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81
GATE ECE 2023 | GA Question: 3
What is the smallest number with distinct digits whose digits add up to $45?$ $123555789$ $123457869$ $123456789$ $99999$
What is the smallest number with distinct digits whose digits add up to $45?$$123555789$$123457869$$123456789$$99999$
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83
GATE ECE 2023 | Question: 10
Consider a narrow band signal, propagating in a lossless dielectric medium $\left(\varepsilon_{r}=4, \mu_{r}=1\right)$, with phase velocity $v_{p}$ and group velocity $v_{g}$. Which of the following statement is true? ($c$ ... $v_{p} > c, v_{g} < c$ $v_{p} < c, v_{g} < c$
Consider a narrow band signal, propagating in a lossless dielectric medium $\left(\varepsilon_{r}=4, \mu_{r}=1\right)$, with phase velocity $v_{p}$ and group velocity $v_...
1 votes
2 answers
85
GATE ECE 2008 | Question: 28
In the Taylor series expansion of $\exp (x)+\sin (x)$ about the point $x=\pi$, the coefficient of $(x-\pi)^{2}$ is $\exp (\pi)$ $0.5 \exp (\pi)$ $\exp (\pi)+1$ $\exp (\pi)-1$
In the Taylor series expansion of $\exp (x)+\sin (x)$ about the point $x=\pi$, the coefficient of $(x-\pi)^{2}$ is$\exp (\pi)$$0.5 \exp (\pi)$$\exp (\pi)+1$$\exp (\pi)-1$...
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86
GATE ECE 2023 | Question: 6
In a semiconductor, if the Fermi energy level lies in the conduction band, then the semiconductor is known as degenerate $\text{n}$-type. degenerate $\text{p}$-type. non-degenerate $\text{n}$-type. non-degenerate $\text{p}$-type.
In a semiconductor, if the Fermi energy level lies in the conduction band, then the semiconductor is known asdegenerate $\text{n}$-type.degenerate $\text{p}$-type.non-deg...
2 votes
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88
GATE ECE 2023 | Question: 24
For the circuit shown below, the propagation delay of each $ \mathrm{NAND}$ gate is $1 \mathrm{~ns}$. The critical path delay, in $\text{ns,}$ is______________(rounded off to the nearest integer).
For the circuit shown below, the propagation delay of each $ \mathrm{NAND}$ gate is $1 \mathrm{~ns}$. The critical path delay, in $\text{ns,}$ is______________(rounded of...
0 votes
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89
GATE ECE 2023 | Question: 2
The rate of increase, of a scalar field $f(x, y, z)=x y z$, in the direction $v=(2,1,2)$ at a point $(0,2,1)$ is $\frac{2}{3}$ $\frac{4}{3}$ $2$ $4$
The rate of increase, of a scalar field $f(x, y, z)=x y z$, in the direction $v=(2,1,2)$ at a point $(0,2,1)$ is$\frac{2}{3}$$\frac{4}{3}$$2$$4$
0 votes
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90
GATE ECE 2023 | Question: 11
In the circuit shown below, $\text{V}_1$ and $\text{V}_2$ are bias voltages. Based on input and output impedances, the circuit behaves as a voltage controlled voltage source. voltage controlled current source. current controlled voltage source. current controlled current source.
In the circuit shown below, $\text{V}_1$ and $\text{V}_2$ are bias voltages. Based on input and output impedances, the circuit behaves as avoltage controlled voltage sour...
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91
GATE ECE 2023 | Question: 4
The value of the contour integral, $\oint_C\left(\frac{z+2}{z^2+2 z+2}\right) d z$, where the contour $\mathrm{C}$ is $\left\{z:\left|z+1-\frac{3}{2} j\right|=1\right\}$, taken in the counter clockwise direction, is $-\pi(1+j)$ $\pi(1+j)$ $\pi(1-j)$ $-\pi(1-j)$
The value of the contour integral, $\oint_C\left(\frac{z+2}{z^2+2 z+2}\right) d z$, where the contour $\mathrm{C}$ is $\left\{z:\left|z+1-\frac{3}{2} j\right|=1\right\}$,...
0 votes
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93
GATE ECE 2023 | Question: 21
The signal-to-noise ratio $\mathrm{SNR}$ of an $\mathrm{ADC}$ with a full-scale sinusoidal input is given to be $61.96 \mathrm{~dB}$. The resolution of the $\mathrm{ADC}$ is_____________bits (rounded off to the nearest integer).
The signal-to-noise ratio $\mathrm{SNR}$ of an $\mathrm{ADC}$ with a full-scale sinusoidal input is given to be $61.96 \mathrm{~dB}$. The resolution of the $\mathrm{ADC}$...
0 votes
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94
GATE ECE 2023 | Question: 14
The synchronous sequential circuit shown below works at a clock frequency $1 \; \mathrm{GHz}$. The throughput, in $\text{Mbits/s,}$ and the latency, in $\text{ns,}$ respectively, are $1000,3$ $333.33,1$ $2000,3$ $333.33,3$
The synchronous sequential circuit shown below works at a clock frequency $1 \; \mathrm{GHz}$. The throughput, in $\text{Mbits/s,}$ and the latency, in $\text{ns,}$ respe...
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97
GATE ECE 2023 | Question: 9
For a $\text{MOS}$ capacitor, $\text{V}_{\mathrm{fb}}$ and $\text{V}_{\mathrm{t}}$ are the flat-band voltage and the threshold voltage, respectively. The variation of the depletion width $\left(\mathrm{W}_{\mathrm{dep}}\right)$ for varying gate voltage $\left(\text{V}_g\right)$ is best represented by
For a $\text{MOS}$ capacitor, $\text{V}_{\mathrm{fb}}$ and $\text{V}_{\mathrm{t}}$ are the flat-band voltage and the threshold voltage, respectively. The variation of the...
1 votes
0 answers
98
GATE ECE 2023 | Question: 30
In the circuit shown below, $D_1$ and $D_2$ are silicon diodes with cut-in voltage of $0.7 \mathrm{~V}$. $\mathrm{V}_{\mathrm{IN}}$ and $\mathrm{V}_{\mathrm{OUT}}$ are input and output voltages in volts. The transfer characteristic is
In the circuit shown below, $D_1$ and $D_2$ are silicon diodes with cut-in voltage of $0.7 \mathrm{~V}$. $\mathrm{V}_{\mathrm{IN}}$ and $\mathrm{V}_{\mathrm{OUT}}$ are in...
0 votes
0 answers
99
GATE ECE 2023 | Question: 16
Consider a system with input $x(t)$ and output $y(t)=x\left(e^{t}\right)$. The system is Causal and time invariant. Non-causal and time varying. Causal and time varying. Non-causal and time invariant.
Consider a system with input $x(t)$ and output $y(t)=x\left(e^{t}\right)$. The system isCausal and time invariant.Non-causal and time varying.Causal and time varying.Non-...
0 votes
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101
GATE ECE 2023 | Question: 8
A series $\text{RLC}$ circuit has a quality factor $\text{Q}$ of $1000$ at a center frequency of $10^{6} \; \mathrm{rad} / \mathrm{s}$. The possible values of $\text{R, L}$ and $\text{C}$ are $R=1 \; \Omega, L=1 \; \mu H$ and $C=1 \; \mu F$ ... $C=1 \; \mu F$ $R=0.001 \; \Omega, L=1 \; \mu H$ and $C=1 \; \mu F$
A series $\text{RLC}$ circuit has a quality factor $\text{Q}$ of $1000$ at a center frequency of $10^{6} \; \mathrm{rad} / \mathrm{s}$. The possible values of $\text{R,...
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102
GATE ECE 2023 | Question: 27
The value of the line integral $\int_{P}^{Q}\left(z^{2} d x+3 y^{2} d y+2 x z \; d z\right)$ along the straight line joining the points $P(1,1,2)$ and $Q(2,3,1)$ is $20$ $24$ $29$ $-5$
The value of the line integral $\int_{P}^{Q}\left(z^{2} d x+3 y^{2} d y+2 x z \; d z\right)$ along the straight line joining the points $P(1,1,2)$ and $Q(2,3,1)$ is$20$$2...
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103
GATE ECE 2023 | Question: 17
Let $m(t)$ be a strictly band-limited signal with bandwidth $B$ and energy $E$. Assuming $\omega_{0}=10 B$, the energy in the $m(t) \cos \omega_{0} t$ is $\frac{E}{4}$ $\frac{E}{2}$ $E$ $2E$
Let $m(t)$ be a strictly band-limited signal with bandwidth $B$ and energy $E$. Assuming $\omega_{0}=10 B$, the energy in the $m(t) \cos \omega_{0} t$ is$\frac{E}{4}$$\f...
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104
GATE ECE 2023 | Question: 18
The Fourier transform $X(\omega)$ of $x(t)=e^{-t^{2}}$ is Note: $\int_{-\infty}^{\infty} e^{-y^{2}} d y=\sqrt{\pi}$ $\sqrt{\pi} e^{\frac{\omega^{2}}{2}}$ $\frac{e^{-\frac{\omega^{2}}{4}}}{2 \sqrt{\pi}}$ $\sqrt{\pi} e^{-\frac{\omega^{2}}{4}}$ $\sqrt{\pi} e^{-\frac{\omega^{2}}{2}}$
The Fourier transform $X(\omega)$ of $x(t)=e^{-t^{2}}$ isNote: $\int_{-\infty}^{\infty} e^{-y^{2}} d y=\sqrt{\pi}$$\sqrt{\pi} e^{\frac{\omega^{2}}{2}}$$\frac{e^{-\frac{\o...
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106
GATE ECE 2023 | Question: 19
In the table shown below, match the signal type with its spectral characteristics. Signal type Spectral characteristics (i) Continuous, aperiodic (a) Continuous, aperiodic (ii) Continuous, periodic (b) Continuous, periodic (iii) Discrete, aperiodic (c) Discrete, aperiodic (iv) ...
In the table shown below, match the signal type with its spectral characteristics. Signal type Spectral characteristics (i) Continuous, aperiodic(a) Continuous, aperiod...
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107
GATE ECE 2023 | Question: 20
For a real signal, which of the following is/are valid power spectral density/densities? $\text{S}_X(\omega)=\frac{2}{9+\omega^2}$ $\text{S}_X(\omega)=e^{-\omega^2} \cos ^2 \omega$
For a real signal, which of the following is/are valid power spectral density/densities?$\text{S}_X(\omega)=\frac{2}{9+\omega^2}$$\text{S}_X(\omega)=e^{-\omega^2} \cos ^2...
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108
GATE ECE 2023 | Question: 22
In the circuit shown below, the current $i$ flowing through $200 \; \Omega$ resistor is___________ $\mathrm{mA}$ (rounded off to two decimal places).
In the circuit shown below, the current $i$ flowing through $200 \; \Omega$ resistor is___________ $\mathrm{mA}$ (rounded off to two decimal places).
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109
GATE ECE 2023 | Question: 29
The $\frac{V_{\text {OUT }}}{V_{\text {IN }}}$ of the circuit shown below is $-\frac{\mathrm{R}_4}{\mathrm{R}_3}$ $\frac{\mathrm{R}_4}{\mathrm{R}_3}$ $1+\frac{\text{R}_4}{\text{R}_3}$ $1-\frac{\mathrm{R}_4}{\mathrm{R}_3}$
The $\frac{V_{\text {OUT }}}{V_{\text {IN }}}$ of the circuit shown below is$-\frac{\mathrm{R}_4}{\mathrm{R}_3}$$\frac{\mathrm{R}_4}{\mathrm{R}_3}$$1+\frac{\text{R}_4}{\t...
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110
GATE ECE 2023 | Question: 54
In the circuit below, the voltage $V_L$ is _________ $\mathrm{V}$ (rounded off to two decimal places).
In the circuit below, the voltage $V_L$ is _________ $\mathrm{V}$ (rounded off to two decimal places).
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111
GATE ECE 2023 | Question: 31
A closed loop system is shown in the figure where $\mathrm{k}>0$ and $\alpha>0$. The steady state error due to a ramp input $\left(\mathrm{R}(\mathrm{s})=\alpha / \mathrm{s}^2\right)$ is given by $\frac{2 \alpha}{\mathrm{k}}$ $\frac{\alpha}{\mathrm{k}}$ $\frac{\alpha}{2 \mathrm{k}}$ $\frac{\alpha}{4 \mathrm{k}}$
A closed loop system is shown in the figure where $\mathrm{k}>0$ and $\alpha>0$. The steady state error due to a ramp input $\left(\mathrm{R}(\mathrm{s})=\alpha / \mathrm...
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112
GATE ECE 2023 | Question: 25
In the circuit shown below, switch $\mathrm{S}$ was closed for a long time. If the switch is opened at $t=0$, the maximum magnitude of the voltage $\mathrm{V}_{\mathrm{R}}, \text{in volts,}$ is_____________ (rounded off to the nearest integer).
In the circuit shown below, switch $\mathrm{S}$ was closed for a long time. If the switch isopened at $t=0$, the maximum magnitude of the voltage $\mathrm{V}_{\mathrm{R}}...
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113
GATE ECE 2023 | Question: 46
In an extrinsic semiconductor, the hole concentration is given to be $1.5 n_{i}$ where $n_{i}$ is the intrinsic carrier concentration of $1 \times 10^{10} \mathrm{~cm}^{-3}$. The ratio of electron to hole mobility for equal hole and electron drift current is given as ________ (rounded off to two decimal places).
In an extrinsic semiconductor, the hole concentration is given to be $1.5 n_{i}$ where $n_{i}$ is the intrinsic carrier concentration of $1 \times 10^{10} \mathrm{~cm}^{-...
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118
GATE ECE 2023 | Question: 51
In a semiconductor device, the Fermi-energy level is $0.35 \; \mathrm{eV}$ above the valence band energy. The effective density of states in the valence band at $T=300 \mathrm{~K}$ is $1 \times 10^{19} \mathrm{~cm}^{-3}$. The thermal equilibrium hole ... $\mathrm{kT}$ at $300 \mathrm{~K}$ is $0.026 \; \mathrm{eV}$.
In a semiconductor device, the Fermi-energy level is $0.35 \; \mathrm{eV}$ above the valence band energy. The effective density of states in the valence band at $T=300 \m...
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120
GATE ECE 2023 | Question: 41
The $S$-parameters of a two-port network is given as $ [S]=\left[\begin{array}{ll} S_{11} & S_{12} \\ S_{21} & S_{22} \end{array}\right] $ with reference to $Z_0$. Two lossless transmission line sections of electrical lengths $\theta_1=\beta l_1$ ...
The $S$-parameters of a two-port network is given as$$[S]=\left[\begin{array}{ll}S_{11} & S_{12} \\S_{21} & S_{22}\end{array}\right]$$with reference to $Z_0$. Two lossles...
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