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1801
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
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 alon...
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1802
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. ... $\text{P-III, Q-II, R-I, S-IV}$ $\text{P-II, Q-IV, R-III, S-I}$
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.$\begin{array}{llrl} & \u...
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1803
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
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 initial...
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1804
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
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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1805
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
The trigonometric Fourier series of an even function does not have thedc termcosine termssine termsodd harmonic terms
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1806
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
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 ...
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1807
GATE ECE 2011 | Question: 7
The logic function implemented by the circuit below is (ground implies a logic $\text{“0”})$ $\text{F=AND(P,Q})$ $\text{F=OR(P,Q})$ $\text{F=XNOR(P,Q})$ $\text{F=XOR(P,Q})$
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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46.4k
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588
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Number Representations
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digital-circuits
multiplexers
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1808
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
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...
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1809
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 $25 \; \mathrm {mV}$
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 bi...
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1810
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 $6.4-\mathrm{j} 4.8$ $6.56-\mathrm{j} 7.87$ $10+\mathrm{j} 0$ $16+\mathrm{j} 0$
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$$6.56-\mathrm{j} 7....
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1811
GATE ECE 2011 | Question: 11
In the circuit shown below, the value of $\mathrm{R}_{\mathrm{L}}$ such that the power transferred to $\mathrm{R}_{\mathrm{L}}$ is maximum is $5\; \Omega$ $10\; \Omega$ $15\; \Omega$ $20\; \Omega$
In the circuit shown below, the value of $\mathrm{R}_{\mathrm{L}}$ such that the power transferred to $\mathrm{R}_{\mathrm{L}}$ is maximum is$5\; \Omega$$10\; \Omega$$15\...
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1812
GATE ECE 2011 | Question: 12
The value of the integral $\oint_c \frac{-3 z+4}{\left(z^2+4 z+5\right)} d z$ where $c$ is the circle $|z|=1$ is given by $0$ $1 / 10$ $4 / 5$ $1$
The value of the integral $\oint_c \frac{-3 z+4}{\left(z^2+4 z+5\right)} d z$ where $c$ is the circle $|z|=1$ is given by$0$$1 / 10$$4 / 5$$1$
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1813
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 $2 \mathrm{~mm}$ ... $1.6 \times 10^8 \mathrm{~m} / \mathrm{s}$ $3 \times 10^8 \mathrm{~m} / \mathrm{s}$
A transmission line of characteristic impedance $50\; \Omega$ is terminated by a $50\; \Omega$ load. When excited by a sinusoidal voltage source at $10\; \mathrm{GHz}$, t...
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1814
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 ... decreases with increasing radial distance from the source
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....
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1815
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 ... $2 \; \text{bits/sec}$ $3 \; \mathrm{bits/sec}$ $4 \; \mathrm{bits/sec}$
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...
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1816
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 $G(s) H(s)=k \frac{s(s+1)}{(s+2)(s+3)}$ $G(s) H(s)=k \frac{(s+1)}{s(s+2)(s+3)^2}$ $G(s) H(s)=k \frac{1}{s(s-1)(s+2)(s+3)}$ $G(s) H(s)=k \frac{(s+1)}{s(s+2)(s+3)}$
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)}$$G(s) H(s)=k...
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1817
GATE ECE 2011 | Question: 17
A system is defined by its impulse response $h(n)=2^n u(n-2)$. The system is stable and causal causal but not stable stable but not causal unstable and noncausal
A system is defined by its impulse response $h(n)=2^n u(n-2)$. The system isstable and causalcausal but not stablestable but not causalunstable and noncausal
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1818
GATE ECE 2011 | Question: 18
If the unit step response of a network is $\left(1-e^{-\alpha t}\right)$, then its unit impulse response is $\alpha e^{-\alpha t}$ $\alpha^{-1} e^{-\alpha t}$ $\left(1-\alpha^{-1}\right) e^{-\alpha t}$ $(1-\alpha) e^{-\alpha t}$
If the unit step response of a network is $\left(1-e^{-\alpha t}\right)$, then its unit impulse response is$\alpha e^{-\alpha t}$$\alpha^{-1} e^{-\alpha t}$$\left(1-\alph...
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1819
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"}$
The output $\mathrm{Y}$ in the circuit below is always $\text{“1"}$ whentwo or more of the inputs $\mathrm{P, Q, R}$ are $\text{“0"}$two or more of the inputs $\mathr...
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Number Representations
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digital-circuits
combinational-circuits
logic-gates
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1820
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
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 inp...
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1821
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
Drift current in semiconductors depends upononly the electric fieldonly the carrier concentration gradientboth the electric field and the carrier concentrationboth the el...
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1822
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
A Zener diode, when used in voltage stabilization circuits, is biased in reverse bias region below the breakdown voltagereverse breakdown regionforward bias regionforward...
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1823
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})$
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{...
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1824
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 $\unicode{x222F}_S \; 5 \vec{r} . \hat{n} d S$ is $3 \mathrm{V}$ $5 \mathrm{V}$ $10 \mathrm{V}$ $15 \mathrm{V}$
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 i...
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1825
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}$
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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Differential Equations
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differential-equations
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1826
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 $\mu_r=1$ ... $\varepsilon_r=3, E_p=360 \pi$ $\varepsilon_r=9, E_p=360 \pi$ $\varepsilon_r=9, E_p=120 \pi$
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 p...
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1827
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 ... $\mathrm{RC} <<1 \;\mu \mathrm{s}$ $\mathrm{RC} >> 0.5 \mathrm{~ms}$
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. Fo...
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1828
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 $\underline{x}$ ...
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 $\und...
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1829
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 $\mathrm{H}_2(z)$ ... $\frac{\left(1-0.4 z^{-1}\right)}{z^{-1}\left(1-0.6 z^{-1}\right)}$
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 f...
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1830
GATE ECE 2011 | Question: 30
An $8085$ ... $8 \mathrm{CH}$ $64 \mathrm{H}$ $23 \mathrm{H}$ $15 \mathrm{H}$
An $8085$ assembly language program is given below. Assume that the carry flag is initially unset. The content of the accumulator after the execution of the program is$$\...
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1831
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$
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 $\...
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1832
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}$
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 ...
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1833
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$
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 \mathr...
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1834
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}$
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 cur...
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1835
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$
The system of equations $$ \begin{aligned} &x+y+z=6 \\ &x+4 y+6 z=20 \\ &x+4 y+\lambda z=\mu \end{aligned} $$ has NO solution for values of $\lambda$ and $\mu$ given by$\...
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Linear Algebra
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linear-algebra
system-of-equations
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1836
GATE ECE 2011 | Question: 36
A fair dice is tossed two times. The probability that the second toss results in a value that is higher than the first toss is $2 / 36$ $2 / 6$ $5 / 12$ $1 / 2$
A fair dice is tossed two times. The probability that the second toss results in a value that is higher than the first toss is$2 / 36$$2 / 6$$5 / 12$$1 / 2$
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Probability and Statistics
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probability-and-statistics
probability
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1837
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 ... $\vec{H}_2=3 \hat{u}_x+30 \hat{u}_y+10 \hat{u}_z \; A / m$
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 \...
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1838
GATE ECE 2011 | Question: 38
A transmission line of characteristic impedance $50 \; \Omega$ is terminated in a load impedance $\text{Z}_\text{L} .$ The $\text{VSWR}$ of the line is measured as $5$ and the first of the voltage maxima in the line is observed at a distance of $\lambda / 4$ from the load. The ... is $10 \; \Omega$ $250 \; \Omega$ $(19.23+j 46.15) \; \Omega$ $(19.23-j 46.15) \; \Omega$
A transmission line of characteristic impedance $50 \; \Omega$ is terminated in a load impedance $\text{Z}_\text{L} .$ The $\text{VSWR}$ of the line is measured as $5$ an...
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1839
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 $(4 \pi^2 f^2+1) \exp (\pi f^2)$ ... $(4 \pi^2 f^2+1) \exp (-\pi f)$ $(4 \pi^2 f^2-1) \exp (-\pi f)$
$\mathrm{X(t)}$ 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 be...
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1840
GATE ECE 2011 | Question: 40
The output of a $3$-stage Johnson (twisted-ring) counter is fed to a digital-to-analog (D/A) converter as shown in the figure below. Assume all states of the counter to be unset initially. The waveform which represents the D/A converter output $\mathrm{V}_{\mathrm{o}}$ is
The output of a $3$-stage Johnson (twisted-ring) counter is fed to a digital-to-analog (D/A) converter as shown in the figure below. Assume all states of the counter to b...
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