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1
GATE EC 2021  Question: 4
Consider a realvalued baseband 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 $\text{15 kHz}$ $\text{30 kHz}$ $\text{60 kHz}$ $\text{20 kHz}$
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GATE EC 2021  Question: 5
Consider two $16$point sequences $x\left [ n \right ]$ and $h\left [ n \right ]$. Let the linear convolution of $x\left [ n \right ]$ and $h\left [ n \right ]$ be denoted by $y\left [ n \right ]$, while $z\left [ n \right ]$ denotes the $16$point inverse discrete Fourier ... $k=0,1,2,,15$ $k=0$ $k=15$ $\text{k=0 and k=15}$
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GATE EC 2021  Question: 6
A bar of silicon is doped with boron concentration of $10^{16} \text{cm}^{3}$ and assumed to be fully ionized. It is exposed to light such that electronhole pairs are generated throughout the volume of the bar at the rate of $10^{20} \text{cm}^{3} s^{1}$. If the ... $2 \times 10^{20} \text{cm}^{6}$ $10^{32} \text{cm}^{6}$ $2 \times 10^{32} \text{cm}^{6}$
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4
GATE EC 2021  Question: 7
The energy band diagram of a $\text{ptype}$ semiconductor bar of length $L$ under equilibrium condition (i.e.. the Fermi energy level $E_{F}$ is constant) is shown in the figure. The valance band $E_{V}$ is sloped since doping is nonuniform along the bar. The difference ... bar is $\frac{\Delta }{qL}$ $\frac{2\Delta }{qL}$ $\frac{\Delta }{2qL}$ $\frac{3\Delta }{2qL}$
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5
GATE EC 2021  Question: 8
In the circuit shown in the figure, the transistors $M_{1}$ and $M_{2}$ are operating in saturation. The channel length modulation coefficients of both the transistors are nonzero. The transconductance of the $\text{MOSFETs}$ $M_{1}$ and $M_{2}$ are $g_{m1}$ ... $g_{m2}\left ( \frac{1}{g_{m1}}\left  \right r_{01}\left  \right r_{02} \right )$
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6
GATE EC 2021  Question: 9
For the circuit with an ideal $\text{OPAMP}$ shown in the figure. $V_{\text{REF}}$ is fixed. If $V_{\text{OUT}}=1$ volt for $V_{\text{IN}}0.1$ volt and $V_{\text{OUT}}=6$ volt for $V_{\text{IN}}=1$ volt, where $V_{\text{OUT}}$ is measured across $R_{L}$ connected at the output of this $\text{OPAMP}$, the value of $R_{F}/R_{\text{IN}}$ is $3.285$ $2.860$ $3.825$ $5.555$
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7
GATE EC 2021  Question: 10
Consider the circuit with an ideal $\text{OPAMP}$ shown in the figure. Assuming $\left  V_{\text{IN}} \right \ll \left  V_{\text{CC}} \right $ and $\left  V_{\text{REF}} \right \ll \left  V_{\text{CC}} \right  $, the condition at which $V_{\text{OUT}}$ equals to ... $V_{\text{IN}}\:=\:2\:V_{\text{REF}}$ $V_{\text{IN}}\:=\:2\:+\:V_{\text{REF}}$
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GATE EC 2021  Question: 14
The complete Nyquist plot of the openloop transfer function $G(s)H(s)$ of a feedback control system in the figure. If $G(s)H(s)$ has one zero in the righthalf of the $s$plane, the number of poles that the closedloop system will have in the righthalf of the $s$plane is $0$ $1$ $4$ $3$
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9
GATE EC 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 ... $\frac{1}{3}$ $\frac{3}{5}$ $\frac{2}{5}$ $\frac{2}{3}$
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10
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 ________ $A$.
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GATE EC 2021  Question: 19
Consider the circuit shown in the figure. The value of $v_{0}$ (rounded off to one decimal place) is _________ $V$.
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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 ___________ $V$.
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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 ________________
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14
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 ______________
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15
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 _____ $\text{kHz}$.
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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 _____ $V$.
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17
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.
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18
GATE EC 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 $0\:V/s$ $3\:V/s$ $3\:V/s$ $5\:V/s$
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19
GATE EC 2021  Question: 29
Consider the twoport network shown in the figure. The admittance parameters, in siemens, are $y_{11}=2,\:y_{12}=4,\:y_{21}=4,\:y_{22}=2$ $y_{11}=1,\:y_{12}=2,\:y_{21}=1,\:y_{22}=3$ $y_{11}=2,\:y_{12}=4,\:y_{21}=1,\:y_{22}=2$ $y_{11}=2,\:y_{12}=4,\:y_{21}=4,\:y_{22}=3$
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20
GATE EC 2021  Question: 30
For an $n$channel silicon $\text{MOSFET}$ with $10\:nm$ gate oxide thickness, the substrate sensitivity $\left ( \partial V_{T}/\partial \left  V_{BS} \right  \right )$ is found to be $50\:mV/V$ at a substrate voltage $\left  V_{BS} \right =2V$, where $V_{T}$ is the ... $4.37\times 10^{15}\:cm^{3}$ $2.37\times 10^{15}\:cm^{3}$ $9.37\times 10^{15}\:cm^{3}$
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21
GATE EC 2021  Question: 32
The content of the registers are $R_{1} = 25H, R_{2} = 30H$ and $R_{3} = 40H$. The following machine instructions are executed. $\text{PUSH } \{R_{1}\}$ $\text{PUSH } \{R_{2}\}$ $\text{PUSH } \{R_{3}\}$ $\text{POP } \{R_{1}\}$ $\text{POP } \{R_{2}\}$ ... $R_{1}=30H,\:R_{2}=40H,\:R_{3}=25H$ $R_{1}=40H,\:R_{2}=25H,\:R_{3}=30H$
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22
GATE EC 2021  Question: 33
The electrical system shown in the figure converts input source current $i_{s}(t)$ to output voltage $v_{o}(t)$ Current i $i_{L}(t)$ in the inductor and voltage $v_{c}(t)$ across the capacitor ... as well as completely observable completely state controllable but not observable completely observable but not state controllable neither state controllable nor observable
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23
GATE EC 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 messagecodeword pairs in this code ($\text{m}_{i}$ ; $\text{c}_{i}$), where $\text{c}_{i}$ is the ... $\text{valid codeword}$ in this code? $1101001$ $1011010$ $0001011$ $0110100$
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24
GATE EC 2021  Question: 35
The impedance matching network shown n the figure is to match a lossless line having characteristic impedance $Z_{0}= 50 \:\Omega$ with a load impedance $Z_{L}$. A quarterwave line having a characteristic impedance $Z_1=75\:\Omega$ is connected to $Z_{L}$. Two stubs having ... the real part of $Z_{L}$ is $112.5\:\Omega$ $75.0\:\Omega$ $50.0\:\Omega$ $33.3\:\Omega$
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25
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 ________________ $\text{ms}$.
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26
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 ______________
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27
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 _________________
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28
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 ___________
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29
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 ______________________ $V$.
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30
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 ______________ $V$.
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31
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 ... $V$.
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32
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 ____________________ $V$.
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33
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 _______________ $A$.
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34
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 ___________________
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35
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 $2$ ... $\text{Hz}$.
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36
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 ____________________ $\text{kHz}$.
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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.
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38
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 _________________________
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39
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 ______ $V$.
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40
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 ________________________
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