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GATE2017220
Let $y^{2}2y+1=x$ and $\sqrt{x}+y=5$. The value of $x+\sqrt{y}$ equals _________. (Give the answer up to three decimal places).
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GATE2017213
A threephase voltage source inverter with ideal devices operating in $180^{\circ}$ conduction mode is feeding a balanced starconnected resistive load. The $DC$ voltage input is $V_{dc}$. The peak of the fundamental component of the phase voltage is $\frac{V_{dc}}{\pi} \\$ $\frac{2V_{dc}}{\pi} \\$ $\frac{3V_{dc}}{\pi} \\$ $\frac{4V_{dc}}{\pi} $
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GATE2017214
A $3$phase, $4$pole, $400$V, $50$Hz squirrelcage induction motor is operating at a slip of $0.02$. The speed of the rotor flux in mechanical rad/sec, sensed by a stationary observer, is closest to $1500$ $1470$ $157$ $154$
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GATE2017215
The figure shows the perphase representation of a phaseshifting transformer connected between buses $1$ and $2$, where $\alpha$ is a complex number with nonzero real and imaginary parts. For the given circuit, $Y_{bus}$ and $Z_{bus}$ are bus admittance matrix and ... is unsymmetric. $Y_{bus}$ is unsymmetric and $Z_{bus}$ is symmetric. Both $Y_{bus}$ and $Z_{bus}$ are unsymmetric.
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GATE2017216
The figure below shows the circuit diagram of a controlled rectifier supplied from a $230$V, $50$Hz, $1$phase voltage source and a $10:1$ ideal transformer. Assume that all devices are ideal. The firing angles of the thyristors $T_{1}$ and $T_{2}$ are $90^{\circ}$ and $270^{\circ}$, respectively. The RMS value of the current through diode $D_{3}$ in amperes is _______.
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6
GATE2017217
Assume that in traffic junction, the cycle of the traffic signal lights is $2$ minutes of green (Vehicle does not stop) and $3$ minutes of red (Vehicle stops). Consider that the arrival time of vehicles at the junction is uniformly distributed over $5$ minute cycle. The expected waiting time (in minutes) for the vehicle at the junction is ________.
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GATE201728
Two resistors with nominal resistance values $R_{1}$ and $R_{2}$ have additive uncertainties $\bigtriangleup R_{1}$ and $\bigtriangleup R_{2}$, respectively. When these resistances are connected in parallel, the standard deviation of the error in the equivalent resistance $R$ ...
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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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Feb 27, 2017
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gate2017ee2
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9
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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GATE201721
An urn contains $5$ red balls and $5$ black balls. In the first draw, one ball is picked at random and discarded without noticing its colour. The probability to get a Red ball in the second draw is $\frac{1}{2} \\$ $\frac{4}{9} \\$ $\frac{5}{9} \\$ $\frac{6}{9} $
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GATE201722
Consider a solid sphere of radius $5$ cm made of a perfect electric conductor. If one million electrons are added to this sphere, these electrons will be distributed Uniformly over the entire volume of the sphere. Uniformly over the outer surface of the sphere. Concentrated around the centre of the sphere. Along a straight line passing through the centre of the sphere.
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GATE201723
The figures show diagramatic representations of vector fields $\vec{X}, \vec{Y}, \text{and} \vec{Z}$ respectively. Which one of the following choices is true? $\bigtriangledown . \vec{X}=0,\bigtriangledown \times \vec{Y} \neq 0, \bigtriangledown \times \vec{Z}=0$ ... $\bigtriangledown . \vec{X}=0,\bigtriangledown \times \vec{Y} = 0, \bigtriangledown \times \vec{Z}=0$
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GATE201724
The polezero plots of three discretetime systems $P, Q$ and $R$ on the $z$plane are shown below. Which one of the following is TRUE about the frequency selectivity of these systems? All three are highpass filters. All three are bandpass filters. All three are lowpass filters. $P$ is lowpass filter. $Q$ is a bandpass filter and $R$ is a highpass filter.
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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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GATE201726
When a unit ramp input is applied to the unity feedback system having closed loop transfer function $\frac{C(s)}{R(s)}=\frac{Ks+b}{s^{2}+as+b}, (a>0, b>0, K>0)$, the steady state error will be $0 \\ $ $\frac{a}{b} \\$ $\frac{a+K}{b} \\$ $\frac{aK}{b}$
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GATE201727
The transfer function $C(s)$ of a compensator is given below. $C(s)=\frac{(1+\frac{s}{0.1})(1+\frac{s}{100})}{(1+s)(1+\frac{s}{10})}$ The frequency range in which the phase (lead) introduced by the compensator reaches the maximum is $0.1 < \omega < 1$ $1 < \omega < 10$ $10 < \omega < 100$ $ \omega > 100$
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GATE2017154
The positive, negative, and zero sequence reactances of a wyeconnected synchronous generator are $0.2$pu, $0.2$pu, and $0.1$pu, respectively. The generator is an open circuit with a terminal voltage of $1$pu. The minimum value of the inductive ... ground fault occurs at the terminals is ___________ (assume fault impedance to be zero). (Give the answer up to one decimal place.)
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GATE2017155
The figure shows the single line diagram of a power system with a double circuit transmission line. The expression for electrical power is $1.5 \sin \delta$, where $\delta$ is the rotor angle. The system is operating at the stable equilibrium point with mechanical power equal to ... $P_{\max}$, in pu is ______. (Give the answer up to three decimal places.)
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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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GATE2017142
Only one of the real roots of $f(x)=x^{6}x1$ lies in the interval $1 \leq x \leq 2$ and bisection method is used to find its value. For achieving an accuracy of $0.001$, the required minimum number of iterations is _________.
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GATE2017143
In the circuit shown below, the maximum power transferred to the resistor $R$ is ______ W.
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GATE2017144
The magnitude of magnetic flux density (B) in micro Teslas $(\mu T)$, at the centre of a loop of wire wound as a regular hexagon of side length $1 m$ carrying a current $(I=1 A)$, and placed in vacuum as shown in the figure is _________. (Give the answer up to two decimal places.)
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23
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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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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32
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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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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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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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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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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38
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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