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GATE EC 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 __________
asked
Feb 20
in
Vector Analysis
by
Arjun
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4.4k
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13
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gateec2021
numericalanswers
vectoranalysis
vectorinplanes
0
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2
GATE EC 2021  Question: 17
Consider the vector field $F\:=\:a_{x}\left ( 4yc_{1}z \right )+a_y\left ( 4x + 2z\right )+a_{z}\left ( 2y +z\right )$ 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 _________________
asked
Feb 20
in
Vector Analysis
by
Arjun
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4.4k
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12
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gateec2021
numericalanswers
vectoranalysis
vectorinplanes
0
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0
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3
GATE EC 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 ________ $A$.
asked
Feb 20
in
Others
by
Arjun
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4.4k
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14
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gateec2021
numericalanswers
0
votes
0
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4
GATE EC 2021  Question: 19
Consider the circuit shown in the figure. The value of $v_{0}$ (rounded off to one decimal place) is _________ $V$.
asked
Feb 20
in
Others
by
Arjun
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4.4k
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11
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gateec2021
numericalanswers
0
votes
0
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5
GATE EC 2021  Question: 20
An $8$bit unipolar (all analog output values are positive) digitaltoanalog converter $\text{(DAC)}$ has a fullscale 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 ___________ $V$.
asked
Feb 20
in
Others
by
Arjun
(
4.4k
points)

12
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gateec2021
numericalanswers
0
votes
0
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6
GATE EC 2021  Question: 21
The autocorrelation function $R_{X}\left ( \tau \right )$ of a widesense stationary random process $X(t)$ is shown in the figure. The average power of $X(t)$ is ________________
asked
Feb 20
in
Others
by
Arjun
(
4.4k
points)

13
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gateec2021
numericalanswers
0
votes
0
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7
GATE EC 2021  Question: 22
Consider a carrier signal which is amplitude modulated by a singletone 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 ______________
asked
Feb 20
in
Others
by
Arjun
(
4.4k
points)

16
views
gateec2021
numericalanswers
0
votes
0
answers
8
GATE EC 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 _____ $\text{kHz}$.
asked
Feb 20
in
Others
by
Arjun
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4.4k
points)

30
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gateec2021
numericalanswers
0
votes
0
answers
9
GATE EC 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 _____ $V$.
asked
Feb 20
in
Others
by
Arjun
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4.4k
points)

12
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gateec2021
numericalanswers
0
votes
0
answers
10
GATE EC 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.
asked
Feb 20
in
Others
by
Arjun
(
4.4k
points)

15
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gateec2021
numericalanswers
0
votes
0
answers
11
GATE EC 2021  Question: 36
A real $2\times2$ nonsingular 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 ________________
asked
Feb 20
in
Linear Algebra
by
Arjun
(
4.4k
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12
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gateec2021
numericalanswers
linearalgebra
eigenvalues
0
votes
0
answers
12
GATE EC 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 ________________
asked
Feb 20
in
Vector Analysis
by
Arjun
(
4.4k
points)

14
views
gateec2021
numericalanswers
vectoranalysis
0
votes
0
answers
13
GATE EC 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 ________________ $\text{ms}$.
asked
Feb 20
in
Others
by
Arjun
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4.4k
points)

12
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gateec2021
numericalanswers
0
votes
0
answers
14
GATE EC 2021  Question: 39
The exponential Fourier series representation of a continuoustime periodic signal $x(t)$ is defined as $x\left ( t \right )=\sum_{k=\infty }^{\infty }a_{k}e^{jk\omega _{0}t}$ where $\omega _0$ is the fundamental angular frequency of $x(t)$ ... $x(t)$ (rounded off to one decimal place) is ______________
asked
Feb 20
in
Others
by
Arjun
(
4.4k
points)

12
views
gateec2021
numericalanswers
0
votes
0
answers
15
GATE EC 2021  Question: 40
For a unit step input $u[n]$, a discretetime $\text{LTI}$ system produces an output signal $\left ( 2\delta \left [ n+1 \right ] +\delta \left [ n \right ]+\delta \left [ n1 \right ]\right )$. 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 _________________
asked
Feb 20
in
Others
by
Arjun
(
4.4k
points)

13
views
gateec2021
numericalanswers
0
votes
0
answers
16
GATE EC 2021  Question: 41
Consider the signals $x\left [ n \right ]=2^{n1}u\left [ n+2 \right ]$ 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 discretetime Fourier ... (rounded off to one decimal place) is ___________
asked
Feb 20
in
Others
by
Arjun
(
4.4k
points)

13
views
gateec2021
numericalanswers
0
votes
0
answers
17
GATE EC 2021  Question: 42
A silicon $PN$ 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 $10\times10^{16}\:cm^{3}$ ... would completely deplete one of the two regions ($P$ or $N$) prior to the other (rounded off to one decimal place) is ______________________ $V$.
asked
Feb 20
in
Others
by
Arjun
(
4.4k
points)

12
views
gateec2021
numericalanswers
0
votes
0
answers
18
GATE EC 2021  Question: 43
An asymmetrical periodic pulse train $v_{in}$ of $10\:V$ amplitude with ontime $T_{\text{ON}}=1\:ms$ and offtime $T_{\text{OFF}}=1\:\mu s$ 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 ______________ $V$.
asked
Feb 20
in
Others
by
Arjun
(
4.4k
points)

12
views
gateec2021
numericalanswers
0
votes
0
answers
19
GATE EC 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 ... $V$.
asked
Feb 20
in
Others
by
Arjun
(
4.4k
points)

13
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gateec2021
numericalanswers
0
votes
0
answers
20
GATE EC 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 ____________________ $V$.
asked
Feb 20
in
Others
by
Arjun
(
4.4k
points)

11
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gateec2021
numericalanswers
0
votes
0
answers
21
GATE EC 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 flipflops is assumed to be zero. The clock ($\text{Clk}$ ... of triggering clock edges after which the flipflop outputs $Q_{2}Q_{1}Q_{0}$ becomes $1\; 0\; 0$ (in integer) is
asked
Feb 20
in
Digital Circuits
by
Arjun
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4.4k
points)

15
views
gateec2021
numericalanswers
digitalcircuits
sequentialcircuit
counters
0
votes
0
answers
22
GATE EC 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 $t = 0$ ... maximum ammeter reading that one will observe after the switch is closed (rounded off to two decimal places) is _______________ $A$.
asked
Feb 20
in
Others
by
Arjun
(
4.4k
points)

18
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gateec2021
numericalanswers
0
votes
0
answers
23
GATE EC 2021  Question: 48
A unity feedback system that uses proportionalintegral ($\text{PI}$) 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 ___________________
asked
Feb 20
in
Others
by
Arjun
(
4.4k
points)

13
views
gateec2021
numericalanswers
0
votes
0
answers
24
GATE EC 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 $2$ ... $\text{Hz}$.
asked
Feb 20
in
Others
by
Arjun
(
4.4k
points)

12
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gateec2021
numericalanswers
0
votes
0
answers
25
GATE EC 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 ____________________ $\text{kHz}$.
asked
Feb 20
in
Others
by
Arjun
(
4.4k
points)

14
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gateec2021
numericalanswers
0
votes
0
answers
26
GATE EC 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.
asked
Feb 20
in
Others
by
Arjun
(
4.4k
points)

13
views
gateec2021
numericalanswers
0
votes
0
answers
27
GATE EC 2021  Question: 52
A message signal having peaktopeak 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 _________________________
asked
Feb 20
in
Others
by
Arjun
(
4.4k
points)

13
views
gateec2021
numericalanswers
0
votes
0
answers
28
GATE EC 2021  Question: 53
Consider a polar nonreturn 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 ______ $V$.
asked
Feb 20
in
Others
by
Arjun
(
4.4k
points)

12
views
gateec2021
numericalanswers
0
votes
0
answers
29
GATE EC 2021  Question: 54
A standard airfilled 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 ________________________
asked
Feb 20
in
Others
by
Arjun
(
4.4k
points)

12
views
gateec2021
numericalanswers
0
votes
0
answers
30
GATE EC 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 ____________________ $\text{V/m}$.
asked
Feb 20
in
Others
by
Arjun
(
4.4k
points)

16
views
gateec2021
numericalanswers
0
votes
0
answers
31
GATE ECE 2020  Question: 15
In the given circuit, the twoport 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 _____________$\Omega$.
asked
Feb 13, 2020
in
Network Solution Methods
by
jothee
(
1.8k
points)

47
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gate2020ec
numericalanswers
networksolutionmethods
twoportnetwork
0
votes
0
answers
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 _______ $\text{H}$.
asked
Feb 13, 2020
in
Network Solution Methods
by
jothee
(
1.8k
points)

40
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gate2020ec
numericalanswers
networksolutionmethods
0
votes
0
answers
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 steadystate output $V_{o}$ ( rounded off to two decimal places) is ______ $V$.
asked
Feb 13, 2020
in
Network Solution Methods
by
jothee
(
1.8k
points)

29
views
gate2020ec
numericalanswers
networksolutionmethods
steadystate
sinusoidal
0
votes
0
answers
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 opamp is __________ $\text{mA}$.
asked
Feb 13, 2020
in
Analog Circuits
by
jothee
(
1.8k
points)

36
views
gate2020ec
numericalanswers
opamps
analogcircuits
0
votes
0
answers
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 ____________ .
asked
Feb 13, 2020
in
Digital Circuits
by
jothee
(
1.8k
points)

33
views
gate2020ec
numericalanswers
digitalcircuits
microprocessor8085
0
votes
0
answers
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 __________ $V$.
asked
Feb 13, 2020
in
Digital Circuits
by
jothee
(
1.8k
points)

49
views
gate2020ec
numericalanswers
digitalcircuits
dataconverters
0
votes
0
answers
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 __________ $\Omega$.
asked
Feb 13, 2020
in
Electromagnetics
by
jothee
(
1.8k
points)

29
views
gate2020ec
numericalanswers
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 __________.
asked
Feb 13, 2020
in
Communications
by
jothee
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1.8k
points)

36
views
gate2020ec
numericalanswers
entropy
communications
0
votes
0
answers
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 ___________.
asked
Feb 13, 2020
in
Network Solution Methods
by
jothee
(
1.8k
points)

46
views
gate2020ec
numericalanswers
networksolutionmethods
transferfunction
0
votes
0
answers
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 twosided power spectral density $S_{W}\left ( f \right )=3 W/Hz$, for all $f$. The variance of $Y$ is ________.
asked
Feb 13, 2020
in
Vector Analysis
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jothee
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1.8k
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33
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gate2020ec
numericalanswers
vectoranalysis
gaussstheorem
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