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GATE2017145
A $375$W, $230$V, $50$Hz, capacitor start singlephase induction motor has the following constants for the main and auxiliary windings (at starting): $Z_{m}=(12.50+j15.75) \Omega$ (main winding), $Z_{a}=(24.50+j12.75) \Omega$ (auxiliary ... the value of the capacitance (in $\mu F$) to be added in series with the auxiliary winding to obtain maximum torque at starting is ________.
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GATE2017146
Two parallel connected, threephase, $50$Hz, $11$kV, starconnected synchronous machines $A$ and $B$, are operating as synchronous condensers. They together supply $50$MVAR to a $11$kV grid. Current supplied by both the machines are equal. Synchronous reactances of ... of excitation current of machine $A$ to that of machine $B$ is _______. (Give the answer up to two decimal places.)
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GATE2017147
A $220$V DC series motor runs drawing a current of $30$ A from the supply. Armature and field circuit resistances are $0.4\Omega$ and $0.1\Omega$, respectively. The load torque varies as the square of the speed. The flux in the motor may be taken as ... %, the resistance in ohms that should be added in series with the armature is ______. (Give the answer up to two decimal places.)
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GATE2017148
A threephase, three winding $\Delta / \Delta / Y (1.1kV/6.6kV/400V)$ transformer is energized from $AC$ mains at the $1.1kV$ side. It supplies $900kVA$ load at $0.8$ power factor lag from the $6.6kV$ winding and $300kVA$ load at $0.6$ power factor ... . The $RMS$ line current in ampere drawn by the $1.1kV$ winding from the mains is ________. (Give the answer up to one decimal place.)
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GATE2017149
A separately excited $DC$ generator supplies $150$A to a $145$V DC grid. The generator is running at $800$RPM. The armature resistance of the generator is $0.1\Omega$. If the speed of the generator is increased to $1000$ RPM, the current in amperes supplied by the generator to the $DC$ grid is ______. (Give the answer up to one decimal place.)
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GATE2017150
For a system having transfer function $G(s)=\frac{s+1}{s+1}$, a unit step input is applied at time $t=0$. The value of the response of the system at $t=1.5 sec$ (rounded off to three decimal places) is ________.
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GATE2017151
Consider a causal and stable $LTI$ system with rational transfer function $H(z)$, whose corresponding impulse response begins at $n=0$. Furthermore, $H(1)=\frac{5}{4}$. The poles of $H(z)$ are $p_{k}=\frac{1}{\sqrt{2}} \text{exp}(j\frac{(2k1)\pi}{4})$ ... all at $z=0$. Let $g[n]=j^{n}h[n]$. The value of $g[8]$ equals __________. (Give the answer up to three decimal places.)
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GATE2017152
The circuit shown in the figure uses matched transistors with a thermal voltage $V_{T}=25$m V. The base currents of the transistors are negligible. The value of the resistance $R$ in $k\Omega$ that is required to provide $1 \mu A$ bias current for the differential amplifier block shown is ________.(Give the answer up to one decimal place.)
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GATE2017153
The figure below shows an uncontrolled diode bridge rectifier supplied from a $220$V, $50$Hz, $I$phase ac source. The load draws a constant current $I_{0}=14A$. The conduction angle of the diode $D_{1}$ in degrees (rounded off to two decimal places) is _______.
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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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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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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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GATE2017134
The load shown in the figure is supplied by a $400$V (linetoline), $3$phase source (RYB sequence). The load is balanced and inductive, drawing $3464$ VA. When the switch $S$ is in position $N$, the three wattmeters $W_{1}, W_{2},$ and $W_{3}$ read $577.35$W each. If ... and $W_2=W_3=0$ $W_1=0$; $W_2=1732$; and $W_3=0$ $W_1=866$; $W_2=0$; and $W_3=866$ $W_1=W_2=0$ and $W_3=1732$
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GATE2017135
The approximate transfer characteristic for the circuit shown below with an ideal operational amplifier and diode will be
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GATE2017136
The output expression for the Karnaugh map shown below is $B \overline{D}+BCD$ $B \overline{D}+AB$ $\overline{B}D+ABC$ $B \overline{D}+ABC$
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GATE2017137
The logical gate implemented using the circuit shown below where $V_{1}$ and $V_{2}$ are inputs (with $0$V as digital $0$ and $5$V as digital $1$) and $V_{out}$ is the output, is NOT NOR NAND XOR
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GATE2017138
The input voltage $V_{DC}$ of the buckboost converter shown below varies from $32$V to $72$V. Assume that all components are ideal, inductor current is continuous, and output voltage is ripple free. The range of duty ratio $D$ of the converter for which the magnitude of the steadystate output ... $0 \leq D \leq 1$ $\frac{1}{3}\leq D \leq \frac{2}{3}$
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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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GATE2017140
The bus admittance matrix for a power system network is $\begin{bmatrix} j39.9 & j20 & j20\\ j20 & j39.9 & j20 \\ j20 & j20 & j39.9 \end{bmatrix} pu.$ There is a transmission line, connected between buses $1$ and $3$, which is represented by ...
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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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GATE2017120
A threephase, $50$Hz, starconnected cylindrical rotor synchronous machine is running as a motor. The machine is operated from a $6.6$ kV grid and draws current at unity power factor (UPF). The synchronous reactance of the motor is $30 \Omega$ per phase. The load angle is $30^{\circ}$. The power delivered to the motor in kW is __________. (Give the answer up to one decimal place).
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GATE2017121
A $10$bus power system consists of four generator buses indexed as $G1, G2, G3, G4$ and six load buses indexed as $L1, L2, L3, L4, L5, L6$. The generatorbus $G1$ is considered as slack bus, and the load buses $L3$ ... reactive power limit. The number of nonlinear equations required for solving the load flow problem using Newton  Raphson method in polar form is ___________.
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GATE2017122
Consider the unity feedback control system shown. The value of $K$ that results in a phase margin of the system to be $30^{\circ}$ is _________. (Give the answer up to two decimal places.)
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GATE2017123
The following measurements are obtained on a single phase load $V=220 V \pm 1$%, $I=5.0 A \pm 1$% and $W=555 W \pm 2$%. If the power factor is calculated using these measurements, the worst case error in the calculated power factor in percent is _______. (Give answer up to one decimal place.)
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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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GATE2017125
A $3$phase voltage source inverter is supplied from a $600V$ DC source as shown in the figure below. For a star connected resistive load of $20\Omega$ per phase, the load power for $120^{\circ}$ device conduction, in kW, is ________.
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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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GATE2017127
Consider the differential equation $(t^{2}81)\frac{dy}{dt}+5t y=\sin(t)$ with $y(1)=2 \pi$. There exists a unique solution for this differential equation when $t$ belongs to the interval $(2, 2)$ $(10, 10)$ $(10, 2)$ $(0, 10)$
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GATE2017128
Consider the line integral $I=\int_{c} (x^{2}+iy^{2})dz$, where $z=x+iy$. The line $c$ is shown in the figure below. The value of $I$ is $\frac{1}{2}i \\ $ $\frac{2}{3}i \\ $ $\frac{3}{4}i \\ $ $\frac{4}{5}i$
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GATE2017129
The passive twoport networks are connected in cascade as shown in figure. A voltage source is connected at port $1$. Given $V_{1}=A_{1}V_{2}+B_{1}I_{2}$ $I_{1}=C_{1}V_{2}+D_{1}I_{2}$ $V_{2}=A_{2}V_{3}+B_{2}I_{3}$ $I_{2}=C_{2}V_{3}+D_{2}I_{3}$ ... $V_{T}=\frac{V_{1}}{A_{1}A_{2}+B_{1}C_{2}}, Z_{T}=\frac{A_{1}B_{2}+B_{1}D_{2}}{A_{1}A_{2}+B_{1}C_{2}}$
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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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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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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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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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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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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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GATE2017116
Consider $g(t)= \begin{cases} t\lfloor t \rfloor, & t \geq 0 \\ t\lceil t \rceil, & \text{otherwise } \end{cases}$, where $t \in \mathbb{R}$. Here, $\lfloor t \rfloor$ represents the largest integer less than or ... the smallest integer greater than or equal to $t$. The coefficient of the second harmonic component of the Fourier series representing $g(t)$ is __________.
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GATE2017117
Let $I= c\int \int _{R} xy^{2} dxdy$, where $R$ is the region shown in the figure and $c= 6 \times 10^{4}$. The value of $I$ equals _________. (Give the answer up to two decimal places.)
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GATE2017118
The power supplied by the $25$V source in the figure shown below is __________ $W$.
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GATE2017119
The equivalent resistance between the terminals $A$ and $B$ is __________ $\Omega$.
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