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Recent questions tagged gate2006-ec
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41
GATE ECE 2006 | Question: 41
For the circuit shown in the following figure, the capacitor $C$ is initially uncharged. At $t=0$, the switch $S$ is closed. The voltage $V_{C}$ across the capacitor at $t=1$ millisecond is In the figure shown above, the $\text{OP AMP}$ ... $\nabla$. $0$ Volts $6.3$ Volts $9.45$ Volts $10$ Volts
For the circuit shown in the following figure, the capacitor $C$ is initially uncharged. At $t=0$, the switch $S$ is closed. The voltage $V_{C}$ across the capacitor at $...
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GATE ECE 2006 | Question: 42
For the circuit shown below, assume that the zener diode is ideal with a breakdown voltage of $6$ Volts. The waveform observed across $R$ is
For the circuit shown below, assume that the zener diode is ideal with a breakdown voltage of $6$ Volts. The waveform observed across $R$ is
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GATE ECE 2006 | Question: 43
A new Binary Coded Pentary (BCP) number system is proposed in which every digit of a base-$5$ number is represented by tis corresponding $3$-bit binary code. For example, the base-$5$ number $24$ ... numbering system, the BCP code $100010011001$ corresponds to the following number in base-$5$ system $423$ $1324$ $2201$ $4231$
A new Binary Coded Pentary (BCP) number system is proposed in which every digit of a base-$5$ number is represented by tis corresponding $3$-bit binary code. For example,...
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GATE ECE 2006 | Question: 44
An $\frac{\mathrm{I}}{\mathrm{O}}$ peripheral device shown in Figure $(b)$ below is to be interfaced to an $8085$ microprocessor. To select the $\frac{\mathrm{I}}{\mathrm{O}}$ device in the $\frac{\mathrm{I}}{\mathrm{O}}$ ... $(a)$ below output $7$ output $5$ output $2$ output $0$
An $\frac{\mathrm{I}}{\mathrm{O}}$ peripheral device shown in Figure $(b)$ below is to be interfaced to an $8085$ microprocessor. To select the $\frac{\mathrm{I}}{\mathrm...
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GATE ECE 2006 | Question: 45
For the circuit shown in figure below, two $4$ ... $\mathrm{S}=1, \mathrm{C}_{0}=0$ $\mathrm{S}=1, \mathrm{C}_{0}=1$
For the circuit shown in figure below, two $4$-bit parallel-in serial-out shift registers loaded with the data shown are used to feed the data to a full adder. Initially,...
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GATE ECE 2006 | Question: 46
A $4$-bit D/A converter is connected to a free-running $3$-bit UP counter, as shown in the following figure. Which of the following waveforms will be observed at $V_{0}$? In the figure shown above, the ground has been shown by the symbol $\nabla$
A $4$-bit D/A converter is connected to a free-running $3$-bit UP counter, as shown in the following figure. Which of the following waveforms will be observed at $V_{0}$?...
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GATE ECE 2006 | Question: 47
Two $\text{D}$-flip-flops, as shown below, are to be connected as a synchronous counter that goes through the following $\mathrm{Q}_{1} \mathrm{Q}_{0}$ sequence $00 \longrightarrow 01 \longrightarrow 11 \longrightarrow 10 \longrightarrow 00 \longrightarrow \dots$ ... $\mathrm{Q}_{1} \mathrm{Q}_{0}$
Two $\text{D}$-flip-flops, as shown below, are to be connected as a synchronous counter that goes through the following $\mathrm{Q}_{1} \mathrm{Q}_{0}$ sequence $00 \long...
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GATE ECE 2006 | Question: 48
Following is the segment of a $8085$ assembly language program $\text{LXISP,EFFFH}$ $\text{CALL 3000 H}$ $3000 \mathrm{H}: \mathrm{LXIH}, 3 \mathrm{CF} 4 \mathrm{H}$ $\text{PUSH PSW}$ $\text{SPIH}$ $\text{POP PSW}$ $\text{RET}$ On completion of $\text{RET}$ execution ... of $\mathrm{SP}$ is $3 \text{CFO H}$ $3 \mathrm{CF} 8 \; \mathrm{H}$ $\text{EFFD H}$ $\text{EFFF H}$
Following is the segment of a $8085$ assembly language program$\text{LXISP,EFFFH}$$\text{CALL 3000 H}$$3000 \mathrm{H}: \mathrm{LXIH}, 3 \mathrm{CF} 4 \mathrm{H}$$\text{P...
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GATE ECE 2006 | Question: 49
The point $\text{P}$ in the following figure is stuck-at-$1$. The output $f$ will be $\overline{\mathrm{AB} \overline{\mathrm{C}}}$ $\overline{\mathrm{A}}$ $\mathrm{AB} \overline{\mathrm{C}}$ $\mathrm{A}$
The point $\text{P}$ in the following figure is stuck-at-$1$. The output $f$ will be$\overline{\mathrm{AB} \overline{\mathrm{C}}}$$\overline{\mathrm{A}}$$\mathrm{AB} \ove...
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GATE ECE 2006 | Question: 50
A signal $m(t)$ with bandwidth $500 \mathrm{~Hz}$ is first multiplied by a signal $g(t)$ where \[ g(t)=\sum_{\mathrm{R}=-\infty}^{\infty}(-1)^{k} \delta\left(t-0.5 \times 10^{-4} k\right) \] The resulting signal is then passed through an ideal ... with bandwidth $1 \; \mathrm{kHz}$. The output of the lowpass filter would be $\delta(t)$ $m(t)$ $0$ $m(t) \delta(t)$
A signal $m(t)$ with bandwidth $500 \mathrm{~Hz}$ is first multiplied by a signal $g(t)$ where\[ g(t)=\sum_{\mathrm{R}=-\infty}^{\infty}(-1)^{k} \delta\left(t-0.5 \times ...
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GATE ECE 2006 | Question: 51
The minimum sampling frequency (in samples/sec) required to reconstruct the following signal from its samples without distortion \[ x(t)=5\left(\frac{\sin 2 \pi 1000 t}{\pi t}\right)^{3}+7\left(\frac{\sin 2 \pi 1000 t}{\pi t}\right)^{2} \] would be $2 \times 10^{3}$ $4 \times 10^{3}$ $6 \times 10^{3}$ $8 \times 10^{3}$
The minimum sampling frequency (in samples/sec) required to reconstruct the following signal from its samples without distortion\[ x(t)=5\left(\frac{\sin 2 \pi 1000 t}{\p...
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GATE ECE 2006 | Question: 52
A uniformly distributed random variable $X$ with probability density function \[ f_{\gamma}(x)=\frac{1}{10}(t r(x+5)-u(x-5)) \] where $u(.)$ is the unit step function is passed through a transformation given in the figure below. The probability density function of the transformed random ...
A uniformly distributed random variable $X$ with probability density function\[ f_{\gamma}(x)=\frac{1}{10}(t r(x+5)-u(x-5)) \]where $u(.)$ is the unit step function is pa...
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GATE ECE 2006 | Question: 53
A system with input $x[n]$ and output $y[n]$ is given as $y[n]=\left(\sin \frac{5}{6} \pi n\right) x(n)$. The system is linear, stable and invertible non-linear, stable and non-invertible linear, stable and non-invertible linear, unstable and invertible
A system with input $x[n]$ and output $y[n]$ is given as $y[n]=\left(\sin \frac{5}{6} \pi n\right) x(n)$.The system islinear, stable and invertiblenon-linear, stable and ...
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GATE ECE 2006 | Question: 54
The unit-step response of a system starting from rest is given by $\qquad C(t)=1-t^{-2 t} \text { for } t \geq 0$ The transfer function of the system is $\frac{1}{1+2 s}$ $\frac{2}{2+s}$ $\frac{1}{2+s}$ $\frac{2 s}{1+2 s}$
The unit-step response of a system starting from rest is given by$\qquad C(t)=1-t^{-2 t} \text { for } t \geq 0$The transfer function of the system is$\frac{1}{1+2 s}$$\f...
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GATE ECE 2006 | Question: 55
The Nyquist plot of $\mathrm{G}(j \omega) \mathrm{H}(j \omega)$ for a closed loop control system, passes through $(-1, j 0)$ point in the $\mathrm{GH}$ plane. The gain margin of the system in $\mathrm{dB}$ is equal to infinite greater than zero. less than zero zero
The Nyquist plot of $\mathrm{G}(j \omega) \mathrm{H}(j \omega)$ for a closed loop control system, passes through $(-1, j 0)$ point in the $\mathrm{GH}$ plane. The gain ma...
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GATE ECE 2006 | Question: 56
The positive values of $\text{“K”}$ and “$a$” so that the system shown in the figure below oscillates at a frequency of $2 \mathrm{rad} / \mathrm{sec}$ respectively are $1,0.75$ $2, 0.75$ $1,1$ $2,2$
The positive values of $\text{“K”}$ and “$a$” so that the system shown in the figure below oscillates at a frequency of $2 \mathrm{rad} / \mathrm{sec}$ respective...
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GATE ECE 2006 | Question: 57
The unit impulse response of a system is \[h(t)=e^{-t}, t \geq 0\] For this system, the steady-state value of the output for unit step input is equal to $-1$ $0$ $1$ $\infty$
The unit impulse response of a system is\[h(t)=e^{-t}, t \geq 0\]For this system, the steady-state value of the output for unit step input is equal to$-1$$0$$1$$\infty$
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GATE ECE 2006 | Question: 58
The transfer function of a phase-lead compensator is given by \[G_{c}(s)=\frac{1+3 T s}{1+T s} \text { where } T>0\] The maximum phase-shift provided by such a compensator is $\frac{\pi}{2}$ $\frac{\pi}{3}$ $\frac{\pi}{4}$ $\frac{\pi}{6}$
The transfer function of a phase-lead compensator is given by\[G_{c}(s)=\frac{1+3 T s}{1+T s} \text { where } T>0\]The maximum phase-shift provided by such a compensator ...
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GATE ECE 2006 | Question: 59
A linear system is described by the following state equation $X(t)=\mathrm{AX}(t)+\mathrm{BU}(t), \mathrm{A}=\left[\begin{array}{cc} 0 & 1 \\ -1 & 0\end{array}\right]$ ... $\left[\begin{array}{cc}\cos t & -\sin t \\ \cos t & \sin t\end{array}\right]$
A linear system is described by the following state equation$$X(t)=\mathrm{AX}(t)+\mathrm{BU}(t), \mathrm{A}=\left[\begin{array}{cc}0 & 1 \\ -1 & 0\end{array}\right]$$The...
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GATE ECE 2006 | Question: 60
The minimum step-size required for a Delta-Modulator operating at $32 \mathrm{~K}$ samples/ $\mathrm{sec}$ to track the signal (here $u(t)$ is the unit-step function) $\begin{array}{l}x(t)=125 t(u(t)-u(t-1))+(250-125 t)(u(t-1) -u(t-2)) \end{array}$ so that slope-overload is avoided, would be $2^{-10}$ $2^{-8}$ $2^{-6}$ $2^{-4}$
The minimum step-size required for a Delta-Modulator operating at $32 \mathrm{~K}$ samples/ $\mathrm{sec}$ to track the signal (here $u(t)$ is the unit-step function)$\be...
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GATE ECE 2006 | Question: 61
A zero- mean white Gaussian noise is passed through an ideal lowpass filter of ban width $10 \; \mathrm{kHz}$. The output is the uniformly sampled with sampling period $t_{s}=0.03 \; \mathrm{msec}$. The samples so obtained would be correlated statistically independent uncorrelated orthogonal
A zero- mean white Gaussian noise is passed through an ideal lowpass filter of ban width $10 \; \mathrm{kHz}$. The output is the uniformly sampled with sampling period $t...
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GATE ECE 2006 | Question: 62
A source generates three symbols with probabilities $0.25,0.25,0.50$ at a rate of $3000$ symbols per second. Assuming independent generation of symbols, the most efficient source encoder would have average bit rate as $6000 \; \mathrm{bits} / \mathrm{sec}$ ... $3000 \; \mathrm{bits} / \mathrm{sec}$ $1500 \; \mathrm{bits} / \mathrm{sec}$
A source generates three symbols with probabilities $0.25,0.25,0.50$ at a rate of $3000$ symbols per second. Assuming independent generation of symbols, the most efficien...
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GATE ECE 2006 | Question: 63
The diagonal clipping in Amplitude Demodulation (using envelope detector) can be avoided if RC time-constant of the envelope detector satisfies the following condition, (here $W$ is message bandwidth and $\omega_{c}$ ... $\mathrm{RC}<\frac{1}{\omega_{c}}$ $\mathrm{RC}>\frac{1}{\omega_{c}}$
The diagonal clipping in Amplitude Demodulation (using envelope detector) can be avoided if RC time-constant of the envelope detector satisfies the following condition, (...
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GATE ECE 2006 | Question: 64
In the following figure the minimum value of the constant ' $C$ ', which is to be added to $y_{1}(t)$ such that $y_{1}(t)$ and $y_{2}(t)$ are different, is $\Delta$ $\frac{\Delta}{2}$ $\frac{\Delta^{2}}{12}$ $\frac{\Delta}{\mathrm{L}}$
In the following figure the minimum value of the constant ' $C$ ', which is to be added to $y_{1}(t)$ such that $y_{1}(t)$ and $y_{2}(t)$ are different, is$\Delta$$\frac{...
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GATE ECE 2006 | Question: 65
A message signal with bandwidth $10 \; \mathrm{kHz}$ is Lower-Side Band SSB modulated with carrier frequency $f_{c 1}=10^{6} \mathrm{~Hz}$. The resulting signal is then passed through a Narrow-Band Frequency Modulator with carrier frequency $f_{c_{2}}=10^{9} \; \mathrm{Hz}$ ... $2 \times 10^{6} \mathrm{~Hz}$ $2 \times 10^{9} \mathrm{~Hz}$ $2 \times 10^{10} \mathrm{~Hz}$
A message signal with bandwidth $10 \; \mathrm{kHz}$ is Lower-Side Band SSB modulated with carrier frequency $f_{c 1}=10^{6} \mathrm{~Hz}$. The resulting signal is then p...
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GATE ECE 2006 | Question: 66
A medium of relative permittivity $\varepsilon_{r 2}=2$ forms an interface with free-space. A point source of electronagnetic energy is located in the medium at a depth of $1$ meter from the interface. Due to the total internal reflection, the transmitted beam has a circular cross-section ... $\frac{\pi}{2} \mathrm{~m}^{2}$ $\pi \; \mathrm{m}^{2}$
A medium of relative permittivity $\varepsilon_{r 2}=2$ forms an interface with free-space. A point source of electronagnetic energy is located in the medium at a depth o...
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GATE ECE 2006 | Question: 67
A medium is divided into regions I and II about $x=0$ plane, as shown in the figure below. An electromagnetic wave with electric field $\mathrm{E}_{1}=4 \hat{a}_{x}+3 \hat{a}_{y}+5 \hat{a}_{z}$ is incident normally on the interface from region-I. The electric field $E_{2}$ in region-II ... $-3 \hat{a}_{x}+3 \hat{a}_{y}+5 \hat{a}$
A medium is divided into regions I and II about $x=0$ plane, as shown in the figure below. An electromagnetic wave with electric field $\mathrm{E}_{1}=4 \hat{a}_{x}+3 \ha...
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GATE ECE 2006 | Question: 68
When a plane wave travelling in free-space is incident normally on a medium having $\varepsilon_{t}=4.0$, then fraction of power transmitted into the medium is given by $\frac{8}{9}$ $\frac{1}{2}$ $\frac{1}{3}$ $\frac{5}{6}$
When a plane wave travelling in free-space is incident normally on a medium having $\varepsilon_{t}=4.0$, then fraction of power transmitted into the medium is given by$\...
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GATE ECE 2006 | Question: 69
A rectangular waveguide having $\mathrm{TE}_{10}$ mode as dominant mode is having a cutoff frequency of $18-\mathrm{GHz}$ for the $\mathrm{TE}_{w,}$ mode. The inner broad-wall dimension of the rectangular waveguide is $\frac{5}{3} \; \mathrm{cms}$ $5 \; \mathrm{cms}$ $\frac{5}{2} \; \mathrm{cms}$ $10 \; \mathrm{cms}$
A rectangular waveguide having $\mathrm{TE}_{10}$ mode as dominant mode is having a cutoff frequency of $18-\mathrm{GHz}$ for the $\mathrm{TE}_{w,}$ mode. The inner broad...
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GATE ECE 2006 | Question: 70
A mast antenna consisting of a $50$ meter long vertical conductor operates over a perfectly conducting ground plane. It is base-fed at a frequency of $600-\mathrm{kHz}$. The radiation resistance of the antenna in ohms is $\frac{2 \pi^{2}}{5}$ $\frac{\pi^{2}}{5}$ $\frac{4 \pi^{2}}{5}$ $20 \pi^{2}$
A mast antenna consisting of a $50$ meter long vertical conductor operates over a perfectly conducting ground plane. It is base-fed at a frequency of $600-\mathrm{kHz}$. ...
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GATE ECE 2006 | Question: 71
Common Data for Questions 71, 72,73: In the transistor amplifier circuit shown in the figure below, the transistor has the following parameters: \[ \beta_{\mathrm{DC}}=60, \mathrm{~V}_{\mathrm{BE}}=0.7 \mathrm{~V}, h_{n^{c}} \longrightarrow \infty, h_{ ... $4.8$ Volts $5.3$ Volts $6.0$ Volts $6.6$ Volts
Common Data for Questions 71, 72,73:In the transistor amplifier circuit shown in the figure below, the transistor has the following parameters:\[ \beta_{\mathrm{DC}}=60, ...
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GATE ECE 2006 | Question: 72
Common Data for Questions 71, 72,73: In the transistor amplifier circuit shown in the figure below, the transistor has the following parameters: \[ \beta_{\mathrm{DC}}=60, \mathrm{~V}_{\mathrm{BE}}=0.7 \mathrm{~V}, h_{n^{c}} \longrightarrow \infty, h_{f c ... $10 \%$ decreases by less than or equal to $10 \%$ increases by more than $10 \%$ decreases by more than $10 \%$
Common Data for Questions 71, 72,73:In the transistor amplifier circuit shown in the figure below, the transistor has the following parameters:\[ \beta_{\mathrm{DC}}=60, ...
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GATE ECE 2006 | Question: 73
Common Data for Questions 71, 72,73: In the transistor amplifier circuit shown in the figure below, the transistor has the following parameters: \[ \beta_{\mathrm{DC}}=60, \mathrm{~V}_{\mathrm{BE}}=0.7 \mathrm{~V}, h_{n^{c}} \longrightarrow \infty, h_{f c} \ ... symbol $\nabla$ The small-signal gain of the amplifier $v_{c} / v_{s}$ is $-10$ $-5.3$ $5.3$ $10$
Common Data for Questions 71, 72,73:In the transistor amplifier circuit shown in the figure below, the transistor has the following parameters:\[ \beta_{\mathrm{DC}}=60, ...
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GATE ECE 2006 | Question: 74
Common Data for Questions 74, 75: Let $g(t)=p(t)^{*} p(t)$, where * denotes convolution and $p(t)=u(t)-u(t-1)$ with $u(t)$ being the unit step function The impulse response of filter matched to the signal $s(t)=g(t)-\delta(t-2)^{*} g(t)$ is given as $s(1-t)$ $-s(1-t)$ $-s(t)$ $s(t)$
Common Data for Questions 74, 75:Let $g(t)=p(t)^{*} p(t)$, where * denotes convolution and $p(t)=u(t)-u(t-1)$ with $u(t)$ being the unit step functionThe impulse response...
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GATE ECE 2006 | Question: 75
Common Data for Questions 74, 75: Let $g(t)=p(t)^{*} p(t)$, where * denotes convolution and $p(t)=u(t)-u(t-1)$ with $u(t)$ being the unit step function An Amplitude Modulated signal is given as \[ x_{\mathrm{AM}}(t)=100(p(t)+0.5 g(t)) \cos \ ... One set of possible values of the modulating signal and modulation index would be $t, 0.5$ $t, 1.0$ $t, 2.0$ $t^{2}, 0.5$
Common Data for Questions 74, 75:Let $g(t)=p(t)^{*} p(t)$, where * denotes convolution and $p(t)=u(t)-u(t-1)$ with $u(t)$ being the unit step function An Amplitude Modul...
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GATE ECE 2006 | Question: 76
statement for Linked Answer Questions 76 and 77 A regulated power supply, shown in figure below, has an unregulated input (UR) of $15$ Volts and generates a regulated output $V_{\text {out }}$. Use the component values shown in the figure. In the figure above, the ... the transistor $\text{Q1}$ shown in the figure is $4.8$ Watts $5.0$ Watts $5.4$ Watts $6.0$ Watts
statement for Linked Answer Questions 76 and 77A regulated power supply, shown in figure below, has an unregulated input (UR) of $15$ Volts and generates a regulated outp...
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GATE ECE 2006 | Question: 77
statement for Linked Answer Questions 76 and 77 A regulated power supply, shown in figure below, has an unregulated input (UR) of $15$ Volts and generates a regulated output $V_{\text {out }}$. Use the component values shown in the figure. In the figure ... across the transistor $\text{Q1}$ increases by $20 \%$ increases by $50 \%$ remains unchanged decreases by $20 \%$
statement for Linked Answer Questions 76 and 77A regulated power supply, shown in figure below, has an unregulated input (UR) of $15$ Volts and generates a regulated outp...
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GATE ECE 2006 | Question: 78
Statement for Linked Answer Questions 78 and 79 The following two questions refer to wide sense stationary stochastic processes It is desired to generate a stochastic process (as voltage process) with power spectral density \[ S(\omega)=\frac{16}{16+\omega^{2}} \] ... filter first order highpass $\mathrm{R-C}$ filter tuned $\text{L-C}$ filter series $\text{R-L}$ filter
Statement for Linked Answer Questions 78 and 79The following two questions refer to wide sense stationary stochastic processesIt is desired to generate a stochastic proce...
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79
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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80
GATE ECE 2006 | Question: 81
Statement for Linked Answer Questions 80 and 81 Consider the following Amplitude Modulated (AM) signal, where $f_{m}<\mathrm{B}$ \[x_{\mathrm{AM}}(t)=10\left(1+0.5 \sin 2 \pi f_{m} t\right) \cos 2 \pi f_{c} t\] The $\text{AM}$ signal gets added to a noise with ... $\frac{25}{2 \mathrm{N}_{0} \mathrm{B}}$ $\frac{25}{\mathrm{N}_{0} \mathrm{B}}$
Statement for Linked Answer Questions 80 and 81Consider the following Amplitude Modulated (AM) signal, where $f_{m}<\mathrm{B}$\[x_{\mathrm{AM}}(t)=10\left(1+0.5 \sin 2 \...
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