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41
GATE IN 2023 | Question: 31
For the given digital circuit, $\mathrm{A}=\mathrm{B}=1$. Assume that $\mathrm{AND}, \mathrm{OR}$, and $\text{NOT}$ gates have propagation delays of $10 \mathrm{~ns}, 10 \mathrm{~ns}$, and $5 \mathrm{~ns}$ respectively. All lines have zero propagation delay. Given that $\mathrm{C}=1$ when the circuit is ... frequency of steady-state oscillation of the output $\mathrm{Y}$ is_____________. $20~ \mathrm{MHz}$ $15 ~\mathrm{MHz}$ $40~ \mathrm{MHz}$ $50 ~\mathrm{MHz}$
For the given digital circuit, $\mathrm{A}=\mathrm{B}=1$. Assume that $\mathrm{AND}, \mathrm{OR}$, and $\text{NOT}$ gates have propagation delays of $10 \mathrm{~ns}, 10 ...
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42
GATE IN 2023 | Question: 32
In the circuit shown, the initial binary content of shift register $A$ is $1101$ and that of shift register $B$ is $1010.$ The shift registers are positive-edge triggered, and the gates have no delay. When the shift control is high, what will be the binary content of the shift registers $A$ and $B$ after four clock pulses? $A=1101, B=1101$ $A=1110, B=1001$ $A=0101, B=1101$ $A=1010, B=1111$
In the circuit shown, the initial binary content of shift register $A$ is $1101$ and that of shift register $B$ is $1010.$ The shift registers are positive-edge triggered...
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May 22, 2023
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43
GATE IN 2023 | Question: 33
The magnitude and phase plots shown in the figure match with the transfer-function______________. $\frac{10000}{s^2+2 s+10000} $ $ \frac{10000}{s^2+2 s+10000} e^{-0.05 s}$ $\frac{10000}{s^2+2 s+10000} e^{-0.5 \times 10^{-12} s} $ $\frac{100}{s^2+2 s+100}$
The magnitude and phase plots shown in the figure match with the transfer-function______________.$\frac{10000}{s^2+2 s+10000} $$ \frac{10000}{s^2+2 s+10000} e^{-0.05 s}$$...
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May 22, 2023
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44
GATE IN 2023 | Question: 34
A continuous real-valued signal $x(t)$ has finite positive energy and $x(t)=0, \forall \; t<0.$ From the list given below, select ALL the signals whose continuous-time Fourier transform is purely imaginary. $x(t)+x(-t)$ $x(t)-x(-t)$ $j(x(t)+x(-t))$ $j(x(t)-x(-t))$
A continuous real-valued signal $x(t)$ has finite positive energy and $x(t)=0, \forall \; t<0.$ From the list given below, select ALL the signals whose continuous-time Fo...
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May 22, 2023
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45
GATE IN 2023 | Question: 35
A silica-glass fiber has a core refractive index of $1.47$ and a cladding refractive index of $1.44.$ If the cladding is completely stripped out and the core is dipped in water having a refractive index of $1.33,$ the numerical aperture of the modified fiber is____________(rounded off to three decimal places).
A silica-glass fiber has a core refractive index of $1.47$ and a cladding refractive index of $1.44.$ If the cladding is completely stripped out and the core is dipped in...
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46
GATE IN 2023 | Question: 36
In the circuit shown, $\omega=100 \pi \mathrm{rad} / \mathrm{s}, \mathrm{R}_1=\mathrm{R}_2=2.2 \Omega$ and $\mathrm{L}=7 \mathrm{mH}$. The capacitance $C$ for which $Y_{\text {in }}$ is purely real is__________________$\mathrm{mF}$ (rounded off to two decimal places).
In the circuit shown, $\omega=100 \pi \mathrm{rad} / \mathrm{s}, \mathrm{R}_1=\mathrm{R}_2=2.2 \Omega$ and $\mathrm{L}=7 \mathrm{mH}$. The capacitance $C$ for which $Y_{\...
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May 22, 2023
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47
GATE IN 2023 | Question: 37
The $\mathrm{R}-\mathrm{L}$ circuit with $\mathrm{R}=10 ~ \mathrm{k} \Omega$ and $\mathrm{L}=1 \mathrm{mH}$ is excited by a step current $\mathrm{I}_{\mathrm{u}} \mathrm{u}(\mathrm{t})$. At $\mathrm{t}=0^{-}$, there is a current $\mathrm{I}_L=\mathrm{I}_0 / 5$ flowing through the inductor. The minimum time taken for the current through the inductor to reach $99 \%$ of its final value is___________$\mu \mathrm{s}$ (rounded off to two decimal places).
The $\mathrm{R}-\mathrm{L}$ circuit with $\mathrm{R}=10 ~ \mathrm{k} \Omega$ and $\mathrm{L}=1 \mathrm{mH}$ is excited by a step current $\mathrm{I}_{\mathrm{u}} \mathrm{...
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May 22, 2023
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48
GATE IN 2023 | Question: 38
Consider a standard negative feedback configuration with $G(s)=\frac{1}{(s-2)(s-3)}$ and the controller $C(s)=K_P+\frac{K_I}{s}+K_D s$. The root-locus of $G(s) C(s)$ is presented in the figure below. The gain $C(j \omega)=2$ at $\omega=1 ~ \mathrm{rad} / \mathrm{s}$. The value of $K_D$ is____________(rounded off to one decimal place).
Consider a standard negative feedback configuration with $G(s)=\frac{1}{(s-2)(s-3)}$ and the controller $C(s)=K_P+\frac{K_I}{s}+K_D s$. The root-locus of $G(s) C(s)$ is p...
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May 22, 2023
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49
GATE IN 2023 | Question: 39
How many five-digit numbers can be formed using the integers $3,4,5$ and $6$ with exactly one digit appearing twice?
How many five-digit numbers can be formed using the integers $3,4,5$ and $6$ with exactly one digit appearing twice?
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50
GATE IN 2023 | Question: 40
The phase margin of the transfer function $G(s)=\frac{2(1-s)}{(1+s)^{2}}$ is____________degrees. (rounded off to the nearest integer).
The phase margin of the transfer function $G(s)=\frac{2(1-s)}{(1+s)^{2}}$ is____________degrees. (rounded off to the nearest integer).
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51
GATE IN 2023 | Question: 41
A wire-wound 'resistive potentiometer type' angle sensor with $72$ turns is used in an application. The first turn of the potentiometer is connected to ground while its last turn is connected to $3.6 \mathrm{~V}$. The width of the wiper covers two turns ensuring makebefore-break. The output (wiper) voltage when the wiper is on top of both the turns $35$ and $36$ is_____________$\text{V}$ (rounded off to two decimal places).
A wire-wound 'resistive potentiometer type' angle sensor with $72$ turns is used in an application. The first turn of the potentiometer is connected to ground while its l...
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May 22, 2023
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GATE IN 2023 | Question: 42
The two secondaries of a linear variable differential transformer (LVDT) showed a magnitude of $2 \mathrm{~V (RMS)}$ for zero displacement position of the core. It is noted that the phase of one of the secondaries has a deviation of one degree from the expected phase. Other than this deviation, the LVDT is ideal. If the ... $\mu \mathrm{m}$ (rounded off to one decimal place).
The two secondaries of a linear variable differential transformer (LVDT) showed a magnitude of $2 \mathrm{~V (RMS)}$ for zero displacement position of the core. It is not...
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53
GATE IN 2023 | Question: 43
Five measurements are made using a weighing machine, and the readings are $80 \mathrm{~kg}, 79 \mathrm{~kg}, 81 \mathrm{~kg}, 79 \mathrm{~kg}$ and $81 \mathrm{~kg}$. The sample standard deviation of the measurement ___________is $\mathrm{kg}$ (rounded off to two decimal places).
Five measurements are made using a weighing machine, and the readings are $80 \mathrm{~kg}, 79 \mathrm{~kg}, 81 \mathrm{~kg}, 79 \mathrm{~kg}$ and $81 \mathrm{~kg}$. The ...
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GATE IN 2023 | Question: 44
Four strain gauges $\mathrm{R}_{\mathrm{A}}, \mathrm{R}_{\mathrm{B}}, \mathrm{R}_{\mathrm{C}}$ and $\mathrm{R}_{\mathrm{D}}$, each with nominal resistance $\mathrm{R}$, are connected in a bridge configuration. When a force is applied, $\mathrm{R}_{\mathrm{A}}$ and $\mathrm{R}_{\mathrm{D}}$ ... $\mathrm{R}_{\mathrm{V}}$ required to balance the bridge is____________$\Omega$ (rounded off to two decimal places).
Four strain gauges $\mathrm{R}_{\mathrm{A}}, \mathrm{R}_{\mathrm{B}}, \mathrm{R}_{\mathrm{C}}$ and $\mathrm{R}_{\mathrm{D}}$, each with nominal resistance $\mathrm{R}$, a...
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May 22, 2023
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GATE IN 2023 | Question: 45
A sinusoidal current of $i_1(t)=1 \sin (200 \pi t) \mathrm{mA}$ is flowing through a $4~ \mathrm{H}$ inductor which is mutually coupled to another $5 ~ \mathrm{H}$ inductor carrying $ \mathrm{i}_2(t)=2 \sin (200 \pi t) \mathrm{~mA} $ as shown in the figure. The coupling coefficient between the inductors is $0.6.$ The peak energy stored in the circuit is_____________$\mu \mathrm{J}$ (rounded off to two decimal places).
A sinusoidal current of $i_1(t)=1 \sin (200 \pi t) \mathrm{mA}$ is flowing through a $4~ \mathrm{H}$ inductor which is mutually coupled to another $5 ~ \mathrm{H}$ induct...
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May 22, 2023
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GATE IN 2023 | Question: 46
The figure below shows a feedback amplifier constructed using an nMOS transistor. Assume that $\mu_{\mathrm{n}} \mathrm{C}_{\mathrm{ox}}=1 \mathrm{~mA} / \mathrm{V}^2$, threshold voltage $\mathrm{V}_{\mathrm{T}}=1 \mathrm{~V}$ and $\mathrm{W} / \mathrm{L}=2$ ... offer zero impedance at the signal frequency. The ratio $\mathrm{V}_{\text {out }} / \mathrm{V}_{\text {in }}$ is___________ (rounded off to two decimal places).
The figure below shows a feedback amplifier constructed using an nMOS transistor. Assume that $\mu_{\mathrm{n}} \mathrm{C}_{\mathrm{ox}}=1 \mathrm{~mA} / \mathrm{V}^2$, t...
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May 22, 2023
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GATE IN 2023 | Question: 47
Consider the real-valued function $g(x)=\max \left\{(x-2)^2,-2 x+7\right\}$, where $x \in(-\infty, \infty)$. The minimum value attained by $g(x)$ is_____________(rounded off to one decimal place).
Consider the real-valued function $g(x)=\max \left\{(x-2)^2,-2 x+7\right\}$, where $x \in(-\infty, \infty)$. The minimum value attained by $g(x)$ is_____________(rounded ...
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May 22, 2023
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GATE IN 2023 | Question: 48
A short-circuit test is conducted on a single-phase transformer by shorting its secondary. The frequency of input voltage is $1 ~ \mathrm{kHz}$. The corresponding wattmeter reading, primary current and primary voltage are $8 \mathrm{~W}, 2 \mathrm{~A}$ and $6 \mathrm{~V}$ respectively. Assume that the no-load losses and ... $\text{A}$ (rounded off to two decimal places).
A short-circuit test is conducted on a single-phase transformer by shorting its secondary. The frequency of input voltage is $1 ~ \mathrm{kHz}$. The corresponding wattmet...
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May 22, 2023
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GATE IN 2023 | Question: 49
The opamps in the circuit are ideal. The input signals are $\mathrm{V}_{\mathrm{S} 1}=3+0.10 \sin (300 t) ~ \mathrm{V} \text { and } \mathrm{V}_{\mathrm{S} 2}=-2+0.11 \sin (300 t) ~ \mathrm{V}$ The average value of the voltage $V_0$ is_____________$\text{V}$ (rounded off to two decimal places).
The opamps in the circuit are ideal. The input signals are$$\mathrm{V}_{\mathrm{S} 1}=3+0.10 \sin (300 t) ~ \mathrm{V} \text { and } \mathrm{V}_{\mathrm{S} 2}=-2+0.11 \si...
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May 22, 2023
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GATE IN 2023 | Question: 50
In the circuit shown, the input voltage $\mathrm{V}_{\text {in }}=100 ~ \mathrm{mV}$. The switch and the opamp are ideal. At time $\mathrm{t}=0$, the initial charge stored in the $10 ~ \mathrm{nF}$ capacitor is $1 ~ \mathrm{nC}$, with the polarity as indicated in the figure. The switch $\mathrm{S}$ is ... $t=20 \mathrm{~ms}$, the magnitude of the voltage $\mathrm{V}_{\mathrm{o}}$ will be______________$\mathrm{mV}$ (rounded off to the nearest integer).
In the circuit shown, the input voltage $\mathrm{V}_{\text {in }}=100 ~ \mathrm{mV}$. The switch and the opamp are ideal. At time $\mathrm{t}=0$, the initial charge store...
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May 22, 2023
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GATE IN 2023 | Question: 51
In the diagram shown, the frequency of the sinusoidal source voltage $\mathrm{V}_{\mathrm{S}}$ is $50 \mathrm{~Hz}$. The load voltage is $230 \mathrm{~V}$ (RMS), and the load impedance is $\frac{230}{\sqrt{2}}+j \frac{230}{\sqrt{2}} \; \Omega$ ... $V_x$ and $V_y$ are the inputs. The magnitude of the average value of the multiplier output $\mathrm{V}_{\mathrm{o}}$ is_______________$V$ (rounded off to one decimal place).
In the diagram shown, the frequency of the sinusoidal source voltage $\mathrm{V}_{\mathrm{S}}$ is $50 \mathrm{~Hz}$. The load voltage is $230 \mathrm{~V}$ (RMS), and the ...
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May 22, 2023
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GATE IN 2023 | Question: 52
In the circuit shown, assuming an ideal opamp, the value of the output voltage $\mathrm{V}_{\mathrm{o}}=$____________$\mathrm{V}$ (rounded off to one decimal place).
In the circuit shown, assuming an ideal opamp, the value of the output voltage$\mathrm{V}_{\mathrm{o}}=$____________$\mathrm{V}$ (rounded off to one decimal place).
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May 22, 2023
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GATE IN 2023 | Question: 53
The rank of the matrix $A$ given below is one. The ratio $\frac{\alpha}{\beta}$ is __________ (rounded off to the nearest integer). $A=\left[\begin{array}{cc} 1 & 4 \\ -3 & \alpha \\ \beta & 6 \end{array}\right]$
The rank of the matrix $A$ given below is one. The ratio $\frac{\alpha}{\beta}$ is __________ (rounded off to the nearest integer).$$A=\left[\begin{array}{cc}1 & 4 \\-3 &...
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GATE IN 2023 | Question: 54
A $1.999 \mathrm{~V}$ True $\text{RMS 3-1/2}$ digit multimeter has an accuracy of $\pm 0.1 \%$ of reading $\pm 2$ digits. It is used to measure $100 \mathrm{~A}$ (RMS) current flowing through a line using a $100:5$ ratio, Class-$1$ current transformer with a burden of $0.1 \Omega \pm 0.5 \%$. The worst-case absolute error in the multimeter output is___________$\mathrm{V}$ (rounded off to three decimal places).
A $1.999 \mathrm{~V}$ True $\text{RMS 3-1/2}$ digit multimeter has an accuracy of $\pm 0.1 \%$ of reading $\pm 2$ digits.It is used to measure $100 \mathrm{~A}$ (RMS) cur...
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May 22, 2023
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GATE IN 2023 | Question: 55
The voltage source $\mathrm{Vs}=10 \sqrt{2} \sin (20000 \pi t) ~ \mathrm{V}$ has an internal resistance of $50~ \Omega$. The RMS value of the current through $\mathrm{R}$ is_________$\text{mA}$ (rounded off to one decimal place). *This option did not appear in $\text{GATE 2023}$ Examination. It appeared as "Turbine flow meter", that is, "Turbine flow meter" option was repeated.
The voltage source $\mathrm{Vs}=10 \sqrt{2} \sin (20000 \pi t) ~ \mathrm{V}$ has an internal resistance of $50~ \Omega$. The RMS value of the current through $\mathrm{R}$...
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