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201
GATE IN 2021 | Question: 40
A toroid made of $\text{CRGO}$ has an inner diameter of $\text{10 cm}$ and an outer diameter of $\text{14 cm}$. The thickness of the toroid is $\text{2 cm}$. $200$ turns of copper wire is wound on the core $\mu_{o} = 4\pi\times10^{-7}$ $\text{H/m}$ and $\mu_{R}$ of $\text{CRGO}$ is $3000$. When a current of $\text{5 mA}$ flows through the winding, the flux density in the core in millitesla is ______________.
A toroid made of $\text{CRGO}$ has an inner diameter of $\text{10 cm}$ and an outer diameter of $\text{14 cm}$. The thickness of the toroid is $\text{2 cm}$. $200$ turns ...
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202
GATE IN 2021 | Question: 41
An air cored coil having a winding resistance of $10\: \Omega$ is connected in series with a variable capacitor $C_{x}$. The series circuit is excited by a $\text{10 V}$ sinusoidal voltage source of angular frequency $1000$ rad/$\text{s}$. As the value of the capacitor is varied, a maximum voltage of $\text{30 V}$ was observed across it. Neglecting skin-effect, the value of the inductance of the coil in millihenry is ___________.
An air cored coil having a winding resistance of $10\: \Omega$ is connected in series with a variable capacitor $C_{x}$. The series circuit is excited by a $\text{10 V}$ ...
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203
GATE IN 2021 | Question: 42
A household fan consumes $\text{60 W}$ and draws a current of $\text{0.3125 A (rms)}$ when connected to a $\text{230 V (rms) ac }$, $\text{50 Hz}$ single phase mains. The reactive power drawn by the fan in $\text{VAr}$ is _______________________ (rounded off to the nearest integer).
A household fan consumes $\text{60 W}$ and draws a current of $\text{0.3125 A (rms)}$ when connected to a $\text{230 V (rms) ac }$, $\text{50 Hz}$ single phase mains. The...
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204
GATE IN 2021 | Question: 43
Given $y\left ( t \right )=e^{-3t}u\left ( t \right )\ast u\left ( t+3 \right )$, where $\ast$ denotes convolution operation. The value of $y\left ( t \right )$ as $t\rightarrow \infty$ is ___________________ (rounded off to two decimal places).
Given $y\left ( t \right )=e^{-3t}u\left ( t \right )\ast u\left ( t+3 \right )$, where $\ast$ denotes convolution operation. The value of $y\left ( t \right )$ as $t\rig...
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205
GATE IN 2021 | Question: 44
The input signal shown below is passed through the filter with the following taps The number of non-zero output samples is ________________.
The input signal shown belowis passed through the filter with the following tapsThe number of non-zero output samples is ________________.
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206
GATE IN 2021 | Question: 45
A sinusoid $\left ( \sqrt{2} \sin t \right ) \: \mu \left ( t \right )$, where $\mu \left ( t \right )$ is the step input, is applied to a system with transfer-function $G\left ( s \right )=\dfrac{1}{s+1}$. The amplitude of the steady state output is __________.
A sinusoid $\left ( \sqrt{2} \sin t \right ) \: \mu \left ( t \right )$, where $\mu \left ( t \right )$ is the step input, is applied to a system with transfer-function $...
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207
GATE IN 2021 | Question: 46
Consider a system with transfer-function $G\left ( s \right )=\dfrac{2}{s+1}$. A unit step function $\mu \left ( t \right )$ is applied to the system, which results in an output $y\left ( t \right )$. If $e\left ( t \right )=y\left ( t \right )-\mu \left ( t \right ),$ then $ \lim\limits_{t\rightarrow \infty }e\left ( t \right )$ is ___________________.
Consider a system with transfer-function $G\left ( s \right )=\dfrac{2}{s+1}$. A unit step function $\mu \left ( t \right )$ is applied to the system, which results in an...
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208
GATE IN 2021 | Question: 47
The circuit shown below uses an ideal $\text{OpAmp}$. Output $V_{O}$ in volt is ____________ (rounded off to one decimal place).
The circuit shown below uses an ideal $\text{OpAmp}$. Output $V_{O}$ in volt is ____________ (rounded off to one decimal place).
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209
GATE IN 2021 | Question: 48
All the transistors used in the circuit are matched and have a current gain $\beta$ of $20$. Neglecting the Early effect, the current $I_{O4}$ in milliamphere is ____________.
All the transistors used in the circuit are matched and have a current gain $\beta$ of $20$. Neglecting the Early effect, the current $I_{O4}$ in milliamphere is ________...
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210
GATE IN 2021 | Question: 49
The power in a $\text{400 V}$ ($\text{rms}$, line-line) three-phase, three-wire $\text{RYB}$ sequence system is measured using the two wattmetters, as shown. The $\text{R}$-line current is $5\angle 60^\circ \:A$. Wattmeter $W_{1}$ in the $\text{R}$-line will read (in watt) ____________.
The power in a $\text{400 V}$ ($\text{rms}$, line-line) three-phase, three-wire $\text{RYB}$ sequence system is measured using the two wattmetters, as shown. The $\text{R...
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211
GATE IN 2021 | Question: 50
A $3$ $^1/_2$ digit, rectifier type digital meter is set to read in its $\text{2000 V}$ range. A symmetrical square wave of frequency $\text{50 Hz}$ and amplitude $\pm 100 \:V$ is measured using the meter. The meter will read ___________.
A $3$ $^1/_2$ digit, rectifier type digital meter is set to read in its $\text{2000 V}$ range. A symmetrical square wave of frequency $\text{50 Hz}$ and amplitude $\pm 10...
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212
GATE IN 2021 | Question: 51
A bar primary current transformer of rating $\text{1000/1 A}$, $\text{5VA}$, $\text{UPF}$ has $995$ secondary turns. It exhibits zero ratio error and phase of $30$ minutes at $\text{1000 A}$ with rated burden. The watt loss component of the primary excitation current in ampere is _______________ (rounded off to one decimal place).
A bar primary current transformer of rating $\text{1000/1 A}$, $\text{5VA}$, $\text{UPF}$ has $995$ secondary turns. It exhibits zero ratio error and phase of $30$ minute...
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213
GATE IN 2021 | Question: 52
In the bridge circuit shown, the voltmeter $\text{V}$ showed zero when the value of the resistors are: $R_{1}=100\:\Omega$, $R_{2}=110\:\Omega$, and $R_{3}=90\:\Omega$. If $\left ( R_{1}/R_{2} \right )=\left ( R_{A}/R_{B} \right )$, the value of $R_{4}$ is ohm is ________.
In the bridge circuit shown, the voltmeter $\text{V}$ showed zero when the value of the resistors are: $R_{1}=100\:\Omega$, $R_{2}=110\:\Omega$, and $R_{3}=90\:\Omega$. I...
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214
GATE IN 2021 | Question: 53
For the full bridge made of linear strain gages with gage factor $2$ as shown in the diagram, $R_{1}=R_{2}=R_{3}=R_{4}=100 \:\Omega$ at $0^{\circ}C$ and strain is $0$. The temperature coefficient of resistance of the strain gages used is $0.005\: per\: ^{\circ}C$. All strain gages are made of ... temperature. While measuring a strain of $0.01$ at a temperature of $50^{\circ}C$, the output $V_{O}$ in millivolt is _______________ (rounded off to two decimal places).
For the full bridge made of linear strain gages with gage factor $2$ as shown in the diagram, $R_{1}=R_{2}=R_{3}=R_{4}=100 \:\Omega$ at $0^{\circ}C$ and strain is $0$. Th...
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215
GATE IN 2021 | Question: 54
A signal having a bandwidth of $\text{5 MHz}$ is transmitted using the Pulse code modulation $\text{(PCM)}$ scheme as follows. The signal is sampled at a rate of $50\%$ above the Nyquist rate and quantized into $256$ levels. The binary pulse rate of the $\text{PCM}$ signal is $\text{M}$bits per second is __________.
A signal having a bandwidth of $\text{5 MHz}$ is transmitted using the Pulse code modulation $\text{(PCM)}$ scheme as follows. The signal is sampled at a rate of $50\%$ a...
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216
GATE IN 2021 | Question: 55
In the figure shown, a large multimode fiber with $n_{\text{core}}=1.5$ and $n_{\text{clad}}=1.2$ is used for sensing. A portion with the cladding removed passes through a liquid with refractive index $n_{\text{liquid}}$. An $\text{LED}$ is used to illuminate the fiber from one end and a paper is placed on ... . The paper shows a spot with radius $\text{1 cm}$. The refractive index $n_{\text{liquid}}$ of the liquid (rounded off to two decimal places) is ______________.
In the figure shown, a large multimode fiber with $n_{\text{core}}=1.5$ and $n_{\text{clad}}=1.2$ is used for sensing. A portion with the cladding removed passes through ...
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217
GATE2020 IN: 21
Assume that the opamp in the circuit shown is ideal. The value of $\frac{V_x}{I_x} (\text{in k}\Omega)$ is ____________.
Assume that the opamp in the circuit shown is ideal.The value of $\frac{V_x}{I_x} (\text{in k}\Omega)$ is ____________.
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218
GATE2020 IN: 22
A sinusoid of $\text{10 kHz}$ is sampled at $\text{15 k samples/s}.$ The resulting signal is passed through an ideal low pass filter $(LPF)$ with cut-off frequency of $\text{25 kHz}$. The maximum frequency component at the output of the $\text{LPF (in kHz)}$ is _________.
A sinusoid of $\text{10 kHz}$ is sampled at $\text{15 k samples/s}.$ The resulting signal is passed through an ideal low pass filter $(LPF)$ with cut-off frequency of $\t...
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GATE2020 IN: 23
A $\text{200 mV}$ full-scale dual-slope analog to digital converter $\text{(DS-ADC)}$ has a reference voltage of $\text{100 mV}$. The first integration time is set as $\text{100 ms.}$ The $\text{DS-ADC}$ is operated in the continuous conversion mode. The conversion time of the $\text{DS-ADC}$ for an input voltage of $\text{123.4 mV (in ms, rounded off to one decimal place)}$ is _____.
A $\text{200 mV}$ full-scale dual-slope analog to digital converter $\text{(DS-ADC)}$ has a reference voltage of $\text{100 mV}$. The first integration time is set as $\t...
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GATE2020 IN: 24
The capacitance $C_x$ of a capacitive type sensor is $(1000x) pF,$ where x is the input to the sensor. As shown in the figure, the sensor is excited by a voltage $\text{10 sin(100}\pi\: t) V$. The other terminal of the sensor is tied to the input of a high input impedance amplifier through a shielded cable, with shield connected ... . The cable capacitance is $\text{100 pF}$. The peak of the voltage $V_A$ at the input of the amplifier when $\text{x=0.1 (in volts)}$ is _________.
The capacitance $C_x$ of a capacitive type sensor is $(1000x) pF,$ where x is the input to the sensor. As shown in the figure, the sensor is excited by a voltage $\text{...
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GATE2020 IN: 25
Two $100\: \Omega$ resistors having tolerance $3\%$ and $4\%$ are connected in series. The effective tolerance of the series combination $\text{(in % rounded off to one decimal place)}$ is ___________.
Two $100\: \Omega$ resistors having tolerance $3\%$ and $4\%$ are connected in series. The effective tolerance of the series combination $\text{(in % rounded off to one d...
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GATE2020 IN: 29
The loop transfer function of a negative feedback system is $G(s)H(s)=\frac{1}{s(s-2)}$. The Nyquist plot for the above system _________. encircles $(-1+j0)$ point once in the clockwise direction encircles $(-1+j0)$ point once in the counterclockwise direction does not encircles $(-1+j0)$ point encircles $(-1+j0)$ point twice in the counterclockwise direction
The loop transfer function of a negative feedback system is $G(s)H(s)=\frac{1}{s(s-2)}$. The Nyquist plot for the above system _________.encircles $(-1+j0)$ point once in...
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223
GATE2020 IN: 30
$I_1,\; I_2\: and \:I_3$ in the figure below are mesh currents. The correct set of mesh equations for these currents, in matrix form, is ____________ $\begin{bmatrix} 3&-1&-2\\-1&3&-1\\-2&-1&3 \end{bmatrix} \begin{bmatrix}I_1\\I_2\\I_3\end{bmatrix}= \begin{bmatrix}V_1\\V_2\\-V_3\end{bmatrix}$ ...
$I_1,\; I_2\: and \:I_3$ in the figure below are mesh currents. The correct set of mesh equations for these currents, in matrix form, is ____________$\begin{bmatrix} 3&-1...
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GATE2020 IN: 33
The rms value of the phasor current $\underline{I}$ in the circuit shown $\text{(in amperes)}$ is _____.
The rms value of the phasor current $\underline{I}$ in the circuit shown $\text{(in amperes)}$ is _____.
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GATE2020 IN: 34
In the circuit shown, the rms value of the voltage across the $ 100 \Omega$ resistor $\text{(in volts)}$ is _________.
In the circuit shown, the rms value of the voltage across the $ 100 \Omega$ resistor $\text{(in volts)}$ is _________.
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GATE2020 IN: 35
Let $g[n]=\left\{ \begin{array}{rcl} 1 & n=0 \\0 &n=\pm 1,\pm 2,\pm 3,\dots \end{array}\right. $ and $h[n]=\left\{ \begin{array}{rcl} 1 & n=0,3,6,9\dots \\0 & otherwise \end{array}\right. $ Consider $y[n]=h[n]\otimes g[n]$, where $\otimes$ denotes the convolution operator. The value of $y[2]$ is ___________
Let $g[n]=\left\{ \begin{array}{rcl} 1 & n=0 \\0 &n=\pm 1,\pm 2,\pm 3,\dots \end{array}\right. $ and $h[n]=\left\{ \begin{array}{rcl} 1 & n=0,3,6,9\dots \\0 & otherwise \...
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GATE2020 IN: 36
The loop transfer function of a negative feedback system is given by $G(s)H(s)=\frac{K}{s(s+2)(s+6)}$, where $K>0$. The value of $K$ at the breakaway point of the root locus for the above system $\text{(rounded off to one decimal place)}$ is __________.
The loop transfer function of a negative feedback system is given by $G(s)H(s)=\frac{K}{s(s+2)(s+6)}$, where $K>0$. The value of $K$ at the breakaway point of the root lo...
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GATE2020 IN: 37
The system shown in Fig.(a) has a time response y(t) to an input $r(t)=10u(t)$ as shown in Fig. (b), $u(t)$ being the unit step input. Both $K, t$ are positive. The gain $K$ of the system is __________
The system shown in Fig.(a) has a time response y(t) to an input $r(t)=10u(t)$ as shown in Fig. (b), $u(t)$ being the unit step input. Both $K, t$ are positive. The gain ...
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GATE2020 IN: 38
Assuming that the opamp used in the circuit shown is ideal, the reading of the $1\;Hz$ bandwidth, permanent magnet moving coil $(PMMC)$ type voltmeter $\text{(in volts)}$ is __________
Assuming that the opamp used in the circuit shown is ideal, the reading of the $1\;Hz$ bandwidth, permanent magnet moving coil $(PMMC)$ type voltmeter $\text{(in volts)}$...
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GATE2020 IN: 39
If the opamps in the circuit shown are ideal and $V_x=0.5\;mV$, the steady state value of $V_\circ \; \text{(in volts, rounded off to two decimal places)}$ is ___________
If the opamps in the circuit shown are ideal and $V_x=0.5\;mV$, the steady state value of $V_\circ \; \text{(in volts, rounded off to two decimal places)}$ is ___________...
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GATE2020 IN: 42
The real power drawn by a balanced load connected to a $\text{400 V, 50 Hz,}$ balanced, symmetrical 3-phase, 3-wire, $RYB$ sequence mains is measured using the two-wattmeter method. Wattmeter $W_1$ is connected in the $R$ line and wattmeter $W_2$ is connected in the $B$ line. The line current is measured as $\frac{1}{\sqrt3}A$. If the wattmeter $W_1$ reads zero, the reading on $W_2$ (in watts) is _______.
The real power drawn by a balanced load connected to a $\text{400 V, 50 Hz,}$ balanced, symmetrical 3-phase, 3-wire, $RYB$ sequence mains is measured using the two-wattme...
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GATE2020 IN: 44
The circuit shown uses ideal opamp powered from a supply $V_{CC}=5 V$. If the charge $q_p$ generated by the piezoelectric sensor is of the form $q_p=0.1 \sin(10000\pi t) \mu C$, the peak detector output after 10 cycles of $q_p$ $\text{(in volts, rounded off to one decimal place)}$ is ______.
The circuit shown uses ideal opamp powered from a supply $V_{CC}=5 V$. If the charge $q_p$ generated by the piezoelectric sensor is of the form $q_p=0.1 \sin(10000\pi t) ...
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GATE2020 IN: 45
A metallic strain gauge of resistance $R_X$ with a gauge factor of 2 is bonded to a structure made of a metal with modulus of elasticity of $200\: GN/m^2$. The value of $R_X$ is $1\:k\Omega$ when no stress is applied. $R_X$ is a part of a quarter bridge with three identical fixed resistors of $1\:k\Omega$ each. The ... of 4 V. The structure is subjected to a stress of $100\:MN/m^2$. Magnitude of the output of the bridge (in mV, rounded off to two decimal places) is _________.
A metallic strain gauge of resistance $R_X$ with a gauge factor of 2 is bonded to a structure made of a metal with modulus of elasticity of $200\: GN/m^2$. The value of $...
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GATE2020 IN: 46
A laser beam of 10 mm beam diameter is focused onto an optical fiber using a thin biconvex lens as shown in the figure. The refractive index of the lens is $1.5$. The refractive indices of the core and cladding of the fiber are $1.55 \;and \;1.54$ respectively. The minimum value of the focal length of the lens to attain he maximum coupling to the fiber $\text{(in mm, rounded off to one decimal place)}$ is ______
A laser beam of 10 mm beam diameter is focused onto an optical fiber using a thin biconvex lens as shown in the figure. The refractive index of the lens is $1.5$. The ref...
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GATE2020 IN: 47
As shown in the figure, a slab of finite thickness $t$ with refractive index $n_2=1.5$, has air $(n_1=1)$ above and below it. Light of free space wavelength $600 nm$ is incident normally from air as shown. For a destructive interference to be observed at R, the minimum value of thickness of the slab t (in nm) is __________.
As shown in the figure, a slab of finite thickness $t$ with refractive index $n_2=1.5$, has air $(n_1=1)$ above and below it. Light of free space wavelength $600 nm$ is i...
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GATE2020 IN: 48
Consider the finite sequence $X=(1,1,1).$ The Inverse Discrete Fourier Transform (IDFT) of X is given as $\text{(x(0), x(1), x(2)).}$ The value of $x(2)$ is _______
Consider the finite sequence $X=(1,1,1).$ The Inverse Discrete Fourier Transform (IDFT) of X is given as $\text{(x(0), x(1), x(2)).}$ The value of $x(2)$ is _______
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GATE2020 IN: 49
A circuit consisting of capacitors, DC voltage source and an amplifier having a voltage gain G=-5 is shown in the figure. The effective capacitance across the nodes A and B $\text{(in $\mu$F, rounded off to one decimal place)}$ is ________
A circuit consisting of capacitors, DC voltage source and an amplifier having a voltage gain G=-5 is shown in the figure. The effective capacitance across the nodes A and...
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GATE2020 IN: 50
Consider the following state variable equations: $\dot{x_1}(t)=x_2(t)$ $\dot{x_2}(t)=-6x_1(t)-5x_2(t)$ The initial conditions are $x_1(0)=0 \:and\: x_2(0)=1.$ At $t=1$ second, the value of $x_2(1)$ $\text{(rounded off to two decimal places)}$ is ___________
Consider the following state variable equations:$\dot{x_1}(t)=x_2(t)$$\dot{x_2}(t)=-6x_1(t)-5x_2(t)$The initial conditions are $x_1(0)=0 \:and\: x_2(0)=1.$ At $t=1$ secon...
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GATE2020 IN: 51
Assume the diodes in the circuit shown are ideal. The current $I_X$ flowing through the $3\: k\Omega$ resistor $\text{(in mA, rounded off to one decimal place)}$ is ___________
Assume the diodes in the circuit shown are ideal. The current $I_X$ flowing through the $3\: k\Omega$ resistor $\text{(in mA, rounded off to one decimal place)}$ is _____...
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GATE2020 IN: 52
A $\text{1000/1 A, 5 VA, UPF}$ bar-primary measuring current transformer has $1000$ secondary turns. The current transformer exhibits a ratio error of $-0.1\%$ and a phase error of $3.438$ minutes when the primary current is $1000 A.$ At this operating condition, the rms value of the magnetization current of the current transformer $\text{(in amperes, rounded off to two decimal places)}$ is _________
A $\text{1000/1 A, 5 VA, UPF}$ bar-primary measuring current transformer has $1000$ secondary turns. The current transformer exhibits a ratio error of $-0.1\%$ and a phas...
soujanyareddy13
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