Recent questions tagged gate2011-ec

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1

GATE ECE 2011 | Question: 1
The modes in a rectangular waveguide are denoted by $\mathrm{TE}_{\mathrm{mn}} / \mathrm{TM}_{\mathrm{mn}}$ where $\mathrm{m}$ and $\mathrm{n}$ are the eigen numbers along the larger and smaller dimensions of the waveguide respectively. Which one of ... frequencies The $\mathrm{TM}_{10}$ and the $\mathrm{TM}_{01}$ modes both exist and have the same cut-off frequencies

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2

GATE ECE 2011 | Question: 2
The Column-1 lists the attributes and the Column-2 lists the modulation systems. Match the attribute to the modulation system that best meets it. ... $\text{P-III, Q-II, R-I, S-IV}$ $\text{P-II, Q-IV, R-III, S-I}$

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GATE ECE 2011 | Question: 3
The differential equation $100 \dfrac{d^2 y}{d t^2}-20 \dfrac{d y}{d t}+y=x(t)$ describes a system with an input $x(t)$ and an output $y(t)$. The system, which is initially relaxed, is excited by a unit step input. The output $y(t)$ can be represented by the waveform

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4

GATE ECE 2011 | Question: 4
For the transfer function $\text{G}(j \omega)=5+j \omega$, the corresponding Nyquist plot for positive frequency has the form

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5

GATE ECE 2011 | Question: 5
The trigonometric Fourier series of an even function does not have the dc term cosine terms sine terms odd harmonic terms

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GATE ECE 2011 | Question: 6
When the output $\mathrm{Y}$ in the circuit below is $\text{“1",}$ it implies that data has changed from $\text{“0"}$ to $\text{“1"}$ changed from $\text{“1"}$ to $\text{“0"}$ changed in either direction not changed

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GATE ECE 2011 | Question: 7
The logic function implemented by the circuit below is (ground implies a logic $\text{“0”})$ $\text{F=AND(P,Q})$ $\text{F=OR(P,Q})$ $\text{F=XNOR(P,Q})$ $\text{F=XOR(P,Q})$

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8

GATE ECE 2011 | Question: 8
The circuit below implements a filter between the input current $\mathrm{i}_{\mathrm{i}}$ and the output voltage $\mathrm{v}_{\mathrm{o}}$. Assume that the opamp is ideal. The filter implemented is a low pass filter band pass filter band stop filter high pass filter

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GATE ECE 2011 | Question: 9
A silicon $\text{PN}$ junction is forward biased with a constant current at room temperature. When the temperature is increased by $10^{\circ} \mathrm{C}$, the forward bias voltage across the $\text{PN}$ junction increases by $60 \; \mathrm{mV}$ decreases by $60 \; \mathrm{mV}$ increases by $25 \; \mathrm{mV}$ decreases by $25 \; \mathrm {mV}$

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10

GATE ECE 2011 | Question: 10
In the circuit shown below, the Norton equivalent current in amperes with respect to the terminals $\mathrm{P}$ and $\mathrm{Q}$ is $6.4-\mathrm{j} 4.8$ $6.56-\mathrm{j} 7.87$ $10+\mathrm{j} 0$ $16+\mathrm{j} 0$

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11

GATE ECE 2011 | Question: 11
In the circuit shown below, the value of $\mathrm{R}_{\mathrm{L}}$ such that the power transferred to $\mathrm{R}_{\mathrm{L}}$ is maximum is $5\; \Omega$ $10\; \Omega$ $15\; \Omega$ $20\; \Omega$

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GATE ECE 2011 | Question: 12
The value of the integral $\oint_c \frac{-3 z+4}{\left(z^2+4 z+5\right)} d z$ where $c$ is the circle $|z|=1$ is given by $0$ $1 / 10$ $4 / 5$ $1$

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GATE ECE 2011 | Question: 13
A transmission line of characteristic impedance $50\; \Omega$ is terminated by a $50\; \Omega$ load. When excited by a sinusoidal voltage source at $10\; \mathrm{GHz}$, the phase difference between two points spaced $2 \mathrm{~mm}$ ... $1.6 \times 10^8 \mathrm{~m} / \mathrm{s}$ $3 \times 10^8 \mathrm{~m} / \mathrm{s}$

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14

GATE ECE 2011 | Question: 14
Consider the following statements regarding the complex Poynting vector $\vec{P}$ for the power radiated by a point source in an infinite homogeneous and lossless medium. $\operatorname{Re}(\vec{P})$ denotes the real part of $\vec{P}, S$ denotes a ... $\oint \oint_S \operatorname{Re}(\vec{P}) . \hat{n} \; dS$ decreases with increasing radial distance from the source

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15

GATE ECE 2011 | Question: 15
An analog signal is band-limited to $4 \; \mathrm{kHz}$, sampled at the Nyquist rate and the samples are quantized into $4$ levels. The quantized levels are assumed to be independent and equally probable. If we transmit two quantized samples per second, the information rate is ... $2 \; \text{bits/sec}$ $3 \; \mathrm{bits/sec}$ $4 \; \mathrm{bits/sec}$

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16

GATE ECE 2011 | Question: 16
The root locus plot for a system is given below. The open loop transfer function corresponding to this plot is given by $G(s) H(s)=k \frac{s(s+1)}{(s+2)(s+3)}$ $G(s) H(s)=k \frac{(s+1)}{s(s+2)(s+3)^2}$ $G(s) H(s)=k \frac{1}{s(s-1)(s+2)(s+3)}$ $G(s) H(s)=k \frac{(s+1)}{s(s+2)(s+3)}$

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GATE ECE 2011 | Question: 17
A system is defined by its impulse response $h(n)=2^n u(n-2)$. The system is stable and causal causal but not stable stable but not causal unstable and noncausal

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18

GATE ECE 2011 | Question: 18
If the unit step response of a network is $\left(1-e^{-\alpha t}\right)$, then its unit impulse response is $\alpha e^{-\alpha t}$ $\alpha^{-1} e^{-\alpha t}$ $\left(1-\alpha^{-1}\right) e^{-\alpha t}$ $(1-\alpha) e^{-\alpha t}$

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19

GATE ECE 2011 | Question: 19
The output $\mathrm{Y}$ in the circuit below is always $\text{“1"}$ when two or more of the inputs $\mathrm{P, Q, R}$ are $\text{“0"}$ two or more of the inputs $\mathrm{P, Q, R}$ are $\text{“1"}$ any odd number of the inputs $\mathrm{P, Q, R}$ is $\text{“0"}$ any odd number of the inputs $\mathrm{P, Q, R}$ is $\text{“1"}$

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20

GATE ECE 2011 | Question: 20
In the circuit shown below, capacitors $\text{C}_1$ and $\text{C}_2$ are very large and are shorts at the input frequency. $\mathrm{v}_{\mathrm{i}}$ is a small signal input. The gain magnitude $\left|\mathrm{v}_{\mathrm{o}} / \mathrm{v}_{\mathrm{i}}\right|$ at $10 \; \mathrm{Mrad} / \mathrm{s}$ is maximum minimum unity zero

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21

GATE ECE 2011 | Question: 21
Drift current in semiconductors depends upon only the electric field only the carrier concentration gradient both the electric field and the carrier concentration both the electric field and the carrier concentration gradient

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22

GATE ECE 2011 | Question: 22
A Zener diode, when used in voltage stabilization circuits, is biased in reverse bias region below the breakdown voltage reverse breakdown region forward bias region forward bias constant current mode

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23

GATE ECE 2011 | Question: 23
The circuit shown below is driven by a sinusoidal input $\mathrm{v}_{\mathrm{i}}=\mathrm{V}_{\mathrm{P}} \cos (\mathrm{t} / \mathrm{RC})$. The steady state output $\text{v}_\text{o}$ is $\left(\mathrm{V}_p / 3\right) \cos (\mathrm{t / R C})$ ... $\left(\mathrm{V}_p / 2\right) \sin (\mathrm{t / R C})$

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24

GATE ECE 2011 | Question: 24
Consider a closed surface $S$ surrounding a volume V. If $\vec{r}$ is the position vector of a point inside $S$, with $\hat{n}$ the unit normal on $S$, the value of the integral $\oint \oint_S 5 \vec{r} . \hat{n} d S$ is $3 \mathrm{V}$ $5 \mathrm{V}$ $10 \mathrm{V}$ $15 \mathrm{V}$

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25

GATE ECE 2011 | Question: 25
The solution of the differential equation $\frac{d y}{d x}=k y, y(0)=c$ is $x=c e^{-k y}$ $x=k e^{c y}$ $y=c e^{k x}$ $y=c e^{-k x}$

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26

GATE ECE 2011 | Question: 26
The electric and magnetic fields for a $\text{TEM}$ wave of frequency $14 \; \mathrm{GHz}$ in a homogeneous medium of relative permittivity $\varepsilon_r$ and relative permeability $\mu_r=1$ ... $\varepsilon_r=3, E_p=360 \pi$ $\varepsilon_r=9, E_p=360 \pi$ $\varepsilon_r=9, E_p=120 \pi$

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27

GATE ECE 2011 | Question: 27
A message signal $m(t)=\cos 2000 \pi t+4 \cos 4000 \pi t$ modulates the carrier $c(t)=\cos 2 \pi f_c t$ where $f_c=1 \; \mathrm{MHz}$ to produce an $\text{AM}$ signal. For demodulating the generated $\text{AM}$ signal using an envelope detector, the time constant ... $\mathrm{RC} <<1 \;\mu \mathrm{s}$ $\mathrm{RC} >> 0.5 \mathrm{~ms}$

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28

GATE ECE 2011 | Question: 28
The block diagram of a system with one input $u$ and two outputs $y_1$ and $y_2$ is given below. A state space model of the above system in terms of the state vector $\underline{x}$ ...

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29

GATE ECE 2011 | Question: 29
Two systems $H_1(z)$ and $H_2(z)$ are connected in cascade as shown below. The overall output $y(n)$ is the same as the input $x(n)$ with a one unit delay. The transfer function of the second system $\mathrm{H}_2(z)$ ... $\frac{\left(1-0.4 z^{-1}\right)}{z^{-1}\left(1-0.6 z^{-1}\right)}$

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30

GATE ECE 2011 | Question: 30
An $8085$ ... $8 \mathrm{CH}$ $64 \mathrm{H}$ $23 \mathrm{H}$ $15 \mathrm{H}$

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31

GATE ECE 2011 | Question: 31
The first six points of the $8$-point $\text{DFT}$ of a real valued sequence are $5,1-\mathrm{j} 3,0,3-\mathrm{j} 4,0$ and $3+\mathrm{j} 4$. The last two points of the $\text{DFT}$ are respectively $0,1-\mathrm{j} 3$ $0,1+\mathrm{j} 3$ $1+\mathrm{j} 3,5$ $1-\mathrm{j} 3,5$

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32

GATE ECE 2011 | Question: 32
For the $\text{BJT Q}_1$ in the circuit shown below, $\beta=\infty, \mathrm{V}_{\mathrm{BEon}}=0.7 \mathrm{V}, \mathrm{V}_{\mathrm{CEsat}}=0.7 \mathrm{V}$. The switch is initially closed. At time $t=0$, the switch is opened. The time $t$ at which $\mathrm{Q}_1$ leaves the active region is $10 \mathrm{~ms}$ $25 \mathrm{~ms}$ $50 \mathrm{~ms}$ $100 \mathrm{~ms}$

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33

GATE ECE 2011 | Question: 33
In the circuit shown below, the network $\mathrm{N}$ is described by the following $Y$ matrix: $Y=\left[\begin{array}{cc}0.1 \mathrm{~S} & -0.01 \mathrm{~S} \\ 0.01 \mathrm{~S} & 0.1 \mathrm{~S}\end{array}\right]$. The voltage gain $\dfrac{V_2}{V_1}$ is $1 / 90$ $ – 1 / 90$ $ – 1 / 99$ $ – 1 / 11$

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34

GATE ECE 2011 | Question: 34
In the circuit shown below, the initial charge on the capacitor is $2.5 \mathrm{~mC}$, with the voltage polarity as indicated. The switch is closed at time $t=0$. The current $i(t)$ at a time $t$ after the switch is closed is $i(t)=15 \exp (-2 \times 10^3 \mathrm{t) \;A}$ ... $i(t)=10 \exp (-2 \times 10^3 \mathrm{t) \;A}$ $i(t)=-5 \exp (-2 \times 10^3 \mathrm{t) \;A}$

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35

GATE ECE 2011 | Question: 35
The system of equations $ \begin{aligned} &x+y+z=6 \\ &x+4 y+6 z=20 \\ &x+4 y+\lambda z=\mu \end{aligned} $ has NO solution for values of $\lambda$ and $\mu$ given by $\lambda=6, \mu=20$ $\lambda=6, \mu \neq 20$ $\lambda \neq 6, \mu=20$ $\lambda \neq 6, \mu \neq 20$

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36

GATE ECE 2011 | Question: 36
A fair dice is tossed two times. The probability that the second toss results in a value that is higher than the first toss is $2 / 36$ $2 / 6$ $5 / 12$ $1 / 2$

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37

GATE ECE 2011 | Question: 37
A current sheet $\vec{J}=10 \hat{u}_y \; A / m$ lies on the dielectric interface $x=0$ between two dielectric media with $\varepsilon_{r 1}=5, \mu_{r 1}=1$ in Region-$1 \; (x<0)$ and $\varepsilon_{r 2}=2, \mu_{r 2}=2$ in Region-$2 \; (x>0)$. If the magnetic field ... $\vec{H}_2=3 \hat{u}_x+30 \hat{u}_y+10 \hat{u}_z \; A / m$

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38

GATE ECE 2011 | Question: 39
$\mathrm{X(t)}$ is a stationary random process with autocorrelation function $R_X(\tau)=\exp \left(-\pi \tau^2\right)$. This process is passed through the system shown below. The power spectral density of the output process $\mathrm{Y}(\mathrm{t})$ is $(4 \pi^2 f^2+1) \exp (\pi f^2)$ ... $(4 \pi^2 f^2+1) \exp (-\pi f)$ $(4 \pi^2 f^2-1) \exp (-\pi f)$

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39

GATE ECE 2011 | Question: 43
An input $\mathrm{x(t)}=\exp (-2 \mathrm{t)u(t})+\delta(\mathrm{t}-6)$ is applied to an LTI system with impulse response $\mathrm{h(t)=u(t})$. The output is $[1-\exp (-2 \mathrm{t)] u(t)+u(t}+6)$ $[1-\exp (-2 \mathrm{t)] u(t)+u(t}-6)$ $0.5[1-\exp (-2 \mathrm{t)] u(t)+u(t}+6)$ $0.5[1-\exp (-2 \mathrm{t)] u(t)+u(t}-6)$

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40

GATE ECE 2011 | Question: 44
For a $\mathrm{BJT}$, the common-base current gain $\alpha=0.98$ and the collector base junction reverse bias saturation current $\mathrm{I}_{\mathrm{CO}}=0.6 \;\; \mu \mathrm{A}$. This $\mathrm{BJT}$ is connected in the common emitter mode and operated in the active ... mode of operation is $0.98 \mathrm{~mA}$ $0.99 \mathrm{~mA}$ $1.0 \mathrm{~mA}$ $1.01 \mathrm{~mA}$

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