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804
GATE2017: 6
A series $\text {R-L-C}$ circuit is excited with a $50\;\text{V}$, $50\;\text{Hz}$ sinusoidal source. The voltages across the resistance and the capacitance are shown in the figure. The voltage across the inductor $\text(V_L)$ is ___________$\text{V}$.
A series $\text {R-L-C}$ circuit is excited with a $50\;\text{V}$, $50\;\text{Hz}$ sinusoidal source. The voltages across the resistance and the capacitance are shown in ...
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805
GATE2017: 13
The term hysteresis is associated with $\text{ON-OFF control}$ $\text{P-I control}$ $\text{Feed-forward control}$ $\text{Ratio control}$
The term hysteresis is associated with $\text{ON-OFF control}$$\text{P-I control}$$\text{Feed-forward control}$$\text{Ratio control}$
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806
GATE2015-60
The open loop transfer function of a system is $G(s)=\frac{s^2+6s+10}{s^2+2s+2}.$ The angles of arrival of its root loci are $\pm \frac{\pi}{4}$ $\pm \frac{\pi}{3}$ $\pm \frac{\pi}{2}$ $\pm \frac{5\pi}{6}$
The open loop transfer function of a system is $G(s)=\frac{s^2+6s+10}{s^2+2s+2}.$ The angles of arrival of its root loci are$\pm \frac{\pi}{4}$$\pm \frac{\pi}{3}$$\pm \fr...
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807
GATE2014-33
A thermistor has a resistance of $1\;k\Omega$ at temperature $298\;K$ and $465\;\Omega$ at temperature $316\;K$. The temperature sensitivity in $K^{-1}[i.e(1/R)(dR/dT),$ where $R$ is the resistance at the temperature $T(in\; K)]$, of this thermistor at $316\;K$ is ___________.
A thermistor has a resistance of $1\;k\Omega$ at temperature $298\;K$ and $465\;\Omega$ at temperature $316\;K$. The temperature sensitivity in $K^{-1}[i.e(1/R)(dR/dT),$ ...
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809
GATE2013-58
Choose the grammatically $\text{CORRECT}$ sentence: Two and two add four Two and two become four Two and two are four Two and two make four
Choose the grammatically $\text{CORRECT}$ sentence:Two and two add fourTwo and two become fourTwo and two are fourTwo and two make four
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810
GATE2013-37
The maximum value of the solution y(t) of the differential equation $y(t)+\ddot{y}(t)=0$ with initial conditions $\dot{y}(0)=1$ and $y(0)=1,$ for $t\underline{>}0$ is $1$ $2$ $\pi$ $\sqrt{2}$
The maximum value of the solution y(t) of the differential equation $y(t)+\ddot{y}(t)=0$ with initial conditions $\dot{y}(0)=1$ and $y(0)=1,$ for $t\underline{>}0$ is $1$...
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812
GATE2012-10
The $i-v$ characteristics of the diode in the circuit given below are $i=\left\{ \begin{array}{rcl} \frac{\text{v}-0.7}{500}\text{A},& \text{v}\geq0.7\text{v}\\ 0\;\text{A}, & \text{v}<0.7\text{v} \end{array}\right.$ $10\;\text{mA}$ $9.3\;\text{mA}$ $6.67\;\text{mA}$ $6.2\;\text{mA}$
The $i-v$ characteristics of the diode in the circuit given below are $$i=\left\{ \begin{array}{rcl} \frac{\text{v}-0.7}{500}\text{A},& \text{v}\geq0.7\text{v}\\ 0\;\text...
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813
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 Fourier transform is purely imaginary. $x(t)+x(-t)$ $x(t)-x(-t)$ $j(x(t)+x(-t))$ $j(x(t)-x(-t))$
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...
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814
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...
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816
GATE2017: 8
A circuit consisting of dependent and independent sources is shown in the figure. If the voltage at $\text{Node-1}$ is $-1\;\text{V}$, then the voltage at $\text{Node-2}$ is _____________ $\text{V}$.
A circuit consisting of dependent and independent sources is shown in the figure. If the voltage at $\text{Node-1}$ is $-1\;\text{V}$, then the voltage at $\text{Node-2}$...
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817
GATE2016-36
For the periodic signal $x(t)$ shown below with period $T=8s$, the power in the 10th harmonic is __________. $0$ $\frac{1}{2} \left (\frac{2}{10\pi} \right)^2$ $\frac{1}{2} \left (\frac{4}{10\pi} \right)^2$ $\frac{1}{2} \left (\frac{4}{5\pi} \right)^2$
For the periodic signal $x(t)$ shown below with period $T=8s$, the power in the 10th harmonic is __________.$0$$\frac{1}{2} \left (\frac{2}{10\pi} \right)^2$$\frac{1}{2} ...
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819
GATE2014-41
An $N-$bit, $ADC$ has an analog reference voltage $V$. Assuming zero mean and uniform distribution of the quantization error, the quantization noise power will be: $\frac{V^2}{12(2^N-1)^2}$ $\frac{V^2}{12(2^N-1)}$ $\frac{V}{12(2^N-1)}$ $\frac{V^2}{\sqrt{12} }$
An $N-$bit, $ADC$ has an analog reference voltage $V$. Assuming zero mean and uniform distribution of the quantization error, the quantization noise power will be:$\frac{...
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820
GATE2014-46
The transfer function of a system is given by $G(s)=\frac{e^{-s/500}}{s+500}$ The input to the system is $x(t)=\sin100\pi t$. In periodic steady state the output of the system is found to be $y(t)=A\sin(100\pi t-\phi).$ The phase angle $(\phi )$ in degree is ___________.
The transfer function of a system is given by$$G(s)=\frac{e^{-s/500}}{s+500}$$The input to the system is $x(t)=\sin100\pi t$. In periodic steady state the output of the s...
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824
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_______________.
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825
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 is doubled, the force per unit length will be____________$\mu \mathrm{N} / \mathrm{m}$ (rounded off to one decimal place).
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...
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827
GATE2017: 29
The current response of a series $\text R-L$ circuit to a unit step voltage is given in the table. The value of $L$ is __________$H$.
The current response of a series $\text R-L$ circuit to a unit step voltage is given in the table. The value of $L$ is __________$H$.
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828
GATE2017: 5
For a first order lowpass filter with unity $\text {d.c}$. gain and $-3\;\text {dB}$ corner frequency of $2000\pi \:\text {rad/s}$,the transfer function $H(j\omega)$ is $\frac{1}{1000+j\omega}$ $\frac{1}{1+j1000\omega}$ $\frac{2000\pi}{2000\pi+j\omega}$ $\frac{1000\omega}{1+j1000\omega}$
For a first order lowpass filter with unity $\text {d.c}$. gain and $-3\;\text {dB}$ corner frequency of $2000\pi \:\text {rad/s}$,the transfer function $H(j\omega)$ is $...
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829
GATE2012-26
A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is $1/3$ $1/2$ $2/3$ $3/4$
A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is$1/3$$1/2$$2/3$$3/4$
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830
GATE IN 2023 | Question: 3
Which of the following flow meters offers the lowest resistance to the flow? Turbine flow meter Orifice flow meter* Venturi meter Electromagnetic flow meter
Which of the following flow meters offers the lowest resistance to the flow? Turbine flow meter Orifice flow meter* Venturi meter Electromagnetic flow meter
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831
GATE IN 2023 | Question: 6
The table shows the present state $\mathrm{Q}(\mathrm{t})$, next state $\mathrm{Q}(\mathrm{t}+1)$ ... $\text{T}$ flip-flop $\text{D}$ flip-flop $\text{SR}$ flip-flop $\text{JK}$ flip-flop
The table shows the present state $\mathrm{Q}(\mathrm{t})$, next state $\mathrm{Q}(\mathrm{t}+1)$, and the control input in a flip-flop. Identify the flip-flop.$$\begin{a...
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832
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 $x[n]=0$ is___________.
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]=...
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833
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 $Y_{\text {in }}$ is purely real is__________________$\mathrm{mF}$ (rounded off to two decimal places).
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_{\...
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835
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
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836
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 each term is $W X+\bar{W} X \bar{Y}+W \bar{X} Y$ $W X+W Y+X \bar{Y}$ $X \bar{Y}+W Y$ $\bar{X} Y+\bar{W} \bar{Y}$
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 ...
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837
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).
The phase margin of the transfer function $G(s)=\frac{2(1-s)}{(1+s)^{2}}$ is____________degrees. (rounded off to the nearest integer).
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838
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?
How many five-digit numbers can be formed using the integers $3,4,5$ and $6$ with exactly one digit appearing twice?
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840
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, the value of $E[X]-E\left[X^{2}\right]$ is_____________(rounded off to one decimal place).
$X$ 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, ...
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