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81
GATE IN 2023 | Question: 6
The table shows the present state $\mathrm{Q}(\mathrm{t})$, next state $\mathrm{Q}(\mathrm{t}+1)$ ... $\text{T}$ flip-flop $\text{D}$ flip-flop $\text{SR}$ flip-flop $\text{JK}$ flip-flop
The table shows the present state $\mathrm{Q}(\mathrm{t})$, next state $\mathrm{Q}(\mathrm{t}+1)$, and the control input in a flip-flop. Identify the flip-flop.$$\begin{a...
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82
GATE IN 2023 | Question: 7
Match the Exclusive-$\text{OR (XOR)}$ operations $\text{(i)}$ to $\text{(iv)}$ with the results $\text{(p)}$ to $\text{(s),}$ where $X$ ... $\text{(i) - (p), (ii) - (s), (iii) - (q), (iv) - (r)}$ $\text{(i) - (q), (ii) - (p), (iii) - (s), (iv) - (r)}$
Match the Exclusive-$\text{OR (XOR)}$ operations $\text{(i)}$ to $\text{(iv)}$ with the results $\text{(p)}$ to $\text{(s),}$ where $X$ is a Boolean input.$$\begin{array}...
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83
GATE IN 2023 | Question: 8
A light emitting diode $\text{(LED)}$ emits light when it is _________ biased. A photodiode provides maximum sensitivity to light when it is _____________ biased. forward, forward forward, reverse reverse, reverse reverse, forward
A light emitting diode $\text{(LED)}$ emits light when it is _________ biased. A photodiode provides maximum sensitivity to light when it is _____________ biased.forward...
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85
GATE IN 2023 | Question: 10
The solution $x(t), t \geq 0$, to the differential equation $\ddot{x}=-k \dot{x}, k>0$ with initial conditions $x(0)=1$ and $\dot{x}(0)=0$ is $x(t)=2 e^{-k t}+2 k t-1$ $x(t)=2 e^{-k t}-1$ $x(t)=1$ $x(t)=2 e^{-k t}-k t-1$
The solution $x(t), t \geq 0$, to the differential equation $\ddot{x}=-k \dot{x}, k>0$ with initial conditions $x(0)=1$ and $\dot{x}(0)=0$ is$x(t)=2 e^{-k t}+2 k t-1$$x(t...
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87
GATE IN 2023 | Question: 12
Choose the fastest logic family among the following: Transistor-Transistor Logic Emitter-Coupled Logic CMOS Logic Resistor-Transistor Logic
Choose the fastest logic family among the following: Transistor-Transistor Logic Emitter-Coupled Logic CMOS LogicResistor-Transistor Logic
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88
GATE IN 2023 | Question: 13
What is $\lim _{x \rightarrow 0} f(x)$, where $f(x)=x \sin \frac{1}{x} ?$ $0$ $1$ $\infty$ Limit does not exist
What is $\lim _{x \rightarrow 0} f(x)$, where $f(x)=x \sin \frac{1}{x} ?$$0$$1$$\infty$Limit does not exist
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89
GATE IN 2023 | Question: 14
The number of zeros of the polynomial $P(s)=s^{3}+2 s^{2}+5 s+80$ in the right- half plane is_________.
The number of zeros of the polynomial $P(s)=s^{3}+2 s^{2}+5 s+80$ in the right- half plane is_________.
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90
GATE IN 2023 | Question: 15
The number of times the Nyquist plot of $G(s) H(s)=\frac{1}{2} \frac{(s-1)(s-2)}{(s+1)(s+2)}$ encircles the origin is_______________.
The number of times the Nyquist plot of $G(s) H(s)=\frac{1}{2} \frac{(s-1)(s-2)}{(s+1)(s+2)}$ encircles the origin is_______________.
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91
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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92
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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93
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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94
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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95
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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96
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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97
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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98
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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104
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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105
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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108
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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109
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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111
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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114
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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115
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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118
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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