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GATE ECE 2021 | Question: 16
If the vectors $(1.0,\:-1.0,\:2.0)$, $(7.0,\:3.0,\:x)$ and $(2.0,\:3.0,\:1.0)$ in $\mathbb{R}^{3}$ are linearly dependent, the value of $x$ is __________
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Vector Analysis
Feb 20
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Arjun
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2
GATE ECE 2021 | Question: 17
Consider the vector field $F\:=\:a_{x}\left ( 4y-c_{1}z \right )+a_y\left ( 4x + 2z\right )+a_{z}\left ( 2y +z\right )$ in a rectangular coordinate system $(x,y,z)$ with unit vectors $a_{x},\:a_{y}$ and $a_{z}$. If the field $F$ is irrotational (conservative), then the constant $c_{1}$ (in integer) is _________________
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Vector Analysis
Feb 20
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Arjun
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numerical-answers
vector-analysis
vector-in-planes
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3
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 ________ $A$.
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Others
Feb 20
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Arjun
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numerical-answers
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0
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4
GATE ECE 2021 | Question: 19
Consider the circuit shown in the figure. The value of $v_{0}$ (rounded off to one decimal place) is _________ $V$.
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Others
Feb 20
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numerical-answers
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5
GATE ECE 2021 | Question: 20
An $8$-bit unipolar (all analog output values are positive) digital-to-analog converter $\text{(DAC)}$ has a full-scale voltage range from $0\; V$ to $7.68\:V$. If the digital input code is $10010110$ (the leftmost bit is $\text{MSB}$), then the analog output voltage of the $\text{DAC}$ (rounded off to one decimal place) is ___________ $V$.
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Others
Feb 20
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Arjun
4.5k
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45
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gateec-2021
numerical-answers
0
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0
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6
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 ________________
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Others
Feb 20
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gateec-2021
numerical-answers
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7
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 ______________
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Others
Feb 20
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numerical-answers
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8
GATE ECE 2021 | Question: 23
A speech signal, band limited to $4\:\text{kHz}$, is sampled at $1.25$ times the Nyquist rate. The speech samples, assumed to be statistically independent and uniformly distributed in the range $-5\:V$ to $+5\:V$, are ... transmission of the signal with arbitrarily small probability of transmission error (rounded off to two decimal places) is _____ $\text{kHz}$.
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Others
Feb 20
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Arjun
4.5k
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99
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gateec-2021
numerical-answers
0
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0
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9
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 _____ $V$.
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Others
Feb 20
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63
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gateec-2021
numerical-answers
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10
GATE ECE 2021 | Question: 25
The refractive indices of the core and cladding of an optical fiber are $1.50$ and $1.48$, respectively. The critical propagation angle, which is defined as the maximum angle that the light beam makes with the axis of the optical fiber to achieve the total internal reflection, (rounded off to two decimal places) is _____ degree.
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Others
Feb 20
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numerical-answers
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11
GATE ECE 2021 | Question: 36
A real $2\times2$ non-singular matrix $A$ with repeated eigenvalue is given as $A=\begin{bmatrix} x & -3.0\\ 3.0 & 4.0 \end{bmatrix}$ where $x$ is a real positive number. The value of $x$ (rounded off to one decimal place) is ________________
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Linear Algebra
Feb 20
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Arjun
4.5k
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43
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gateec-2021
numerical-answers
linear-algebra
eigen-values
0
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12
GATE ECE 2021 | Question: 37
For a vector field $D=\rho\cos^{2}\:\varphi \:a_{\rho }+z^{2}\sin^{2}\:\varphi \:a_{\varphi }$ in a cylindrical coordinate system $\left ( \rho ,\varphi ,z \right )$ with unit vectors $a_{\rho },a_{\varphi }$ and $a_{z}$, the ... $\left ( \rho =3, 0\leq z\leq 2 \right )$ (rounded off to two decimal places) is ________________
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Vector Analysis
Feb 20
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Arjun
4.5k
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32
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gateec-2021
numerical-answers
vector-analysis
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13
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 ________________ $\text{ms}$.
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Others
Feb 20
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Arjun
4.5k
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34
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gateec-2021
numerical-answers
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0
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14
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 ______________
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Others
Feb 20
by
Arjun
4.5k
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33
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gateec-2021
numerical-answers
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0
answers
15
GATE ECE 2021 | Question: 40
For a unit step input $u[n]$, a discrete-time $\text{LTI}$ system produces an output signal $\left ( 2\delta \left [ n+1 \right ] +\delta \left [ n \right ]+\delta \left [ n-1 \right ]\right )$. Let $y[n]$ be the output of the system for an input $\left ( \left ( \dfrac{1}{2} \right )^n u\left [ n \right ]\right )$. The value of $y[0]$ is _________________
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Others
Feb 20
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Arjun
4.5k
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26
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gateec-2021
numerical-answers
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0
answers
16
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 ___________
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Others
Feb 20
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22
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gateec-2021
numerical-answers
0
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0
answers
17
GATE ECE 2021 | Question: 42
A silicon $P-N$ junction is shown in the figure. The doping in the $P$ region is $5\times10^{16}\:cm^{-3}$ and doping in the $N$ region is $10\times10^{16}\:cm^{-3}$ ... completely deplete one of the two regions ($P$ or $N$) prior to the other (rounded off to one decimal place) is ______________________ $V$.
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Others
Feb 20
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Arjun
4.5k
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27
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gateec-2021
numerical-answers
0
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0
answers
18
GATE ECE 2021 | Question: 43
An asymmetrical periodic pulse train $v_{in}$ of $10\:V$ amplitude with on-time $T_{\text{ON}}=1\:ms$ and off-time $T_{\text{OFF}}=1\:\mu s$ is applied to the circuit shown in the figure. The diode $D_{1}$ is ideal. The difference between the maximum voltage and minimum voltage of the output waveform $v_{o}$ (in integer) is ______________ $V$.
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Others
Feb 20
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Arjun
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gateec-2021
numerical-answers
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0
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19
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 ... $V$.
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Others
Feb 20
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Arjun
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30
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gateec-2021
numerical-answers
0
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0
answers
20
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 ____________________ $V$.
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Others
Feb 20
by
Arjun
4.5k
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22
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gateec-2021
numerical-answers
0
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0
answers
21
GATE ECE 2021 | Question: 46
The propagation delay of the exclusive$-\text{OR}$ ($\text{XOR}$) gate in the circuit in the figure is $3\:ns$. The propagation delay of all the flip-flops is assumed to be zero. The clock ($\text{Clk}$ ... of triggering clock edges after which the flip-flop outputs $Q_{2}Q_{1}Q_{0}$ becomes $1\; 0\; 0$ (in integer) is
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Digital Circuits
Feb 20
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Arjun
4.5k
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55
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gateec-2021
numerical-answers
digital-circuits
sequential-circuit
counters
0
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0
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22
GATE ECE 2021 | Question: 47
The circuit in the figure contains a current source driving a load having an inductor and a resistor in series, with a shunt capacitor across the load. The ammeter is assumed to have zero resistance. The switch is closed at time ... maximum ammeter reading that one will observe after the switch is closed (rounded off to two decimal places) is _______________ $A$.
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Others
Feb 20
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Arjun
4.5k
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41
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gateec-2021
numerical-answers
0
votes
0
answers
23
GATE ECE 2021 | Question: 48
A unity feedback system that uses proportional-integral ($\text{PI}$) control is shown in the figure. The stability of the overall system is controlled by tuning the $\text{PI}$ control parameters $K_{P}$ and $K_{I}$. The maximum ... as to keep the overall system stable or, in the worst case, marginally stable (rounded off to three decimal places) is ___________________
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Others
Feb 20
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Arjun
4.5k
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41
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gateec-2021
numerical-answers
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0
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24
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 $2$ ... $\text{Hz}$.
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Others
Feb 20
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Arjun
4.5k
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28
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gateec-2021
numerical-answers
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0
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25
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 ____________________ $\text{kHz}$.
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Others
Feb 20
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Arjun
4.5k
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31
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gateec-2021
numerical-answers
0
votes
0
answers
26
GATE ECE 2021 | Question: 51
In a high school having equal number of boy students and girl students, $75\%$ of the students study Science and the remaining $25\%$ students study Commerce. Commerce students are two times more likely to be a boy than are ... gained in knowing that a randomly selected girl student studies Commerce (rounded off to three decimal places) is _____________________ bits.
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Others
Feb 20
by
Arjun
4.5k
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36
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gateec-2021
numerical-answers
0
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0
answers
27
GATE ECE 2021 | Question: 52
A message signal having peak-to-peak value of $2\:V$, root mean square value of $0.1\:V$ and bandwidth of $\text{5 kHz}$ is sampled and fed to a pulse code modulation ($\text{PCM}$) system that uses a uniform quantizer. ... signal to quantization noise ratio that can be obtained by the $\text{PCM}$ system (rounded off to two decimal places) is _________________________
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Feb 20
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Arjun
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numerical-answers
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0
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28
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 ______ $V$.
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Feb 20
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29
GATE ECE 2021 | Question: 54
A standard air-filled rectangular waveguide with dimensions $\text{a=8 cm, b=4 cm}$, operates at $\text{3.4 GHz}$. For the dominant mode of wave propagation, the phase velocity of the signal in $v_{p}$. The value (rounded off to two decimal places) of $v_{p}/c$, where $c$ denotes the velocity of light, is ________________________
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Feb 20
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30
GATE ECE 2021 | Question: 55
An antenna with a directive gain of $6\text{ dB}$ is radiating a total power of $\text{16 kW}$. The amplitude of the electric field in free space at a distance of $\text{8 km}$ from the antenna in the direction of $\text{6 dB}$ gain (rounded off to three decimal places) is ____________________ $\text{V/m}$.
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Feb 20
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31
GATE ECE 2020 | Question: 15
In the given circuit, the two-port network has the impedance matrix $\begin{bmatrix} Z \end{bmatrix}=\begin{bmatrix} 40 & 60\\ 60& 120 \end{bmatrix}$. The value of $Z_{L}$ for which maximum power is transferred to the load is _____________$\Omega$.
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Network Solution Methods
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32
GATE ECE 2020 | Question: 16
The current in the $\text{RL}$-circuit shown below is $i\left ( t \right )=10\cos\left ( 5t-\pi /4 \right )A$. The value of the inductor $\text{(rounded off to two decimal places)}$ is _______ $\text{H}$.
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Network Solution Methods
Feb 13, 2020
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jothee
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74
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gate2020-ec
numerical-answers
network-solution-methods
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0
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33
GATE ECE 2020 | Question: 17
In the circuit shown below, all the components are ideal and the input voltage is sinusoidal. The magnitude of the steady-state output $V_{o}$ ( rounded off to two decimal places) is ______ $V$.
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Network Solution Methods
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jothee
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59
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numerical-answers
network-solution-methods
steady-state
sinusoidal
1
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0
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34
GATE ECE 2020 | Question: 18
In the circuit shown below, all the components are ideal. If $V_{i}$ is $+2\:V$, the current $I_{o}$ sourced by the op-amp is __________ $\text{mA}$.
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Analog Circuits
Feb 13, 2020
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jothee
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71
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gate2020-ec
numerical-answers
op-amps
analog-circuits
0
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0
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35
GATE ECE 2020 | Question: 19
In an $8085$ microprocessor, the number of address lines required to access a $16$ K byte memory bank is ____________ .
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Digital Circuits
Feb 13, 2020
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jothee
1.9k
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53
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gate2020-ec
numerical-answers
digital-circuits
microprocessor-8085
0
votes
0
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36
GATE ECE 2020 | Question: 20
A $10$-bit D/A converter is calibrated over the full range from $0$ to $10$ V. If the input to the D/A converter is $13 \:A$ (in hex), the output ( rounded off to three decimal places) is __________ $V$.
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Digital Circuits
Feb 13, 2020
by
jothee
1.9k
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77
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gate2020-ec
numerical-answers
digital-circuits
data-converters
0
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0
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37
GATE ECE 2020 | Question: 21
A transmission line of length $3\lambda /4$ and having a characteristic impedance of $50$ $\Omega$ is terminated with a load of $400 \Omega$. The impedance (rounded off to two decimal places) seen at the input end of the transmission line is __________ $\Omega$.
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Electromagnetics
Feb 13, 2020
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jothee
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50
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numerical-answers
impedance
electromagnetics
0
votes
0
answers
38
GATE ECE 2020 | Question: 22
A binary random variable $X$ takes the value $+2$ or $-2$. The probability $P(X=+2)=\alpha $. The value of $\alpha$ (rounded off to one decimal place), for which the entropy of $X$ is maximum, is __________.
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Communications
Feb 13, 2020
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jothee
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70
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numerical-answers
entropy
communications
0
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0
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39
GATE ECE 2020 | Question: 23
The loop transfer function of a negative feedback system is $G\left ( s \right )H\left ( s \right )=\frac{K(s+11)}{s(s+2)(s+8)}.$ The value of $K$, for which the system is marginally stable, is ___________.
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Network Solution Methods
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jothee
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85
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numerical-answers
network-solution-methods
transfer-function
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0
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40
GATE ECE 2020 | Question: 24
The random variable $Y=\int_{-\infty }^{\infty }W\left ( t \right )\phi \left ( t \right )dt, \text{ where } \phi \left ( t \right )=\begin{cases} 1; & 5\leq t\leq 7 &\\ 0; & \text{otherwise} \end{cases}$ and $W(t)$ is ... noise process with two-sided power spectral density $S_{W}\left ( f \right )=3 W/Hz$, for all $f$. The variance of $Y$ is ________.
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Vector Analysis
Feb 13, 2020
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jothee
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vector-analysis
gausss-theorem
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