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921
GATE ECE 2004 | Question: 22
The Fourier transform of a conjugate symmetric function is always imaginary conjugate anti-symmetric real conjugate symmetric
The Fourier transform of a conjugate symmetric function is alwaysimaginaryconjugate anti-symmetricrealconjugate symmetric
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922
GATE ECE 2004 | Question: 23
The gain margin for the system with open-loop transfer function $\mathrm{G}(s) \mathrm{H}(z)=\frac{2(1+z)}{s^{2}}$, is $\infty$ $0$ $1$ $-\infty$
The gain margin for the system with open-loop transfer function $\mathrm{G}(s) \mathrm{H}(z)=\frac{2(1+z)}{s^{2}}$, is$\infty$$0$$1$$-\infty$
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923
GATE ECE 2004 | Question: 24
Given $\mathrm{G}(s) \mathrm{H}(z)=\frac{\mathrm{K}}{s(s+1)(s+3)}$, the point of intersection of the asymptotes of the root loci with the real axis is $-4$ $1.33$ $-1.33$ $4$
Given $\mathrm{G}(s) \mathrm{H}(z)=\frac{\mathrm{K}}{s(s+1)(s+3)}$, the point of intersection of the asymptotes of the root loci with the real axis is$-4$$1.33$$-1.33$$4$...
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924
GATE ECE 2004 | Question: 25
In a $\text{PCM}$ system, if the code word length is increased from $6$ to $8$ bits, the signal to quantization noise ratio improves by the factor $8 / 6$ $12$ $16$ $8$
In a $\text{PCM}$ system, if the code word length is increased from $6$ to $8$ bits, the signal to quantization noise ratio improves by the factor$8 / 6$$12$$16$$8$
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926
GATE ECE 2004 | Question: 27
An AM signal and a narrow-band FM signal with identical carriers, modulating signals and modulation indices of $0.1$ are added together. The resultant signal can be closely approximated by broadband FM SSB with carrier DSB-SC SSB without carrier
An AM signal and a narrow-band FM signal with identical carriers, modulating signals and modulation indices of $0.1$ are added together. The resultant signal can be close...
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928
GATE ECE 2004 | Question: 29
The phase velocity of an electromagnetic wave propagating in a hollow metallic rectangular waveguide in the $\mathrm{TE}_{10}$ mode is equal to its group velocity less than the velocity of light in free space equal to the velocity of light in free space greater than the velocity of light in free space
The phase velocity of an electromagnetic wave propagating in a hollow metallic rectangular waveguide in the $\mathrm{TE}_{10}$ mode isequal to its group velocityless than...
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929
GATE ECE 2004 | Question: 30
Consider a lossless antenna with a directive gain of $+6 \mathrm{~dB}$. If $1 \mathrm{~mW}$ of power is fed to it the total power radiated to the antenna will be $4 \mathrm{~mW}$ $1 \mathrm{~mW}$ $7 \mathrm{~mW}$ $1 / 4 \mathrm{~mW}$
Consider a lossless antenna with a directive gain of $+6 \mathrm{~dB}$. If $1 \mathrm{~mW}$ of power is fed to it the total power radiated to the antenna will be$4 \mathr...
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930
GATE ECE 2004 | Question: 31
For the lattice circuit shown in the figure, $Z_{a}=j 2 \Omega$ and $Z_{b}=2 \Omega$. The values of the open circuit impedance parameters $Z=\left[\begin{array}{ll}z_{11} & z_{12} \\ z_{21} & z_{22}\end{array}\right]$ ... $\left[\begin{array}{cc}1+j & -1+j \\ -1-j & 1-j\end{array}\right]$
For the lattice circuit shown in the figure, $Z_{a}=j 2 \Omega$ and $Z_{b}=2 \Omega$. The values of the open circuit impedance parameters $Z=\left[\begin{array}{ll}z_{11}...
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932
GATE ECE 2004 | Question: 33
Consider the Bode magnitude plot shown in the given figure. The transfer function $\mathrm{H}(s)$ is $\frac{(s+10)}{(s+1)(s+100)}$ $\frac{10(s+1)}{(s+1)(s+100)}$ $\frac{10^{2}(s+1)}{(s+10)(s+100)}$ $\frac{10^{3}(s+100)}{(s+1)(s+10)}$
Consider the Bode magnitude plot shown in the given figure. The transfer function $\mathrm{H}(s)$ is$\frac{(s+10)}{(s+1)(s+100)}$$\frac{10(s+1)}{(s+1)(s+100)}$$\frac{10^{...
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933
GATE ECE 2004 | Question: 34
The transfer function $H(s)=\frac{V_{0}(s)}{V_{i}(s)}$ of an R-L-C circuit is given by \[H(s)=\frac{10^{6}}{s^{2}+20 s+10^{6}}\] The Quality factor (Q-factor) of this circuit is $25$ $50$ $100$ $5000$
The transfer function $H(s)=\frac{V_{0}(s)}{V_{i}(s)}$ of an R-L-C circuit is given by\[H(s)=\frac{10^{6}}{s^{2}+20 s+10^{6}}\]The Quality factor (Q-factor) of this circu...
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934
GATE ECE 2004 | Question: 35
For the circuit shown in the figure, the initial conditions are zero. Its transfer function $ H(s) = \frac{V_{c}(s)}{V_{i}(s)}$ $\frac{1}{s^{2}+10^{6} s+10^{6}}$ $\frac{10^{6}}{s^{2}+10^{3} s+10^{6}}$ $\frac{10^{3}}{s^{2}+10^{3} s+10^{6}}$ $\frac{10^{6}}{s^{2}+10^{6} s+10^{6}}$
For the circuit shown in the figure, the initial conditions are zero. Its transfer function$$ H(s) = \frac{V_{c}(s)}{V_{i}(s)}$$$\frac{1}{s^{2}+10^{6} s+10^{6}}$$\frac{10...
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941
GATE ECE 2004 | Question: 42
The drain of an $n$-channel MOSFET is shorted to the gate so that $V_{G S}=V_{D s}$. The threshold voltage $\left(V_{T}\right)$ of MOSFET is $1 \mathrm{~V}$. If the drain current $\left(\mathrm{I}_{\mathrm{D}}\right)$ is $1 \mathrm{~mA}$ ... $2 \mathrm{~mA}$ $3 \mathrm{~mA}$ $9 \mathrm{~mA}$ $4 \mathrm{~mA}$
The drain of an $n$-channel MOSFET is shorted to the gate so that $V_{G S}=V_{D s}$. The threshold voltage $\left(V_{T}\right)$ of MOSFET is $1 \mathrm{~V}$. If the drain...
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943
GATE ECE 2004 | Question: 45
Assuming that the $\beta$ of the transistor is extremely large and $\text{V}_{\text{B E}}=0.7 \mathrm{~V}, \text{I}_{\text{C}}$ and $\text{V}_{\text{CE}}$ ... $\mathrm{I}_{\mathrm{C}}=0.5 \mathrm{~mA}, \mathrm{~V}_{\mathrm{CE}}=3.9 \mathrm{~V}$
Assuming that the $\beta$ of the transistor is extremely large and $\text{V}_{\text{B E}}=0.7 \mathrm{~V}, \text{I}_{\text{C}}$ and $\text{V}_{\text{CE}}$ in the circuit ...
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944
GATE ECE 2004 | Question: 46
A bipolar transistor is operating in the active region with a collector current of $1 \mathrm{~mA}$. Assuming that the $\beta$ of the transistor is $100$ and the thermal voltage $\left(\mathrm{V}_{\mathrm{T}}\right)$ is $25 \; \mathrm{mV}$ ... $g_{m}=40 \mathrm{~mA} / \mathrm{V}$ and $r_{n}=2.5 \; \mathrm{k} \Omega$
A bipolar transistor is operating in the active region with a collector current of $1 \mathrm{~mA}$. Assuming that the $\beta$ of the transistor is $100$ and the thermal ...
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945
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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946
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}}}$$\frac{v_{s}...
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948
GATE ECE 2004 | Question: 50
In a full-wave rectifier using two ideal diodes, $V_{d i}$ and $V_{i d}$ are the $d c$ ...
In a full-wave rectifier using two ideal diodes, $V_{d i}$ and $V_{i d}$ are the $d c$ and peak values of the voltage respectively across a resistive load. If PIV is the ...
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949
GATE ECE 2004 | Question: 51
The minimum number of $2$-to-$1$ multiplexers required to realize a $4$-to $1$ mulitiplexer is $1$ $2$ $3$ $4$
The minimum number of $2$-to-$1$ multiplexers required to realize a $4$-to $1$ mulitiplexer is$1$$2$$3$$4$
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950
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}$$\overline{\math...
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951
GATE ECE 2004 | Question: 53
$11001, 1001$ and $111001$ correspond to the $2$'s complement representation of which one of the following sets of number ? $25, 9$ and $57$ respectively $-6,-6$ and $-6$ respectively $-7,-7$ and $-7$ respectively $-25, -9$ and $-57$ respectively
$11001, 1001$ and $111001$ correspond to the $2$'s complement representation of which one of the following sets of number ?$25, 9$ and $57$ respectively$-6,-6$ and $-6$ r...
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953
GATE ECE 2004 | Question: 55
The number of memory cycles required to execute the following $8085$ instructions $\text{LDA 3000 H}$ $\text{LXI D, FOF 1 H}$ would be $2$ for (I) and $2$ for (II) $4$ for (I) and $3$ for (II) $3$ for (I) and $3$ for (II) $3$ for (I) and $4$ for (II)
The number of memory cycles required to execute the following $8085$ instructions$\text{LDA 3000 H}$$\text{LXI D, FOF 1 H}$would be$2$ for (I) and $2$ for (II)$4$ for (I)...
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956
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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957
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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958
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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959
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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960
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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