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281
GATE Electrical 2019 | Question: 15
The characteristic equation of a linear time-invariant (LTI) system is given by $\Delta(s)=s^{4}+3s^{3}+3s^{2}+s+k=0$ The system is BIBO stable if $0<K<\frac{12}{9}$ $k>3$ $0<k<\frac{8}{9}$ $k>6$
The characteristic equation of a linear time-invariant (LTI) system is given by$$\Delta(s)=s^{4}+3s^{3}+3s^{2}+s+k=0$$The system is BIBO stable if$0<K<\frac{12}{9}$$k>3$$...
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GATE Electrical 2019 | Question: 9
A six-pulse thyristor bridge rectifier is connected to a balanced three-phase, $50Hz$ AC source. Assuming that the DC output current of the rectifier is constant, the lowest harmonic component in the AC input current is $100 Hz$ $150 Hz$ $250 Hz$ $300 Hz$
A six-pulse thyristor bridge rectifier is connected to a balanced three-phase, $50Hz$ AC source. Assuming that the DC output current of the rectifier is constant, the low...
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GATE Electrical 2019 | Question: 7
The symbols, $a$ and $T,$ represent positive quantities, and $u(t)$ is the unit step function. Which one of the following impulse responses is NOT the output of a causal linear time-invariant system? $e^{+at}u(t)$ $e^{-a(t+T)}u(t)$ $1+e^{-at}u(t)$ $e^{-a(t-T)}u(t)$
The symbols, $a$ and $T,$ represent positive quantities, and $u(t)$ is the unit step function. Which one of the following impulse responses is NOT the output of a causal ...
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GATE Electrical 2019 | Question: 52
In a $132$ kV system, the series inductance up to the point of circuit breaker location is $50$ mH. The shunt capacitance at the circuit breaker terminal is $0.05 \: \mu F$. The critical value of resistance in ohms required to be connected across the circuit breaker contacts which will give no transient oscillation is ______
In a $132$ kV system, the series inductance up to the point of circuit breaker location is $50$ mH. The shunt capacitance at the circuit breaker terminal is $0.05 \: \mu ...
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GATE Electrical 2019 | Question: 8
A $5kVA, 50V/100V,$ single-phase transformer has a secondary terminal voltage of $95V$ when loaded. The regulation of the transformer is $4.5\%$ $9\%$ $5\%$ $1\%$
A $5kVA, 50V/100V,$ single-phase transformer has a secondary terminal voltage of $95V$ when loaded. The regulation of the transformer is$4.5\%$$9\%$$5\%$$1\%$
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GATE Electrical 2019 | Question: 21
The $Y_{\text{bus}}$ matrix of a two-bus power system having two identical parallel lines connected between them in pu is given as $Y_{\text{bus}} = \begin{bmatrix} -j8 & j20 \\ j20& -j8 \end{bmatrix}$The magnitude of the series reactance of each line in pu (round off upto one decimal place) is__________.
The $Y_{\text{bus}}$ matrix of a two-bus power system having two identical parallel lines connected between them in pu is given as $$Y_{\text{bus}} = \begin{bmatrix} -j8 ...
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GATE Electrical 2019 | Question: 6
A system transfer function is $H(s)= \frac{a_{1}s^{2}+b_{1}s+c_{1}}{a_{2}s^{2}+b_{2}s+c_{2}}.$ If $a_{1}=b_{1}=0,$ and all the other coefficient are positive, the transfer function represents a low pass filter high pass filter band pass filter notch filter
A system transfer function is $H(s)= \frac{a_{1}s^{2}+b_{1}s+c_{1}}{a_{2}s^{2}+b_{2}s+c_{2}}.$ If $a_{1}=b_{1}=0,$ and all the other coefficient are positive, the transfe...
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GATE Electrical 2019 | Question: 11
A three-phase synchronous motor draws $200 A$ from the line at unity power factor at rated load. Considering the same line voltage and load, the line current at a power factor of $0.5$ leading is $100 \: A$ $200 \: A$ $300 \: A$ $400 \: A$
A three-phase synchronous motor draws $200 A$ from the line at unity power factor at rated load. Considering the same line voltage and load, the line current at a power f...
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GATE Electrical 2019 | Question: 49
A three-phase $50$ Hz, $400$ kV transmission line is $300$ km long. The line inductance is $1$ mH/km per phase, and the capacitance is $0.01 \: \mu F/km$ per phase. The line is under open circuit condition at the receiving end and energized with $400$ kV at the sending end, the receiving end line voltage in kV (round off to two decimal places) will be _________
A three-phase $50$ Hz, $400$ kV transmission line is $300$ km long. The line inductance is $1$ mH/km per phase, and the capacitance is $0.01 \: \mu F/km$ per phase. The l...
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GATE Electrical 2019 | Question: 51
In the single machine infinite bus system shown below, the generator is delivering the real power of $0.8$ pu at $0.8$ power factor lagging to the infinite bus. The power angle of the generator in degrees (round off to one decimal place) is _________
In the single machine infinite bus system shown below, the generator is delivering the real power of $0.8$ pu at $0.8$ power factor lagging to the infinite bus. The power...
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GATE Electrical 2019 | Question: 32
A moving coil instrument having a resistance of $10 \: \Omega$, gives a full-scale deflection when the current is $10$ mA. What should be the value of the series resistance, so that it can be used as a voltmeter for measuring potential difference up to $100$ V? $9 \: \Omega$ $99 \: \Omega$ $990 \: \Omega$ $9990 \: \Omega$
A moving coil instrument having a resistance of $10 \: \Omega$, gives a full-scale deflection when the current is $10$ mA. What should be the value of the series resistan...
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GATE Electrical 2019 | Question: 12
In the circuit shown below, the switch is closed at $t=0$. The value of $\theta$ in degrees which will give the maximum value of DC offset of the current at the time of switching is $60$ $-45$ $90$ $-30$
In the circuit shown below, the switch is closed at $t=0$. The value of $\theta$ in degrees which will give the maximum value of DC offset of the current at the time of s...
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GATE Electrical 2019 | Question: 48
A $220$ V(line), three-phase, Y-connected, synchronous motor has a synchronous impedance of $(0.25+j2.5) \: \Omega/\text{phase}$. The motor draws the rated current of $10$ A at $0.8$ pf leading. The rms value of line-to-line internal voltage in volts (round off to two decimal places) is _________
A $220$ V(line), three-phase, Y-connected, synchronous motor has a synchronous impedance of $(0.25+j2.5) \: \Omega/\text{phase}$. The motor draws the rated current of $10...
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GATE Electrical 2019 | Question: 45
A single-phase transformer of rating $25$ kVA, supplies a $12$ kW load at power factor of $0.6$ lagging. The additional load at unity power factor in kW (round off to two decimal places) that may be added before this transformer exceeds its rated kVA is ________
A single-phase transformer of rating $25$ kVA, supplies a $12$ kW load at power factor of $0.6$ lagging. The additional load at unity power factor in kW (round off to two...
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GATE Electrical 2019 | Question: 43
The voltage across and the current through a load are expressed as follows $v(t)=-170 \sin \bigg( 377t- \frac{\pi}{6} \bigg) V$ $i(t) =8 \cos \bigg( 377t + \frac{\pi}{6} \bigg) A$ The average power in watts (round off to one decimal place) consumed by the load is _________.
The voltage across and the current through a load are expressed as follows$v(t)=-170 \sin \bigg( 377t- \frac{\pi}{6} \bigg) V$$i(t) =8 \cos \bigg( 377t + \frac{\pi}{6} \b...
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GATE Electrical 2019 | Question: 30
The transfer function of a phase lead compensator is given by $D(s) = \frac{3 \bigg( s+ \frac{1}{3T} \bigg)}{ \bigg( s+ \frac{1}{T} \bigg)}$ The frequency (in rad/sec), at which $\angle D(j \omega)$ is maximum, is $\sqrt{\frac{3}{T^2}}$ $\sqrt{\frac{1}{3T^2}}$ $\sqrt{3T}$ $\sqrt{3T^2}$
The transfer function of a phase lead compensator is given by$$D(s) = \frac{3 \bigg( s+ \frac{1}{3T} \bigg)}{ \bigg( s+ \frac{1}{T} \bigg)}$$The frequency (in rad/sec), a...
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GATE Electrical 2019 | Question: 53
In a DC-DC boost converter, the duty ratio is controlled to regulate the output voltage at $48$ V. The input DC voltage is $24$ V. The output power is $120$ W. The switching frequency is $50$ kHz. Assume ideal components ... operates at the boundary between continuous and discontinuous conduction modes. The value of the boost inductor (in $\mu H$) is ________
In a DC-DC boost converter, the duty ratio is controlled to regulate the output voltage at $48$ V. The input DC voltage is $24$ V. The output power is $120$ W. The switch...
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GATE Electrical 2019 | Question: 38
The line currents of a three-phase four wire system are square waves with amplitude of $100$ A. These three currents are phase shifted by $120^{\circ}$ with respect to each other. The rms value of neutral current is $0$ A $\frac{100}{\sqrt{3}}$ A $100$ A $300$ A
The line currents of a three-phase four wire system are square waves with amplitude of $100$ A. These three currents are phase shifted by $120^{\circ}$ with respect to ea...
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GATE Electrical 2019 | Question: 16
Given, $V_{gs}$ is the gate-source voltage, $V_{ds}$ is the drain source voltage, and $V_{th}$ is the threshold voltage of an enhancement type NMOS transistor, the conditions for transistor to be biased in saturation are $V_{gs}<V_{th};V_{ds}\geq V_{gs}-V_{th}$ ... $V_{gs}>V_{th};V_{ds}\leq V_{gs}-V_{th}$ $V_{gs}<V_{th};V_{ds}\leq V_{gs}-V_{th}$
Given, $V_{gs}$ is the gate-source voltage, $V_{ds}$ is the drain source voltage, and $V_{th}$ is the threshold voltage of an enhancement type NMOS transistor, the condit...
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GATE Electrical 2019 | Question: 55
A single-phase fully-controlled thyristor converter is used to obtain an average voltage of $180$ V with $10$ A constant current to feed a DC load. It is fed from single-phase AC supply of $230$ V, $50$ Hz. Neglect the source impedance. The power factor (round off to two decimal places) of AC mains is _________
A single-phase fully-controlled thyristor converter is used to obtain an average voltage of $180$ V with $10$ A constant current to feed a DC load. It is fed from single-...
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GATE Electrical 2019 | Question: 37
A DC-DC buck converter operates in continuous conduction mode. It has $48$ V input voltage, and it feeds a resistive load of $24 \: \Omega$. The switching frequency of the converter is $250$ Hz. If switch-on duration is $1$ ms, the load power is $6$ W $12$ W $24$ W $48$ W
A DC-DC buck converter operates in continuous conduction mode. It has $48$ V input voltage, and it feeds a resistive load of $24 \: \Omega$. The switching frequency of th...
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GATE Electrical 2019 | Question: 31
Consider a state-variable model of a system $\begin{bmatrix} x_1 \\ x_2 \end{bmatrix} = \begin{bmatrix} 0 & 1 \\ -\alpha & - 2 \beta \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} + \begin{bmatrix} 0 \\ \alpha \end{bmatrix} r $ ... $\omega_n = \sqrt{\beta}$ $\xi = \sqrt{\beta} $; $\omega_n = \sqrt{\alpha} $
Consider a state-variable model of a system$\begin{bmatrix} x_1 \\ x_2 \end{bmatrix} = \begin{bmatrix} 0 & 1 \\ -\alpha & – 2 \beta \end{bmatrix} \begin{bmatrix} x_1 \...
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GATE Electrical 2019 | Question: 54
A fully-controlled three-phase bridge converter is working from a $415$ V, $50$ Hz AC supply. It is supplying constant current of $100$ A a $400$ V to a DC load. Assume large inductive smoothing and neglect overlap. The rms value of the AC line current in amperes (round off to two decimal places) is _______
A fully-controlled three-phase bridge converter is working from a $415$ V, $50$ Hz AC supply. It is supplying constant current of $100$ A a $400$ V to a DC load. Assume l...
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GATE Electrical 2019 | Question: 46
A $220$ V DC shunt motor takes $3$ A at no-load. It draws $25$ A when running at full-load at $1500$ rpm. The armature and shunt resistance are $0.5 \: \Omega$ and $220 \: \Omega$, respectively. The no-load speed in rpm (round off to two decimal places) is _____.
A $220$ V DC shunt motor takes $3$ A at no-load. It draws $25$ A when running at full-load at $1500$ rpm. The armature and shunt resistance are $0.5 \: \Omega$ and $220 \...
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GATE Electrical 2019 | Question: 34
In the circuit below, the operational amplifier is ideal. If $V_1=10$ mV and $V_2=50$ mV, he output voltage $(V_{\text{out}})$ is $100$ mV $400$ mV $500$ mV $600$ mV
In the circuit below, the operational amplifier is ideal. If $V_1=10$ mV and $V_2=50$ mV, he output voltage $(V_{\text{out}})$ is$100$ mV$400$ mV$500$ mV$600$ mV
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GATE Electrical 2019 | Question: 41
A $0.1 \mu F$ capacitor charged to $100$ V is discharged through a $1 \: k \Omega$ resistor. The time in ms (round off to two decimal places) required for the voltage across the capacitor to drop to $1$ V is _________
A $0.1 \mu F$ capacitor charged to $100$ V is discharged through a $1 \: k \Omega$ resistor. The time in ms (round off to two decimal places) required for the voltage acr...
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GATE Electrical 2019 | Question: 47
A delta-connected, $3.7$ kW, $400$ V(line), three-phase, $4$-pole, $50$-Hz squirrel-cage induction moor has the following equivalent circuit parameters per phase referred to the stator: $R_1=5.39 \: \Omega$, $R_2=5.72 \: \Omega$ ... (round off to two decimal places) when it is connected to a $100$ V(line), $10$ Hz, three-phase AC source is _______
A delta-connected, $3.7$ kW, $400$ V(line), three-phase, $4$-pole, $50$-Hz squirrel-cage induction moor has the following equivalent circuit parameters per phase referred...
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GATE Electrical 2019 | Question: 50
A $30$ kV, $50$ Hz, $50$ MVA generator has the positive, negative, and zero sequence reactances of $0.25$ pu, $0.15$ pu, and $0.05$ pu, respectively. The neutral of the generator is grounded with a reactance so that ... three-phase fault at the generator terminal are equal. The value of grounding reactance in ohms (round off to one decimal place) is ___________
A $30$ kV, $50$ Hz, $50$ MVA generator has the positive, negative, and zero sequence reactances of $0.25$ pu, $0.15$ pu, and $0.05$ pu, respectively. The neutral of the g...
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GATE Electrical 2019 | Question: 42
The current $I$ flowing in the circuit shown in amperes is ____________
The current $I$ flowing in the circuit shown in amperes is ____________
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GATE Electrical 2012 | Question: 35
In the circuit shown, an ideal switch $S$ is operated at $100$ kHz with a duty ratio of $50 \%$. Given that $\Delta i_c$ is $1.6$ A peak-to-peak and $I_0$ is $5$ A dc, the peak current in $S$ is $6.6$ A $5.0$ A $5.8$ A $4.2$ A
In the circuit shown, an ideal switch $S$ is operated at $100$ kHz with a duty ratio of $50 \%$. Given that $\Delta i_c$ is $1.6$ A peak-to-peak and $I_0$ is $5$ A dc, th...
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GATE Electrical 2012 | Question: 52
In the circuit shown, the three voltmeter readings are $V_1 =220$ V, $V_2=122$ V, $V_3=136$ V. The power factor of the load is $0.45$ $0.50$ $0.55$ $0.60$
In the circuit shown, the three voltmeter readings are $V_1 =220$ V, $V_2=122$ V, $V_3=136$ V.The power factor of the load is$0.45$$0.50$$0.55$$0.60$
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GATE Electrical 2012 | Question: 34
A cylindrical rotor generator delivers $0.5$ pu power in the steady-state to an infinite bus through a transmission line of reactance $0.5$ pu. The generator no-load voltage is $1.5$ pu and the infinite bus voltage is $1$ pu. The inertia constant of ... degrees, for a three-phase dead short circuit fault at the generator terminal is $53.5$ $60.2$ $70.8$ $79.6$
A cylindrical rotor generator delivers $0.5$ pu power in the steady-state to an infinite bus through a transmission line of reactance $0.5$ pu. The generator no-load volt...
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GATE Electrical 2012 | Question: 45
An analog voltmeter uses external multiplier settings. With a multiplier setting of $20 \: k \Omega$, it reads $440$ V and with a multiplier setting of $80 \: k \Omega$, it reads $352$ V. For a multiplier setting of $40 \: k \Omega$, the voltmeter reads $371$ V $383$ V $394$ V $406$ V
An analog voltmeter uses external multiplier settings. With a multiplier setting of $20 \: k \Omega$, it reads $440$ V and with a multiplier setting of $80 \: k \Omega$, ...
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GATE Electrical 2012 | Question: 46
The locked rotor current in a $3$-phase, star connected $15$ kW, $4$-pole, $230$ V, $50$ Hz induction motor at rated conditions is $50$ A. Neglecting losses and magnetizing current, the approximate locked rotor line current drawn when the motor is connected to a $236$ V, $57$ Hz supply is $58.5$ A $45.0$ A $42.7$ A $55.6$ A
The locked rotor current in a $3$-phase, star connected $15$ kW, $4$-pole, $230$ V, $50$ Hz induction motor at rated conditions is $50$ A. Neglecting losses and magnetizi...
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GATE Electrical 2012 | Question: 33
For the system shown below, $S_{D1}$ and $S_{D2}$ are complex power demands at bus $1$ and bus $2$ respectively. If $\mid V_2 \mid =1$ pu, the VAR rating of the capacitor $(Q_{G2})$ connected at bus $2$ is $0.2$ pu $0.268$ pu $0.312$ pu $0.4$ pu
For the system shown below, $S_{D1}$ and $S_{D2}$ are complex power demands at bus $1$ and bus $2$ respectively. If $\mid V_2 \mid =1$ pu, the VAR rating of the capacitor...
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GATE Electrical 2012 | Question: 47
A single phase $10$ kVA, $50$ Hz transformer with $1$ kV primary winding draws $0.5$ A and $55$ W, at rated voltage and frequency, on no load. A second transformer has a core with all its linear dimensions $\sqrt{2}$ times the corresponding dimensions of the first transformer. The core ... are $0.7$ A, $77.8$ W $0.7$ A, $155.6$ W $1$ A, $110$ W $1$ A, $220$ W
A single phase $10$ kVA, $50$ Hz transformer with $1$ kV primary winding draws $0.5$ A and $55$ W, at rated voltage and frequency, on no load. A second transformer has a ...
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GATE Electrical 2012 | Question: 9
The bus admittance matrix of a three-bus three-line system is $Y=j \begin{bmatrix} -13 & 10 & 5 \\ 10 & -18 & 10 \\ 5 & 10 & -13 \end{bmatrix}$ If each transmission line between the two buses is represented by an equivalent $\pi$-network, the magnitude of the shunt susceptance of the line connecting bus $1$ and $2$ is $4$ $2$ $1$ $0$
The bus admittance matrix of a three-bus three-line system is $Y=j \begin{bmatrix} -13 & 10 & 5 \\ 10 & -18 & 10 \\ 5 & 10 & -13 \end{bmatrix}$ If each transmission line ...
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GATE Electrical 2012 | Question: 48
In the $3$-phase inverter circuit shown, the load is balanced and the gating scheme is $180^{\circ}$-conduction mode. All the switching devices are ideal. The rms value of load phase voltage is $106.1$ V $141.4$ V $212.2$ V $282.8$ V
In the $3$-phase inverter circuit shown, the load is balanced and the gating scheme is $180^{\circ}$-conduction mode. All the switching devices are ideal.The rms value of...
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GATE Electrical 2012 | Question: 39
Consider the differential equation $\dfrac{d^2y(t)}{dt^2} + 2 \dfrac{dy(t)}{dt} + y(t)=\delta (t)$ with $y(t) \bigg \vert_{t=0^-}= -2$ and $\dfrac{dy}{dt} \bigg \vert _{t=0^-} =0$. The numerical value of $\dfrac{dy}{dt} \bigg \vert _{t=0^+}$ is $-2$ $-1$ $0$ $1$
Consider the differential equation $\dfrac{d^2y(t)}{dt^2} + 2 \dfrac{dy(t)}{dt} + y(t)=\delta (t)$ with $y(t) \bigg \vert_{t=0^-}= -2$ and $\dfrac{dy}{dt} \bigg \vert _{t...
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GATE Electrical 2012 | Question: 8
If $x[n]=(1/3)^{\mid n \mid} – (1/2)^n \: u[n]$, then the region of convergence (ROC) of its $Z$-transform in the $Z$-plane will be $\dfrac{1}{3} < \mid z \mid < 3 \\$ $\dfrac{1}{3} < \mid z \mid < \dfrac{1}{2} \\$ $\dfrac{1}{2} < \mid z \mid < 3 \\$ $\dfrac{1}{3} < \mid z \mid $
If $x[n]=(1/3)^{\mid n \mid} – (1/2)^n \: u[n]$, then the region of convergence (ROC) of its $Z$-transform in the $Z$-plane will be$\dfrac{1}{3} < \mid z \mid < 3 \\$$\...
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