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1
GATE ECE 2000 | Question 19
Zero mean white Gaussian noise with a two-sided power spectral density of $4 \mathrm{~W} / \mathrm{kHz}$ is passed through an ideal lowpass filter with a cut-off frequency of $2 \; \mathrm{kHz}$ and a passband gain of $1$, to produce the noise ... $n\left(t_{1}\right) n\left(t_{2}\right)$ has the most negative expected value and obtain this most negative expected value.
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GATE ECE 2000 | Question 18
A bandlimited signal $x(t)$ with $a^{\prime}$ spectrum $X(f)$ as shown in first figure is processed as shown in second figure is $p(t)$ ... Fourier Transform of $p(t)$. Obtain and sketch the spectrum of $x_{s}(t)$. Obtain and sketch the spectrum of $y(t)$.
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GATE ECE 2000 | Question 17
(a) The program and machine code for an $8085$ ... $\text{LDA} \; 2000 \; \mathrm{H}$ (c) Write an instruction which takes the minimum possible time to clear the accumulator of the $8085$.
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GATE ECE 2000 | Question 15
The operating conditions $(O N=1, O F F=0)$ of three pumps $(x, y, z)$ are to be monitored. $x=1$ implies that pump $X$ is on. It is required that the indicator $\text{(LED)}$ on the panel should glow when a majority of the pumps fail. Enter the logical ... is $1 \mathrm{~V}$. Assume that $P$ can source or sink $10 \mathrm{~mA}$ and a $5 \mathrm{~V}$ supply is available.
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GATE ECE 2000 | Question 20
Given $\mathrm{E}=10 e^{-f(4 x-k t)} \bar{y} \; \mathrm{V} / \mathrm{m}$ in free space: Write all the four Maxwell's equations in free space. Find $\nabla \times E$. Find $\mathrm{H}$.
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GATE ECE 2000 | Question 22
Designa lossless impedance matching network shown in figure to transform $Z_{L}=10+ j 10 \; \Omega$ to $Z_{\text {in }}=50 \; \Omega$. Find the values of $\text{L, C}$ and quality factor $(\mathrm{Q})$ of the circuit at $f=1 \; \mathrm{GHz}$.
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GATE ECE 2000 | Question 14
For the $\text{CMOS}$ monostable multivibrator of given figure, $\mathrm{R}=50 \mathrm{~kW}, \mathrm{C}=0.01 \; \mu \mathrm{F}, \mathrm{V}_{\mathrm{DD}}=5 \mathrm{~V}$, and the $\text{CMOS NOR}$ ... $v_{\mathrm{R}}(t)$, for $t>0$. Find the time period of the output pulse.
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GATE ECE 2000 | Question 11
For the amplifier of given figure, $I_{C}=1.3 \mathrm{~mA}$, $R_{C}=2 \; \mathrm{k} \Omega, R_{\mathrm{E}}=500 \; \Omega, \mathrm{V}_{\mathrm{T}}=\mathrm{T} / q=26 \; \mathrm{mV}, \beta=100$ ... is the approximate $\mathrm{A}_{v'}$ if $\mathrm{C}_{c}$ is removed ? What will $v_{o}$ be if $\mathrm{C}_{b}$ is short circuited?
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GATE ECE 2000 | Question 12
For a feedback amplifier, the open loop transfer function has three poles at $100 \; k \; \mathrm{rad} / \mathrm{s}, 1 \; \mathrm{M} \; \mathrm{rad} / \mathrm{s}$ and $10 \; \mathrm{M} \; \mathrm{rad} / \mathrm{s}$. The low ... is $1000$ and the feedback factor $(\beta)$ is $1$. Use Bode plots to determine the phase margin of the amplifier. Is the amplifier stable?
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GATE ECE 2000 | Question 7
For the linear, time-invariant system whose block diagram is shown in figure with input $x(t)$ and output $y(t)$, Find the transfer function. For the step response of the system [i.e. find $y(t)$ when $x(t)$ is a unit step function and the initial conditions are zero.] Find $y(t)$, if $x(t)$ is as shown in figure and the initial conditions are zero.
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GATE ECE 2000 | Question 6
The network $\mathrm{N}$ in given figure consists only of two elements: a resistor of $1 \; \Omega$ and an inductor of $\text{L}$ Henry. A $5 \mathrm{~V}$ source is connected at the input at $t=0$ seconds. The inductor current ... voltage transfer function of the network. Find $\text{L}$, and draw the configuration of the network. Find the impulse response of the network.
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GATE ECE 2000 | Question 3
For the circuit in given figure, Find the Thevenin equivalent of the sub circuit faced by the capacitor across the terminals $a, b$. Find $v_{c}(t), t>0$, given $v_{c}(0)=0$. Find $i(t), t>0$.
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GATE ECE 2000 | Question 2.25
Two coaxial cables $1$ and $2$ are filled with different dielectric constants $\varepsilon_{r 1}$ and $\varepsilon_{r 2}$ respectively. The ratio of the wavelengths in the two cables, $\left(\lambda_{1} / \lambda_{2}\right)$ ... $\varepsilon_{r 1} / \varepsilon_{r 2}$ $\varepsilon_{r 2} / \varepsilon_{r 1}$
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GATE ECE 2000 | Question 2.24
A rectangular waveguide has dimensions $1 \mathrm{~cm} \times 0.5 \mathrm{~cm}$. Its cut-off frequency is $5 \; \mathrm{GHz}$ $10 \; \mathrm{GHz}$ $15 \; \mathrm{GHz}$ $20 \; \mathrm{GHz}$
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GATE ECE 2000 | Question 2.22
For an $8$ feet $(2.4 \mathrm{~m})$ parabolic dish antenna operating at $4 \; \mathrm{GHz}$, the minimum distance required for far field measurement is closest to $7.5 \mathrm{~cm}$ $15 \mathrm{~cm}$ $15 \mathrm{~m}$ $150 \mathrm{~m}$
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GATE ECE 2000 | Question 2.23
A rectangular waveguide has dimensions $1 \mathrm{~cm} \times 0.5 \mathrm{~cm}$. Its cut-off frequency is $2 \mathrm{~dB}$ $5 \mathrm{~dB}$ $8 \mathrm{~dB}$ $12 \mathrm{~dB}$
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GATE ECE 2000 | Question 2.21
A uniform plane wave in air impinges at $45^{\circ}$ angle on a lossless dielectric material with dielectric constant $\varepsilon_{r}$. The transmitted wave propagates in a $30^{\circ}$ direction with respect to the normal. The value of $\varepsilon_{r}$ is $1.5$ $\sqrt{1.5}$ $2$ $\sqrt{2}$
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GATE ECE 2000 | Question 2.20
In an $\text{FM}$ system, a carrier of $100\; \mathrm{MHz}$ is modulated by a sinusoidal signal of $5 \; \mathrm{kHz}$. The bandwidth by Carson's approximation is $1 \; \mathrm{MHz}$. If $y(t)=(\text {modulated waveform})^{3}$, then by using Carson's approximation, ... $3 \; \mathrm{MHz}, 15 \; \mathrm{kHz}$ $1 \; \mathrm{MHz}, 5 \; \mathrm{kHz}$
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GATE ECE 2000 | Question 2.18
A system has a phase response given by $\phi(\omega)$, where $w$ is the angular frequency. The phase delay and group delay at $\omega=\omega_{0}$ ... $\omega_{o} \phi\left(\omega_{o}\right)_{1} \int_{-\infty}^{\omega_{\infty}} \phi(\lambda) d \lambda$
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GATE ECE 2000 | Question 2.17
The Hilbert transform of $\cos \omega_{1} t+\sin \omega_{2} t$ is $\sin \omega_{1} t-\cos \omega_{2} t$ $\sin \omega_{1} t+\cos \omega_{2} t$ $\cos \omega_{1} t-\sin \omega_{2} t$ $\sin \omega_{1} t+\sin \omega_{2} t$
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GATE ECE 2000 | Question 2.15
In a digital communication system employing Frequency Shift Keying $\text{(FSK)}$, the $0$ and $1$ bit are represented by sine waves of $10 \; \mathrm{kHz}$ and $25 \; \mathrm{kHz}$ respectively. These waveforms will be orthogonal for a bit interval of $45 \; \mu \mathrm{sec}$ $200 \; \mu \mathrm{sec}$ $50 \; \mu \mathrm{sec}$ $250 \; \mu \mathrm{sec}$
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GATE ECE 2000 | Question 2.16
A message $m(t)$ bandlimited to the frequency $f_{m}$ has a power of $P_{m}$. The power of the output signal in given figure is $\frac{\mathrm{P}_{m} \cos \theta}{2}$ $\frac{\mathrm{P}_{m}}{4}$ $\frac{P_{m} \sin ^{2} \theta}{4}$ $\frac{P_{m} \cos ^{2} \theta}{4}$
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GATE ECE 2000 | Question 2.14
In given figure, the steady state output voltage corresponding to the input voltage $3+4 \sin 100 t \mathrm{~V}$ is $3+\frac{4}{\sqrt{2}} \sin \left(100 t-\frac{\pi}{4}\right) \mathrm{V}$ $3+4 \sqrt{2} \sin \left(100 t-\frac{\pi}{4}\right) \mathrm{V}$ ... $3+4 \sin \left(100 t \div \frac{\pi}{4}\right) \mathrm{V}$
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GATE ECE 2000 | Question 2.12
One period $(0, T)$ each of two periodic waveforms $W_{1}$ and $W_{2}$ are shown in figure. The magnitudes of the $n$th Fourier series coefficients of $W_{1}$ and $W_{2}$. for $n \geq 1, n$ odd, are respectively proportional to $n^{-3} \mid$ and $n^{-2} \mid$ $n^{-2} \mid$ and $n^{-3} \mid$ $n^{-1}$ and $n^{-2} \mid$ $n^{-4} \mid$ and $n^{-2} \mid$
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GATE ECE 2000 | Question 2.11
In given figure, the $J$ and $K$ inputs of all the four Flip-Flips are made high. The frequency of the signal at output $Y$ is $0.833 \; \mathrm{kHz}$ $1.0 \; \mathrm{kHz}$ $0.91 \; \mathrm{kHz}$ $0.77 \; \mathrm{kHz}$
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GATE ECE 2000 | Question 2.10
The contents of Register $\text{(B)}$ and Accumulator $\text{(A)}$ of $8085$ microprocessor are $49 \mathrm{H}$ and $3 \mathrm{AH}$ respectively. The contents of $\mathrm{A}$ and the slatus of carry flag $(C Y)$ and sign flag $(S)$ after executing $\text{SUB B}$ ... $\mathrm{A}=1 \mathrm{F}, \mathrm{CY}=1, \text{S}=1$
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GATE ECE 2000 | Question 2.9
A sequential circuit using $D$ Flip-Flop and logic gates is shown in figure, where $X$ and $Y$ are the inputs and $Z$ is the output. The circuit is $S-R$ Flip-Flop with inputs $X=R$ and $Y=S$ $S-R$ Flip-Flop with inputs $X=S$ and $Y=R$ $J-K$ Flip-Flop with inputs $X=J$ and $Y=K$ $J-K$ Flip-Flop with inputs $X=K$ and $Y=J$
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GATE ECE 2000 | Question 2.8
For the $4$ bit $\text{DAC}$ shown, the output voltage $v_{0}$ is $10 \mathrm{~V}$ $5 \mathrm{~V}$ $4 \mathrm{~V}$ $8 \mathrm{~V}$
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GATE ECE 2000 | Question 2.7
For the logic circuit shown in, the simplified Boolean expression for the output $Y$ is $\mathrm{A}+\mathrm{B}+\mathrm{C}$ $\mathrm{A}$ $\mathrm{B}$ $\mathrm{C}$
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GATE ECE 2000 | Question 2.6
if the $\text{op-amp}$ in given figure, has an input offset voltage of $5 \; \mathrm{mV}$ and an open-loop voltage gain of $10,000,$ then $v_{0}$ will be $0 \mathrm{~V}$ $5 \; \mathrm{mV}$ $+15 \mathrm{~V}$ or $-15 \mathrm{~V}$ $+50 \mathrm{~V}$ or $-50 \mathrm{~V}$
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GATE ECE 2000 | Question 2.1
The eigen values of the matrix $\left[\begin{array}{rrrr}2 & -1 & 0 & 0 \\ 0 & 3 & 0 & 0 \\ 0 & 0 & -2 & 0 \\ 0 & 0 & -1 & 4\end{array}\right]$ are $2,-2,1,-1$ $2, 3, -2, 4$ $2,3,1,4$ None of these
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GATE ECE 2000 | Question 2.4
A linear time invariant system has an impulse response $e^{2 t}, t>0$. If the initial conditions are zero and the input is $e^{3 t}$, then output for $t>0$ is $e^{3 t}-e^{2 t}$ $\mathrm{e}^{5 t}$ $e^{3 t}+e^{2 t}$ None of these
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GATE ECE 2000 | Question 2.3
For the circuit in the figure, the voltage $v_{0}$ is $2 \mathrm{~V}$ $\text{1 V}$ $-1 \mathrm{~V}$ None of these
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GATE ECE 2000 | Question 1.25
The circuit of the figure represents a low pass filter high pass filter band pass filter band reject filter
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GATE ECE 2000 | Question 1.24
If the diameter of a $\frac{\lambda}{2}$ dipole antenna is increased $\operatorname{from} \frac{\lambda}{100}$ to $\frac{\lambda}{50}$, then its bandwidth increases bandwidth decreases gain increases gain decreases
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GATE ECE 2000 | Question 1.23
The frequency range for satellite communication is $1 \; \mathrm{kHz}$ to $100\; \mathrm{kHz}$ $100 \; \mathrm{kHz}$ to $10 \; \mathrm{kHz}$ $10 \; \mathrm{MHz}$ to $30 \; \mathrm{MHz}$ $1 \; \mathrm{GHz}$ to $30 \; \mathrm{GHz}$
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GATE ECE 2000 | Question 1.22
A $\text{TEM}$ wave is incident normally upon a perfect conductor. The $\mathrm{E}$ and $\mathrm{H}$ fields at the boundary will be, respectively, minimum and minimum maximum and maximum minimum and maximum maximum and minimum
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GATE ECE 2000 | Question 1.21
The magnitudes of the open-circuit and short-circuit input impedance of a transmission line are $100 \; \Omega$ and $25 \; \Omega$ respectively. The characteristic impedance of the line is, $25 \; \Omega$ $50 \; \Omega$ $75 \; \Omega$ $100 \; \Omega$
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GATE ECE 2000 | Question 1.20
In the $8085$ microprocessor, the $\text{RST6}$ instruction transfers the program execution to the following location: $30 \mathrm{~H}$ $24 \mathrm{~H}$ $48 \mathrm{~H}$ $60 \mathrm{~H}$
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GATE ECE 2000 | Question 1.16
The number of hardware interrupts (which require an external signal to interrupt) present in an $8085$ microprocessor are $1$ $4$ $5$ $13$
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