Recent questions tagged gate2015-ee-2

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GATE2015-2-52
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 $h$. $\frac{x_{k+1}-x_{k}}{h}=y_{k}$ ... stable for $0 < h <\frac{1}{2\pi}$ The system is stable for $\frac{1}{2\pi}<h<\frac{1}{\pi}$

asked Feb 12, 2017 in new by makhdoom ghaya (9.3k points)

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GATE2015-2-53
The unit step response of a system with the transfer function $G(s)=\frac{1-2s}{1+s}$ is given by which one of the following waveforms?

asked Feb 12, 2017 in new by makhdoom ghaya (9.3k points)

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GATE2015-2-51
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 _______.

asked Feb 12, 2017 in new by makhdoom ghaya (9.3k points)

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GATE2015-2-55
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 $3(s+1)/(s^{2}-2s+2)$ $3(2s+1)/(s^{2}-2s+1)$ $(s+1)/(s^{2}-2s+1)$ $3(2s+1)/(s^{2}-2s+2)$

asked Feb 12, 2017 in new by makhdoom ghaya (9.3k points)

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5

GATE2015-2-54
An open loop transfer function $G(s)$ of a system is $G(s)=\frac{k}{s(s+1)(s+2)}$ 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

asked Feb 12, 2017 in new by makhdoom ghaya (9.3k points)

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GATE2015-2-47
A three-winding transformer is connected to an $AC$ voltage source as shown in the figure. The number of turns are as follows: $N_{1} = 100, N_{2} = 50, N_{3} = 50$. If the magnetizing current is neglected, and the currents in two windings are $\bar{I}_{2}=2\angle 30^{\circ}$ ... $1\angle 90^{\circ}$ $1\angle 270^{\circ}$ $4\angle 90^{\circ}$ $4\angle 270^{\circ}$

asked Feb 12, 2017 in new by makhdoom ghaya (9.3k points)

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GATE2015-2-50
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 is $225$ % of ... of external resistance (in Ohm) which must be inserted in a rotor phase if the maximum torque is to occur at start is _________.

asked Feb 12, 2017 in new by makhdoom ghaya (9.3k points)

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GATE2015-2-49
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 motor has a ... the load torque is increased so that the stator current is $120$ A, then the load angle (in degrees) at this load is __________.

asked Feb 12, 2017 in new by makhdoom ghaya (9.3k points)

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9

GATE2015-2-48
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 torque of the ... speed. Neglecting rotational losses, the value of the armature voltage (in Volt) which will reduce the rotor speed to $500$ rpm is _________.

asked Feb 12, 2017 in new by makhdoom ghaya (9.3k points)

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GATE2015-2-46
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 ________.

asked Feb 12, 2017 in new by makhdoom ghaya (9.3k points)

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GATE2015-2-45
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 ______.

asked Feb 12, 2017 in new by makhdoom ghaya (9.3k points)

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GATE2015-2-41
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 __________.

asked Feb 12, 2017 in new by makhdoom ghaya (9.3k points)

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GATE2015-2-40
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 $\frac{dC_{1}}{dP_{1}}=0.2P_{1}+50$ $\frac{dC_{2}}{dP_{2}}=0.24P_{2}+40$ ... Rs/MWh and $dC_{2}/dP_{2} = 68.8$ Rs/MWh. If the generations are rescheduled to minimize the total cost, then $P_{2}$ is ________.

asked Feb 12, 2017 in new by makhdoom ghaya (9.3k points)

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GATE2015-2-44
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 $173.2\angle -60^{\circ}$ $173.2\angle 120^{\circ}$ $100.0\angle -60^{\circ}$ $100.0\angle 120^{\circ}$

asked Feb 12, 2017 in new by makhdoom ghaya (9.3k points)

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GATE2015-2-39
The saturation voltage of the ideal op-amp shown below is $\pm 10$ V. The output voltage $v_{0}$ 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

asked Feb 12, 2017 in new by makhdoom ghaya (9.3k points)

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GATE2015-2-43
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 side. If the magnetizing current is ... $50\angle 30$° $50\angle- 30$° $50\sqrt{3}\angle 30$° $200\angle 30$°

asked Feb 12, 2017 in new by makhdoom ghaya (9.3k points)

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17

GATE2015-2-42
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 $300$ A as shown in figure. $i_{1}=1\sqrt{3}A, i_{2}=0A$ $i_{1}=0A, i_{2}=0A$ $i_{1}=0A, i_{2}=1\sqrt{3}A$ $i_{1}=1\sqrt{3}A, i_{2}=1\sqrt{3}A$

asked Feb 12, 2017 in new by makhdoom ghaya (9.3k points)

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18

GATE2015-2-37
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 $00$ $01$ $10$ $11$

asked Feb 12, 2017 in new by makhdoom ghaya (9.3k points)

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GATE2015-2-29
Consider a signal defined by $x(t)= = \begin{cases} e^{j10 t} & \text{for} |t|\leq 1 \\ 0& \text{for } |t| > 1 \end{cases}$ Its Fourier Transform is $\frac{2 \sin (\omega -10)}{\omega - 10}$ $2e^{j10}\frac{ \sin (\omega -10)}{\omega - 10}$ $\frac{2 \sin \omega}{\omega - 10}$ $e^{j10 \omega }\frac{2 \sin\omega }{\omega }$

asked Feb 12, 2017 in Signals and Systems by makhdoom ghaya (9.3k points)

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GATE2015-2-27
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 following is TRUE? The coin tosses are independent. R is fair, S is not. S is fair, R is not. The coin tosses are dependent.

asked Feb 12, 2017 in Probability & Statistics by makhdoom ghaya (9.3k points)

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21

GATE2015-2-35
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 $2z+2-8/z+7/z^{2}-3/z^{3}$ $-2z+2-6/z+1/z^{2}-3/z^{3}$ $-2z-2+8/z-7/z^{2}+3/z^{3}$ $4z-2-8/z-1/z^{2}+3/z^{3}$

asked Feb 12, 2017 in Signals and Systems by makhdoom ghaya (9.3k points)

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GATE2015-2-36
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 $\frac{Q^{2}}{4\pi \in_{0}} \frac{Q}{d^{2}}$, where $K$ is given by $0$ ... $\frac{1-2\sqrt{2}}{8\sqrt{2}} \hat{t}+\frac{1-2\sqrt{2}}{8\sqrt{2}} \hat{j}$

asked Feb 12, 2017 in new by makhdoom ghaya (9.3k points)

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23

GATE2015-2-28
A differential equation $\frac{di}{dt}-0.2i=0$ is applicable over $−10 < t < 10$. If $i(4) = 10$, then $i(−5)$ is _________.

asked Feb 12, 2017 in Differential Equations by makhdoom ghaya (9.3k points)

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24

GATE2015-2-38
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 $S_{2} S_{1} S_{0}$ ... $D, 1, D, 1, 1, 1, \bar{D}, D$ $\bar{D}, 0, \bar{D}, 0, 0, 0,D, \bar{D}$

asked Feb 12, 2017 in new by makhdoom ghaya (9.3k points)

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25

GATE2015-2-31
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 $V_{0}$ is $36$ V. Assume that all the components are ideal, and that the output voltage is ripple-free. The value of $R$ (in Ohm) that will make the inductor current ($i_{L}$) just continuous is _________.

asked Feb 12, 2017 in Analog and Digital Electronics by makhdoom ghaya (9.3k points)

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26

GATE2015-2-34
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

asked Feb 12, 2017 in Signals and Systems by makhdoom ghaya (9.3k points)

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27

GATE2015-2-32
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 ________.

asked Feb 12, 2017 in Analog and Digital Electronics by makhdoom ghaya (9.3k points)

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28

GATE2015-2-30
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 ________.

asked Feb 12, 2017 in Electrical Circuits by makhdoom ghaya (9.3k points)

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29

GATE2015-2-33
In the given rectifier, the delay angle of the thyristor $T_{1}$ measured from the positive going zero crossing of $V_{s}$ is $30$°. If the input voltage $V_{s}$ is $100 \sin(100 \pi t) V$, the average voltage across $R$ (in Volt) under steady-state is _________.

asked Feb 12, 2017 in Analog and Digital Electronics by makhdoom ghaya (9.3k points)

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30

GATE2015-2-21
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 load torque $T_{L}$ ... . Neglecting rotational losses, the steady-state speed (in radian/second) of the motor, when it drives this load, is _________.

asked Feb 12, 2017 in Electrical Machines by makhdoom ghaya (9.3k points)

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31

GATE2015-2-26
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 ________.

asked Feb 12, 2017 in Calculus by makhdoom ghaya (9.3k points)

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32

GATE2015-2-24
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 ________.

asked Feb 12, 2017 in Control Systems by makhdoom ghaya (9.3k points)

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33

GATE2015-2-22
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 _________.

asked Feb 12, 2017 in Electrical Machines by makhdoom ghaya (9.3k points)

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34

GATE2015-2-19
The current $i$ (in Ampere) in the $2 \Omega$ resistor of the given network is ________.

asked Feb 12, 2017 in Electrical Circuits by makhdoom ghaya (9.3k points)

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35

GATE2015-2-15
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 $CB$ junction is forward biased and the $BE$ junction ... forward biased. Both the $CB$ and $BE$ junctions are forward biased. Both the $CB$ and $BE$ junctions are reverse biased.

asked Feb 12, 2017 in Analog and Digital Electronics by makhdoom ghaya (9.3k points)

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36

GATE2015-2-16
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 constant. If one ... transient. Which one of the following waveforms of the rotor angle $\delta$ shows the transient correctly?

asked Feb 12, 2017 in Power Systems by makhdoom ghaya (9.3k points)

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37

GATE2015-2-17
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 capacitance of all transmission ... $−j7.0$ $−j8.5$ $−j7.5$ $−j9.0$

asked Feb 12, 2017 in Power Systems by makhdoom ghaya (9.3k points)

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38

GATE2015-2-18
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 $\frac{d^{2}i}{dt^{2}}$ at $t=0^{+}$ is $\frac{V}{L}$ $\frac{-V}{R}$ $0$ $\frac{-RV}{L^{2}}$

asked Feb 12, 2017 in Electrical Circuits by makhdoom ghaya (9.3k points)

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39

GATE2015-2-20
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. $a = 0.5, b = 2.0$ $a = 2.0, b = 0.5$ $a = 1.0, b = 1.0$ $a = 4.0, b = 0.5$

asked Feb 12, 2017 in Power Systems by makhdoom ghaya (9.3k points)

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40

GATE2015-2-23
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 power (in kW) ... if the field circuit is left unchanged ? $230$ and $5$ $115$ and $5$ $115$ and $2.5$ $230$ and $2.5$

asked Feb 12, 2017 in Electrical Machines by makhdoom ghaya (9.3k points)