Recent questions in Electromagnetics / GO Electronics

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41

GATE ECE 2014 Set 4 | Question: 24
For an antenna radiating in free space, the electric field at a distance of $1$ km is found to be $12 \: mV/m$. Given that intrinsic impedance of the free space is $120 \pi \: \Omega$, the magnitude of average power density due to this antenna at a distance of $2$ km from the antenna (in $nW/m^2$) is _________.

For an antenna radiating in free space, the electric field at a distance of $1$ km is found to be $12 \: mV/m$. Given that intrinsic impedance of the free space is $120 \...

Milicevic3306

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42

GATE ECE 2014 Set 4 | Question: 25
Match column A with column B. ... $ 1 \rightarrow R; \: 2 \rightarrow Q; \: 3 \rightarrow P;$

Match column A with column B.$\begin{array}{ll} \textbf{Column A} & \textbf{Column B} \\ \text{1. Point electromagnetic source} & \text{P. Highly directional} \\ \text{2....

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43

GATE ECE 2014 Set 4 | Question: 33
For the two-port network shown in the figure, the impedance (Z) matrix (in $\Omega$) is $\begin{bmatrix} 6 & 24 \\ 42 & 9 \end{bmatrix}$ $\begin{bmatrix} 9 & 8 \\ 8 & 24 \end{bmatrix}$ $\begin{bmatrix} 9 & 6 \\ 6 & 24 \end{bmatrix}$ $\begin{bmatrix} 42 & 6 \\ 6 & 60 \end{bmatrix}$

For the two-port network shown in the figure, the impedance (Z) matrix (in $\Omega$) is$\begin{bmatrix} 6 & 24 \\ 42 & 9 \end{bmatrix}$$\begin{bmatrix} 9 & 8 \\ 8 & 24 \e...

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44

GATE ECE 2014 Set 4 | Question: 41
A $16$ – bit ripple carry adder is realized using $16$ identical full adders (FA) as shown in the figure. The carry-propagation delay of each FA is $12$ ns and the sum-propagation delay of each FA is $15$ ns. The worst case delay (in ns) of this $16$-bit adder will be _______

A $16$ – bit ripple carry adder is realized using $16$ identical full adders (FA) as shown in the figure. The carry-propagation delay of each FA is $12$ ns and the sum-...

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45

GATE ECE 2014 Set 4 | Question: 53
The electric field (assumed to be one-dimensional) between two points $A$ and $B$ is shown. Let $\psi _A$ and $\psi _B$ be the electrostatic potentials at $A$ and $B$, respectively. The value of $\psi _B – \psi _A$ in Volts is ____________

The electric field (assumed to be one-dimensional) between two points $A$ and $B$ is shown. Let $\psi _A$ and $\psi _B$ be the electrostatic potentials at $A$ and $B$, re...

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46

GATE ECE 2014 Set 4 | Question: 55
If $\overrightarrow{E} = -(2y^3 – 3yz^2)\hat{x} – (6xy^2-3xz^2) \hat{y}+(6xyz) \hat{z}$ is the electric field in a source free region, a valid expression for the electrostatic potential is $xy^3 – yz^2$ $2xy^3-xyz^2$ $y^3+xyz^2$ $2xy^3-3xyz^2$

If $\overrightarrow{E} = -(2y^3 – 3yz^2)\hat{x} – (6xy^2-3xz^2) \hat{y}+(6xyz) \hat{z}$ is the electric field in a source free region, a valid expression for the ele...

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47

GATE ECE 2014 Set 3 | Question: 17
Let $x(t)= \cos(10\pi t)+\cos(30\pi t)$ be sampled at $20 Hz$ and reconstructed using an ideal low-pass filter with cut-off frequency of $20 Hz$. The frequency/frequencies present in the reconstructed signal is/are $5$ Hz and $15$ Hz only $10$ Hz and $15$ Hzonly $5$ Hz, $10$ Hz and $15$Hz only $5$ Hz only

Let $x(t)= \cos(10\pi t)+\cos(30\pi t)$ be sampled at $20 Hz$ and reconstructed using an ideal low-pass filter with cut-off frequency of $20 Hz$. The frequency/frequencie...

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48

GATE ECE 2014 Set 3 | Question: 22
The phase response of a passband waveform at the receiver is given by $\varphi (f)= -2\pi \alpha (f-f_{c})-2\pi \beta f_{c}$ where $f_{c}$ is the centre frequency, and $\alpha$ and $\beta$ are positive constants. The actual signal propagation delay from the ... $\frac{\alpha\beta }{\alpha +\beta } \\$ $\alpha \\$ $\beta$

The phase response of a passband waveform at the receiver is given by $$\varphi (f)= -2\pi \alpha (f-f_{c})-2\pi \beta f_{c}$$where $f_{c}$ is the centre frequency, and $...

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49

GATE ECE 2014 Set 3 | Question: 24
Consider an air filled rectangular waveguide with a cross-section of $5 \: cm \times 3 \: cm $. For this waveguide, the cut-off frequency (in MHz) of $TE_{21}$ mode is __________.

Consider an air filled rectangular waveguide with a cross-section of $5 \: cm \times 3 \: cm $. For this waveguide, the cut-off frequency (in MHz) of $TE_{21}$ mode is __...

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50

GATE ECE 2014 Set 3 | Question: 25
In the following figure, the transmitter $Tx$ sends a wideband modulated $RF$ signal via a coaxial cable to the receiver $Rx$. The output impedance $Z_{T}$ of $Tx$, the characteristic impedance $Z_{0}$ of the cable and the input impedance ... $Z_{R}\neq Z_{0}$ Impedance mismatches do NOT result in signal distortion but reduce power transfer efficiency

In the following figure, the transmitter $Tx$ sends a wideband modulated $RF$ signal via a coaxial cable to the receiver $Rx$. The output impedance $Z_{T}$ of $Tx$, the ...

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51

GATE ECE 2014 Set 3 | Question: 32
In the circuit shown in the figure, the angular frequency $\omega$ (in rad/s), at which the Norton equivalent impedance as seen from terminals $b-b'$ is purely resistive, is ________.

In the circuit shown in the figure, the angular frequency $\omega$ (in rad/s), at which the Norton equivalent impedance as seen from terminals $b-b'$ is purely resistive,...

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52

GATE ECE 2014 Set 3 | Question: 55
Assume that a plane wave in air with an electric field $\overrightarrow{E}= 10\cos ( \omega t-3x-\sqrt{3}z )\hat{a_{y}}V/m$ is incident on a non-magnetic dielectric slab of relative permittivity $3$ which covers the region $z > 0$. The angle of transmission in the dielectric slab is _________ degrees.

Assume that a plane wave in air with an electric field $\overrightarrow{E}= 10\cos ( \omega t-3x-\sqrt{3}z )\hat{a_{y}}V/m$ is incident on a non-magnetic dielectric slab...

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53

GATE ECE 2014 Set 2 | Question: 13
A cascade connection of two voltage amplifier $A1$ and $A2$ is shown in the figure. The open-loop gain $A_{V0}$, input resistance $R_{in}$, and output resistance $R_{o}$ ... $V_{out}/V_{in}$ is __________.

A cascade connection of two voltage amplifier $A1$ and $A2$ is shown in the figure. The open-loop gain $A_{V0}$, input resistance $R_{in}$, and output resistance $R_{o}$ ...

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54

GATE ECE 2014 Set 2 | Question: 19
Consider the periodic square wave in the figure shown. The ratio of the power in the $7^{th}$ harmonic to the power in the $5^{th}$ harmonic for this waveform is closest in value to ________.

Consider the periodic square wave in the figure shown. The ratio of the power in the $7^{th}$ harm...

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55

GATE ECE 2014 Set 2 | Question: 24
To maximum power transfer, a lossless transmission line is to be matched to a resistive load impedance via a $\lambda/4$ transformer as shown. The characteristic impedance (in $\Omega$) of the $\lambda$/4 transformer is ___________.

To maximum power transfer, a lossless transmission line is to be matched to a resistive load impedance via a $\lambda/4$ transformer as shown. The c...

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56

GATE ECE 2014 Set 2 | Question: 25
Which one of the following field patterns represents a TEM wave travelling in the position $x$ direction? $E= +8\hat{y,} \: H = -4\hat{z}$ $E= -2\hat{y,} H = -3\hat{z}$ $E= +2\hat{y,} H = +2\hat{y}$ $E= -3\hat{y,} H = +4\hat{z}$

Which one of the following field patterns represents a TEM wave travelling in the position $x$ direction?$E= +8\hat{y,} \: H = -4\hat{z}$$E= -2\hat{y,} H = -3\hat{z}$$E= ...

Milicevic3306

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57

GATE ECE 2014 Set 2 | Question: 53
If the electric field of a plane wave is $\overrightarrow{E}(z,t)= \hat{x}3 \cos(\omega t-kz+30^{\circ}) – \hat{y} 4 \sin(\omega t – kz+45^{\circ}) (mV/m),$ the polarization state of the plane wave is left elliptical left circular right elliptical right circular

If the electric field of a plane wave is $$\overrightarrow{E}(z,t)= \hat{x}3 \cos(\omega t-kz+30^{\circ}) – \hat{y} 4 \sin(\omega t – kz+45^{\circ}) (mV/m),$$ the pol...

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58

GATE ECE 2014 Set 2 | Question: 54
In the transmission line shown, the impedance $Z_{\text{in}}$ (in ohms) between node A and the ground is _________.

In the transmission line shown, the impedance $Z_{\text{in}}$ (in ohms) between node A and the ground is _________.

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59

GATE ECE 2014 Set 2 | Question: 55
For a rectangular waveguide of internal dimension $a\times b \: (a> b)$, the cut-off frequency for the $TE_{11}$ mode is the arithmetic mean of the cut-off frequencies for $TE_{10}$ mode and $TE_{20}$ mode. If $a= \sqrt{5}$ cm, the value of $b$ (in cm) is ______.

For a rectangular waveguide of internal dimension $a\times b \: (a b)$, the cut-off frequency for the $TE_{11}$ mode is the arithmetic mean of the cut-off frequencies for...

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60

GATE ECE 2014 Set 1 | Question: 6
For maximum power transfer between two cascaded sections of an electrical network, the relationship between the output impedance $Z_{1}$ of the first section to the input impedance $Z_{2}$ of the second section is $Z_{2} = Z_{1}$ $Z_{2} = -Z_{1}$ $Z_{2} = Z_{1}^{\ast}$ $Z_{2} = -Z_{1}^{\ast}$

For maximum power transfer between two cascaded sections of an electrical network, the relationship between the output impedance $Z_{1}$ of the first section to the input...

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61

GATE ECE 2014 Set 1 | Question: 11
A good current buffer has low input impedance and low output impedance low input impedance and high output impedance high input impedance and low output impedance high input impedance and high output impedance

A good current buffer haslow input impedance and low output impedancelow input impedance and high output impedancehigh input impedance and low output impedancehigh input ...

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62

GATE ECE 2014 Set 1 | Question: 54
For a parallel plate transmission line, let $v$ be the speed of propagation and $Z$ be the characteristic impedance. Neglecting fringe effects, a reduction of the spacing between the plates by a factor of two results in halving of $v$ and no change in $Z$ no changes in $v$ and halving of $Z$ no change in both $v$ and $Z$ halving of both $v$ and $Z$

For a parallel plate transmission line, let $v$ be the speed of propagation and $Z$ be the characteristic impedance. Neglecting fringe effects, a reduction of the spacin...

Milicevic3306

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63

GATE ECE 2014 Set 1 | Question: 55
The input impedance of a $\dfrac{\lambda}{8}$ section of a lossless transmission line of characteristic impedance $50\: \Omega$ is found to be real when the other end is terminated by a load $Z_{L} (=R + jX)\Omega.$ If $X$ is $30\:\Omega ,$ the value of $R ( \text{in} \:\Omega )$ is _______.

The input impedance of a $\dfrac{\lambda}{8}$ section of a lossless transmission line of characteristic impedance $50\: \Omega$ is found to be real when the other end is...

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64

GATE ECE 2013 | Question: 23
A source $v_{s}(t) = V\cos100\:\pi t$ has an internal impedance of $(4 + j3)\:\Omega.$ If a purely resistive load connected to this source has to extract the maximum power out of the source, its value in $\Omega$ should be $3$ $4$ $5$ $7$

A source $v_{s}(t) = V\cos100\:\pi t$ has an internal impedance of $(4 + j3)\:\Omega.$ If a purely resistive load connected to this source has to extract the maximum powe...

Milicevic3306

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65

GATE ECE 2013 | Question: 15
In a voltage-voltage feedback as shown below, which one of the following statements is TRUE if the gain $k$ is increased? The input impedance increases and output impedance decreases The input impedance increases and output ... also increases The input impedance decreases and output impedance also decreases The input impedance decreases and output impedance increases

In a voltage-voltage feedback as shown below, which one of the following statements is TRUE if the gain $k$ is increased? The input impedance increases and output impedan...

Milicevic3306

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66

GATE ECE 2012 | Question: 40
The magnetic field along the propagation direction inside a rectangular waveguide with the cross-section shown in the figure is $H_Z=3\:\cos(2.094\times10^2x)\:\cos(2.618\times10^2y)\:\cos(6.283\times10^{10}t-\beta z)$ The phase velocity $v_p$ of the wave inside the waveguide satisfies $v_p\gt c$ $v_p=c$ $0\lt v_p\lt c$ $v_p=0$

The magnetic field along the propagation direction inside a rectangular waveguide with the cross-section shown in the figure is$$H_Z=3\:\cos(2.094\times10^2x)\:\cos(2.618...

Milicevic3306

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67

GATE ECE 2012 | Question: 28
A trasmission line with a characteristic impedance of $100\:\Omega$ is used to match a $50\:\Omega$ section to a $200\:\Omega$ section. If the matching is to be done both at $429\:MHz$ and $1\:GHz$, the length of the transmission line can be approximately $82.5\:cm$ $1.05\:m$ $1.58\:m$ $1.75\:m$

A trasmission line with a characteristic impedance of $100\:\Omega$ is used to match a $50\:\Omega$ section to a $200\:\Omega$ section. If the matching is to be done both...

Milicevic3306

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68

GATE ECE 2012 | Question: 21
The impedance looking into nodes $1$ and $2$ in the given circuit is $50\:\Omega$ $100\:\Omega$ $5\:k\Omega$ $10.1\:k\Omega$

The impedance looking into nodes $1$ and $2$ in the given circuit is$50\:\Omega$$100\:\Omega$$5\:k\Omega$$10.1\:k\Omega$

Milicevic3306

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69

GATE ECE 2012 | Question: 17
The radiation pattern of an antenna in spherical co-ordinates is given by $F(\theta)=\cos^4\theta\:\:\:;\:\:\:0\le \theta\le \frac{\pi}{2}$ The directivity of the antenna is $10\:dB$ $12.6\:dB$ $11.5\:dB$ $18\:dB$

The radiation pattern of an antenna in spherical co-ordinates is given by$$F(\theta)=\cos^4\theta\:\:\:;\:\:\:0\le \theta\le \frac{\pi}{2}$$The directivity of the antenna...

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70

GATE ECE 2012 | Question: 16
A coaxial cable with an inner diameter of $1\:mm$ and outer diameter of $2.4\:mm$ is filled with a dielectric of relative permittivity $10.89$. Given $\mu_0=4\pi\times10^{-7}\:H/m$, $\varepsilon_0=\frac{10^{-9}}{36\pi}\:F/m$, the characteristic impedance of the cable is $330\:\Omega$ $100\:\Omega$ $143.3\:\Omega$ $43.4\:\Omega$

A coaxial cable with an inner diameter of $1\:mm$ and outer diameter of $2.4\:mm$ is filled with a dielectric of relative permittivity $10.89$. Given $\mu_0=4\pi\times10^...

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71

GATE ECE 2012 | Question: 10
The average power delivered to an impedance $(4-j3)\:\Omega$ by a current $5\cos(100\pi t+100)\:A$ is $44.2\:W$ $50\:W$ $62.5\:W$ $125\:W$

The average power delivered to an impedance $(4-j3)\:\Omega$ by a current $5\cos(100\pi t+100)\:A$ is$44.2\:W$$50\:W$$62.5\:W$$125\:W$

Milicevic3306

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72

GATE ECE 2012 | Question: 5
The electric field of a uniform plane electromagnetic wave in free space, along the positive $x$ direction, is given by $\overrightarrow{E}=10(\hat{a}_y+j\hat{a}_z)e^{-j\:25x}$. The frequency and polarization of the wave, respectively, are $1.2\:GHz$ and left circular $4\:Hz$ and left circular $1.2\:GHz$ and right circular $4\:Hz$ and right circular

The electric field of a uniform plane electromagnetic wave in free space, along the positive $x$ direction, is given by $\overrightarrow{E}=10(\hat{a}_y+j\hat{a}_z)e^{-j\...

Milicevic3306

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73

GATE ECE 2012 | Question: 4
A plane wave propagating in air with $\overrightarrow{E}=(8\hat{a}_x+6\hat{a}_y+5\hat{a}_z)e^{j(\omega t+3x-4y)}\:V/m$ is incident on a perfectly conducting slab positioned at $x\le0$ . The $\overrightarrow{E}$ ... $(-8\hat{a}_x+6\hat{a}_y-5\hat{a}_z)e^{j(\omega t-3x-4y)}\:V/m$

A plane wave propagating in air with $\overrightarrow{E}=(8\hat{a}_x+6\hat{a}_y+5\hat{a}_z)e^{j(\omega t+3x-4y)}\:V/m$ is incident on a perfectly conducting slab position...

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74

GATE ECE 2018 | Question: 49
A uniform plane wave traveling in free space and having the electric field ... ) as shown in the figure and there is no reflected wave. The relative permittivity (correct to two decimal places) of the dielectric medium is __________.

A uniform plane wave traveling in free space and having the electric field$$\overrightarrow{E} =\left ( \sqrt{2}\:\hat{a}_{x} -\hat{a}_{z}\right )cos\left [ 6\sqrt{3}\: \...

gatecse

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75

GATE ECE 2018 | Question: 48
The cutoff frequency of $TE_{01}$ mode of an air filled rectangular waveguide having inner dimensions $a\:\text{cm} \: \times \: b\: \text{cm}\:\left ( a> b \right )$ is twice that of the dominant $TE_{10}$ mode. When the waveguide is operated ... the guide wavelength is found to be $4\:\text{cm}$. The value of $b$ (in cm, correct to two decimal places) is ________.

The cutoff frequency of $TE_{01}$ mode of an air filled rectangular waveguide having inner dimensions $a\:\text{cm} \: \times \: b\: \text{cm}\:\left ( a b \right )$ is t...

gatecse

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76

GATE ECE 2018 | Question: 21
A lossy transmission line has resistance per unit length $R=0.05\:\Omega/m.$ The line is distortionless and has characteristic impedance of $50\:\Omega.$ The attenuation constant (in $\text{Np/m}$, correct to three decimal places) of the line is ________.

A lossy transmission line has resistance per unit length $R=0.05\:\Omega/m.$ The line is distortionless and has characteristic impedance of $50\:\Omega.$ The attenuation ...

gatecse

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77

GATE ECE 2018 | Question: 10
The points $\text{P, Q, and R}$ shown on the Smith chart (normalized impedance chart) in the following figure represent: $\text{P: Open Circuit, Q: Short Circuit, R: Matched Load}$ $\text{P: Open Circuit, Q: Matched Load, R: Short Circuit}$ $\text{P: Short Circuit, Q: Matched Load, R: Open Circuit}$ $\text{P: Short Circuit, Q: Open Circuit, R: Matched Load}$

The points $\text{P, Q, and R}$ shown on the Smith chart (normalized impedance chart) in the following figure represent: $\text{P: Open Circu...

gatecse

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78

GATE ECE 2018 | Question: 3
A good transimpedance amplifier has low input impedance and high output impedance high input impedance and high output impedance high input impedance and low output impedance low input impedance and low output impedance

A good transimpedance amplifier haslow input impedance and high output impedancehigh input impedance and high output impedancehigh input impedance and low output impedanc...

gatecse

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79

GATE ECE 2017 Set 2 | Question: 55
The permittivity of water at optical frequencies is $1.75 \varepsilon _0$. It is found that an isotropic light source at a distance $d$ under water forms an illuminated circular area of radius $5$ m, as shown in the figure. The critical angle is $\theta _c$. The value of $d$ (in meter) is _______________

The permittivity of water at optical frequencies is $1.75 \varepsilon _0$. It is found that an isotropic light source at a distance $d$ under water forms an illuminated c...

admin

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80

GATE ECE 2017 Set 2 | Question: 54
Standard air-filled rectangular waveguides of dimensions $a=2.29$ cm and $b=1.02 $ cm are designed for radar applications. It is desired that these waveguides operate only in the dominant $TE_{10}$ mode with the operating frequency at least $25 \%$ ... $6.55 \: GHz \leq f \leq 13.1 \: GHz$ $1.64 \: GHz \leq f \leq 10.24 \: GHz$

Standard air-filled rectangular waveguides of dimensions $a=2.29$ cm and $b=1.02 $ cm are designed for radar applications. It is desired that these waveguides operate onl...

admin

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admin asked Nov 25, 2017