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GATE ECE 2001 | Question: 1.1
This question consists of TWENTY FIVE sub-questions $(1.1 - 1.25)$ of ONE mark each. For each of these sub-questions, four possible answers ( $\text{A, B, C}$ and $\text{D}$ ) are given, out of which only one is correct. Answer each sub-question by darkening the appropriate ... $2 \mathrm{~V}$ $\frac{4}{3} \mathrm{~V}$ $4 \mathrm{~V}$ $8 \mathrm{~V}$
This question consists of TWENTY FIVE sub-questions $(1.1 - 1.25)$ of ONE mark each. For each of these sub-questions, four possible answers ( $\text{A, B, C}$ and $\text{...
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GATE ECE 2001 | Question: 1.2
If each branch of a Delta circuit has impedance $\sqrt{3} Z$, then each branch of the equivalent Wye circuit has impedance. $\frac{Z}{\sqrt{3}}$ $3 Z$ $3 \sqrt{3} \mathrm{Z}$ $\frac{Z}{3}$
If each branch of a Delta circuit has impedance $\sqrt{3} Z$, then each branch of the equivalent Wye circuit has impedance.$\frac{Z}{\sqrt{3}}$$3 Z$$3 \sqrt{3} \mathrm{Z}...
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GATE ECE 2001 | Question: 1.3
The transfer function of a system is given by $H(s)=\frac{1}{s^{2}(s-2)}$. The impulse response of the system is $\left(t^{2 *} e^{-2 t}\right) \mathrm{U}(t)$ (* denotes convolution, and $\mathrm{U}(t)$ is unit step function) $\left(t^{*} e^{2 t}\right) \mathrm{U}(t)$ $\left(t e^{-2} t\right) \mathrm{U}(t)$ $\left(t e^{-2 t}\right) \mathrm{U}(t)$
The transfer function of a system is given by $H(s)=\frac{1}{s^{2}(s-2)}$. The impulse response of the system is$\left(t^{2 *} e^{-2 t}\right) \mathrm{U}(t)$ (* denotes c...
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GATE ECE 2001 | Question: 1.4
The admittance parameter $\mathrm{Y}_{12}$ in the $2$-port network in the figure, $-0.2 \; \mathrm{mho}$ $0.1 \; \mathrm{mho}$ $-0.05 \; \mathrm{mho}$ $0.05 \; \mathrm{mho}$
The admittance parameter $\mathrm{Y}_{12}$ in the $2$-port network in the figure,$-0.2 \; \mathrm{mho}$$0.1 \; \mathrm{mho}$$-0.05 \; \mathrm{mho}$$0.05 \; \mathrm{mho}$
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GATE ECE 2001 | Question: 1.5
The region of convergence of the $z$-transform of a unit step function is $|z|>1$ $|z|<1$ (Real part of $z)>0$ ( Real part of $z)<0$
The region of convergence of the $z$-transform of a unit step function is$|z|>1$$|z|<1$(Real part of $z)>0$( Real part of $z)<0$
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GATE ECE 2001 | Question: 1.6
The current gain of a BJT is $g_{m} r_{\circ}$ $\frac{g_{m}}{r_{\circ}}$ $g_{m} r_{\pi}$ $\frac{g_{m}}{r_{\pi}}$
The current gain of a BJT is$g_{m} r_{\circ}$$\frac{g_{m}}{r_{\circ}}$$g_{m} r_{\pi}$$\frac{g_{m}}{r_{\pi}}$
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GATE ECE 2001 | Question: 1.7
MOSFET can be used as a current controlled capacitor voltage controlled capacitor current controlled inductor voltage controlled inductor
MOSFET can be used as acurrent controlled capacitorvoltage controlled capacitorcurrent controlled inductorvoltage controlled inductor
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GATE ECE 2001 | Question: 1.8
The effective channel length of a MOSFET in saturation decreases with increase in gate voltage drain voltage source voltage body voltage
The effective channel length of a MOSFET in saturation decreases with increase ingate voltagedrain voltagesource voltagebody voltage
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GATE ECE 2001 | Question: 1.9
The ideal $\text{OP-AMP}$ has the following characteristics. $\mathrm{R}_{\mathrm{i}}=\infty, \mathrm{A}=\infty, \mathrm{R}_{0}=0$ $\mathrm{R}_{\mathrm{i}}=0, \mathrm{~A}=\infty, \mathrm{R}_{0}=0$ $\mathrm{R}_{\mathrm{i}}=\infty, \mathrm{A}=\infty, \mathrm{R}_{0}=\infty$ $\mathrm{R}_{1}=0, \mathrm{~A}=\infty, \mathrm{R}_{0}=\infty$
The ideal $\text{OP-AMP}$ has the following characteristics.$\mathrm{R}_{\mathrm{i}}=\infty, \mathrm{A}=\infty, \mathrm{R}_{0}=0$$\mathrm{R}_{\mathrm{i}}=0, \mathrm{~A}=\...
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GATE ECE 2001 | Question: 1.10
The $2$'s complement representation of $-17$ is $01110$ $01111$ $11110$ $10001$
The $2$'s complement representation of $-17$ is$01110$$01111$$11110$$10001$
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GATE ECE 2001 | Question: 1.11
Consider the following two statements : $\text{Statement 1: A}$ stable multivibrator can be used for generating square wave. $\text{Statement 1: B}$ stable multivibrator can be used for storing binary information. Only statement $1$ is correct Only statement $2$ is correct Both the statements $1$ and $2$ are correct Both the statements $1$ and $2$ are incorrect
Consider the following two statements :$\text{Statement 1: A}$ stable multivibrator can be used for generating square wave.$\text{Statement 1: B}$ stable multivibrator c...
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GATE ECE 2001 | Question: 1.12
For the ring oscillator shown in the figure, the propagation delay of each inverter is $100$ pico sec. What is the fundamental frequency of the oscillator output? $10 \; \mathrm{MHz}$ $100 \; \mathrm{MHz}$ $1 \; \mathrm{GHz}$ $2 \; \mathrm{GHz}$
For the ring oscillator shown in the figure, the propagation delay of each inverter is $100$ pico sec. What is the fundamental frequency of the oscillator output?$10 \; \...
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GATE ECE 2001 | Question: 1.13
An $8085$ microprocessor based system uses a $4 \mathrm{K} \times 8 \text{bit RAM}$ whose starting address is $\text{AA00 H}$. The address of the last byte in this $\text{RAM}$ is $\text{OFFF H}$ $1000 \; \mathrm{H}$ $\text{B9FF H}$ $\text{BAOO H}$
An $8085$ microprocessor based system uses a $4 \mathrm{K} \times 8 \text{bit RAM}$ whose starting address is $\text{AA00 H}$. The address of the last byte in this $\text...
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GATE ECE 2001 | Question: 1.14
The equivalent of the block diagram in the figure, given in
The equivalent of the block diagram in the figure, given in
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GATE ECE 2001 | Question: 1.15
If the characteristic equation of a closed-loop system is $s^{2}+2 s+2=0$, then the system is overdamped critically damped underdamped undamped
If the characteristic equation of a closed-loop system is $s^{2}+2 s+2=0$, then the system isoverdampedcritically dampedunderdampedundamped
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GATE ECE 2001 | Question: 1.16
The root-locus diagram for a closed-loop feedback system is shown in the figure is. The system is overdamped. only if $0 \leq \mathrm{K} \leq 1$ only if $1 < \text{K} < 5$ only if $\mathrm{K} > 5$ if $0 \leq \text{K} < 1$ or $\text{K} > 5$
The root-locus diagram for a closed-loop feedback system is shown in the figure is. The system is overdamped.only if $0 \leq \mathrm{K} \leq 1$only if $1 < \text{K} < 5$o...
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GATE ECE 2001 | Question: 1.17
The Nyquist plot for the open-loop transfer function $G(s)$ of a unity negative feedback system is shown in the figure, if $G(s)$ has no pole in the right-half of $s$-plane, the number of roots of the system characteristic equation in the right-half of $s$-plane is $0$ $1$ $2$ $3$
The Nyquist plot for the open-loop transfer function $G(s)$ of a unity negative feedback system is shown in the figure, if $G(s)$ has no pole in the right-half of $s$-pla...
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GATE ECE 2001 | Question: 1.18
Let $\delta(t)$ denote the delta function. The value of the integral $\int_{-\infty}^{\infty} \delta(t) \cos \left(\frac{3 t}{2}\right) d t$ is $1$ $-1$ $0$ $\frac{\pi}{2}$
Let $\delta(t)$ denote the delta function. The value of the integral $\int_{-\infty}^{\infty} \delta(t) \cos \left(\frac{3 t}{2}\right) d t$ is$1$$-1$$0$$\frac{\pi}{2}$
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GATE ECE 2001 | Question: 1.19
A bandlimited signal is sampled at the Nyquist rate. The signal can be recovered by passing the samples through an RC filter an envelope detector a PLL an ideal low-pass filter with the appropriate bandwidth.
A bandlimited signal is sampled at the Nyquist rate. The signal can be recovered by passing the samples throughan RC filteran envelope detectora PLLan ideal low-pass filt...
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GATE ECE 2001 | Question: 1.20
The PDF of a Gaussian random variable $X$ is given by $\operatorname{Px}(x)=\frac{1}{3 \sqrt{2 \pi}} e^{\frac{-(x-4)^{2}}{18}}$ The probability of the event $\{X=4\}$ is $\frac{1}{2}$ $\frac{1}{3 \sqrt{2 \pi}}$ $0$ $\frac{1}{4}$
The PDF of a Gaussian random variable $X$ is given by $\operatorname{Px}(x)=\frac{1}{3 \sqrt{2 \pi}} e^{\frac{-(x-4)^{2}}{18}}$ The probability of the event $\{X=4\}$ is$...
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GATE ECE 2001 | Question: 1.21
If a signal $f(t)$ has energy $E$, the energy of the signal $f(2 t)$ is equal to $\text{E}$ $\frac{\mathrm{E}}{2}$ $2 \mathrm{E}$ $4 \mathrm{E}$
If a signal $f(t)$ has energy $E$, the energy of the signal $f(2 t)$ is equal to$\text{E}$$\frac{\mathrm{E}}{2}$$2 \mathrm{E}$$4 \mathrm{E}$
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GATE ECE 2001 | Question: 1.22
A transmission line is distortionless if $\mathrm{RL}=\frac{1}{\mathrm{GC}}$ $\mathrm{RL}=\mathrm{GC}$ $\mathrm{LG}=\mathrm{RC}$ $\mathrm{RG}=\mathrm{LC}$
A transmission line is distortionless if$\mathrm{RL}=\frac{1}{\mathrm{GC}}$$\mathrm{RL}=\mathrm{GC}$$\mathrm{LG}=\mathrm{RC}$$\mathrm{RG}=\mathrm{LC}$
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GATE ECE 2001 | Question: 1.23
If a plane electromagnetic wave satisfies the equation $\frac{\partial^{2} \mathrm{E}_{\mathrm{x}}}{\partial \mathrm{z}^{2}}=\mathrm{c}^{2} \frac{\partial^{2} \mathrm{E}_{\mathrm{x}}}{\partial \mathrm{t}^{2}}$, the wave propagates in the $x$-direction $z$-direction $y$-direction $x y$ plane at an angle of $45^{\circ}$ between the $x$ and $z$ directions
If a plane electromagnetic wave satisfies the equation $\frac{\partial^{2} \mathrm{E}_{\mathrm{x}}}{\partial \mathrm{z}^{2}}=\mathrm{c}^{2} \frac{\partial^{2} \mathrm{E}_...
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GATE ECE 2001 | Question: 1.24
The phase velocity of waves propagating in a hollow metal waveguide is greater than the velocity of light in free space. less than the velocity of light in free space. equal to the velocity of light in free space. equal to the group velocity.
The phase velocity of waves propagating in a hollow metal waveguide isgreater than the velocity of light in free space.less than the velocity of light in free space.equal...
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GATE ECE 2001 | Question: 1.25
The dominant mode in a rectangular waveguide is $\text{TE10,}$ because this mode has no attenuation no cut-off no magnetic field component the highest cut-off wavelength
The dominant mode in a rectangular waveguide is $\text{TE10,}$ because this mode hasno attenuationno cut-offno magnetic field componentthe highest cut-off wavelength
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GATE ECE 2001 | Question: 2.1
This question consists of TWENTY FIVE subquestions $(2.1-2.25)$ of TWO marks each. For each of these sub-questions, four possible answers ( $\text{A, B, C}$ and $\text{D}$) are given, out of which only one is correct. Answer each sub-question by darkening the appropriate ... $e_{0}$ in the figure, $48 \mathrm{~V}$ $24 \mathrm{~V}$ $36 \mathrm{~V}$ $28 \mathrm{~V}$
This question consists of TWENTY FIVE subquestions $(2.1-2.25)$ of TWO marks each. For each of these sub-questions, four possible answers ( $\text{A, B, C}$ and $\text{D}...
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GATE ECE 2001 | Question: 2.2
In the figure, the value of the load resistor $R$ which maximizes the power delivered to it is $14.14 \; \Omega$ $10 \; \Omega$ $200 \; \Omega$ $28.28 \; \Omega$
In the figure, the value of the load resistor $R$ which maximizes the power delivered to it is$14.14 \; \Omega$$10 \; \Omega$$200 \; \Omega$$28.28 \; \Omega$
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GATE ECE 2001 | Question: 2.3
When the angular frequency $\omega$ in the figure, varied from $0$ to $\infty$, the locus of the current phasor $\mathrm{I}_{2}$ is given by
When the angular frequency $\omega$ in the figure, varied from $0$ to $\infty$, the locus of the current phasor $\mathrm{I}_{2}$ is given by
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GATE ECE 2001 | Question: 2.4
The $Z$ parameters $Z_{11}$ and $Z_{21}$ for the $2$-port network in the figure, $Z_{11}=-\frac{6}{11} \; \Omega ; Z_{21}=\propto \frac{16}{11} \; \Omega$; $Z_{11}=\frac{6}{11} \; \Omega ; Z_{21}=\frac{4}{11} \; \Omega$; $Z_{11}=\frac{6}{11} \; \Omega ; Z_{21}=-\frac{16}{11} \; \Omega$; $Z_{11}=\frac{4}{11} \; \Omega ; Z_{21}=\frac{4}{11} \; \Omega$;
The $Z$ parameters $Z_{11}$ and $Z_{21}$ for the $2$-port network in the figure,$Z_{11}=-\frac{6}{11} \; \Omega ; Z_{21}=\propto \frac{16}{11} \; \Omega$;$Z_{11}=\frac{6}...
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GATE ECE 2001 | Question: 2.5
An npn $\text{BJT}$ has $\mathrm{gm}=38 \mathrm{~m} \mathrm{~A} / \mathrm{V}, \mathrm{C}_{u}=10^{-14} \mathrm{~F}$, $C_{\pi}=4 \times 10^{-13} \mathrm{~F}$, and $D C$ current gain $\beta_{0}=90$. For this transistor $f_{\mathrm{T}}$ ... $f_{\mathrm{T}}=1.47 \times 10^{10} \mathrm{~Hz}$ and $f_{\beta}=1.33 \times 10^{12} \mathrm{~Hz}$
An npn $\text{BJT}$ has $\mathrm{gm}=38 \mathrm{~m} \mathrm{~A} / \mathrm{V}, \mathrm{C}_{u}=10^{-14} \mathrm{~F}$, $C_{\pi}=4 \times 10^{-13} \mathrm{~F}$, and $D C$ cur...
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GATE ECE 2001 | Question: 2.6
The transistor shunt regulator shown in the figure is has a regulated output voltage of $10 \mathrm{~V}$, when the input varies from $20 \mathrm{~V}$ to $30 \mathrm{~V}$ ... $\mathrm{P}_{\mathrm{Z}}=115 \mathrm{~mW}, \mathrm{P}_{\mathrm{T}}=11.9 \mathrm{~W}$
The transistor shunt regulator shown in the figure is has a regulated output voltage of $10 \mathrm{~V}$, when the input varies from $20 \mathrm{~V}$ to $30 \mathrm{~V}$....
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GATE ECE 2001 | Question: 2.7
The oscillator circuit shown in the figure, Hartley oscillator with $f_{\text {oscillation }}=79.6 \; \mathrm{MHz}$ Colpitts oscillator with $f_{\text {oscillation }}=79.6 \; \mathrm{MHz}$ Hartley oscillator with $f_{\text {oscillation }}=159.2 \; \mathrm{MHz}$ Colpitts oscillator with $f_{\text {oscillation }}=159.2 \; \mathrm{MHz}$
The oscillator circuit shown in the figure,Hartley oscillator with $f_{\text {oscillation }}=79.6 \; \mathrm{MHz}$Colpitts oscillator with $f_{\text {oscillation }}=79.6 ...
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GATE ECE 2001 | Question: 2.8
The inverting OP-AMP shown in the figure has an open-loop gain of $100.$ The closed-loop gain $\frac{v_{0}}{v_{s}}$ is $-8$ $-9$ $-10$ $-11$
The inverting OP-AMP shown in the figure has an open-loop gain of $100.$ The closed-loop gain $\frac{v_{0}}{v_{s}}$ is$-8$$-9$$-10$$-11$
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GATE ECE 2001 | Question: 2.9
In the figure, assume the OP-AMPs to be ideal. The output $v_{0}$ of the circuit is $10 \cos (100 t)$ $10 \int_{0}^{1} \cos (100 \tau) d \tau$ $10^{-4} \int_{0}^{t} \cos (100 \tau) d \tau$ $10^{-4} \frac{d}{d t} \cos (100 t)$
In the figure, assume the OP-AMPs to be ideal. The output $v_{0}$ of the circuit is$10 \cos (100 t)$$10 \int_{0}^{1} \cos (100 \tau) d \tau$$10^{-4} \int_{0}^{t} \cos (10...
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GATE ECE 2001 | Question: 2.10
In the figure, the $\text{LED}$ emits light when both $S_{1}$ and $S_{2}$ are closed. emits light when both $S_{1}$ and $S_{2}$ are open. emits light when only of $S_{1}$ or $S_{2}$ is closed. does not emit light, irrespective of the switch positions.
In the figure, the $\text{LED}$emits light when both $S_{1}$ and $S_{2}$ are closed.emits light when both $S_{1}$ and $S_{2}$ are open.emits light when only of $S_{1}$ or...
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GATE ECE 2001 | Question: 2.11
In the TTL circuit in the figure, $\mathrm{S}_{2}$ to $\mathrm{S}_{0}$ are select lines and $\text{X}_{7}$ to $\text{X}_{0}$ are input lines. $\text{S}_{0}$ and $\text{X}_{0}$ are LSBs. The output $Y$ ... $\overline{\mathrm{C}} \cdot(\overline{\mathrm{A} \oplus \mathrm{B}})+\mathrm{C} \cdot(\mathrm{A} \oplus \mathrm{B})$
In the TTL circuit in the figure, $\mathrm{S}_{2}$ to $\mathrm{S}_{0}$ are select lines and $\text{X}_{7}$ to $\text{X}_{0}$ are input lines. $\text{S}_{0}$ and $\text{X}...
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GATE ECE 2001 | Question: 2.12
The digital block in the figure, realized using two positive edge triggered D-flip-flops. Assume that for that for $t < t_{0}, Q_{1} =Q_{2} = 0.$ The circuit in the digital block is given by
The digital block in the figure, realized using two positive edge triggered D-flip-flops. Assume that for that for $t < t_{0}, Q_{1} =Q_{2} = 0.$ The circuit in the digit...
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GATE ECE 2001 | Question: 2.13
In the $\text{DRAM}$ cell in the figure is the $V_{t}$ of the $\text{NMOSFET}$ is $1 \mathrm{~V}$. For the following three combinations of $\mathrm{WL}$ and $\mathrm{BL}$ voltages. $5 \mathrm{~V} ; 3 \mathrm{~V} ; 7 \mathrm{~V}$ ... $5 \mathrm{~V} ; 5 \mathrm{~V} ; 5 \mathrm{~V}$ $4 \mathrm{~V} ; 4 \mathrm{~V} ; 4 \mathrm{~V}$
In the $\text{DRAM}$ cell in the figure is the $V_{t}$ of the $\text{NMOSFET}$ is $1 \mathrm{~V}$. For the following three combinations of $\mathrm{WL}$ and $\mathrm{BL}$...
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GATE ECE 2001 | Question: 2.14
The impulse response functions of four linear systems $\mathrm{S}_{1}, \mathrm{~S}_{2}, \mathrm{~S}_{3}, \mathrm{~S}_{4}$ ... of these systems is time invariant, causal, and stable? $\mathrm{S}_{1}$ $\mathrm{S}_{2}$ $\mathrm{S}_{3}$ $\mathrm{S}_{4}$
The impulse response functions of four linear systems $\mathrm{S}_{1}, \mathrm{~S}_{2}, \mathrm{~S}_{3}, \mathrm{~S}_{4}$ are given respectively by$\begin{array}{ll} h_{1...
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GATE ECE 2001 | Question: 2.16
The open-loop $\text{DC}$ gain of a unity negative feedback system with closed-loop transfer function $\frac{s+4}{s^{2}+7 s+13}$ is $\frac{4}{13}$ $\frac{4}{9}$ $4$ $13$
The open-loop $\text{DC}$ gain of a unity negative feedback system with closed-loop transfer function $\frac{s+4}{s^{2}+7 s+13}$ is$\frac{4}{13}$$\frac{4}{9}$$4$$13$
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