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1

GATE ECE 2004 | Question: 1
Consider the network graph shown in the figure. Which one of the following is NOT a 'tree' of this graph?

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2

GATE ECE 2004 | Question: 2
The equivalent inductance measured between the terminals $1$ and $2$ for the circuit shown in the figure is $\mathrm{L}_{1}+\mathrm{L}_{2}+\mathrm{M}$ $\mathrm{L}_{1}+\mathrm{L}_{2}-\mathrm{M}$ $\mathrm{L}_{1}+\mathrm{L}_{2}+2 \mathrm{M}$ $\mathrm{L}_{1}+\mathrm{L}_{2}-2 \mathrm{M}$

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3

GATE ECE 2004 | Question: 3
The circuit shown in in the figure, with $R=\frac{1}{3} \Omega$, $\mathrm{L}=\frac{1}{4} \mathrm{H}, \mathrm{C}=3 \mathrm{~F}$ has input voltage $v(t)=\sin 2 t$. The resulting current $i(t)$ is $5 \sin (2t + 53.1^{\circ})$ $5 \sin (2t - 53.1^{\circ})$ $25 \sin (2t + 53.1^{\circ})$ $25 \sin (2t - 53.1^{\circ})$

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4

GATE ECE 2004 | Question: 4
For the circuit shown in in the figure, the time constant $\text{RC}=1 \mathrm{~ms}$. The input voltage is $v_{i}(t)=\sqrt{2}$ $\sin 10^{3} t$. The output voltage $v_{0}(t)$ is equal to $\sin \left(10^{3} t-45^{\circ}\right)$ $\sin \left(10^{3} t+45^{\circ}\right)$ $\sin \left(10^{3} t-53^{\circ}\right)$ $\sin \left(10^{3} t+53^{\circ}\right)$

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5

GATE ECE 2004 | Question: 5
For the R-L circuit shown in the figure, the input voltage $v_{i}(t)=u(t)$. The current $i(t)$ is

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6

GATE ECE 2004 | Question: 6
The impurity commonly used for realizing the base region of a silicon $n-p-n$ transistor is Gallium Indium Boron Phosphorus

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7

GATE ECE 2004 | Question: 7
If for a silicon $n-p-n$ transistor, the base-to-emitter voltage $\left(\mathrm{V}_{\mathrm{KE}}\right)$ is $0.7 \mathrm{~V}$ and the collector-to-base voltage $\left(\mathrm{V}_{\text{CB}}\right)$ is $0.2 \mathrm{~V}$, then the transistor is operating in the normal active mode saturation mode inverse active mode cutoff mode

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8

GATE ECE 2004 | Question: 8
Consider the following statements $\mathrm{S} 1$ and $\mathrm{S} 2$. $\text{S1 :}$ The $\beta$ of a bipolar transistor reduces if the base width is increased. $\text{S2 :}$ The $\beta$ of a bipolar transistor increases if the doping concentration in the base is ... are TRUE Both $\text{S1}$ and $\text{S2}$ are FALSE $\mathrm{S} 1$ is TRUE and $\mathrm{S} 2$ is FALSE

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9

GATE ECE 2004 | Question: 9
An ideal op-amp is an ideal voltage controlled current source voltage controlled voltage source current controlled current source current contolled voltage source

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10

GATE ECE 2004 | Question: 10
Voltage series feedback (also called series-shunt feedback) results in increase in both input and output impedances decrease in both input and output impedances increase in input impedance and decrease in output impedance decrease in input impedance and increase in output impedance

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11

GATE ECE 2004 | Question: 11
The circuit in the given figure is a low-pass filter high-pass filter band-pass filter band-reject filter

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12

GATE ECE 2004 | Question: 12
Assuming $\mathrm{V}_{\text {CEsat }}=0.2 \mathrm{~V}$ and $\beta=50$, the minimum base current $\left(I_{v}\right)$ required to drive the transistor in the given figure to saturation is $56 \; \mu \mathrm{A}$ $140 \mathrm{~mA}$ $60 \mu \mathrm{A}$ $3 \; \mathrm{~mA}$

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13

GATE ECE 2004 | Question: 13
A master-slave flip-flop has the characteristic that change in the input immediately reflected in the output change in the output occurs when the state of the master is affected change in the output occurs when the state of the slave is affected both the master and the slave states are affected at the same time

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14

GATE ECE 2004 | Question: 14
The range of signed decimal numbers that can be represented by $6$-bite $1$'s complement number is $-31$ to $+31$ $-63$ to $+64$ $-64$ to $+63$ $-32$ to $+31$

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15

GATE ECE 2004 | Question: 15
A digital system is required to amplify a binary-encoded audio signal. The user should be able to control the gain of the amplifier from a minimum to a maximum in $100$ increments. The minimum number of bits required to encode, in straight binary, is $8$ $6$ $5$ $7$

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16

GATE ECE 2004 | Question: 16
Choose the correct one from among the alternatives $A, B, C, D$ after matching an item from Group $1$ with the most appropriate item in Group $2.$ ... $\mathrm{P}-2, \mathrm{Q}-1, \mathrm{R}-3$ $\text{P - 1, Q - 2, R - 2}$

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17

GATE ECE 2004 | Question: 17
Figure given below shows the internal schematic of a TTL AND-OR -Invert (AOI) gate. For the inputs shown in the given figure, the output $Y$ is $0$ $1$ $\mathrm{AB}$ $\overline{\mathrm{AB}}$

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18

GATE ECE 2004 | Question: 18
Given figure is the voltage transfer characteristic of an NMOS inverter with enhancement mode transistor as load an NMOS inverter with depletion mode transistor as load a CMOS inverter a BJT inverter

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19

GATE ECE 2004 | Question: 19
The impulse response $h[n]$ of a linear time-invariant system is given by \[h[n]=u[n+3]+u[n-2]-2 u[n-7]\] where $u[n]$ is the unit step sequence. The above system is stable but not causal stable and causal causal but unstable unstable and not causal

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20

GATE ECE 2004 | Question: 20
The distribution function $\mathrm{F}_{1}(x)$ of a random variable $\mathrm{X}$ is shown in the figure. The probability that $X=1$ is zero $0.25$ $0.55$ $0.30$

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21

GATE ECE 2004 | Question: 21
The $z$-transform of a system is $H(z)=\frac{z}{z-0.2}.$ If the ROC is $|z|<0.2$, then the impulse response of the system is $(0.2)^{n} u[n]$ $(0.2)^{n} u[-n-1]$ $-(0.2)^{n} u[n]$ $-(0.2)^{n} u[-n-1]$

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22

GATE ECE 2004 | Question: 22
The Fourier transform of a conjugate symmetric function is always imaginary conjugate anti-symmetric real conjugate symmetric

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23

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 $\infty$ $0$ $1$ $-\infty$

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24

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 $-4$ $1.33$ $-1.33$ $4$

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25

GATE ECE 2004 | Question: 25
In a 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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26

GATE ECE 2004 | Question: 26
An AM signal is detected using an envelope detector. The carrier frequency and modulating signal frequency are $1 \; \mathrm{MHz}$ and $2 \; \mathrm{kHz}$ respectively. An appropriate value for the time constant of the envelope detector is $500 \; \mu \mathrm{sec}$ $20 \; \mu \mathrm{sec}$ $0.2 \; \mu \mathrm{sec}$ $1 \; \mu \mathrm{sec}$

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27

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

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28

GATE ECE 2004 | Question: 28
In the output of a DM speech encoder, the consecutive pulses are of opposite polarity during time interval $t_{1} < t < t_{2}.$ This indicates that during this interval the input to the modulator is essentially constant the modulator is going through slope overload the accumulator is in saturation the speech signal is being sampled at the Nyquist rate

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29

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

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30

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 $4 \mathrm{~mW}$ $1 \mathrm{~mW}$ $7 \mathrm{~mW}$ $1 / 4 \mathrm{~mW}$

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31

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 $Z=\left[\begin{array}{ll}z_{11} & z_{12} \\ z_{21} & z_{22}\end{array}\right]$ ... $\left[\begin{array}{cc}1+j & -1+j \\ -1-j & 1-j\end{array}\right]$

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32

GATE ECE 2004 | Question: 32
The circuit shown in the figure has initial current $i_{t}\left(0^{-}\right)=1 \mathrm{~A}$ through the inductor and an initial voltage $v_{c}\left(0^{-}\right)=-1 \mathrm{~V}$ across the capacitor. For input $v(t)=u(t)$, the Laplace transform of the current $i(t)$ for $t \geq 0$ ... $\frac{s+2}{s^{2}+s+1}$ $\frac{s-2}{s^{2}+s+1}$ $\frac{s-2}{s^{2}+s+1}$

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33

GATE ECE 2004 | Question: 33
Consider the Bode magnitude plot shown in the given figure. The transfer function $\mathrm{H}(s)$ is $\frac{(s+10)}{(s+1)(s+100)}$ $\frac{10(s+1)}{(s+1)(s+100)}$ $\frac{10^{2}(s+1)}{(s+10)(s+100)}$ $\frac{10^{3}(s+100)}{(s+1)(s+10)}$

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34

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 $25$ $50$ $100$ $5000$

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35

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)}$ $\frac{1}{s^{2}+10^{6} s+10^{6}}$ $\frac{10^{6}}{s^{2}+10^{3} s+10^{6}}$ $\frac{10^{3}}{s^{2}+10^{3} s+10^{6}}$ $\frac{10^{6}}{s^{2}+10^{6} s+10^{6}}$

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36

GATE ECE 2004 | Question: 36
A system described by the following differential equation $\frac{d^{2} y}{d t^{2}}+3 \frac{d y}{d t}+2 y=x(t)$ is initially at rest. For input $x(t)=2 u(t)$, the output $y(t)$ is $\left(1-2 e^{-t}+e^{-2 t}\right) u(t)$ $\left(1+2 e^{-t}-2 e^{-2 t}\right) u(t)$ $\left(0.5+e^{-t}+1.5 e^{-2 t}\right) u(t)$ $\left(0.5+2 e^{-1}+2 e^{-2 t}\right) u(t)$

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37

GATE ECE 2004 | Question: 37
Consider the following statements $\text{S1}$ and $\text{S2}$ $\text{S1} : $ At the resonant frequency the impedance of a series $\mathrm{R}-\mathrm{L}-\mathrm{C}$ circuit is zero. $\text{S2} : $ In a parallel $\mathrm{G}-\mathrm{L}-\mathrm{C}$ circuit, ... $\text{S2}$ are TRUE $\text{S1}$ is TRUE and $\text{S2}$ is FALSE Both $\text{S1}$ and $\text{S2}$ are FALSE

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38

GATE ECE 2004 | Question: 38
In an abrupt $p-n$ junction, doping concentrations on $p$-side and $n$-side are $\mathrm{N}_{\mathrm{A}}=9 \times 10^{16} / \mathrm{cm}^{3}$ and $N_{0}=1 \times 10^{16} / \mathrm{cm}^{3}$ respectively. The $p-n$ junction is reverse biased and the total depletion width is ... $0.3 \; \mu \mathrm{m}$ $2.25 \; \mu \mathrm{m}$ $0.75 \; \mu \mathrm{m}$

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39

GATE ECE 2004 | Question: 39
The resistivity of a uniformloy doped $n$-type silicon sample is $0.5 \; \Omega-\mathrm{cm}$. If the electron mobility $\left(\mu_{n}\right)$ is $1250 \mathrm{~cm}^{2} / \mathrm{V}$-sec and the charge of an electron is $1.6 \times 10^{-19}$ Coulomb, the donor impurity ... $2.5 \times 10^{15} / \mathrm{cm}^{3}$ $2 \times 10^{15} / \mathrm{cm}^{3}$

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40

GATE ECE 2004 | Question: 40
Consider an abrupt p-junction. Let $V_{\text {in }}$ be the built-in potential of this junction and $\mathrm{V}_{\mathrm{R}}$ be the applied reverse bias. If the junction capacitance $\left(\mathrm{C}_{t}\right)$ is $1 \; \mathrm{pF}$ ... $4 \; \mathrm{pF}$ $2 \; \mathrm{pF}$ $0.25 \; \mathrm{pF}$ $0.5 \; \mathrm{pF}$

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