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GATE201725
If a synchronous motor is running at a leading power factor, its excitation induced voltage $(E_{f})$ is Equal to terminal voltage $V_{t}$ Higher than the terminal voltage $V_{t}$ Less than terminal voltage $V_{t}$ Dependent upon supply voltage $V_{t}$
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2
GATE2017210
For a $3$input logic circuit shown below, the output $Z$ can be expressed as $Q+\overline{R}$ $P\overline{Q}+R$ $\overline{Q}+R$ $P+\overline{Q}+R$
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3
GATE2017112
The slope and level detector circuit in a $CRO$ has a delay of $100$ns. The start  stop sweep generator has a response time of $50$ns. In order to display correctly, a delay line of $150$ns has to be inserted into the $y$channel $150$ns has to be inserted ... channel $150$ns has to be inserted into both $x$ and $y$channels $100$ns has to be inserted into both $x$ and $y$channels
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GATE2017114
For the circuit shown in the figure below, assume that diodes $D_{1}, D_{2}$ and $D_{3}$ are ideal. The $DC$ components of voltages $v_{1}$ and $v_{2}$, respectively are $0$V and $1$V $0.5$V and $0.5$V $1$V and $0.5$V $1$V and $1$V
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GATE2017124
In the converter circuit shown below, the switches are controlled such that the load voltage $v_{0}(t)$ is a $400$ Hz square wave. The RMS value of the fundamental component of $v_{0}(t)$ in volts is ________.
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numericalanswers
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GATE2017130
Let a causal LTI system be characterised by the following differential equation, with initial rest condition $\frac{d^{2}y}{dt^{2}}+7\frac{dy}{dt}+10y (t)=4x(t)+5\frac{dx(t)}{dt}$ where, $x(t)$ and $y(t)$ are the input and output respectively. The impulse response of the system is ($u(t)$ is the ... $2e^{2t}u(t)+7e^{5t}u(t)$ $7e^{2t}u(t)2e^{5t}u(t)$ $7e^{2t}u(t)+2e^{5t}u(t)$
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7
GATE2017131
Let the signal $x(t)=\sum_{k=\infty }^{+\infty } (1)^{k} \delta (t\frac{k}{2000})$ be passed through an LTI system with frequency response $H(\omega )$ ... $2000+2000\cos (2000 \pi t)+2000\cos (4000 \pi t)$ $4000\cos (2000 \pi t)$ $2000\cos (2000 \pi t)$
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8
GATE2017132
In the system whose signal flow graph is shown in the figure, $U_{1}(s)$ and $U_{2}(s)$ are inputs. The transfer function $\frac{Y(s)}{U_{1}(s)}$ is $\frac{k_{1}}{J Ls^{2}+J Rs+k_{1}k_{2}}$ $\frac{k_{1}}{J Ls^{2}J Rsk_{1}k_{2}}$ $\frac{k_{1}U_{2}(R+sL)}{J Ls^{2}+(J RU_{2}L)s+k_{1}k_{2}U_{2}R}$ $\frac{k_{1}U_{2}(sLR)}{J Ls^{2}(J R+U_{2}L)sk_{1}k_{2}+U_{2}R}$
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9
GATE2017133
The transfer function of the system $Y(s)/U(s)$ ... $\frac{(s4)}{(s^{2}+s4)} \\ $ $\frac{(s+4)}{(s^{2}s4)} \\$
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10
GATE2017139
A load is supplied by a $230$ V, $50$ Hz source. The active power $P$ and the reactive power $Q$ consumed by the load are such that $1kW \leq P \leq 2kW$ and $1kVAR \leq Q \leq 2kVAR$ ... case power factor after power factor correction is $0.447 \text{ lag}$ $0.707 \text{ lag}$ $0.894 \text{ lag}$ $1$
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11
GATE2017141
The switch in the figure below was closed for a long time. It is opened at $t=0$. The current in the inductor of $2$H for $t \geq 0$, is $2.5e^{4t}$ $5e^{4t}$ $2.5e^{0.25t}$ $5e^{0.25t}$
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12
GATE201711
The matrix $A=\begin{bmatrix} \frac{3}{2} &0 & \frac{1}{2}\\ 0& 1 &0 \\ \frac{1}{2} & 0 & \frac{3}{2} \end{bmatrix}$ has three distinct eigenvalues and one of its eigenvectors is $\begin{bmatrix} 1\\ 0\\ 1 \end{bmatrix}$. Which one of the ... $\begin{bmatrix} 1\\ 0\\ 1 \end{bmatrix}$ $\begin{bmatrix} 1\\ 1\\ 1 \end{bmatrix}$
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13
GATE201712
For a complex number $z, \lim_{z \rightarrow i} \frac{z^{2}+1}{z^{3}+2zi (z^{2}+2)}$ is $2i$ $i$ $i$ $2i$
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14
GATE201716
The transfer function of a system is given by, $\frac{V_{0}(s)}{V_{i}(s)}=\frac{1s}{1+s}$ Let the output of the system be $v_{0}(t)=V_{m} \sin (\omega t + \varphi )$ for the input, $v_{i}(t)=V_{m} \sin (\omega t )$. Then the minimum and maximum values of $\varphi$ (in ... respectively $\frac{\pi}{2}$ and $\frac{\pi}{2}$ $\frac{\pi}{2}$ and $0$ $0$ and $\frac{\pi}{2}$ $\pi$ and $0$
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15
GATE2017113
The Boolean expression $AB+A\bar{C}+BC$ simplifies to $BC + A\bar{C}$ $AB + A\bar{C} + B$ $AB + A\bar{C}$ $AB + BC$
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16
GATE2017126
A function $f(x)$ is defined as $f(x)= \begin{cases} e^{x}, & x < 1 \\ \text{In } x+ax^{2}+bx, & x\geq 1 \end{cases}$, where $x \in \mathbb{R}$ Which one of the following statement is TRUE? $f(x)$ is NOT differentiable at $x=1$ for any values of $a$ ... $x=1$ for all values of $a$ and $b$ such that $a+b=e$. $f(x)$ is differentiable at $x=1$ for all values of $a$ and $b$.
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17
GATE2017230
In the circuit shown below, the value of capacitor $C$ required for maximum power to be transferred to the load is $1$ nF $1 \mu F$ $1$ mF $10$ mF
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18
GATE201729
A stationary closed Lissajous pattern on an oscilloscope has $3$ horizontal tangencies and $2$ vertical tangencies for a horizontal input with frequency $3$kHz. The frequency of the vertical input is $1.5$kHz $2$kHz $3$kHz $4.5$kHz
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19
GATE2017111
A closed loop system has the characteristic equation given by $s^{3}+Ks^{2}+(K+2)s+3=0$. For this system to be stable, which one of the following conditions should be satisfied? $0 < K < 0.5$ $0.5 < K < 1$ $0 < K < 1$ $K > 1$
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20
GATE2017115
For the power semiconductor devices $IGBT, MOSFET$, Diode and Thyristor, which one of the following statements is TRUE? All the four are majority carrier devices. All the four are minority carrier devices. $IGBT$ and $MOSFET$ are majority carrier ... are minority carrier devices. $MOSFET$ is majority carrier device, whereas $IGBT$, Diode, Thyristor are minority carrier devices.
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