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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 t...
admin
3.2k
points
asked
May 22, 2023
Measurements
gatein-2023
electrical-circuits-and-machines
numerical-answers
+
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0
0 votes
0
0 answers
GATE IN 2023 | Question: 6
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.$$\begin{a...
admin
3.2k
points
asked
May 22, 2023
Digital Electronics
gatein-2023
digital-electronics
sequential-circuit
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0
0 votes
0
0 answers
GATE IN 2023 | Question: 7
Match the Exclusive-$\text{OR (XOR)}$ operations $\text{(i)}$ to $\text{(iv)}$ with the results $\text{(p)}$ to $\text{(s),}$ where $X$ is a Boolean input.$$\begin{array}...
admin
3.2k
points
asked
May 22, 2023
Digital Electronics
gatein-2023
digital-electronics
boolean-algebra
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0
0 votes
0
0 answers
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...
admin
3.2k
points
asked
May 22, 2023
Analog Electronics
gatein-2023
analog-electronics
measurements
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–
0
0 votes
0
0 answers
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) } |...
admin
3.2k
points
asked
May 22, 2023
Analysis of complex variables
gatein-2023
analysis-of-complex-variables
calculus
numerical-answers
+
–
0
0 votes
0
0 answers
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$$x(t...
admin
3.2k
points
asked
May 22, 2023
Differential equations
gatein-2023
differential-equations
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0
0 votes
0
0 answers
GATE IN 2023 | Question: 11
A system has the transfer-function$\frac{Y(s)}{X(s)}=\frac{s-\pi}{s+\pi}$Let $u(t)$ be the unit-step function. The input $x(t)$ that results in a steady-state output $y(t...
admin
3.2k
points
asked
May 22, 2023
Control Systems
gatein-2023
control-systems
signals-and-systems
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0
0 votes
0
0 answers
GATE IN 2023 | Question: 12
Choose the fastest logic family among the following: Transistor-Transistor Logic Emitter-Coupled Logic CMOS LogicResistor-Transistor Logic
admin
3.2k
points
asked
May 22, 2023
Digital Electronics
gatein-2023
digital-electronics
analytical-aptitude
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–
0
0 votes
0
0 answers
GATE IN 2023 | Question: 13
What is $\lim _{x \rightarrow 0} f(x)$, where $f(x)=x \sin \frac{1}{x} ?$$0$$1$$\infty$Limit does not exist
admin
3.2k
points
asked
May 22, 2023
Calculus
gatein-2023
calculus
numerical-answers
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0
0 votes
0
0 answers
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_________.
admin
3.2k
points
asked
May 22, 2023
Control Systems
gatein-2023
control-systems
numerical-answers
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–
0
0 votes
0
0 answers
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_______________.
admin
3.2k
points
asked
May 22, 2023
Control Systems
gatein-2023
control-systems
numerical-answers
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–
0
0 votes
0
0 answers
GATE IN 2023 | Question: 16
The opamp in the circuit shown is ideal, except that it has an input bias current of $1 ~ \mathrm{nA}$ and an input offset voltage of $10 ~ \mu \mathrm{V}$. The resulting...
admin
3.2k
points
asked
May 22, 2023
Analog Electronics
gatein-2023
analog-electronics
numerical-answers
+
–
0
0 votes
0
0 answers
GATE IN 2023 | Question: 17
The force per unit length between two infinitely long parallel conductors, with a gap of $2 \mathrm{~cm} $ between them is $10~ \mu \mathrm{N} / \mathrm{m}.$ When the gap...
admin
3.2k
points
asked
May 22, 2023
Electricity and Magnetism
gatein-2023
electrical-circuits-and-machines
numerical-answers
+
–
0
0 votes
0
0 answers
GATE IN 2023 | Question: 18
Consider the discrete-time signal $x[n]=u[-n+5]-u[n+3],$ where $u[n]=\left\{\begin{array}{l}1 ; n \geq 0 \\ 0 ; n<0\end{array}\right . $ The smallest $n$ for which $x[n]=...
admin
3.2k
points
asked
May 22, 2023
Signals and Systems
gatein-2023
signals-and-systems
numerical-answers
+
–
0
0 votes
0
0 answers
GATE IN 2023 | Question: 19
Let $y(t)=x(4 t),$ where $x(t)$ is a continuous-time periodic signal with fundamental period of $100 \mathrm{~s}.$ The fundamental period of $ y(t)$ is___________$s$ (rou...
admin
3.2k
points
asked
May 22, 2023
Signals and Systems
gatein-2023
signals-and-systems
numerical-answers
+
–
0
0 votes
0
0 answers
GATE IN 2023 | Question: 20
When the bridge given below is balanced, the current through the resistor $\mathrm{R}_{\mathrm{a}}$ is____________ $\mathrm{mA}$ (rounded off to two decimal places).
admin
3.2k
points
asked
May 22, 2023
Electrical Circuits and Machines
gatein-2023
electrical-circuits-and-machines
numerical-answers
+
–
0
0 votes
0
0 answers
GATE IN 2023 | Question: 21
In the circuit given, the Thevenin equivalent resistance $\mathrm{R}_{\mathrm{th}}$ across the terminals '$\mathrm{a}$' and ' $\mathrm{b}$' is____________$\Omega$ (rounde...
admin
3.2k
points
asked
May 22, 2023
Electrical Circuits and Machines
gatein-2023
electrical-circuits-and-machines
numerical-answers
+
–
0
0 votes
0
0 answers
GATE IN 2023 | Question: 22
$X$ is a discrete random variable which takes values $0,1$ and $2.$ The probabilities are $P(X=0)=0.25$ and $P(X=1)=0.5$. With $E[ .]$ denoting the expectation operator, ...
admin
3.2k
points
asked
May 22, 2023
Probability and Statistics
gatein-2023
probability-and-statistics
numerical-answers
+
–
0
0 votes
0
0 answers
GATE IN 2023 | Question: 23
The diode in the circuit is ideal. The current source $\mathrm{i}_{\mathrm{s}}(t)=\pi \sin (3000 \pi \mathrm{t}) \mathrm{~mA}.$ The magnitude of the average current flowi...
admin
3.2k
points
asked
May 22, 2023
Analog Electronics
gatein-2023
analog-electronics
numerical-answers
+
–
0
0 votes
0
0 answers
GATE IN 2023 | Question: 24
The full-scale range of the wattmeter shown in the circuit is $100 \mathrm{~W}$. The turns ratio of the individual transformers are indicated in the figure. The RMS value...
admin
3.2k
points
asked
May 22, 2023
Electrical Circuits and Machines
gatein-2023
electrical-circuits-and-machines
numerical-answers
+
–
0
0 votes
0
0 answers
GATE IN 2023 | Question: 25
The no-load steady-state output voltage of a $\text{DC}$ shunt generator is $200 \mathrm{~V}$ when it is driven in the clockwise direction at its rated speed. If the same...
admin
3.2k
points
asked
May 22, 2023
Electrical Circuits and Machines
gatein-2023
electrical-circuits-and-machines
numerical-answers
+
–
0
0 votes
0
0 answers
GATE IN 2023 | Question: 26
The impulse response of an LTI system is $h(t)=\delta(t)+0.5 \delta(t-4)$, where $\delta(t)$ is the continuous-time unit impulse signal. If the input signal $x(t)=\cos \l...
admin
3.2k
points
asked
May 22, 2023
Signals and Systems
gatein-2023
signals-and-systems
numerical-answers
+
–
0
0 votes
0
0 answers
GATE IN 2023 | Question: 27
The Laplace transform of the continuous-time signal $x(t)=e^{-3 t} u(t-5)$ is_____________, where $u(t)$ denotes the continuous-time unit step signal.$\frac{e^{-5 s}}{s+3...
admin
3.2k
points
asked
May 22, 2023
Signals and Systems
gatein-2023
signals-and-systems
laplace-transform
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–
0
0 votes
0
0 answers
GATE IN 2023 | Question: 28
In a $p-i-n$ photodiode, a pulse of light containing $8 \times 10^{12}$ incident photons at wavelength $\lambda_0=1.55~ \mu \mathrm{m}$ gives rise to an average $4 \times...
admin
3.2k
points
asked
May 22, 2023
Sensors and Industrial Instrumentation
gatein-2023
communication-and-optical-instrumentation
numerical-answers
+
–
0
0 votes
0
0 answers
GATE IN 2023 | Question: 29
Let $f(z)=j \frac{1-z}{1+z}$, where $z$ denotes a complex number and $j$ denotes $\sqrt{-1}$. The inverse function $f^{-1}(z)$ maps the real axis to the___________.unit c...
admin
3.2k
points
asked
May 22, 2023
Analysis of complex variables
gatein-2023
analysis-of-complex-variables
complex-function
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–
0
0 votes
0
0 answers
GATE IN 2023 | Question: 30
The simplified form of the Boolean function $\mathrm{F}(W, X, Y, Z)=\Sigma(4,5,10,11,12,13$, $14,15)$ with the minimum number of terms and smallest number of literals in ...
admin
3.2k
points
asked
May 22, 2023
Digital Electronics
gatein-2023
digital-electronics
boolean-algebra
boolean-functions
numerical-answers
+
–
0
0 votes
0
0 answers
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 ...
admin
3.2k
points
asked
May 22, 2023
Digital Electronics
gatein-2023
digital-electronics
analytical-aptitude
+
–
0
0 votes
0
0 answers
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...
admin
3.2k
points
asked
May 22, 2023
Digital Electronics
gatein-2023
digital-electronics
analytical-aptitude
+
–
0
0 votes
0
0 answers
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} $$ \frac{10000}{s^2+2 s+10000} e^{-0.05 s}$$...
admin
3.2k
points
asked
May 22, 2023
Control Systems
gatein-2023
control-systems
numerical-answers
+
–
0
0 votes
0
0 answers
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 Fo...
admin
3.2k
points
asked
May 22, 2023
Signals and Systems
gatein-2023
signals-and-systems
analytical-aptitude
+
–
0
0 votes
0
0 answers
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...
admin
3.2k
points
asked
May 22, 2023
Communication and Optical Instrumentation
gatein-2023
communication-and-optical-instrumentation
numerical-answers
+
–
0
0 votes
0
0 answers
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_{\...
admin
3.2k
points
asked
May 22, 2023
Electrical Circuits and Machines
gatein-2023
electrical-circuits-and-machines
numerical-answers
+
–
0
0 votes
0
0 answers
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{...
admin
3.2k
points
asked
May 22, 2023
Signals and Systems
gatein-2023
electrical-circuits-and-machines
numerical-answers
+
–
0
0 votes
0
0 answers
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 p...
admin
3.2k
points
asked
May 22, 2023
Control Systems
gatein-2023
control-systems
numerical-answers
+
–
0
0 votes
0
0 answers
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?
admin
3.2k
points
asked
May 22, 2023
Quantitative Aptitude
gatein-2023
combinatorics
quantitative-aptitude
+
–
0
0 votes
0
0 answers
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).
admin
3.2k
points
asked
May 22, 2023
Control Systems
gatein-2023
control-systems
numerical-answers
+
–
0
0 votes
0
0 answers
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 l...
admin
3.2k
points
asked
May 22, 2023
Sensors and Industrial Instrumentation
gatein-2023
analog-electronics
numerical-answers
+
–
0
0 votes
0
0 answers
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 not...
admin
3.2k
points
asked
May 22, 2023
Sensors and Industrial Instrumentation
gatein-2023
analog-electronics
numerical-answers
measurements
+
–
0
0 votes
0
0 answers
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 ...
admin
3.2k
points
asked
May 22, 2023
Probability and Statistics
gatein-2023
measurements
probability-and-statistics
numerical-answers
+
–
0
0 votes
0
0 answers
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 $\mathrm{R}$, a...
admin
3.2k
points
asked
May 22, 2023
Sensors and Industrial Instrumentation
gatein-2023
numerical-answers
measurements
+
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