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801
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}$$2 \pi \...
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802
GATE ECE 2004 | Question: 48
In the $\text{op-amp}$ circuit given in the figure, the load current $i_{\text{L}}$ is $-\frac{v_{s}}{R_{2}}$ $\frac{v_{s}}{R_{2}}$ $-\frac{v_{s}}{R_{\text{L}}}$ $\frac{v_{s}}{R_{1}}$
In the $\text{op-amp}$ circuit given in the figure, the load current $i_{\text{L}}$ is$-\frac{v_{s}}{R_{2}}$$\frac{v_{s}}{R_{2}}$$-\frac{v_{s}}{R_{\text{L}}}$$\frac{v_{s}...
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803
GATE ECE 2004 | Question: 49
In the voltage regulator shown in the given figure, the load current can vary from $100 \mathrm{~mA}$ to $500 \mathrm{~mA}$. Assuming that the Zener diode is ideal (i.e., the Zener knee current is negligibly small and Zener resistance is zero in the breakdown region), the value of $R$ is $7 \; \Omega$ $70 \; \Omega$ $\frac{70}{3} \; \Omega$ $14 \; \Omega$
In the voltage regulator shown in the given figure, the load current can vary from $100 \mathrm{~mA}$ to $500 \mathrm{~mA}$. Assuming that the Zener diode is ideal (i.e.,...
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804
GATE ECE 2004 | Question: 50
In a full-wave rectifier using two ideal diodes, $V_{d i}$ and $V_{i d}$ are the $d c$ ...
In a full-wave rectifier using two ideal diodes, $V_{d i}$ and $V_{i d}$ are the $d c$ and peak values of the voltage respectively across a resistive load. If PIV is the ...
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805
GATE ECE 2004 | Question: 51
The minimum number of $2$-to-$1$ multiplexers required to realize a $4$-to $1$ mulitiplexer is $1$ $2$ $3$ $4$
The minimum number of $2$-to-$1$ multiplexers required to realize a $4$-to $1$ mulitiplexer is$1$$2$$3$$4$
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806
GATE ECE 2004 | Question: 52
The Boolean expression $\text{AC + B} \overline{\text{C}}$ is equivalent to $\overline{\mathrm{A}} \mathrm{C}+\mathrm{B} \overline{\mathrm{C}}+\mathrm{AC}$ ...
The Boolean expression $\text{AC + B} \overline{\text{C}}$ is equivalent to$\overline{\mathrm{A}} \mathrm{C}+\mathrm{B} \overline{\mathrm{C}}+\mathrm{AC}$$\overline{\math...
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807
GATE ECE 2004 | Question: 53
$11001, 1001$ and $111001$ correspond to the $2$'s complement representation of which one of the following sets of number ? $25, 9$ and $57$ respectively $-6,-6$ and $-6$ respectively $-7,-7$ and $-7$ respectively $-25, -9$ and $-57$ respectively
$11001, 1001$ and $111001$ correspond to the $2$'s complement representation of which one of the following sets of number ?$25, 9$ and $57$ respectively$-6,-6$ and $-6$ r...
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808
GATE ECE 2004 | Question: 54
The $8255$ Programmable Peripheral Interface is used as described below. An A/D converter is interfaced to a microprocessor through $8255.$ The conversion is initiated by a signal from the $8255$ on Port C. A signal on Port C causes data to be strobed into Port A. Two computers ... II) Mode $2$ for (I) and Mode $0$ for (II) Mode $2$ for (I) and Mode $1$ for (II)
The $8255$ Programmable Peripheral Interface is used as described below.An A/D converter is interfaced to a microprocessor through $8255.$ The conversion is initiated by ...
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809
GATE ECE 2004 | Question: 55
The number of memory cycles required to execute the following $8085$ instructions $\text{LDA 3000 H}$ $\text{LXI D, FOF 1 H}$ would be $2$ for (I) and $2$ for (II) $4$ for (I) and $3$ for (II) $3$ for (I) and $3$ for (II) $3$ for (I) and $4$ for (II)
The number of memory cycles required to execute the following $8085$ instructions$\text{LDA 3000 H}$$\text{LXI D, FOF 1 H}$would be$2$ for (I) and $2$ for (II)$4$ for (I)...
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810
GATE ECE 2004 | Question: 56
In the modulo-$6$ ripple counter shown in the given figure, the output of the $2$-input gate is used to clear the J-K flip-flops. The $2$-input gate is a NAND gate a NOR gate an OR gate an AND gate
In the modulo-$6$ ripple counter shown in the given figure, the output of the $2$-input gate is used to clear the J-K flip-flops.The $2$-input gate isa NAND gatea NOR gat...
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811
GATE ECE 2004 | Question: 57
Consider the sequence of $8085$ instructions given below. $\text{LXI H, 9258, MOV A, M, CMA, MOV M, A}$ Which one of the following is performed by this sequence? Contents of location $9258$ are moved to the accumulator Contents of ... location $8529$ are complemented and stored in location $8529$ Contents of location $5892$ are complemented and stored in location $5892$
Consider the sequence of $8085$ instructions given below.$\text{LXI H, 9258, MOV A, M, CMA, MOV M, A}$Which one of the following is performed by this sequence?Contents of...
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812
GATE ECE 2004 | Question: 58
A Boolean function $f$ of two variables $x$ and $y$ is defined as follows: \[f(0,0)=f(0,1)=f(1,1)=1 ; \quad f(1,0)=0\] Assuming complements of $x$ and $y$ are not available, a minimum cost solution for realizing $f$ using only $2$-input NOR gates and $2$-input OR gates (each having unit cost) would have a total cost of $1$ unit $4$ unit $3$ unit $2$ unit
A Boolean function $f$ of two variables $x$ and $y$ is defined as follows:\[f(0,0)=f(0,1)=f(1,1)=1 ; \quad f(1,0)=0\]Assuming complements of $x$ and $y$ are not available...
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813
GATE ECE 2004 | Question: 59
It is desired to multiply the numbers $0 \mathrm{AH}$ by $0 \mathrm{BH}$ and store the result in the accumulator. The numbers are available in registers $B$ and $C$ respectively. A Part of the $8085$ ... $\text{ADD B, JNZ LOOP, DCR C}$ $\text{DCR C, JNZ LOOP, ADD B}$ $\text{ADD B, DCR C, JNZ LOOP}$
It is desired to multiply the numbers $0 \mathrm{AH}$ by $0 \mathrm{BH}$ and store the result in the accumulator. The numbers are available in registers $B$ and $C$ respe...
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814
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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815
GATE ECE 2004 | Question: 61
A rectangular pulse train $s(t)$ as shown in the figure is convolved with the signal $\cos ^{2}\left(4 p \times 10^{3} t\right)$. The convolved signal will be a $\text{DC}$ $12 \; \mathrm{kHz}$ sinusoid $8 \; \mathrm{kHz}$ sinusoid $14 \; \mathrm{kHz}$ sinusoid
A rectangular pulse train $s(t)$ as shown in the figure is convolved with the signal $\cos ^{2}\left(4 p \times 10^{3} t\right)$. The convolved signal will be a$\text{DC}...
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816
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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817
GATE ECE 2004 | Question: 63
A causal $\text{LTI}$ system is described by the difference equation \[2 y[n]=\alpha y[n-2]-2 x[n]+\beta x[n-1]\] The system is stable only if $|\alpha|=2, \quad|\beta|<2$ $|\alpha|>2, \quad|\beta|>2$ $|\alpha|<2$, any value of $\beta$ $|\beta \mid<2,$ any value of $\alpha$
A causal $\text{LTI}$ system is described by the difference equation\[2 y[n]=\alpha y[n-2]-2 x[n]+\beta x[n-1]\]The system is stable only if$|\alpha|=2, \quad|\beta|<2$$|...
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818
GATE ECE 2004 | Question: 64
A causal system having the transfer function $\mathrm{H}(s)=\frac{1}{s+2}$ is excited with $10 u(t)$. The time at which the output reaches $99 \%$ of its steady state value is $2.7 \; \mathrm{sec}$ $2.5 \; \mathrm{sec}$ $2.5 \; \mathrm{sec}$ $2.1 \; \mathrm{sec}$
A causal system having the transfer function $\mathrm{H}(s)=\frac{1}{s+2}$ is excited with $10 u(t)$. The time at which the output reaches $99 \%$ of its steady state val...
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819
GATE ECE 2004 | Question: 65
The impulse response $h|n|$ ... $4 \sqrt{2} e^{j \pi n / 4}$ $4 e^{j \pi n / 4}$ $-4 e^{j \pi n / 4}$
The impulse response $h|n|$ of a linear time invariant system is given as\[h[n]=\left\{\begin{array}{cc}-2 \sqrt{2} & n=1,-1 \\4 \sqrt{2} & n=2,-2 \\0, & \text { otherwis...
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820
GATE ECE 2004 | Question: 66
Let $x(t)$ and $y(t)$ (with Fourier transforms $X(f)$ and $Y(f)$ respectively) be related as shown in the given figure. Then $Y(f)$ is $-\frac{1}{2} X(f / 2) e^{-j 2 \pi f}$ $-\frac{1}{2} X(f / 2) e^{j 2 \pi f}$ $-X(f / 2) e^{j 2 \pi f}$ $-\mathrm{X}(f / 2) e^{-j2 \pi f}$
Let $x(t)$ and $y(t)$ (with Fourier transforms $X(f)$ and $Y(f)$ respectively) be related as shown in the given figure.Then $Y(f)$ is$-\frac{1}{2} X(f / 2) e^{-j 2 \pi f}...
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821
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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822
GATE ECE 2004 | Question: 68
Consider the signal flow graph shown in the figure below. The gain $\frac{x_{5}}{x_{1}}$ is $\frac{1-\left(b e+c f+d g\right)}{a b c}$ $\frac{b e d g}{1-(b e+c f+d g)}$ $\frac{a b c d}{1-\left(b e+c f+d g\right)+bedg}$ $\frac{1-\left(b e+cf+d g\right)+b ed g}{a b c d}$
Consider the signal flow graph shown in the figure below. The gain $\frac{x_{5}}{x_{1}}$ is$\frac{1-\left(b e+c f+d g\right)}{a b c}$$\frac{b e d g}{1-(b e+c f+d g)}$$\fr...
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823
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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824
GATE ECE 2004 | Question: 70
The open-loop transfer function of a unity feedback system is $G(s)=\frac{K}{s\left(s^{2}+s+2\right)(s+3)}$ The range of $\mathrm{K}$ for which the system is stable is $\frac{21}{44}>\mathrm{K}>0$ $13>\mathrm{K}>0$ $\frac{21}{4}<\mathrm{K}<\infty$ $-6<\mathrm{K}<\infty$
The open-loop transfer function of a unity feedback system is $G(s)=\frac{K}{s\left(s^{2}+s+2\right)(s+3)}$The range of $\mathrm{K}$ for which the system is stable is$\fr...
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825
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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826
GATE ECE 2004 | Question: 72
The state variable equations of a system are: $\begin{array}{l} 1. \; x_{1}=-3 x_{1}-x_{2}+u \\ 2. \; x_{2}=2 x_{1} \\ \quad y=x_{1}+u \end{array}$ The system is controllable but not observable observable but not controllable neither controllable nor observable controllable and observable
The state variable equations of a system are:$\begin{array}{l} 1. \; x_{1}=-3 x_{1}-x_{2}+u \\ 2. \; x_{2}=2 x_{1} \\ \quad y=x_{1}+u \end{array}$The system iscontrollabl...
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827
GATE ECE 2004 | Question: 73
Given $A=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$, the state transition matrix $e^{A t}$ is given by $\left[\begin{array}{cc}0 & e^{-t} \\ e^{-t} & 0\end{array}\right]$ ... $\left[\begin{array}{cc}0 & e^{t} \\ e^{t} & 0\end{array}\right]$
Given $A=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$, the state transition matrix $e^{A t}$ is given by$\left[\begin{array}{cc}0 & e^{-t} \\ e^{-t} & 0\end{a...
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828
GATE ECE 2004 | Question: 74
Consider the signal $x(t)$ shown in the figure. Let $h(t)$ denote the impulse response of the filter matched to $x(t)$, with $h(t)$ being non-zero only in the interval 0 to $4 \; \mathrm{sec}$. The slope of $h(t)$ in the interval $3 < t < \text{sec}.$ is $\frac{1}{2} \sec ^{-1}$ $-1 \sec ^{-1}$ $-\frac{1}{2} \sec ^{-1}$ $1 \; \mathrm{sec}^{-1}$
Consider the signal $x(t)$ shown in the figure. Let $h(t)$ denote the impulse response of the filter matched to $x(t)$, with $h(t)$ being non-zero only in the interval 0 ...
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829
GATE ECE 2004 | Question: 75
A $1 \mathrm{~mW}$ video signal having a bandwidth of $100 \; \mathrm{MHz}$ is transmitted to a receiver through a cable that has $40 \mathrm{~dB}$ loss. If the effective one-sided noise spectral density at the receiver is $10^{-20}$ Watt $/ \mathrm{Hz}$, ... signal-to-noise ratio at the receiver is $50 \mathrm{~dB}$ $30 \mathrm{~dB}$ $40 \mathrm{~dB}$ $60 \mathrm{~dB}$
A $1 \mathrm{~mW}$ video signal having a bandwidth of $100 \; \mathrm{MHz}$ is transmitted to a receiver through a cable that has $40 \mathrm{~dB}$ loss. If the effective...
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830
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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831
GATE ECE 2004 | Question: 77
Two sinusoidal signals of same amplitude and frequencies $10 \; \mathrm{kHz}$ and $10.1 \; \mathrm{kHz}$ are added together. The combined signal is given to an ideal frequency detector. The output of the detector is $0.1 \; \mathrm{kHz}$ sinusoid $20.1 \; \mathrm{kHz}$ sinusoid a linear function of time a constant
Two sinusoidal signals of same amplitude and frequencies $10 \; \mathrm{kHz}$ and $10.1 \; \mathrm{kHz}$ are added together. The combined signal is given to an ideal freq...
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832
GATE ECE 2004 | Question: 78
Consider a binary digital communication system with equally likely $0$'s and $1$'s. When binary 0 is transmitted the voltage at the detector input can lie between the levels $-0.25 \mathrm{~V}$ and $+0.25 \mathrm{~V}$ with equal probability: when binary $1$ is ... $1$), the average bit error probability is $0.15$ $0.2$ $0.05$ $0.5$
Consider a binary digital communication system with equally likely $0$'s and $1$'s. When binary 0 is transmitted the voltage at the detector input can lie between the lev...
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833
GATE ECE 2004 | Question: 79
A random variable $\mathrm{X}$ with uniform density in the interval $0$ to $1$ ... $\text{X}$. The root-mean square value of the quantization noise is $0.573$ $0.198$ $2.205$ $0.266$
A random variable $\mathrm{X}$ with uniform density in the interval $0$ to $1$ is quantized as follows:$\begin{array}{ll} \qquad \text{If 0 < X < 0.3,} & \text{x}_{4} = 0...
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834
GATE ECE 2004 | Question: 80
Choose the correct one from among the alternatives $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$ after matching an item from Group $1$ with the most appropriate item in Group $2.$ ... $\text{1-S, 2-P, 3-U, 4-Q}$ $\text{1-U, 2-R, 3-S, 4-Q}$
Choose the correct one from among the alternatives $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$ after matching an item from Group $1$ with the most appropriate item i...
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835
GATE ECE 2004 | Question: 81
Three analog signals, having bandwidths $1200 \mathrm{~Hz}$, $600 \mathrm{~Hz}$ and $600 \mathrm{~Hz}$, are sampled at their respective Nyquist rates, encoded with $12$ bit words, and time division multiplexed. The bit rate for the multiplexed signal is $115.2 \; \mathrm{kbps}$ $28.8 \; \mathrm{kbps}$ $57.6 \; \mathrm{kbps}$ $38.4 \; \mathrm{kbps}$
Three analog signals, having bandwidths $1200 \mathrm{~Hz}$, $600 \mathrm{~Hz}$ and $600 \mathrm{~Hz}$, are sampled at their respective Nyquist rates, encoded with $12$ b...
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836
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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837
GATE ECE 2004 | Question: 83
A parallel plate air-filled capacitor has plate area of $10^{-1} \mathrm{~m}^{2}$ and plate separation of $10^{-3} \mathrm{~m}$. It is connected to a $0.5 \mathrm{~V}, 3.6 \; \mathrm{GHz}$ ... $10 \mathrm{~mA}$ $100 \mathrm{~mA}$ $10 \mathrm{~A}$ $1.59 \mathrm{~mA}$
A parallel plate air-filled capacitor has plate area of $10^{-1} \mathrm{~m}^{2}$ and plate separation of $10^{-3} \mathrm{~m}$. It is connected to a $0.5 \mathrm{~V}, 3....
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GATE ECE 2004 | Question: 84
A source produces binary data at the rate of $\text{10 kbps.}$ The binary symbols are represented as shown in the figure given below. The source output is transmitted using two modulation schemes, namely Bìnary PSK (BPSK) and Quadrature PSK (QPSK). Let $\mathrm{B}_{1}$ ... $\mathrm{B}_{1}=20 \; \mathrm{kHz}, \mathrm{B}_{2}=10 \; \mathrm{kHz}$
A source produces binary data at the rate of $\text{10 kbps.}$ The binary symbols are represented as shown in the figure given below.The source output is transmitted usin...
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GATE ECE 2004 | Question: 85
Consider a $300 \; \Omega$, quarter-wave long (at $1 \; \mathrm{GHz}$ ) transmission line as shown in the figure. It is connected to a $10 \mathrm{~V}, 50 \; \Omega$ source at one end and is left open circuited at the other end. The magnitude of the voltage at the open circuit end of the line is $10 \mathrm{~V}$ $5 \mathrm{~V}$ $60 \mathrm{~V}$ $60 / 7 \mathrm{~V}$
Consider a $300 \; \Omega$, quarter-wave long (at $1 \; \mathrm{GHz}$ ) transmission line as shown in the figure. It is connected to a $10 \mathrm{~V}, 50 \; \Omega$ sour...
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GATE ECE 2004 | Question: 86
In a microwave test bench, why is the microwave signal amplitude modulated at $1 \; \mathrm{kHz}$? To increase the sensitivity of measurement To transmit the signal to a far-off place To study amplitude modulation Because crystal detector fails at microwave frequencies
In a microwave test bench, why is the microwave signal amplitude modulated at $1 \; \mathrm{kHz}$?To increase the sensitivity of measurementTo transmit the signal to a fa...
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