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41
GATE IN 2024 | Question: 41
In the figure shown, $\mathrm{R}=4.5 \mathrm{k} \Omega, \Delta \mathrm{R}=1.5 \mathrm{k} \Omega$, and $\mathrm{INA}$ is assumed to be ideal. The equivalent resistance between $\mathrm{A}$ and $\mathrm{B}$ is $\mathrm{k} \Omega$ (rounded off to nearest integer).
In the figure shown, $\mathrm{R}=4.5 \mathrm{k} \Omega, \Delta \mathrm{R}=1.5 \mathrm{k} \Omega$, and $\mathrm{INA}$ is assumed to be ideal. The equivalent resistance bet...
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Feb 16
Others
gatein-2024
numerical-answers
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42
GATE IN 2024 | Question: 42
Consider the capacitive sensor circuit and its output voltage shown in the figure. The circuit is switched $\mathrm{ON}$ at $\mathrm{t}=0$. Assuming the opamp to be ideal, the frequency of the output voltage $\mathrm{V}_{0}$ is $\mathrm{kHz}$ (rounded off to two decimal places).
Consider the capacitive sensor circuit and its output voltage shown in the figure. The circuit is switched $\mathrm{ON}$ at $\mathrm{t}=0$. Assuming the opamp to be ideal...
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Feb 16
Others
gatein-2024
numerical-answers
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43
GATE IN 2024 | Question: 43
The 4-point DFTs of two sequences $x[n]$ and $y[n]$ are $X[k]=[1,-j, 1, j]$ and $Y[k]=[1,3 j, 1,-3 j]$, respectively. Assuming $z[n]$ represents the 4 -point circular convolution of $x[n]$ and $y[n]$, the value of $z[0]$ is (rounded off to nearest integer). Note: The DFT of a $N$-point sequence $x[n]$ is defined as \[ X[k]=\sum_{n=0}^{N-1} x[n] e^{\frac{-j 2 \pi n k}{N}} \]
The 4-point DFTs of two sequences $x[n]$ and $y[n]$ are $X[k]=[1,-j, 1, j]$ and $Y[k]=[1,3 j, 1,-3 j]$, respectively. Assuming $z[n]$ represents the 4 -point circular con...
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Feb 16
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gatein-2024
numerical-answers
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44
GATE IN 2024 | Question: 44
Consider the figure shown. For zero deflection in the galvanometer, the required value of resistor $R_{x}$ is $\Omega$ (rounded off to nearest integer).
Consider the figure shown. For zero deflection in the galvanometer, the required value of resistor $R_{x}$ is $\Omega$ (rounded off to nearest integer).
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Feb 16
Others
gatein-2024
numerical-answers
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45
GATE IN 2024 | Question: 45
Consider a unity negative feedback system with its open-loop pole-zero map as shown in the figure. If the point $s=j \alpha, \alpha>0$, lies on the root locus, the value of $\alpha$ is (rounded off to nearest integer). Note: The poles are marked with $x$ in the figure.
Consider a unity negative feedback system with its open-loop pole-zero map as shown in the figure. If the point $s=j \alpha, \alpha>0$, lies on the root locus, the value ...
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Feb 16
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gatein-2024
numerical-answers
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46
GATE IN 2024 | Question: 46
A shielded cable with $\mathrm{C}_{\text {stray }}=20 \mathrm{pF}$ and $\mathrm{R}_{\text {wire }}=10 \Omega$ is used to connect the inductive sensors as shown in the figure. The RMS value of $V_{\text {out }}$ is $\mathrm{V}$ (rounded off to two decimal places). Note: Assume all components are ideal, and sensors are not magnetically coupled.
A shielded cable with $\mathrm{C}_{\text {stray }}=20 \mathrm{pF}$ and $\mathrm{R}_{\text {wire }}=10 \Omega$ is used to connect the inductive sensors as shown in the fig...
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Feb 16
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gatein-2024
numerical-answers
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47
GATE IN 2024 | Question: 47
In the figure shown, the diode current is given by $I_{D}=I_{S} e^{\frac{\alpha V_{D}}{T}} \cdot V_{D}$ is the diode voltage in volts, $T$ is the absolute temperature in Kelvin, $\alpha=1.16 \times 10^{4} \mathrm{~K} / \mathrm{V}$, and $I_{S}=10^{-15} \mathrm{~A}$ is the saturation ... independent. The change in the output voltage $\left(\mathrm{V}_{\text {out }}\right.$ ) per Kelvin change in temperature is $\mathrm{mV}$ (rounded off to one decimal place).
In the figure shown, the diode current is given by $I_{D}=I_{S} e^{\frac{\alpha V_{D}}{T}} \cdot V_{D}$ is the diode voltage in volts, $T$ is the absolute temperature in ...
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Feb 16
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48
GATE IN 2024 | Question: 48
An ADC has a full scale voltage of $1.4 \mathrm{~V}$, resolution of $200 \mathrm{mV}$, and produces binary output data. The input signal of the ADC has a bandwidth of $500 \mathrm{MHz}$, and it samples the data at the Nyquist rate. The parallel data output is converted to a serial bit stream using a parallel-to-serial converter. The data rate at the output of the parallel-to-serial converter is Gbps (rounded off to nearest integer).
An ADC has a full scale voltage of $1.4 \mathrm{~V}$, resolution of $200 \mathrm{mV}$, and produces binary output data. The input signal of the ADC has a bandwidth of $50...
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Feb 16
Others
gatein-2024
numerical-answers
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49
GATE IN 2024 | Question: 49
In the circuit shown, assume the opamp is ideal and the initial charge on the capacitor is zero. The output voltage at time $t=2 \mathrm{~ms}$ is $\mathrm{V}$ (rounded off to one decimal place).
In the circuit shown, assume the opamp is ideal and the initial charge on the capacitor is zero. The output voltage at time $t=2 \mathrm{~ms}$ is $\mathrm{V}$ (rounded of...
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Feb 16
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gatein-2024
numerical-answers
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50
GATE IN 2024 | Question: 50
In the figure shown, $\mathrm{Sw}$ is a switch whose position changes from 1 to 0 when $\mathrm{Vc}$ changes from logic HIGH to LOW and vice versa. The bandwidth of the permanent magnet moving coil (PMMC) type voltmeter is $1 \mathrm{~Hz}$ ... $\mathrm{V}$ (rounded off to nearest integer). Note: Assume all components are ideal.
In the figure shown, $\mathrm{Sw}$ is a switch whose position changes from 1 to 0 when $\mathrm{Vc}$ changes from logic HIGH to LOW and vice versa. The bandwidth of the p...
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Feb 16
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gatein-2024
numerical-answers
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51
GATE IN 2024 | Question: 51
A $50 \mathrm{kVA}$ transformer has an efficiency of $95 \%$ at full load and unity power factor. Assume the core losses are negligible. The efficiency of the transformer at $75 \%$ of the full load and 0.8 power factor is $\%$ (rounded off to one decimal place).
A $50 \mathrm{kVA}$ transformer has an efficiency of $95 \%$ at full load and unity power factor. Assume the core losses are negligible. The efficiency of the transformer...
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Feb 16
Others
gatein-2024
numerical-answers
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52
GATE IN 2024 | Question: 52
A three-phase squirrel-cage induction motor has a starting torque of $100 \%$ of the full load torque and a maximum torque of $300 \%$ of the full load torque. Neglecting the stator impedance, the slip at the maximum torque is $\%$ (rounded off to two decimal places).
A three-phase squirrel-cage induction motor has a starting torque of $100 \%$ of the full load torque and a maximum torque of $300 \%$ of the full load torque. Neglecting...
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Feb 16
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53
GATE IN 2024 | Question: 53
Two magnetically coupled coils, when connected in series-aiding configuration, have a total inductance of $500 \mathrm{mH}$. When connected in series-opposing configuration, the coils have a total inductance of $300 \mathrm{mH}$. If the self-inductance of both the coils are equal, then the coupling coefficient is (rounded off to two decimal places).
Two magnetically coupled coils, when connected in series-aiding configuration, have a total inductance of $500 \mathrm{mH}$. When connected in series-opposing configurati...
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Feb 16
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54
GATE IN 2024 | Question: 54
The solution of an ordinary differential equation $y^{\prime \prime \prime}+3 y^{\prime \prime}+3 y^{\prime}+y=30 e^{-t}$ is \[ y(t)=\left(c_{0}+c_{1} t-c_{2} t^{2}+c_{3} t^{3}\right) e^{-t} \] Given $y(0)=3, y^{\prime}(0)=-3$ and $y^{\prime \prime}(0)=-47$, the value of $\left(c_{0}+c_{1}+c_{2}+c_{3}\right)$ is (rounded off ... $c_{0}, c_{1}, c_{2}, c_{3}$ are constants.
The solution of an ordinary differential equation $y^{\prime \prime \prime}+3 y^{\prime \prime}+3 y^{\prime}+y=30 e^{-t}$ is\[y(t)=\left(c_{0}+c_{1} t-c_{2} t^{2}+c_{3} t...
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Feb 16
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55
GATE IN 2024 | Question: 55
A random variable $X$ has a probability density function \[ f_{X}(x)=\left\{\begin{array}{cc} e^{-x}, & x \geq 0 \\ 0, & \text { otherwise } \end{array}\right. \] The probability of $X>2$ is (rounded off to three decimal places).
A random variable $X$ has a probability density function\[f_{X}(x)=\left\{\begin{array}{cc}e^{-x}, & x \geq 0 \\0, & \text { otherwise }\end{array}\right.\]The probabilit...
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Feb 16
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56
GATE IN 2023 | GA Question: 1
The village was nestled in a green spot, __________ the ocean and the hills. through in at between
The village was nestled in a green spot, __________ the ocean and the hills.throughin atbetween
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May 22, 2023
Verbal Aptitude
gatein-2023
verbal-aptitude
english-grammar
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57
GATE IN 2023 | GA Question: 2
Disagree : Protest: : Agree: __________ (By word meaning) Refuse Pretext Recommend Refute
Disagree : Protest: : Agree: __________(By word meaning)RefusePretextRecommendRefute
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May 22, 2023
Verbal Aptitude
gatein-2023
verbal-aptitude
word-pairs
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58
GATE IN 2023 | GA Question: 3
A 'frabjous' number is defined as a $3$ digit number with all digits odd, and no two adjacent digits being the same. For example, $137$ is a frabjous number, while $133$ is not. How many such frabjous numbers exist? $125$ $720$ $60$ $80$
A 'frabjous' number is defined as a $3$ digit number with all digits odd, and no two adjacent digits being the same. For example, $137$ is a frabjous number, while $133$ ...
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May 22, 2023
Quantitative Aptitude
gatein-2023
quantitative-aptitude
number-theory
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59
GATE IN 2023 | GA Question: 4
Which one among the following statements must be $\text{TRUE}$ about the mean and the median of the scores of all candidates appearing for $\text{GATE }2023?$ The median is at least as large as the mean. The mean is at least as large as the median. At most half the candidates have a score that is larger than the median At most half the candidates have a score that is larger than the mean.
Which one among the following statements must be $\text{TRUE}$ about the mean and the median of the scores of all candidates appearing for $\text{GATE }2023?$The median i...
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May 22, 2023
Quantitative Aptitude
gatein-2023
quantitative-aptitude
statistics
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60
GATE IN 2023 | GA Question: 5
In the given diagram, ovals are marked at different heights $(h)$ of a hill. Which one of the following options $\mathbf{P}, \mathbf{Q}, \mathbf{R}$, and $\mathbf{S}$ depicts the top view of the hill? $\mathbf{P}$ $\mathbf{Q}$ $\mathbf{R}$ $\mathbf{S}$
In the given diagram, ovals are marked at different heights $(h)$ of a hill. Which one of the following options $\mathbf{P}, \mathbf{Q}, \mathbf{R}$, and $\mathbf{S}$ dep...
asked
May 22, 2023
Quantitative Aptitude
gatein-2023
quantitative-aptitude
curves
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61
GATE IN 2023 | GA Question: 6
Residency is a famous housing complex with many well-established individuals among its residents. A recent survey conducted among the residents of the complex revealed that all of those residents who are well established in their respective fields happen to be academicians. The survey also revealed that most of ... are residents of the complex who are well established in their fields. Some academicians residing in the complex are well established in their fields.
Residency is a famous housing complex with many well-established individuals among its residents. A recent survey conducted among the residents of the complex revealed th...
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May 22, 2023
Analytical Aptitude
gatein-2023
analytical-aptitude
logical-reasoning
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62
GATE IN 2023 | GA Question: 7
Ankita has to climb $5$ stairs starting at the ground, while respecting the following rules: At any stage, Ankita can move either one or two stairs up. At any stage, Ankita cannot move to a lower step. Let $F(N)$ denote the number of possible ways in which Ankita can reach the $N^{\text {th}}$ stair. For example, $F(1)=1, F(2)=2, F(3)=3$. The value of $F(5)$ is__________. $8$ $7$ $6$ $5$
Ankita has to climb $5$ stairs starting at the ground, while respecting the following rules:At any stage, Ankita can move either one or two stairs up.At any stage, Ankita...
asked
May 22, 2023
Quantitative Aptitude
gatein-2023
quantitative-aptitude
functions
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63
GATE IN 2023 | GA Question: 8
The information contained in DNA is used to synthesize proteins that are necessary for the functioning of life. DNA is composed of four nucleotides: Adenine (A), Thymine (T), Cytosine (C), and Guanine (G). The information contained in DNA can then be thought of as a sequence of these four nucleotides: A, T, C, and G. DNA has coding ... of proteins. The function of about $98 \%$ of human DNA is not understood. only (i) only (ii) both (i) and (ii) neither (i) nor (ii)
The information contained in DNA is used to synthesize proteins that are necessary for the functioning of life. DNA is composed of four nucleotides: Adenine (A), Thymine ...
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May 22, 2023
Analytical Aptitude
gatein-2023
analytical-aptitude
logical-reasoning
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64
GATE IN 2023 | GA Question: 9
Which one of the given figures $\text{P, Q, R}$ and $\text{S}$ represents the graph of the following function? $f(x)=|| x+2|-| x-1||$ $\text{P}$ $\text{Q}$ $\text{R}$ $\text{S}$
Which one of the given figures $\text{P, Q, R}$ and $\text{S}$ represents the graph of the following function?$$f(x)=|| x+2|-| x-1||$$ $\text{P}$$\text{Q}$$\text{R}$$\te...
asked
May 22, 2023
Quantitative Aptitude
gatein-2023
quantitative-aptitude
absolute-value
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65
GATE IN 2023 | GA Question: 10
An opaque cylinder (shown below) is suspended in the path of a parallel beam of light, such that its shadow is cast on a screen oriented perpendicular to the direction of...
asked
May 22, 2023
Spatial Aptitude
gatein-2023
spatial-aptitude
figure-in-three-dimension
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66
GATE IN 2023 | Question: 1
Choose solution set $S$ corresponding to the systems of two equations $\begin{array}{r} x-2 y+z=0 \\ x-z=0 \end{array}$ Note: $\mathscr{R}$ denotes the set of real numbers $S=\left\{\alpha\left(\begin{array}{l}1 \\ 1 \\ 1\end{array}\right) \mid \alpha \in \mathscr{R}\right\}$ ... $S=\left\{\alpha\left(\begin{array}{l}1 \\ 0 \\ 1\end{array}\right) \mid \alpha \in \mathscr{R}\right\}$
Choose solution set $S$ corresponding to the systems of two equations$$\begin{array}{r}x-2 y+z=0 \\x-z=0\end{array}$$Note: $\mathscr{R}$ denotes the set of real numbers$S...
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May 22, 2023
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67
GATE IN 2023 | Question: 2
Inductance of a coil is measured as $10 ~ \mathrm{mH}$, using an LCR meter, when no other objects are present near the coil. The LCR meter uses a sinusoidal excitation at $10 ~ \mathrm{kHz}$. If a pure copper sheet is brought near the coil, the same LCR meter will read ________. less than $10 ~ \mathrm{mH}$ $10~ \mathrm{mH}$ more than $10 ~\mathrm{mH}$ less than $10~ \mathrm{mH}$ initially and then stabilizes to more than $10~ \mathrm{mH}$
Inductance of a coil is measured as $10 ~ \mathrm{mH}$, using an LCR meter, when no other objects are present near the coil. The LCR meter uses a sinusoidal excitation at...
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May 22, 2023
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68
GATE IN 2023 | Question: 3
Which of the following flow meters offers the lowest resistance to the flow? Turbine flow meter Orifice flow meter* Venturi meter Electromagnetic flow meter
Which of the following flow meters offers the lowest resistance to the flow? Turbine flow meter Orifice flow meter* Venturi meter Electromagnetic flow meter
asked
May 22, 2023
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69
GATE IN 2023 | Question: 4
Pair the quantities $\text{(p)}$ to $\text{(s)}$ with the measuring devices $\text{(i)}$ to $\text{(iv)}$ ... $\text{(i) - (q), (ii) - (s), (iii) - (p), (iv) - (r)}$
Pair the quantities $\text{(p)}$ to $\text{(s)}$ with the measuring devices $\text{(i)}$ to $\text{(iv)}$.$\begin{array}{|l|l|}\hline \text{(i) Linear Variable Differenti...
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May 22, 2023
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70
GATE IN 2023 | Question: 5
Capacitance ' $\text{C}$ ' of a parallel plate structure is calculated as $20 ~ \mathrm{pF}$ using $C=\frac{\varepsilon_0 \varepsilon_r A}{d}$, where $\varepsilon_o$ is the permittivity of free space, $\varepsilon_r$ is the relative permittivity of the dielectric, $A$ is the overlapping area of the electrodes and $d$ is the ... the following readings is likely to be correct? $20.5 ~ \mathrm{pF}$ $20 ~ \mathrm{pF}$ $19.5~ \mathrm{pF}$ $10 ~ \mathrm{pF}$
Capacitance ' $\text{C}$ ' of a parallel plate structure is calculated as $20 ~ \mathrm{pF}$ using $C=\frac{\varepsilon_0 \varepsilon_r A}{d}$, where $\varepsilon_o$ is t...
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May 22, 2023
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71
GATE IN 2023 | Question: 6
The table shows the present state $\mathrm{Q}(\mathrm{t})$, next state $\mathrm{Q}(\mathrm{t}+1)$ ... $\text{T}$ flip-flop $\text{D}$ flip-flop $\text{SR}$ flip-flop $\text{JK}$ flip-flop
The table shows the present state $\mathrm{Q}(\mathrm{t})$, next state $\mathrm{Q}(\mathrm{t}+1)$, and the control input in a flip-flop. Identify the flip-flop.$$\begin{a...
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May 22, 2023
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72
GATE IN 2023 | Question: 7
Match the Exclusive-$\text{OR (XOR)}$ operations $\text{(i)}$ to $\text{(iv)}$ with the results $\text{(p)}$ to $\text{(s),}$ where $X$ ... $\text{(i) - (p), (ii) - (s), (iii) - (q), (iv) - (r)}$ $\text{(i) - (q), (ii) - (p), (iii) - (s), (iv) - (r)}$
Match the Exclusive-$\text{OR (XOR)}$ operations $\text{(i)}$ to $\text{(iv)}$ with the results $\text{(p)}$ to $\text{(s),}$ where $X$ is a Boolean input.$$\begin{array}...
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May 22, 2023
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73
GATE IN 2023 | Question: 8
A light emitting diode $\text{(LED)}$ emits light when it is _________ biased. A photodiode provides maximum sensitivity to light when it is _____________ biased. forward, forward forward, reverse reverse, reverse reverse, forward
A light emitting diode $\text{(LED)}$ emits light when it is _________ biased. A photodiode provides maximum sensitivity to light when it is _____________ biased.forward...
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May 22, 2023
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74
GATE IN 2023 | Question: 9
$F(z)=\frac{1}{1-z}$, when expanded as a power series around $z=2$, would result in $F(z)=\sum_{k=0}^{\infty} a_k(z-2)^k$, with the region of convergence $\text{(ROC) } |z-2|<1$. The coefficients $a_k, k \geq 0$, are given by the expression _____________. $(-1)^k$ $(-1)^{k+1}$ $\left(\frac{1}{2}\right)^k$ $\left(\frac{-1}{2}\right)^{k+1}$
$F(z)=\frac{1}{1-z}$, when expanded as a power series around $z=2$, would result in $F(z)=\sum_{k=0}^{\infty} a_k(z-2)^k$, with the region of convergence $\text{(ROC) } |...
asked
May 22, 2023
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75
GATE IN 2023 | Question: 10
The solution $x(t), t \geq 0$, to the differential equation $\ddot{x}=-k \dot{x}, k>0$ with initial conditions $x(0)=1$ and $\dot{x}(0)=0$ is $x(t)=2 e^{-k t}+2 k t-1$ $x(t)=2 e^{-k t}-1$ $x(t)=1$ $x(t)=2 e^{-k t}-k t-1$
The solution $x(t), t \geq 0$, to the differential equation $\ddot{x}=-k \dot{x}, k>0$ with initial conditions $x(0)=1$ and $\dot{x}(0)=0$ is$x(t)=2 e^{-k t}+2 k t-1$$x(t...
asked
May 22, 2023
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76
GATE IN 2023 | Question: 11
A system has the transfer-function $\frac{Y(s)}{X(s)}=\frac{s-\pi}{s+\pi}$ Let $u(t)$ be the unit-step function. The input $x(t)$ that results in a steady-state output $y(t)=\sin \pi t$ is ____________. $x(t)=\sin (\pi t) u(t)$ $x(t)=\sin \left(\pi t+\frac{\pi}{2}\right) u(t)$ $x(t)=\sin \left(\pi t-\frac{\pi}{2}\right) u(t)$ $x(t)=\cos \left(\pi t+\frac{\pi}{4}\right) u(t)$
A system has the transfer-function$\frac{Y(s)}{X(s)}=\frac{s-\pi}{s+\pi}$Let $u(t)$ be the unit-step function. The input $x(t)$ that results in a steady-state output $y(t...
asked
May 22, 2023
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77
GATE IN 2023 | Question: 12
Choose the fastest logic family among the following: Transistor-Transistor Logic Emitter-Coupled Logic CMOS Logic Resistor-Transistor Logic
Choose the fastest logic family among the following: Transistor-Transistor Logic Emitter-Coupled Logic CMOS LogicResistor-Transistor Logic
asked
May 22, 2023
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78
GATE IN 2023 | Question: 13
What is $\lim _{x \rightarrow 0} f(x)$, where $f(x)=x \sin \frac{1}{x} ?$ $0$ $1$ $\infty$ Limit does not exist
What is $\lim _{x \rightarrow 0} f(x)$, where $f(x)=x \sin \frac{1}{x} ?$$0$$1$$\infty$Limit does not exist
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May 22, 2023
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79
GATE IN 2023 | Question: 14
The number of zeros of the polynomial $P(s)=s^{3}+2 s^{2}+5 s+80$ in the right- half plane is_________.
The number of zeros of the polynomial $P(s)=s^{3}+2 s^{2}+5 s+80$ in the right- half plane is_________.
asked
May 22, 2023
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80
GATE IN 2023 | Question: 15
The number of times the Nyquist plot of $G(s) H(s)=\frac{1}{2} \frac{(s-1)(s-2)}{(s+1)(s+2)}$ encircles the origin is_______________.
The number of times the Nyquist plot of $G(s) H(s)=\frac{1}{2} \frac{(s-1)(s-2)}{(s+1)(s+2)}$ encircles the origin is_______________.
asked
May 22, 2023
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