mH}$. The capacitance $C$ for which $Y_{\...
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104
GATE IN 2023 | Question: 39
How many five-digit numbers can be formed using the integers $3,4,5$ and $6$ with exactly one digit appearing twice?
How many five-digit numbers can be formed using the integers $3,4,5$ and $6$ with exactly one digit appearing twice?
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105
GATE IN 2023 | Question: 40
The phase margin of the transfer function $G(s)=\frac{2(1-s)}{(1+s)^{2}}$ is____________degrees. (rounded off to the nearest integer).
The phase margin of the transfer function $G(s)=\frac{2(1-s)}{(1+s)^{2}}$ is____________degrees. (rounded off to the nearest integer).
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108
GATE IN 2023 | Question: 43
Five measurements are made using a weighing machine, and the readings are $80 \mathrm{~kg}, 79 \mathrm{~kg}, 81 \mathrm{~kg}, 79 \mathrm{~kg}$ and $81 \mathrm{~kg}$. The sample standard deviation of the measurement ___________is $\mathrm{kg}$ (rounded off to two decimal places).
Five measurements are made using a weighing machine, and the readings are $80 \mathrm{~kg}, 79 \mathrm{~kg}, 81 \mathrm{~kg}, 79 \mathrm{~kg}$ and $81 \mathrm{~kg}$. The ...
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112
GATE IN 2023 | Question: 47
Consider the real-valued function $g(x)=\max \left\{(x-2)^2,-2 x+7\right\}$, where $x \in(-\infty, \infty)$. The minimum value attained by $g(x)$ is_____________(rounded off to one decimal place).
Consider the real-valued function $g(x)=\max \left\{(x-2)^2,-2 x+7\right\}$, where $x \in(-\infty, \infty)$. The minimum value attained by $g(x)$ is_____________(rounded ...
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114
GATE IN 2023 | Question: 49
The opamps in the circuit are ideal. The input signals are $\mathrm{V}_{\mathrm{S} 1}=3+0.10 \sin (300 t) ~ \mathrm{V} \text { and } \mathrm{V}_{\mathrm{S} 2}=-2+0.11 \sin (300 t) ~ \mathrm{V}$ The average value of the voltage $V_0$ is_____________$\text{V}$ (rounded off to two decimal places).
The opamps in the circuit are ideal. The input signals are$$\mathrm{V}_{\mathrm{S} 1}=3+0.10 \sin (300 t) ~ \mathrm{V} \text { and } \mathrm{V}_{\mathrm{S} 2}=-2+0.11 \si...
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117
GATE IN 2023 | Question: 52
In the circuit shown, assuming an ideal opamp, the value of the output voltage $\mathrm{V}_{\mathrm{o}}=$____________$\mathrm{V}$ (rounded off to one decimal place).
In the circuit shown, assuming an ideal opamp, the value of the output voltage$\mathrm{V}_{\mathrm{o}}=$____________$\mathrm{V}$ (rounded off to one decimal place).
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118
GATE IN 2023 | Question: 53
The rank of the matrix $A$ given below is one. The ratio $\frac{\alpha}{\beta}$ is __________ (rounded off to the nearest integer). $A=\left[\begin{array}{cc} 1 & 4 \\ -3 & \alpha \\ \beta & 6 \end{array}\right]$
The rank of the matrix $A$ given below is one. The ratio $\frac{\alpha}{\beta}$ is __________ (rounded off to the nearest integer).$$A=\left[\begin{array}{cc}1 & 4 \\-3 &...
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