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482
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 $\frac{\mathrm{P}_{m} \cos \theta}{2}$ $\frac{\mathrm{P}_{m}}{4}$ $\frac{P_{m} \sin ^{2} \theta}{4}$ $\frac{P_{m} \cos ^{2} \theta}{4}$
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}$$\fra...
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483
GATE ECE 2000 | Question 2.17
The Hilbert transform of $\cos \omega_{1} t+\sin \omega_{2} t$ is $\sin \omega_{1} t-\cos \omega_{2} t$ $\sin \omega_{1} t+\cos \omega_{2} t$ $\cos \omega_{1} t-\sin \omega_{2} t$ $\sin \omega_{1} t+\sin \omega_{2} t$
The Hilbert transform of $\cos \omega_{1} t+\sin \omega_{2} t$ is$\sin \omega_{1} t-\cos \omega_{2} t$$\sin \omega_{1} t+\cos \omega_{2} t$$\cos \omega_{1} t-\sin \omega_...
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484
GATE ECE 2000 | Question 2.18
A system has a phase response given by $\phi(\omega)$, where $w$ is the angular frequency. The phase delay and group delay at $\omega=\omega_{0}$ ... $\omega_{o} \phi\left(\omega_{o}\right)_{1} \int_{-\infty}^{\omega_{\infty}} \phi(\lambda) d \lambda$
A system has a phase response given by $\phi(\omega)$, where $w$ is the angular frequency. The phase delay and group delay at $\omega=\omega_{0}$ are respectively given b...
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485
GATE ECE 2000 | Question 2.19
A system described by the transfer function $\mathrm{H}(s)=\frac{1}{s^{3}+\alpha s^{2}+k s+3}$ is stable. The constraints on $\alpha$ and $k$ are $\alpha>0, \alpha k<3$ $\alpha>0, \alpha k>3$ $\alpha<0, \alpha k>0$ $\alpha>0, \alpha k<0$
A system described by the transfer function$\mathrm{H}(s)=\frac{1}{s^{3}+\alpha s^{2}+k s+3}$ is stable. The constraints on $\alpha$ and $k$ are$\alpha>0, \alpha k<3$$\al...
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487
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 $1.5$ $\sqrt{1.5}$ $2$ $\sqrt{2}$
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 i...
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488
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 $7.5 \mathrm{~cm}$ $15 \mathrm{~cm}$ $15 \mathrm{~m}$ $150 \mathrm{~m}$
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 \ma...
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489
GATE ECE 2000 | Question 2.23
A rectangular waveguide has dimensions $1 \mathrm{~cm} \times 0.5 \mathrm{~cm}$. Its cut-off frequency is $2 \mathrm{~dB}$ $5 \mathrm{~dB}$ $8 \mathrm{~dB}$ $12 \mathrm{~dB}$
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}$$12 \mathrm{~dB}$...
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490
GATE ECE 2000 | Question 2.24
A rectangular waveguide has dimensions $1 \mathrm{~cm} \times 0.5 \mathrm{~cm}$. Its cut-off frequency is $5 \; \mathrm{GHz}$ $10 \; \mathrm{GHz}$ $15 \; \mathrm{GHz}$ $20 \; \mathrm{GHz}$
A rectangular waveguide has dimensions $1 \mathrm{~cm} \times 0.5 \mathrm{~cm}$. Its cut-off frequency is$5 \; \mathrm{GHz}$$10 \; \mathrm{GHz}$$15 \; \mathrm{GHz}$$20 \;...
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491
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, $\left(\lambda_{1} / \lambda_{2}\right)$ ... $\varepsilon_{r 1} / \varepsilon_{r 2}$ $\varepsilon_{r 2} / \varepsilon_{r 1}$
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 th...
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492
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 $i(t), t>0$.
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)=...
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494
GATE ECE 2000 | Question 5
For the given circuit, write the state equations using $v_{c}$ and $i_{\mathrm{L}}$ as state variables.
For the given circuit, write the state equations using $v_{c}$ and $i_{\mathrm{L}}$ as state variables.
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498
GATE ECE 2000 | Question 9
The block diagram of a feedback system is shown in the figure. Find the closed loop transfer function. Find the minimum value of $G$ for which the step response of the system would exhibit an overshoot, as shown in figure. For G equal to twice this minimum value, find the time period $T$ indicated in the figure.
The block diagram of a feedback system is shown in the figure.Find the closed loop transfer function.Find the minimum value of $G$ for which the step response of the syst...
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502
GATE ECE 2000 | Question 13
The figure shows a common base amplifier. (a) Write expressions for the time-constants associated with the capacitors, $C_{B}$ and $C_{S}$. (b) What is the approximate lower cut-off frequency of the amplifier?
The figure shows a common base amplifier.(a) Write expressions for the time-constants associated with the capacitors, $C_{B}$ and $C_{S}$.(b) What is the approximate lowe...
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503
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.
For the $\text{CMOS}$ monostable multivibrator of given figure, $\mathrm{R}=50 \mathrm{~kW}, \mathrm{C}=0.01 \; \mu \mathrm{F}, \mathrm{V}_{\mathrm{DD}}=5 \mathrm{~V}$, a...
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506
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 $8085$.
(a) The program and machine code for an $8085$ microprocessor are given by$\begin{array}{lll}3 \mathrm{E} & \text {MVI} & \text {A} \\ \text {C3} & & \\ 00 & \text {NOP} ...
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507
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 $y(t)$.
A bandlimited signal $x(t)$ with $a^{\prime}$ spectrum $X(f)$ as shown in first figure is processed as shown in second figure is $p(t)$ is a periodic train of impulses as...
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509
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 $\mathrm{H}$.
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 $\...
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511
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 $f=1 \; \mathrm{GHz}$.
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 $\text{L, C}$ an...
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512
GATE ECE 1999 | Question 1.1
Identify which of the following is $\text{NOT}$ a true of the graph shown in the given figure is $begh$ $defg$ $adfg$ $aegh$
Identify which of the following is $\text{NOT}$ a true of the graph shown in the given figure is$begh$$defg$$adfg$$aegh$
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513
GATE ECE 1999 | Question 1.2
The $z$-transform $\mathrm{F}(z)$ of the function $f(n \mathrm{T})=a^{\prime \prime T}$ is $\frac{z}{z-a^{\mathrm{T}}}$ $\frac{z}{z+a^{\mathrm{T}}}$ $\frac{\mathrm{z}}{\mathrm{z}-\mathrm{a}^{-\mathrm{T}}}$ $\frac{z}{z+a^{-T}}$
The $z$-transform $\mathrm{F}(z)$ of the function $f(n \mathrm{T})=a^{\prime \prime T}$ is$\frac{z}{z-a^{\mathrm{T}}}$$\frac{z}{z+a^{\mathrm{T}}}$$\frac{\mathrm{z}}{\math...
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514
GATE ECE 1999 | Question 1.3
If $[f(t)]=\mathrm{F}(s)$, then $[f(t-\mathrm{T})]$ is equal to $e^{s \mathrm{T}} \mathrm{~F}(s)$ $e^{-s \mathrm{T}} \mathrm{~F}(s)$ $\frac{\mathrm{F}(s)}{1-e^{s T}}$ $\frac{\mathrm{F}(s)}{1-e^{-\mathrm{sT}}}$
If $[f(t)]=\mathrm{F}(s)$, then $[f(t-\mathrm{T})]$ is equal to$e^{s \mathrm{T}} \mathrm{~F}(s)$$e^{-s \mathrm{T}} \mathrm{~F}(s)$$\frac{\mathrm{F}(s)}{1-e^{s T}}$$\frac{...
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515
GATE ECE 1999 | Question 1.4
A $2$-port network is shown in the given figure. The parameter $h_{21}$ for this network can be given by $-1 / 2$ $+1 / 2$ $-3 / 2$ $+3 / 2$
A $2$-port network is shown in the given figure. The parameter $h_{21}$ for this network can be given by$-1 / 2$$+1 / 2$$-3 / 2$$+3 / 2$
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516
GATE ECE 1999 | Question 1.5
The early effect in a bipolar junction transistor is caused by fast turn-on fast turn-off large collector-base reverse bias large emitter-base forward bias
The early effect in a bipolar junction transistor is caused byfast turn-onfast turn-offlarge collector-base reverse biaslarge emitter-base forward bias
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517
GATE ECE 1999 | Question 1.6
The first dominant pole encountered in the frequency response of a compensated $\text{op - amp}$ is approximately at $5 \; \mathrm{~Hz}$ $10 \; \mathrm{kHz}$ $1 \; \mathrm{MHz}$ $100 \; \mathrm{MHz}$
The first dominant pole encountered in the frequency response of a compensated $\text{op - amp}$ is approximately at$5 \; \mathrm{~Hz}$$10 \; \mathrm{kHz}$$1 \; \mathrm{M...
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518
GATE ECE 1999 | Question 1.7
Negative feedback in an amplifier reduces gain increases frequency and phase distortions reduces bandwidth increases noise
Negative feedback in an amplifierreduces gainincreases frequency and phase distortionsreduces bandwidthincreases noise
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520
GATE ECE 1999 | Question 1.9
Crossover distortion behaviour is characteristic of Class $\text{A}$ output stage Class $\text{B}$ output stage Class $\mathrm{AB}$ output stage Common - base output stage
Crossover distortion behaviour is characteristic ofClass $\text{A}$ output stageClass $\text{B}$ output stageClass $\mathrm{AB}$ output stageCommon - base output stage
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