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3041
GATE ECE 1998 | Question 4
A voltage source of internal impedance $R_{s}+j X_{s}$ supplies power to a load of impedance $R_{L}+j X_{L}$ in which only $R_{L}$ is variable. Determine the value of $R_{L}$ for maximum power transfer from the source to the load. Also, find the numerical value of $R_{L}$ if the source impedance is $3.0 \; \Omega$ (purely resistive) and $X_{1}$ is $4.0 \; \Omega$.
A voltage source of internal impedance $R_{s}+j X_{s}$ supplies power to a load of impedance $R_{L}+j X_{L}$ in which only $R_{L}$ is variable. Determine the value of $R_...
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Sep 26, 2022
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3042
GATE ECE 1998 | Question 16
For the $\text{TTL}$ circuit shown in the figure is find the current through the collector of transistor $Q_{4}$ when $V_{0}=0.2 \mathrm{~V}$. Assume $V_{C E(\text {sat)}}=0.2 \mathrm{~V}, \beta=100$ and $V_{BE(\text {sat})}=0.7 \mathrm{~V}$. The $\alpha$ of $Q_{1}$ in its inverse active mode is $0.01$.
For the $\text{TTL}$ circuit shown in the figure is find the current through the collector of transistor $Q_{4}$ when $V_{0}=0.2 \mathrm{~V}$. Assume $V_{C E(\text {sat)}...
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Sep 26, 2022
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3043
GATE ECE 2003 | Question: 49
The action of a $\text{JFET}$ in its equivalent circuit can best be represented as a Current Controlled Current Source Current Controlled Voltage Source Voltage Controlled Voltage Source Voltage Controlled Current Source
The action of a $\text{JFET}$ in its equivalent circuit can best be represented as aCurrent Controlled Current SourceCurrent Controlled Voltage SourceVoltage Controlled V...
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Sep 26, 2022
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3044
GATE ECE 2004 | Question: 47
The value of $\mathrm{C}$ required for sinusoidal oscillations of frequency $1 \; \mathrm{kHz}$ in the circuit of given figure is $\frac{1}{2 \pi} \; \mu \text{F}$ $2 \pi \; \mu \text{F}$ $\frac{1}{2 \pi \sqrt{6}} \; \mu \text{F}$ $2 \pi \sqrt{6} \; \mu \text{F}$
The value of $\mathrm{C}$ required for sinusoidal oscillations of frequency $1 \; \mathrm{kHz}$ in the circuit of given figure is$\frac{1}{2 \pi} \; \mu \text{F}$$2 \pi \...
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Sep 25, 2022
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3045
GATE ECE 2004 | Question: 60
A $1 \; \mathrm{kHz}$ sinusoidal signal is ideally sampled at $1500$ samples/sec and the sampled signal is passed through an ideal low-pass filter with cut-off frequencey $800 \mathrm{~Hz}$. The output signal has the frequency zero $\text{Hz}$ $0.75 \; \mathrm{kHz}$ $0.5 \; \mathrm{kHz}$ $0.25 \; \mathrm{kHz}$
A $1 \; \mathrm{kHz}$ sinusoidal signal is ideally sampled at $1500$ samples/sec and the sampled signal is passed through an ideal low-pass filter with cut-off frequencey...
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Sep 25, 2022
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3046
GATE ECE 2004 | Question: 67
A system has poles at $0.01 \mathrm{~Hz}, 1 \mathrm{~Hz}$ and $80 \mathrm{~Hz}$; zeros at $5 \mathrm{~Hz}, 100 \mathrm{~Hz}$ and $200 \mathrm{~Hz}$. The approximate phase of the system response at $20 \mathrm{~Hz}$ is $-90^{\circ}$ $0^{\circ}$ $90^{\circ}$ $-180^{\circ}$
A system has poles at $0.01 \mathrm{~Hz}, 1 \mathrm{~Hz}$ and $80 \mathrm{~Hz}$; zeros at $5 \mathrm{~Hz}, 100 \mathrm{~Hz}$ and $200 \mathrm{~Hz}$. The approximate phase...
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Sep 25, 2022
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3047
GATE ECE 2004 | Question: 76
A $100 \; \mathrm{MHz}$ carrier of $1 \mathrm{~V}$ amplitude and a $1 \; \mathrm{MHz}$ modulating signal of $1 \mathrm{~V}$ ... $\sqrt{5 / 4+\cos \left(2 \pi \times 10^{6} t\right)}$
A $100 \; \mathrm{MHz}$ carrier of $1 \mathrm{~V}$ amplitude and a $1 \; \mathrm{MHz}$ modulating signal of $1 \mathrm{~V}$ amplitude are fed to a balanced modulator. The...
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Sep 25, 2022
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3048
GATE ECE 2004 | Question: 82
Consider a system shown in the figure. Let $X(f)$ and $Y(f)$ denote the Fourier transforms of $X(t)$ and $y(t)$ respectively. The ideal HPF has the cutoff frequency $10 \mathrm{kHz}$. The positive frequencies where $Y(f)$ has spectral peaks are $1 \; \mathrm{kHz}$ ... $1 \; \mathrm{kHz}$ and $14 \; \mathrm{kHz}$ $2 \; \mathrm{kHz}$ and $14 \; \mathrm{kHz}$
Consider a system shown in the figure. Let $X(f)$ and $Y(f)$ denote the Fourier transforms of $X(t)$ and $y(t)$ respectively. The ideal HPF has the cutoff frequency $10 \...
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Sep 25, 2022
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3049
GATE ECE 2005 | Question: 77
Two identical and parallel dipole antennas are kept apart by a distance of $\frac{\lambda}{4}$ in the H-plane. They are fed with equal currents but the right most antenna has a phase shift of $+90^{\circ}$. The radiation pattern is given as
Two identical and parallel dipole antennas are kept apart by a distance of $\frac{\lambda}{4}$ in the H-plane. They are fed with equal currents but the right most antenna...
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Sep 22, 2022
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3050
GATE ECE 1995 | Question 1.47
Copper behaves as a conductor always conductor or dielectric depending on the applied electric field strength conductor or dielectric depending on the frequency conductor or dielectric depending on the electric current density
Copper behaves as aconductor alwaysconductor or dielectric depending on the applied electric field strengthconductor or dielectric depending on the frequencyconductor or ...
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Sep 21, 2022
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3051
GATE ECE 2006 | Question: 79
Statement for Linked Answer Questions 78 and 79 The following two questions refer to wide sense stationary stochastic processes The parameters of the system obtained in $\text{Q.78}$ would be first order $\text{R-L}$ ... lowpass filter would have $\mathrm{R}=1 \Omega, \mathrm{L}=4 \mathrm{H}, \mathrm{C}=4 \mathrm{F}$
Statement for Linked Answer Questions 78 and 79The following two questions refer to wide sense stationary stochastic processesThe parameters of the system obtained in $\t...
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Sep 20, 2022
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3052
GATE ECE 1994 | Question 3.5
Channel current is reduced on application of a more positive voltage to the gate of a depletion mode $n$-channel $\text{MOSFET}$.
Channel current is reduced on application of a more positive voltage to the gate of a depletion mode $n$-channel $\text{MOSFET}$.
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Sep 19, 2022
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3053
GATE ECE 1994 | Question 3.9
Noise figure of an amplifier is always greater than $1$ .
Noise figure of an amplifier is always greater than $1$ .
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Sep 19, 2022
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3054
GATE ECE 2007 | Question: 51
The $z$-transform $X[z]$ of a sequence $x[n]$ is given by $X[z]=\dfrac{0.5}{1-2 z^{-1}}$. It is given that the region of convergence of $X[z]$ includes the unit circle. The value of $x[0]$ is $-0.5$ $0$ $0.25$ $0.5$
The $z$-transform $X[z]$ of a sequence $x[n]$ is given by $X[z]=\dfrac{0.5}{1-2 z^{-1}}$. It is given that the region of convergence of $X[z]$ includes the unit circle. T...
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3055
GATE ECE 2007 | Question: 71
The figure shows the high-frequency capacitance-voltage (C-V) characteristics of a $\mathrm{Metal} / \mathrm{SiO}_{2} / \text{silicon (MOS)}$ capacitor having an area of $1 \times 10^{-4} \mathrm{~cm}^{2}$ ... is $50 \; \mathrm{~nm}$ $143 \; \mathrm{~nm}$ $350 \; \mathrm{~nm}$ $1 \; \mu \mathrm{m}$
The figure shows the high-frequency capacitance-voltage (C-V) characteristics of a $\mathrm{Metal} / \mathrm{SiO}_{2} / \text{silicon (MOS)}$ capacitor having an area of ...
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3056
GATE ECE 2007 | Question: 79
An $8085$ assembly language program is given below. Line 1: MVI A, B5H 2: MVI B, 0EH 3: XRI 69H 4: ADD B 5: ANI 9BH 6: CPI 9FH 7: STA 3010H 8: HLT After execution of line $7$ of the program, the status of the $\text{CY}$ and $\mathrm{Z}$ flags will be $\mathrm{CY}=0, \mathrm{Z}=0$ $\text{CY=0, Z=1}$ $\mathrm{CY}=1, \mathrm{Z}=0$ $\mathrm{CY}=1, \mathrm{Z}=1$
An $8085$ assembly language program is given below.Line 1: MVI A, B5H 2: MVI B, 0EH 3: XRI 69H 4: ADD B 5: ANI 9BH 6: CPI 9FH 7: STA 3010H 8: HLT After execution of line ...
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Sep 19, 2022
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3057
GATE ECE 2008 | Question: 68
Four messages band limited to $\text{W, W, 2W}$ and $\text{3W}$ respectively are to be multiplexed using $\text{Time Division Multiplexing (TDM)}.$ The minimum bandwidth required for transmission of this $\text{TDM}$ signal is $\mathrm{W}$ $3 \mathrm{W}$ $6 \mathrm{W}$ $7 \mathrm{W}$
Four messages band limited to $\text{W, W, 2W}$ and $\text{3W}$ respectively are to be multiplexed using $\text{Time Division Multiplexing (TDM)}.$ The minimum bandwidth ...
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Sep 17, 2022
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3058
GATE ECE 2008 | Question: 81
In the following transistor circuit, $V_{B E}=0.7 \mathrm{~V}, r_{e}=25 \; \mathrm{mV} / I_{E},$ and $\beta$ and all the capacitances are very large. The mid-band voltage gain of the amplifier is approximately $-180$ $-120$ $-90$ $-60$
In the following transistor circuit, $V_{B E}=0.7 \mathrm{~V}, r_{e}=25 \; \mathrm{mV} / I_{E},$ and $\beta$ and all the capacitances are very large.The mid-band voltage ...
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Sep 17, 2022
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3059
GATE ECE 2008 | Question: 83
In the following circuit, the comparator output is logic $\text{ 1 }$ if $\mathrm{V}_{1}>\mathrm{V}_{2}$ and is logic $\text{ 0 }$ otherwise. The D/A conversion is done as per the relation $V_{\mathrm{DAC}}=\displaystyle{}\sum_{n=0}^{3} 2^{n-1} b_{n}$ ... magnitude of the error between $V_{D A C}$ and $V_{i n}$ at steady state in volts is $0.2$ $0.3$ $0.5$ $1.0$
In the following circuit, the comparator output is logic $\text{“1”}$ if $\mathrm{V}_{1}>\mathrm{V}_{2}$ and is logic $\text{“0”}$ otherwise. The D/A conversion i...
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Sep 17, 2022
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3060
GATE ECE 1993 | Question 6.17
In a microcomputer, wait states are used to make the processor wait during a $\text{DMA}$ operation make the processor wait during an interrupt processing make the processor wait during a power shutdown interface slow peripherals to the processor
In a microcomputer, wait states are used tomake the processor wait during a $\text{DMA}$ operationmake the processor wait during an interrupt processingmake the processor...
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Sep 16, 2022
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3061
TIFR ECE 2019 | Question: 14
Consider the circle of radius $1$ centred at the origin in two dimensions. Choose two points $x$ and $y$ independently at random so that both are uniformly distributed on the circle. Let the vectors joining the origin to $x$ and $y$ be $X$ and $Y$, respectively. Let $\theta$ be ... $\mathbf{E}\left[|x-y|^{2}\right]=\sqrt{3}$ $\mathbf{E}\left[|x-y|^{2}\right]=1$
Consider the circle of radius $1$ centred at the origin in two dimensions. Choose two points $x$ and $y$ independently at random so that both are uniformly distributed on...
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Nov 30, 2022
Probability and Statistics
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3062
TIFR ECE 2016 | Question: 12
Recall that the Shannon entropy of a random variables $X$ taking values in a finite set $S$ is given by \[H[X]=-\sum_{x \in S} \operatorname{Pr}[X=x] \log _{2} \operatorname{Pr}[X=x] .\] (We set $0 \log _{2} 0=0$.) For a pair of random variables $(X, Y)$ taking ... $H\left[R_{513}, C_{513} \mid R_{1}, R_{2}, \ldots, R_{512}\right]?$ $\log _{2} 513$ $9$ $10$ $19$ $81$
Recall that the Shannon entropy of a random variables $X$ taking values in a finite set $S$ is given by\[H[X]=-\sum_{x \in S} \operatorname{Pr}[X=x] \log _{2} \operatorna...
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Nov 29, 2022
Probability and Statistics
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3063
GATE ECE 1999 | Question 2.20
The input to a matched filter is given by $s(t) = \left\{\begin{matrix} 10\\ 0 \end{matrix}\right. \begin{array}{ll} \sin \left(2 \pi \times 10^{6} t\right) & 0<1<10^{-4} \mathrm{sec} \\ & \text{otherwise} \end{array}$ The peak amplitude of the filter output is $10$ volts $5$ volts $10$ millivolts $5$ millivolts
The input to a matched filter is given by$s(t) = \left\{\begin{matrix} 10\\ 0 \end{matrix}\right. \begin{array}{ll} \sin \left(2 \pi \times 10^{6} t\right) & 0<1<10^{-4} ...
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Sep 29, 2022
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3064
GATE ECE 2002 | Question: 2.17
The system with the open loop transfer function $\mathrm{G}(\mathrm{s}) \mathrm{H}(s)=\frac{1}{s\left(s^{2}+s+1\right)}$ has a gain margin of $-6 \mathrm{~dB}$ $0 \mathrm{~dB}$ $3.5 \mathrm{~dB}$ $6 \mathrm{~dB}$
The system with the open loop transfer function $\mathrm{G}(\mathrm{s}) \mathrm{H}(s)=\frac{1}{s\left(s^{2}+s+1\right)}$ has a gain margin of$-6 \mathrm{~dB}$$0 \mathrm{~...
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Sep 27, 2022
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3065
GATE ECE 1998 | Question 2.5
The threshold voltage for each transistor in the figure is $2 \mathrm{V}$. For this circuit to work as an inverter, $V_{i}$ must take the values $-5 \mathrm{~V}$ and $0 \mathrm{~V}$ $-5 \mathrm{~V}$ and $5 \mathrm{~V}$ $-0 \mathrm{~V}$ and $3 \mathrm{~V}$ $3 \mathrm{~V}$ and $5 \mathrm{~V}$
The threshold voltage for each transistor in the figure is $2 \mathrm{V}$. For this circuit to work as an inverter, $V_{i}$ must take the values$-5 \mathrm{~V}$ and $0 \m...
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Sep 26, 2022
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3066
GATE ECE 1998 | Question 2.13
The $K$-map for a Boolean function is shown in the figure is The number of essential prime implicants for this function is $4$ $5$ $6$ $8$
The $K$-map for a Boolean function is shown in the figure is The number of essential prime implicants for this function is$4$$5$$6$$8$
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3067
GATE ECE 1998 | Question 2.23
The Fourier transform of a voltage signal $x(t)$ is $X(f)$. The unit of $|X(f)|$ is volt volt-sec volt/sec volt $^{2}$
The Fourier transform of a voltage signal $x(t)$ is $X(f)$. The unit of $|X(f)|$ isvoltvolt-secvolt/secvolt $^{2}$
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Sep 26, 2022
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3068
GATE ECE 1998 | Question 2.26
The spectral density of a real valued random process has an even symmetry an odd symmetry a conjugate symmetry no symmetry
The spectral density of a real valued random process hasan even symmetryan odd symmetrya conjugate symmetryno symmetry
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3069
GATE ECE 2003 | Question: 43
When the gate-to-source voltage $\left(\mathrm{V}_{\mathrm{GS}}\right)$ of a MOSFET with threshold voltage of $400 \; \mathrm{mV}$, working in saturation is $900 \; \mathrm{mV}$, the drain current is observed to be $1 \mathrm{~mA}$. Neglecting the channel width modulation ... $0.5 \mathrm{~mA}$ $2.0 \mathrm{~mA}$ $3.5 \mathrm{~mA}$ $4.0 \mathrm{~mA}$
When the gate-to-source voltage $\left(\mathrm{V}_{\mathrm{GS}}\right)$ of a MOSFET with threshold voltage of $400 \; \mathrm{mV}$, working in saturation is $900 \; \math...
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Sep 26, 2022
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3070
GATE ECE 2003 | Question: 60
In an $8085$ microprocessor, the instruction CMP $B$ has been executed while the content of the accumulator is less than that of register $B$. As a result Carry flag will be set but Zero flag will be reset Carry flag will be reset but Zero flag will be set Both Carry flag and Zero flag will be reset Both Carry flag and Zero flag will be set
In an $8085$ microprocessor, the instruction CMP $B$ has been executed while the content of the accumulator is less than that of register $B$. As a resultCarry flag will ...
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Sep 26, 2022
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3071
GATE ECE 2004 | Question: 62
Consider the sequence $x[n]=\left[\begin{array}{lll}-4- \uparrow{j} 5 & 1+j 2 & 4\end{array}\right]$ The conjugate anti-symmetric part of the sequence is $[-4-j 2.5 \quad j 2 \quad 4-j 2.5]$ $[-j 2.5 \quad 1 \quad j 2.5]$ $[-j 5 \quad j 2 \quad 0]$ $\left[\begin{array}{lll}-4 & 1 & 4\end{array}\right]$
Consider the sequence $x[n]=\left[\begin{array}{lll}-4- \uparrow{j} 5 & 1+j 2 & 4\end{array}\right]$The conjugate anti-symmetric part of the sequence is$[-4-j 2.5 \quad j...
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Sep 25, 2022
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3072
GATE ECE 2004 | Question: 71
For the polynomial $P(s)=s^{5}+s^{4}+2 s^{3}+2 s^{2}+3 s+15$, the number of roots which lie in the right half of the s-plane is $4$ $2$ $3$ $1$
For the polynomial $P(s)=s^{5}+s^{4}+2 s^{3}+2 s^{2}+3 s+15$, the number of roots which lie in the right half of the s-plane is$4$$2$$3$$1$
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Sep 25, 2022
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3073
GATE ECE 1994 | Question 3.3
If $G(s)$ is a stable transfer function, then $F(s)=\frac{1}{G(s)}$ is always a stable transfer function.
If $G(s)$ is a stable transfer function, then $F(s)=\frac{1}{G(s)}$ is always a stable transfer function.
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Sep 19, 2022
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3074
GATE ECE 2008 | Question: 66
Noise with double-sided power spectral density of $\mathrm{K}$ over all frequencies is passed through a $\text{RC}$ low pass filter with $3 \mathrm{~dB}$ cut-off frequency of $f_{c}$. The noise power at the filter output is $\mathrm{K}$ $\mathrm{K} f_{c}$ $\mathrm{K} \pi f_{c}$ $\infty$
Noise with double-sided power spectral density of $\mathrm{K}$ over all frequencies is passed through a $\text{RC}$ low pass filter with $3 \mathrm{~dB}$ cut-off frequenc...
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Sep 17, 2022
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3075
GATE ECE 2008 | Question: 79
In the following network, the switch is closed at $t=0$ - and the sampling starts from $t=0$. The sampling frequency is $10 \mathrm{~Hz}$. The expression and the region of convergence of the z-transform of the sampled signal are $\frac{5 z}{z-e^{-5}},|z|<e^{-5}$ ... $\frac{5 z}{z-e^{-0.05}},|z|>e^{-0.05}$ $\frac{5 z}{z-e^{-5}},|z|>e^{-5}$
In the following network, the switch is closed at $t=0$ - and the sampling starts from $t=0$. The sampling frequency is $10 \mathrm{~Hz}$.The expression and the region of...
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Sep 17, 2022
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3076
GATE ECE 1999 | Question 2.25
A plane wave propagating through a medium $\left[\varepsilon_{\mathrm{r}}=8, v_{\mathrm{r}}=2\right.$, and $\left.\sigma=0\right]$ ... $377$ $198.5 \angle 180^{\circ}$ $182.9 \angle 14^{\circ}$ $133.3$
A plane wave propagating through a medium $\left[\varepsilon_{\mathrm{r}}=8, v_{\mathrm{r}}=2\right.$, and $\left.\sigma=0\right]$ has its electric field given by $\overr...
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Sep 29, 2022
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3077
GATE ECE 1999 | Question 5
A coil with a quality factor $(Q)$ of $10$ is put in series with a capacitor $\mathrm{C}_{1}$ of $10 \; \mu \mathrm{F}$, and the combination is found to draw maximum current when a sinusoidal voltage of frequency $50 \mathrm{~Hz}$ is applied. ... $100 \mathrm{~Hz}$ if the applied voltage is $100 \mathrm{~V}(\mathrm{rms})$
A coil with a quality factor $(Q)$ of $10$ is put in series with a capacitor $\mathrm{C}_{1}$ of $10 \; \mu \mathrm{F}$, and the combination is found to draw maximum curr...
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3078
GATE ECE 1999 | Question 7
A $\text{JFET}$ having $\mu=50$ and $r_{d}=10 \mathrm{~K} \Omega$ is used in a common - source configuration as shown in the given figure. The $\text{JFET}$ capacitances are $C_{s^{s}}=5 \; pF$, $C_{g d}=2 \; p \mathrm{F}$ ... midband voltage gain $\left(\mathrm{V}_{0} / \mathrm{V}_{s}\right)$ and the upper $-3 \; d \mathrm{B}$ frequency of the circuit.
A $\text{JFET}$ having $\mu=50$ and $r_{d}=10 \mathrm{~K} \Omega$ is used in a common - source configuration as shown in the given figure. The $\text{JFET}$ capacitances ...
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3079
GATE ECE 2003 | Question: 55
A $4$ bit ripple counter and a $4$ bit synchronous counter are made using flip flops having a propagation delay of $10 \mathrm{~ns}$ each. If the worst case delay in the ripple counter and the synchronous counter be $R$ and $S$ ... $\mathrm{R}=30 \mathrm{~ns}, \mathrm{~S}=10 \mathrm{~ns}$
A $4$ bit ripple counter and a $4$ bit synchronous counter are made using flip flops having a propagation delay of $10 \mathrm{~ns}$ each. If the worst case delay in the ...
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3080
GATE ECE 2004 | Question: 69
If $A=\left[\begin{array}{cc}-2 & 2 \\ 1 & -3\end{array}\right]$, then $\sin A t$ ...
If $A=\left[\begin{array}{cc}-2 & 2 \\ 1 & -3\end{array}\right]$, then $\sin A t$ is$\frac{1}{3}\left[\begin{array}{cc}\sin (-4 t)+2 \sin (-t) & -2 \sin (-4 t)+2 \sin (-t...
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