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GATE Electrical 2015 Set 2 | Question: 54
An open loop transfer function $G(s)$ of a system is $G(s)=\dfrac{k}{s(s+1)(s+2)}$ For a unity feedback system, the breakaway point of the root loci on the real axis occurs at, $−0.42$ $−1.58$ $−0.42$ and $−1.58$ None of the above

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GATE Electrical 2015 Set 2 | Question: 53
The unit step response of a system with the transfer function $G(s)=\dfrac{1-2s}{1+s}$ is given by which one of the following waveforms?

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GATE Electrical 2015 Set 2 | Question: 52
The following discrete-time equations result from the numerical integration of the differential equations of an un-damped simple harmonic oscillator with state variables $x$ and $y$. The integration time step is $h$. $\dfrac{x_{k+1}-x_{k}}{h}=y_{k}$ ... $\dfrac{1}{2\pi}<h<\dfrac{1}{\pi}$

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GATE Electrical 2015 Set 2 | Question: 51
Two three-phase transformers are realized using single-phase transformers as shown in the figure. The phase difference (in degree) between voltages $V_{1}$ and $V_{2}$ is _______.

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GATE Electrical 2015 Set 2 | Question: 55
For the system governed by the set of equations: $dx_{1}/dt=2x_{1}+x_{2}+u$ $dx_{2}/dt=-2x_{1}+u$ $y=3 x_{1}$ the transfer function $Y(s)/U(s)$ is given by $3(s+1)/(s^{2}-2s+2)$ $3(2s+1)/(s^{2}-2s+1)$ $(s+1)/(s^{2}-2s+1)$ $3(2s+1)/(s^{2}-2s+2)$

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GATE Electrical 2015 Set 2 | Question: 39
The saturation voltage of the ideal op-amp shown below is $\pm 10$ V. The output voltage $v_{o}$ of the following circuit in the steady-state is Square wave of period $0.55$ ms. Triangular wave of period $0.55$ ms. square Square wave of period $0.25$ ms. Triangular wave of period $0.25$ ms

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GATE Electrical 2015 Set 2 | Question: 50
A $220$ V, $3$-phase, $4$-pole, $50$ Hz inductor motor of wound rotor type is supplied at rated voltage and frequency. The stator resistance, magnetizing reactance, and core loss are negligible. The maximum torque produced by the rotor ... resistance (in Ohm) which must be inserted in a rotor phase if the maximum torque is to occur at start is _________.

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GATE Electrical 2015 Set 2 | Question: 47
A three-winding transformer is connected to an $AC$ voltage source as shown in the figure. The number of turns are as follows: $N_{1} = 100, N_{2} = 50, N_{3} = 50$ ... in Ampere? $1\angle 90^{\circ}$ $1\angle 270^{\circ}$ $4\angle 90^{\circ}$ $4\angle 270^{\circ}$

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GATE Electrical 2015 Set 2 | Question: 40
The incremental costs (in Rupees/MWh) of operating two generating units are functions of their respective powers $P_{1}$ and $P_{2}$ in $MW$, and are given by $\dfrac{dC_{1}}{dP_{1}}=0.2P_{1}+50$ ... $dC_{2}/dP_{2} = 68.8$ Rs/MWh. If the generations are rescheduled to minimize the total cost, then $P_{2}$ is ________.

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GATE Electrical 2015 Set 2 | Question: 45
A symmetrical square wave of $50\%$ duty cycle has amplitude of $\pm15$ V and time period of $0.4\pi$ ms. This square wave is applied across a series $RLC$ circuit with $R = 5 \Omega$, $L = 10$ mH, and $C = 4 \mu F$. The amplitude of the $5000$ rad/s component of the capacitor voltage (in Volt) is ______.

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11

GATE Electrical 2015 Set 2 | Question: 43
A balanced (positive sequence) three-phase $AC$ voltage source is connected to a balanced, star connected load through a star-delta transformer as shown in the figure. The line-to-line voltage rating is $230$ V on the star side, and $115$ V on the delta ... Ampere? $50\angle 30^\circ$ $50\angle- 30^\circ$ $50\sqrt{3}\angle 30^\circ$ $200\angle 30^\circ$

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12

GATE Electrical 2015 Set 2 | Question: 49
A three-phase, $11$ kV, $50$ Hz, $2$ pole, star connected, cylindrical rotor synchronous motor is connected to an $11$ kV, $50$ Hz source. Its synchronous reactance is $50 \Omega$ per phase, and its stator resistance is negligible. The ... torque is increased so that the stator current is $120$ A, then the load angle (in degrees) at this load is __________.

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13

GATE Electrical 2015 Set 2 | Question: 48
With an armature voltage of $100$ V and rated field winding voltage, the speed of a separately excited $DC$ motor driving a fan is $1000$ rpm, and its armature current is $10$ A. The armature resistance is $1 \Omega$. The load ... rotational losses, the value of the armature voltage (in Volt) which will reduce the rotor speed to $500$ rpm is _________.

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14

GATE Electrical 2015 Set 2 | Question: 46
Two identical coils each having inductance $L$ are placed together on the same core. If an overall inductance of $\alpha L$ is obtained by interconnecting these two coils, the minimum value of $\alpha$ is ________.

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15

GATE Electrical 2015 Set 2 | Question: 41
A composite conductor consists of three conductors of radius $R$ each. The conductors are arranged as shown below. The geometric mean radius $(GMR)$ (in cm) of the composite conductor is $kR$. The value of $k$ is __________.

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16

GATE Electrical 2015 Set 2 | Question: 44
In the given network $V_{1}=100\angle 0^{\circ}V, V_{2}=100\angle -120^{\circ}V, V_{3}=100\angle +120^{\circ}V$. The phasor current $i$ (in Ampere) is $173.2\angle -60^{\circ}$ $173.2\angle 120^{\circ}$ $100.0\angle -60^{\circ}$ $100.0\angle 120^{\circ}$

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17

GATE Electrical 2015 Set 2 | Question: 42
A 3-phase transformer rated for $33 kV/11 kV$ is connected in delta/star as shown in figure. The current transformers ($CTs$) on low and high voltage sides have a ratio of $500/5$. Find the currents $i_{1}$ and $i_{2}$, if the fault current is $300$ ... $i_{1}=0A, i_{2}=1\sqrt{3}A$ $i_{1}=1\sqrt{3}A, i_{2}=1\sqrt{3}A$

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18

GATE Electrical 2015 Set 2 | Question: 38
A Boolean function $f(A, B, C, D) = \prod (1,5,12,15)$ is to be implemented using an $8 \times 1$ multiplexer ($A$ is $MSB$). The inputs $ABC$ are connected to the select inputs $S_{2} S_{1} S_{0}$ of the multiplexer respectively. Which one of the following ... $D, 1, D, 1, 1, 1, \overline{D}, D$ $\overline{D}, 0, \overline{D}, 0, 0, 0,D, \overline{D}$

makhdoom ghaya asked in Analog and Digital Electronics Feb 12, 2017

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19

GATE Electrical 2015 Set 2 | Question: 37
In the following sequential circuit, the initial state (before the first clock pulse) of the circuit is $Q_{1}Q_{0}=00$. The state $(Q_{1}Q_{0})$, immediately after the $333^{rd}$ clock pulse is $00$ $01$ $10$ $11$

makhdoom ghaya asked in Analog and Digital Electronics Feb 12, 2017

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20

GATE Electrical 2015 Set 2 | Question: 28
A differential equation $\dfrac{di}{dt}-0.2i=0$ is applicable over $−10 < t < 10$. If $i(4) = 10$, then $i(−5)$ is _________.

makhdoom ghaya asked in Differential Equations Feb 12, 2017

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21

GATE Electrical 2015 Set 2 | Question: 27
Two coins $R$ and $S$ are tossed. The $4$ joint events $H_{R}H_{S}, T_{R}T_{S}, H_{R}T_{S}, T_{R}H_{S}$ have probabilities $0.28, 0.18, 0.30, 0.24$, respectively, where $H$ represents head and $T$ represents tail. Which one of the ... is TRUE? The coin tosses are independent. $R$ is fair, $S$ is not. $S$ is fair, $R$ is not. The coin tosses are dependent.

makhdoom ghaya asked in Probability & Statistics Feb 12, 2017

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22

GATE Electrical 2015 Set 2 | Question: 33
In the given rectifier, the delay angle of the thyristor $T_{1}$ measured from the positive going zero crossing of $V_{s}$ is $30^\circ$. If the input voltage $V_{s}$ is $100 \sin(100 \pi t) V$, the average voltage across $R$ (in Volt) under steady-state is _________.

makhdoom ghaya asked in Analog and Digital Electronics Feb 12, 2017

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23

GATE Electrical 2015 Set 2 | Question: 36
Two semi-infinite conducting sheets are placed at right angles to each other as shown in the figure. A point charge of $+Q$ is placed at a distance of $d$ from both sheets. The net force on the charge is $\dfrac{Q^{2}}{4\pi \in_{0}} \frac{Q}{d^{2}}$, where $K$ is ... $\dfrac{1-2\sqrt{2}}{8\sqrt{2}} \hat{t}+\dfrac{1-2\sqrt{2}}{8\sqrt{2}} \hat{j}$

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24

GATE Electrical 2015 Set 2 | Question: 31
A buck converter feeding a variable resistive load is shown in the figure. The switching frequency of the switch $S$ is $100$ kHz and the duty ratio is $0.6$. The output voltage $V_{o}$ is $36$ V. Assume that all the components are ideal ... is ripple-free. The value of $R$ (in Ohm) that will make the inductor current ($i_{L}$) just continuous is _________.

makhdoom ghaya asked in Analog and Digital Electronics Feb 12, 2017

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25

GATE Electrical 2015 Set 2 | Question: 29
Consider a signal defined by $x(t)= \begin{cases} e^{j10 t} & \text{for } \mid t \mid \leq 1 \\ 0& \text{for } \mid t \mid > 1\end{cases}$ Its Fourier Transform is $\dfrac{2 \sin (\omega -10)}{\omega - 10}\\$ ... $\dfrac{2 \sin \omega}{\omega - 10} \\$ $e^{j10 \omega }\dfrac{2 \sin\omega }{\omega }$

makhdoom ghaya asked in Signals and Systems Feb 12, 2017

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26

GATE Electrical 2015 Set 2 | Question: 34
For linear time invariant systems, that are Bounded Input Bounded Output stable, which one of the following statements is TRUE? The impulse response will be integrable, but may not be absolutely integrable. The unit impulse response will have finite support. The unit step response will be absolutely integrable. The unit step response will be bounded

makhdoom ghaya asked in Signals and Systems Feb 12, 2017

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27

GATE Electrical 2015 Set 2 | Question: 32
For the switching converter shown in the following figure, assume steady-state operation. Also assume that the components are ideal, the inductor current is always positive and continuous and switching period is $T_{s}$. If the voltage $V_{L}$ is as shown, the duty cycle of the switch $S$ is ________.

makhdoom ghaya asked in Analog and Digital Electronics Feb 12, 2017

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28

GATE Electrical 2015 Set 2 | Question: 30
The coils of a wattmeter have resistances $0.01 \Omega$ and $1000 \Omega$; their inductances may be neglected. The wattmeter is connected as shown in the figure, to measure the power consumed by a load, which draws $25 A$ at power factor $0.8$. The voltage across the load terminals is $30 V$. The percentage error on the wattmeter reading is ________.

makhdoom ghaya asked in Electric Circuits Feb 12, 2017

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29

GATE Electrical 2015 Set 2 | Question: 35
The $z$-Transform of a sequence $x[n]$ is given as $X(z)=2z+4-4/z+3/z^{2}$. If $y[n]$ is the first difference of $x[n]$, then $Y(z)$ is given by $2z+2-8/z+7/z^{2}-3/z^{3}$ $-2z+2-6/z+1/z^{2}-3/z^{3}$ $-2z-2+8/z-7/z^{2}+3/z^{3}$ $4z-2-8/z-1/z^{2}+3/z^{3}$

makhdoom ghaya asked in Signals and Systems Feb 12, 2017

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30

GATE Electrical 2015 Set 2 | Question: 26
The volume enclosed by the surface $f(x, y) = e^{x}$ over the triangle bounded by the lines $x = y; x = 0; y = 1$ in the $xy$ plane is ________.

makhdoom ghaya asked in Calculus Feb 12, 2017

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31

GATE Electrical 2015 Set 2 | Question: 18
A series $RL$ circuit is excited at $t = 0$ by closing a switch as shown in the figure. Assuming zero initial conditions, the value of $\dfrac{d^{2}i}{dt^{2}}$ at $t=0^{+}$ is $\dfrac{V}{L} \\$ $\dfrac{-V}{R} \\$ $0 \\$ $\dfrac{-RV}{L^{2}}$

makhdoom ghaya asked in Electric Circuits Feb 12, 2017

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32

GATE Electrical 2015 Set 2 | Question: 17
A $3$-bus power system network consists of 3 transmission lines. The bus admittance matrix of the uncompensated system is $\begin{bmatrix} -j6 &j3 &j4 \\ j3&-j7 &j5 \\ j4& j5 & -j8 \end{bmatrix}$ pu. If the shunt ... $−j7.0$ $−j8.5$ $−j7.5$ $−j9.0$

makhdoom ghaya asked in Power Systems Feb 12, 2017

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33

GATE Electrical 2015 Set 2 | Question: 24
An open loop control system results in a response of $e^{-2t}(\sin 5t+\cos 5t)$ for a unit impulse input. The $DC$ gain of the control system is ________.

makhdoom ghaya asked in Control Systems Feb 12, 2017

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34

GATE Electrical 2015 Set 2 | Question: 22
The figure shows the per-phase equivalent circuit of a two-pole three-phase induction motor operating at $50$ Hz. The “air-gap” voltage, $V_{g}$ across the magnetizing inductance, is $210$ V rms, and the slip, $s$, is $0.05$. The torque (in Nm) produced by the motor is _________.

makhdoom ghaya asked in Electrical Machines Feb 12, 2017

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35

GATE Electrical 2015 Set 2 | Question: 21
A shunt-connected $DC$ motor operates at its rated terminal voltage. Its no-load speed is $200$ radian/second. At its rated torque of $500$ Nm, its speed is $180$ radian/second. The motor is used to directly drive a load whose ... . Neglecting rotational losses, the steady-state speed (in radian/second) of the motor, when it drives this load, is _________.

makhdoom ghaya asked in Electrical Machines Feb 12, 2017

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36

GATE Electrical 2015 Set 2 | Question: 19
The current $i$ (in Ampere) in the $2 \Omega$ resistor of the given network is ________.

makhdoom ghaya asked in Electric Circuits Feb 12, 2017

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37

GATE Electrical 2015 Set 2 | Question: 15
When a bipolar junction transistor is operating in the saturation mode, which one of the following statements is TRUE about the state of its collector-base $(CB)$ and the base-emitter $(BE)$ junctions? The $CB$ ... . Both the $CB$ and $BE$ junctions are forward biased. Both the $CB$ and $BE$ junctions are reverse biased.

makhdoom ghaya asked in Analog and Digital Electronics Feb 12, 2017

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38

GATE Electrical 2015 Set 2 | Question: 16
The synchronous generator shown in the figure is supplying active power to an infinite bus via two short, lossless transmission lines, and is initially in steady state. The mechanical power input to the generator and the voltage magnitude $E$ are ... . Which one of the following waveforms of the rotor angle $\delta$ shows the transient correctly?

makhdoom ghaya asked in Power Systems Feb 12, 2017

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39

GATE Electrical 2015 Set 2 | Question: 20
Find the transformer ratios $a$ and $b$ such that the impedance ($Z_{in}$) is resistive and equals $2.5 \Omega$ when the network is excited with a sine wave voltage of angular frequency of $5000$ rad/s. $a = 0.5, b = 2.0$ $a = 2.0, b = 0.5$ $a = 1.0, b = 1.0$ $a = 4.0, b = 0.5$

makhdoom ghaya asked in Power Systems Feb 12, 2017

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40

GATE Electrical 2015 Set 2 | Question: 23
A $4$-pole, separately excited, wave wound $DC$ machine with negligible armature resistance is rated for $230$ V and $5$ kW at a speed of $1200$ rpm. If the same armature coils are reconnected to form a lap winding, what is the rated voltage (in volts) and ... field circuit is left unchanged ? $230$ and $5$ $115$ and $5$ $115$ and $2.5$ $230$ and $2.5$

makhdoom ghaya asked in Electrical Machines Feb 12, 2017

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