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121
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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122
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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123
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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124
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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125
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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126
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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127
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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128
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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May 22, 2023
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129
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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130
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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May 22, 2023
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131
GATE IN 2022 | Question: 1
The input $x(t)$ to a system is related to its output $y(t)$ as $\frac{dy(t)}{dt} + y(t) = 3x (t-3)u (t-3)$ Here $u(t)$ represents a unit-step function. The transfer function of this system is __________ $\dfrac{e^{-3s}}{s+3}$ $\dfrac{3e^{-3s}}{s+1}$ $\dfrac{3e^{- (s/3)}}{s+1}$ $\dfrac{e^{-(s/3)}}{s+3}$
The input $x(t)$ to a system is related to its output $y(t)$ as$$\frac{dy(t)}{dt} + y(t) = 3x (t-3)u (t-3)$$Here $u(t)$ represents a unit-step function.The transfer funct...
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132
GATE IN 2022 | Question: 2
A pneumatic nozzle-flapper system is conventionally used to convert __________ Small changes in flapper’s velocity to large changes in output temperature Small changes in flapper’s displacement to large changes in output temperature Small changes in flapper’s velocity to large changes in output pressure Small changes in flapper’s displacement to large changes in output pressure
A pneumatic nozzle-flapper system is conventionally used to convert __________Small changes in flapper’s velocity to large changes in output temperatureSmall changes in...
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133
GATE IN 2022 | Question: 3
A periodic function $f(x),$ with period $2,$ is defined as $f(x) = \left\{\begin{matrix} -1 -x & -1 \leq x < 0 \\ 1 – x & 0 < x \leq 1 \end{matrix}\right. $ The Fourier series of this function contains ___________ Both $\cos (n \pi x)$ and $\sin (n \pi x)$ where $ n = 1, 2, 3, \dots $ Only $\sin (n \pi x)$ where $ n = 1, 2, 3, \dots $ Only $\cos (n \pi x)$ where $ n = 1, 2, 3, \dots $ Only $\cos (2n \pi x)$ where $ n = 1, 2, 3, \dots $
A periodic function $f(x),$ with period $2,$ is defined as$f(x) = \left\{\begin{matrix} -1 -x & -1 \leq x < 0 \\ 1 – x & 0 < x \leq 1 \end{matrix}\right. $The Fourier s...
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134
GATE IN 2022 | Question: 4
The output of a system $y(t)$ is related to its input $x(t)$ according to the relation $y(t) = x(t) \sin (2 \pi t).$ This system is __________ Linear and time-variant Non-linear and time-invariant Linear and time-invariant Non-linear and time-variant
The output of a system $y(t)$ is related to its input $x(t)$ according to the relation $y(t) = x(t) \sin (2 \pi t).$ This system is __________Linear and time-variantNon-l...
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135
GATE IN 2022 | Question: 5
A unity-gain negative-feedback control system has a loop-gain $L(s)$ given by $L(s) = \frac{6}{s(s-5)}$ The closed-loop system is _________ Causal and stable Causal and unstable Non-causal and stable Non-causal and unstable
A unity-gain negative-feedback control system has a loop-gain $L(s)$ given by$$L(s) = \frac{6}{s(s-5)}$$The closed-loop system is _________Causal and stableCausal and uns...
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136
GATE IN 2022 | Question: 6
A sinusoidal carrier wave with amplitude $A_{c}$ and frequency $f_{c}$ is amplitude modulated with a message signal $m(t)$ having frequency $0 < f_{m} \ll f_{c}$ to generate the modulated wave $s(t)$ given by $ s(t) = A_{c} [1+m(t)] \cos (2 \pi f_{c}t) $ ... $m(t) = 1.5 \sin (2 \pi f_{m} t)$ $m(t) = 2 \sin (4 \pi f_{m} t)$ $m(t) = 2 \cos (4 \pi f_{m} t)$
A sinusoidal carrier wave with amplitude $A_{c}$ and frequency $f_{c}$ is amplitude modulated with a message signal $m(t)$ having frequency $0 < f_{m} \ll f_{c}$ to gener...
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137
GATE IN 2022 | Question: 7
A Hall sensor is based on the principle of ___________ Photoelectric effect Seebeck effect Piezoelectric effect Lorentz force
A Hall sensor is based on the principle of ___________Photoelectric effectSeebeck effectPiezoelectric effectLorentz force
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138
GATE IN 2022 | Question: 8
A signal $x(t)$ is band-limited between $100 \; \text{Hz}$ and $200 \; \text{Hz}.$ A signal $y(t)$ is related to $x(t)$ as follows: $y(t) = x (2t – 5)$ The statement that is always true is _______ $y(t)$ is band-limited between $50 \; \text{Hz}$ and $100 \; \text{Hz}$ $y(t)$ is band-limited between $100 \; \text{Hz}$ and $200 \; \text{Hz}$ $y(t)$ is band-limited between $200 \; \text{Hz}$ and $400 \; \text{Hz}$ $y(t)$ is not band-limited
A signal $x(t)$ is band-limited between $100 \; \text{Hz}$ and $200 \; \text{Hz}.$A signal $y(t)$ is related to $x(t)$ as follows:$$y(t) = x (2t – 5)$$The statement tha...
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139
GATE IN 2022 | Question: 9
The figure shows a Chromel-Alumel thermocouple, where the junction $A$ is held at temperature $T_{A},$ and a thermal emf $E_{1}$ is measured using an ideal voltmeter between the open ends $\text{B1}$ and $\text{B2},$ both held at temperature $T_{B}.$ Two identical copper wires are introduced between $\text{B1-C1}$ and $\text{B2-C2}$ as shown in the ... reads a thermal emf $E_{2}.$ Then, _________ $E_{1} < E_{2}$ $E_{1} > E_{2}$ $E_{1} = 2E_{2}$ $E_{1} = E_{2}$
The figure shows a Chromel-Alumel thermocouple, where the junction $A$ is held at temperature $T_{A},$ and a thermal emf $E_{1}$ is measured using an ideal voltmeter betw...
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Mar 20, 2022
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140
GATE IN 2022 | Question: 10
The resistance of a pure copper wire of length $10 \; \text{cm}$ and diameter $1 \; \text{mm}$ is to be measured. The most suitable method from amongst the choices given below is _________ Two wire method Three wire method Four wire method Ellipsometry
The resistance of a pure copper wire of length $10 \; \text{cm}$ and diameter $1 \; \text{mm}$ is to be measured. The most suitable method from amongst the choices given ...
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141
GATE IN 2022 | Question: 11
The logic block shown has an output $F$ given by ________ $A + B$ $A \cdot \overline{B}$ $A + \overline{B}$ $\overline{B}$
The logic block shown has an output $F$ given by ________$A + B$$A \cdot \overline{B}$$A + \overline{B}$$\overline{B}$
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142
GATE IN 2022 | Question: 12
In which of the following bridge(s) is the balancing condition frequency-independent? Maxwell bridge Wien bridge Schering bridge Wheatstone bridge
In which of the following bridge(s) is the balancing condition frequency-independent?Maxwell bridgeWien bridgeSchering bridgeWheatstone bridge
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143
GATE IN 2022 | Question: 13
The output $\text{F}$ of the digital circuit shown can be written in the form(s) __________ $\overline{A \cdot B}$ $\overline{A} + \overline{B}$ $\overline{A+B}$ $\overline{A} \cdot \overline{B}$
The output $\text{F}$ of the digital circuit shown can be written in the form(s) __________$\overline{A \cdot B}$$\overline{A} + \overline{B}$$\overline{A+B}$$\overline{A...
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144
GATE IN 2022 | Question: 14
Given $\text{M} = \begin{bmatrix} 2 & 3 & 7 \\ 6 & 4 & 7 \\ 4 & 6 & 14 \end{bmatrix},$ Which of the following statement(s) is/are correct? The rank of $\text{M}$ is $2$ The rank of $\text{M}$ is $3$ The rows of $\text{M}$ are linearly independent The determinant of $\text{M}$ is $0$
Given $\text{M} = \begin{bmatrix} 2 & 3 & 7 \\ 6 & 4 & 7 \\ 4 & 6 & 14 \end{bmatrix},$ Which of the following statement(s) is/are correct?The rank of $\text{M}$ is $2$The...
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145
GATE IN 2022 | Question: 15
An analog-to-digital converter with resolution $0.01 \; \text{V}$ converts analog signals between $0 \; \text{V}$ to $+10 \; \text{V}$ to an unsigned binary output. The minimum number of bits (in integer) in the output is _________
An analog-to-digital converter with resolution $0.01 \; \text{V}$ converts analog signals between $0 \; \text{V}$ to $+10 \; \text{V}$ to an unsigned binary output. The m...
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146
GATE IN 2022 | Question: 16
Consider $24$ voice signals being transmitted without latency using time-division multiplexing. If each signal is sampled at $12 \; \text{kHz}$ and represented by an $8$-bit word, the bit-duration (in microseconds) is __________ (round off to two decimal places)
Consider $24$ voice signals being transmitted without latency using time-division multiplexing. If each signal is sampled at $12 \; \text{kHz}$ and represented by an $8$-...
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147
GATE IN 2022 | Question: 17
A photodiode is made of a semiconductor with a bandgap of $1.42 \; \text{eV}.$ Given that Plank’s constant is $6.626 \times 10^{-34} \; \text{Js,}$ the speed of light in vacuum is $3 \times 10^{8} \; \text{m/s,}$ and $1 \; \text{eV} = 1.6 \times 10^{-19} \; \text{J,}$ the cut-off wavelength (in nanometers) of the photodiode is _________ (round off to one decimal place)
A photodiode is made of a semiconductor with a bandgap of $1.42 \; \text{eV}.$ Given that Plank’s constant is $6.626 \times 10^{-34} \; \text{Js,}$ the speed of light i...
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148
GATE IN 2022 | Question: 18
The global minimum of $x^{3} e^{-|x|}$ for $x \in (-\infty, \infty)$ occurs at $x = $ _________ (round off to one decimal place)
The global minimum of $x^{3} e^{-|x|}$ for $x \in (-\infty, \infty)$ occurs at $x = $ _________ (round off to one decimal place)
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149
GATE IN 2022 | Question: 19
A $\text{440 V, 8 kW, 4-pole, 50 Hz,}$ star-connected induction motor has a full load slip of $0.04.$ The rotor speed (in rpm) at full load is ________ (round off to one decimal place)
A $\text{440 V, 8 kW, 4-pole, 50 Hz,}$ star-connected induction motor has a full load slip of $0.04.$ The rotor speed (in rpm) at full load is ________ (round off to one ...
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150
GATE IN 2022 | Question: 20
The transfer function of a system is: $\frac{(s+1)(s+3)}{(s+5)(s+7)(s+9)}$ In the state-space representation of the system, the minimum number of state variables (in integer) necessary is _________
The transfer function of a system is:$$\frac{(s+1)(s+3)}{(s+5)(s+7)(s+9)}$$In the state-space representation of the system, the minimum number of state variables (in inte...
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151
GATE IN 2022 | Question: 21
A Zener diode is used as a $4 \; \text{V}$ voltage regulator in the circuit shown. Given that the diode requires a minimum current of $4 \; \text{mA}$ for voltage regulation, the maximum current (in milliamperes) permitted to flow through the load $R_{L}$ is __________ (round off to one decimal place)
A Zener diode is used as a $4 \; \text{V}$ voltage regulator in the circuit shown. Given that the diode requires a minimum current of $4 \; \text{mA}$ for voltage regulat...
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152
GATE IN 2022 | Question: 22
A bag contains six red balls and four blue balls. If three balls are drawn in succession without replacement, the probability that the second and third balls drawn are red is ____________ (round off to two decimal places)
A bag contains six red balls and four blue balls. If three balls are drawn in succession without replacement, the probability that the second and third balls drawn are re...
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153
GATE IN 2022 | Question: 23
In the bandpass filter circuit shown, $R_{0} = 50\; \Omega, L_{0} = 1 \; \text{mH,} \; C_{0} = 10 \; \text{nF.}$ The $\text{Q}$ factor of the filter is _________ (round off to two decimal places)
In the bandpass filter circuit shown, $R_{0} = 50\; \Omega, L_{0} = 1 \; \text{mH,} \; C_{0} = 10 \; \text{nF.}$ The $\text{Q}$ factor of the filter is _________ (round o...
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154
GATE IN 2022 | Question: 24
The Newton-Raphson method is applied to determine the solution of $f(x) = 0$ where $f(x) = x – \cos (x).$ If the initial guess of the solution is $x_{0} = 0,$ the value of the next approximation $x_{1}$ is ________ (round off to two decimal places)
The Newton-Raphson method is applied to determine the solution of $f(x) = 0$ where $f(x) = x – \cos (x).$ If the initial guess of the solution is $x_{0} = 0,$ the value...
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155
GATE IN 2022 | Question: 25
An $\text{OPAMP}$ has a gain of $10^{4},$ an input impedance of $10 \; \text{M} \Omega$ and an output impedance of $100 \; \Omega.$ The $\text{OPAMP}$ is used in unity-gain feedback configuration in a voltage buffer circuit. The closed-loop output impedance of the $\text{OPAMP}$ (in milliohms) in the circuit is ___________ (round off to one decimal place)
An $\text{OPAMP}$ has a gain of $10^{4},$ an input impedance of $10 \; \text{M} \Omega$ and an output impedance of $100 \; \Omega.$ The $\text{OPAMP}$ is used in unity-g...
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156
GATE IN 2022 | Question: 26
A signal $V_{in} (t)$ shown is applied from $t = 0 \; \text{ms}$ to $t = 6 \; \text{ms}$ to the circuit shown. Given the initial voltage across the capacitor is $0.3 \; \text{V},$ and that the diode is ideal, the open circuit voltage $V_{out}(t)$ at $t = 5 \; \text{ms}$ is ___________ $0.3 \; \text{V}$ $0.6 \; \text{V}$ $0.7 \; \text{V}$ $1.0 \; \text{V}$
A signal $V_{in} (t)$ shown is applied from $t = 0 \; \text{ms}$ to $t = 6 \; \text{ms}$ to the circuit shown. Given the initial voltage across the capacitor is $0.3 \; \...
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157
GATE IN 2022 | Question: 27
The signal flow graph of a system is shown. The expression for $Y(s)/X(s)$ is ___________ $\frac{2G_{1}(s) G_{2}(s) + 2G_{1}(s) G_{3}(s)} {1 + G_{2}(s) + G_{3}(s)}$ $2 + G_{1}(s) + G_{3}(s) + \frac{G_{2}(s)}{1 + G_{2}(s)}$ $ G_{1}(s) + G_{3}(s) - \frac{G_{2}(s)}{2 + G_{2}(s)}$ $\frac{2G_{1}(s) G_{2}(s) + 2G_{1}(s) G_{3}(s) – G_{1}(s)} {1 + G_{2}(s) + G_{3}(s)}$
The signal flow graph of a system is shown. The expression for $Y(s)/X(s)$ is ___________ $\frac{2G_{1}(s) G_{2}(s) + 2G_{1}(s) G_{3}(s)} {1 + G_{2}(s) + G_{3}(s)}$$2 + G...
Lakshman Bhaiya
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Lakshman Bhaiya
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Mar 20, 2022
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158
GATE IN 2022 | Question: 28
Consider the transfer function $H_{c}(S) = \frac{1}{(s+1)(s+3)}$ Bilinear transformation with a sampling period of $0.1 \; \text{s}$ is employed to obtain the discrete-time transfer function $H_{d}(z).$ Then $H_{d}(z)$ is __________ $\frac{(1+z^{-1})^{2}} {(19-21z^{-1}) (23-17z^{-1})}$ $\frac{(1-z^{-1})^{2}} {(21-19z^{-1}) (17-23z^{-1})}$ $\frac{(1+z^{-1})^{2}} {(21-19z^{-1}) (23-17z^{-1})}$ $\frac{(1+z^{-1})^{2}} {(21-19z^{-1}) (17-23z^{-1})}$
Consider the transfer function$$H_{c}(S) = \frac{1}{(s+1)(s+3)}$$Bilinear transformation with a sampling period of $0.1 \; \text{s}$ is employed to obtain the discrete-ti...
Lakshman Bhaiya
2.4k
points
Lakshman Bhaiya
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Mar 20, 2022
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159
GATE IN 2022 | Question: 29
A car is moving collinearly with a laser beam emitted by a transceiver. A laser pulse emitted at $t=0 \; \text{s}$ is received back by the transceiver $100 \; \text{ns}$ (nanoseconds) later after reflection from the car. A second pulse emitted at $t=0.1 \; \text{s}$ is received back $90 \; \text{ns}$ ... $108 \; \text{kmph,}$ moving towards the transceiver $54 \; \text{kmph,}$ moving away from the transceiver $108 \; \text{kmph,}$ moving away from the transceiver
A car is moving collinearly with a laser beam emitted by a transceiver. A laser pulse emitted at $t=0 \; \text{s}$ is received back by the transceiver $100 \; \text{ns}$ ...
Lakshman Bhaiya
2.4k
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Lakshman Bhaiya
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Mar 20, 2022
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160
GATE IN 2022 | Question: 30
The signal $x(t) = (t-1)^{2}u(t-1),$ where $u(t)$ is the unit-step function, has the Laplace transform $X(s).$ The value of $X(1)$ is ________ $\frac{1}{e}$ $\frac{2}{e}$ $2e$ $e^{2}$
The signal $x(t) = (t-1)^{2}u(t-1),$ where $u(t)$ is the unit-step function, has the Laplace transform $X(s).$ The value of $X(1)$ is ________$\frac{1}{e}$$\frac{2}{e}$$2...
Lakshman Bhaiya
2.4k
points
Lakshman Bhaiya
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Mar 20, 2022
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