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1722
GATE ECE 2021 | Question: 4
Consider a real-valued base-band signal $x(t)$, band limited to $\text{10 kHz}$. The Nyquist rate for the signal $y\left ( t \right )=x\left ( t \right )x\left ( 1+\dfrac{t}{2} \right )$ is $\text{15 kHz}$ $\text{30 kHz}$ $\text{60 kHz}$ $\text{20 kHz}$
Consider a real-valued base-band signal $x(t)$, band limited to $\text{10 kHz}$. The Nyquist rate for the signal $y\left ( t \right )=x\left ( t \right )x\left ( 1+\dfrac...
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1729
GATE ECE 2021 | Question: 14
The complete Nyquist plot of the open-loop transfer function $G(s)H(s)$ of a feedback control system in the figure. If $G(s)H(s)$ has one zero in the right-half of the $s$-plane, the number of poles that the closed-loop system will have in the right-half of the $s$-plane is $0$ $1$ $4$ $3$
The complete Nyquist plot of the open-loop transfer function $G(s)H(s)$ of a feedback control system in the figure.If $G(s)H(s)$ has one zero in the right-half of the $s$...
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1730
GATE ECE 2021 | Question: 15
Consider a rectangular coordinate system $(x,y,z)$ with unit vectors $a_{x}\:a_{y}$ and $a_{z}$. A plane wave traveling in the region $z\geq 0$ with electric field vector $E=10\cos\left ( 2\times 10^{8}t\:+\:\beta z\right )a_{y}$ is incident normally on the ... $\frac{1}{3}$ $\frac{3}{5}$ $\frac{2}{5}$ $\frac{2}{3}$
Consider a rectangular coordinate system $(x,y,z)$ with unit vectors $a_{x}\:a_{y}$ and $a_{z}$. A plane wave traveling in the region $z\geq 0$ with electric field vector...
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1731
GATE ECE 2021 | Question: 18
Consider the circuit shown in the figure. The current $I$ flowing through the $7\:\Omega$ resistor between $P$ and $Q$ (rounded off to one decimal place) is ________ $A$.
Consider the circuit shown in the figure.The current $I$ flowing through the $7\:\Omega$ resistor between $P$ and $Q$ (rounded off to one decimal place) is ________ $A$.
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1732
GATE ECE 2021 | Question: 19
Consider the circuit shown in the figure. The value of $v_{0}$ (rounded off to one decimal place) is _________ $V$.
Consider the circuit shown in the figure.The value of $v_{0}$ (rounded off to one decimal place) is _________ $V$.
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1734
GATE ECE 2021 | Question: 21
The autocorrelation function $R_{X}\left ( \tau \right )$ of a wide-sense stationary random process $X(t)$ is shown in the figure. The average power of $X(t)$ is ________________
The autocorrelation function $R_{X}\left ( \tau \right )$ of a wide-sense stationary random process $X(t)$ is shown in the figure.The average power of $X(t)$ is _________...
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1735
GATE ECE 2021 | Question: 22
Consider a carrier signal which is amplitude modulated by a single-tone sinusoidal message signal with a modulation index of $50\%$. If the carrier and one of the sidebands are suppressed in the modulated signal, the percentage of power saved (rounded off to one decimal place) is ______________
Consider a carrier signal which is amplitude modulated by a single-tone sinusoidal message signal with a modulation index of $50\%$. If the carrier and one of the sideban...
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1737
GATE ECE 2021 | Question: 24
A $4\:kHz$ sinusoidal message signal having amplitude $4\:V$ is fed to a delta modulator ($DM$) operating at a sampling rate of $32\:\text{kHz}$. The minimum step size required to avoid slope overload noise in the $DM$ (rounded off to two decimal places) is _____ $V$.
A $4\:kHz$ sinusoidal message signal having amplitude $4\:V$ is fed to a delta modulator ($DM$) operating at a sampling rate of $32\:\text{kHz}$. The minimum step size re...
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1739
GATE ECE 2021 | Question: 28
The switch in the circuit in the figure is in position $P$ for a long time and then moved to position $Q$ at time $t=0$. The value of $\dfrac{dv\left ( t \right )}{dt}$ at $t=0^{+}$ is $0\:V/s$ $3\:V/s$ $-3\:V/s$ $-5\:V/s$
The switch in the circuit in the figure is in position $P$ for a long time and then moved to position $Q$ at time $t=0$.The value of $\dfrac{dv\left ( t \right )}{dt}$ at...
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1740
GATE ECE 2021 | Question: 29
Consider the two-port network shown in the figure. The admittance parameters, in siemens, are $y_{11}=2,\:y_{12}=-4,\:y_{21}=-4,\:y_{22}=2$ $y_{11}=1,\:y_{12}=-2,\:y_{21}=-1,\:y_{22}=3$ $y_{11}=2,\:y_{12}=-4,\:y_{21}=-1,\:y_{22}=2$ $y_{11}=2,\:y_{12}=-4,\:y_{21}=-4,\:y_{22}=3$
Consider the two-port network shown in the figure.The admittance parameters, in siemens, are$y_{11}=2,\:y_{12}=-4,\:y_{21}=-4,\:y_{22}=2$$y_{11}=1,\:y_{12}=-2,\:y_{21}=-1...
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1744
GATE ECE 2021 | Question: 34
A digital transmission system uses a ($7,4$) systematic linear Hamming code for transmitting data over a noisy channel. If three of the message-codeword pairs in this code ($\text{m}_{i}$ ; $\text{c}_{i}$), where $\text{c}_{i}$ is the ... $\text{valid codeword}$ in this code? $1101001$ $1011010$ $0001011$ $0110100$
A digital transmission system uses a ($7,4$) systematic linear Hamming code for transmitting data over a noisy channel. If three of the message-codeword pairs in this cod...
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1746
GATE ECE 2021 | Question: 38
In the circuit shown in the figure, the switch is closed at time $t=0$, while the capacitor is initially charged to $-5\:V$ (i.e., $v_{c}(0)=-5V$). The time after which the voltage across the capacitor becomes zero (rounded off to three decimal places) is ________________ $\text{ms}$.
In the circuit shown in the figure, the switch is closed at time $t=0$, while the capacitor is initially charged to $-5\:V$ (i.e., $v_{c}(0)=-5V$).The time after which th...
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1747
GATE ECE 2021 | Question: 39
The exponential Fourier series representation of a continuous-time periodic signal $x(t)$ is defined as $x\left ( t \right )=\sum_{k=-\infty }^{\infty }a_{k}e^{jk\omega _{0}t}$ where $\omega _0$ ... $x(t)$ (rounded off to one decimal place) is ______________
The exponential Fourier series representation of a continuous-time periodic signal $x(t)$ is defined as$$x\left ( t \right )=\sum_{k=-\infty }^{\infty }a_{k}e^{jk\omega _...
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1749
GATE ECE 2021 | Question: 41
Consider the signals $x\left [ n \right ]=2^{n-1}u\left [ -n+2 \right ]$ and $y\left [ n \right ]=2^{-n+2}u\left [ n+1 \right ]$, where $u[n]$ is the unit step sequence. Let $X(e^{jw})$ and $Y(e^{jw})$ be the discrete-time Fourier ... (rounded off to one decimal place) is ___________
Consider the signals $x\left [ n \right ]=2^{n-1}u\left [ -n+2 \right ]$ and $y\left [ n \right ]=2^{-n+2}u\left [ n+1 \right ]$, where $u[n]$ is the unit step sequence. ...
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1752
GATE ECE 2021 | Question: 44
For the transistor $M_{1}$ in the circuit shown in the figure, $\mu_{n} C_{\text{ox}} = 100\:\mu A/V^{2}$ and $(W/L)=10$, where $\mu_{n}$ is the mobility of electron, $C_{\text{ox}}$ is the oxide capacitance ... $V$.
For the transistor $M_{1}$ in the circuit shown in the figure, $\mu_{n} C_{\text{ox}} = 100\:\mu A/V^{2}$ and $(W/L)=10$, where $\mu_{n}$ is the mobility of electron, $C_...
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1753
GATE ECE 2021 | Question: 45
A circuit with an ideal $\text{OPAMP}$ is shown in the figure. A pulse $V_{\text{IN}}$ of $20\:ms$ duration is applied to the input. The capacitors are initially uncharged. The output voltage $V_{\text{OUT}}$ of this circuit at $t=0^{+}$ (in integer) is ____________________ $V$.
A circuit with an ideal $\text{OPAMP}$ is shown in the figure. A pulse $V_{\text{IN}}$ of $20\:ms$ duration is applied to the input. The capacitors are initially uncharge...
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1756
GATE ECE 2021 | Question: 49
A sinusoidal message signal having root mean square value of $4\:V$ and frequency of $\text{1 kHz}$ is fed to a phase modulator with phase deviation constant $2$ ... $\text{Hz}$.
A sinusoidal message signal having root mean square value of $4\:V$ and frequency of $\text{1 kHz}$ is fed to a phase modulator with phase deviation constant $2$ rad/ vol...
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1757
GATE ECE 2021 | Question: 50
Consider a superheterodyne receiver tuned to $600 \text{ kHz}$. If the local oscillator feeds a $1000 \text{ kHz}$ signal to the mixer, the image frequency (in integer) is ____________________ $\text{kHz}$.
Consider a superheterodyne receiver tuned to $600 \text{ kHz}$. If the local oscillator feeds a $1000 \text{ kHz}$ signal to the mixer, the image frequency (in integer) i...
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1760
GATE ECE 2021 | Question: 53
Consider a polar non-return to zero ($\text{NRZ}$) waveform, using $+2\:V$ and $-2\:V$ for representing binary $1$' and $0$ ... the optimum threshold voltage for a maximum a posteriori ($\text{MAP}$) receiver (rounded off to two decimal places) is ______ $V$.
Consider a polar non-return to zero ($\text{NRZ}$) waveform, using $+2\:V$ and $-2\:V$ for representing binary ‘$1$’ and ‘$0$’ respectively, is transmitted in the...
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