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41
GATE IN 2021 | Question: 31
Boolean function $\text{F}$ of three variable $\text{X, Y,}$ and $\text{Z}$ ... $F\left ( X, Y, Z \right )={X}' {Z}' + Y {Z}'$ $F\left ( X, Y, Z \right )={X}' {Y}' Z + XYZ$
Boolean function $\text{F}$ of three variable $\text{X, Y,}$ and $\text{Z}$ is given as$F\left ( X, Y, Z \right )=\left ( {X}' + Y + Z \right )\cdot \left ( X + {Y}' + {Z...
Arjun
2.9k
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Arjun
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Feb 19, 2021
Digital Electronics
gatein-2021
digital-electronics
boolean-algebra
boolean-functions
products-of-sum-form
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42
GATE IN 2021 | Question: 32
A $10$ $^1/_2$ digit Counter-timer is set in the 'frequency mode' of operation (with $T_{s}=1 s$). For a specific input, the reading obtained is $1000$. Without disconnecting this input, the Counter-timer is changed to operate in the 'Period mode' and the range selected is microseconds ($\mu s$, with $f_{s} = 1\text{ MHz}$). The counter will then display $0$ $10$ $100$ $1000$
A $10$ $^1/_2$ digit Counter-timer is set in the 'frequency mode' of operation (with $T_{s}=1 s$). For a specific input, the reading obtained is $1000$. Without disconnec...
Arjun
2.9k
points
Arjun
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Feb 19, 2021
Digital Electronics
gatein-2021
digital-electronics
sequential-circuit
counters
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43
GATE IN 2021 | Question: 33
A $\text{J}$-type thermocouple has an output voltage $V_{\theta }=\left ( 13650+50\: \theta _{x} \right ) \mu \;V$, where $\theta _{x}$ is the junction temperature in Celsius ($^{\circ}C$ ... $V_{o}$ of the instrumentation amplifier in millivolt is $\text{98 mV}$ $\text{99 mV}$ $\text{100 mV}$ $\text{101 mV}$
A $\text{J}$-type thermocouple has an output voltage $V_{\theta }=\left ( 13650+50\: \theta _{x} \right ) \mu \;V$, where $\theta _{x}$ is the junction temperature in Cel...
Arjun
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Arjun
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Feb 19, 2021
Others
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44
GATE IN 2021 | Question: 34
A laser pulse is sent from ground level to the bottom of a concrete water tank at normal incidence. The tank is filled with water up to $\text{2 m}$ below the ground level. The reflected pulse from the bottom of the tank travels back and hits the detector. The round-trip time elapsed between sending the laser pulse, the pulse hitting the bottom of the tank ... $n_{\text{water}}=1.3$ and velocity of light in air $c_{\text{air}}=3 \times 10^{8}\: m/s$) $9$ $10$ $11$ $12$
A laser pulse is sent from ground level to the bottom of a concrete water tank at normal incidence. The tank is filled with water up to $\text{2 m}$ below the ground leve...
Arjun
2.9k
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Arjun
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Feb 19, 2021
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45
GATE IN 2021 | Question: 35
A $4 \times 1$ multiplexer with two selector lines is used to realize a Boolean function $\text{F}$ having four Boolean variables $\text{X, Y, Z}$ and $\text{W}$ as shown below. $S_{0}$ and $S_{1}$ denote the least significant bit $\text{(LSB)}$ and most significant bit $\text{(MSB)}$ ... $F\left ( X,Y,Z,W \right )=\sum \text{m}\left ( 1,3,7,9,15 \right )$
A $4 \times 1$ multiplexer with two selector lines is used to realize a Boolean function $\text{F}$ having four Boolean variables $\text{X, Y, Z}$ and $\text{W}$ as shown...
Arjun
2.9k
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Arjun
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Feb 19, 2021
Digital Electronics
gatein-2021
digital-electronics
combinational-circuits
multiplexers
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46
GATE IN 2021 | Question: 36
Given below is the diagram of a synchronous sequential circuit with one $\text{J-K}$ flip-flop and one $\text{T}$ flip-flop with their outputs denotes as $\text{A}$ and $\text{B}$ ... $00\rightarrow 10\rightarrow 01\rightarrow 11\rightarrow 00 \cdots$ $00\rightarrow 10\rightarrow 11\rightarrow 01\rightarrow 00 \cdots$ $00\rightarrow 01\rightarrow 11\rightarrow 00 \cdots$
Given below is the diagram of a synchronous sequential circuit with one $\text{J-K}$ flip-flop and one $\text{T}$ flip-flop with their outputs denotes as $\text{A}$ and $...
Arjun
2.9k
points
Arjun
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Feb 19, 2021
Digital Electronics
gatein-2021
digital-electronics
sequential-circuit
counters
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47
GATE IN 2021 | Question: 37
Consider that $\text{X}$ and $\text{Y}$ are independent continuous valued random variables with uniform $\text{PDF}$ given by $X\sim U\left ( 2,3 \right )$ and $Y\sim U\left ( 1,4 \right )$. Then $P\left ( Y\leq X \right )$ is equal to __________________ (rounded off to two decimal places).
Consider that $\text{X}$ and $\text{Y}$ are independent continuous valued random variables with uniform $\text{PDF}$ given by $X\sim U\left ( 2,3 \right )$ and $Y\sim U\l...
Arjun
2.9k
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Arjun
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Feb 19, 2021
Probability and Statistics
gatein-2021
numerical-answers
probability-and-statistics
probability
probability-density-function
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48
GATE IN 2021 | Question: 38
Given $A=\begin{pmatrix} 2 & 5\\ 0 & 3 \end{pmatrix}$. The value of the determinant $\left | A^{4}-5A^{3}+6A^{2}+2I \right |=$ _______________.
Given $A=\begin{pmatrix} 2 & 5\\ 0 & 3 \end{pmatrix}$. The value of the determinant $\left | A^{4}-5A^{3}+6A^{2}+2I \right |=$ _______________.
Arjun
2.9k
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Arjun
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Feb 19, 2021
Linear Algebra
gatein-2021
numerical-answers
linear-algebra
matrices
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49
GATE IN 2021 | Question: 39
The figure below shows an electrically conductive bar of square cross-section resting on a plane surface. The bar of mass of $\text{1 kg}$ has a depth of $\text{0.5 m}$ along the $\text{y}$ direction. The coefficient of friction between the bar and the surface is $0.1$. Assume the acceleration due to gravity to be ... onto the bar and is maintained. When the bar has moved by $\text{1 m}$, its speed in metre per second is ___________ (rounded off to one decimal place).
The figure below shows an electrically conductive bar of square cross-section resting on a plane surface. The bar of mass of $\text{1 kg}$ has a depth of $\text{0.5 m}$ a...
Arjun
2.9k
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Arjun
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Others
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numerical-answers
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50
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 ...
Arjun
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Arjun
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numerical-answers
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51
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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Arjun
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numerical-answers
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52
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...
Arjun
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Arjun
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numerical-answers
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53
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...
Arjun
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Arjun
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numerical-answers
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54
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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Arjun
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Others
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numerical-answers
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55
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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Arjun
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numerical-answers
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56
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...
Arjun
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Arjun
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57
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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Arjun
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numerical-answers
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58
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 ________...
Arjun
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Arjun
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Feb 19, 2021
Others
gatein-2021
numerical-answers
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59
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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60
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...
Arjun
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Arjun
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numerical-answers
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61
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...
Arjun
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Arjun
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Feb 19, 2021
Others
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numerical-answers
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62
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...
Arjun
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Arjun
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Feb 19, 2021
Others
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numerical-answers
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63
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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Arjun
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64
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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65
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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Arjun
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