GATE EE 2015 Set 2
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GATE EE

In the following circuit, the input voltage $${V_{in}}$$ is $$100\sin \left( {100\pi t} \right).$$ For $$100\pi RC = 50,
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When a bipolar junction transistor is operating in the saturation mode, which one of the following statements is TRUE ab
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In the following circuit, the transistor is in active mode and $${V_C} = 2V.$$ To get $${V_C} = 4V,$$ we replace $${R_C}
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The operational amplifier shown in the figure is ideal. The input voltage (in Volt) is $${V_i} = 2\sin \left( {2\pi \ti
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The filters $${F_1}$$ and $${F_2}$$ having characteristics as shown in figures $$(a)$$ and $$(b)$$ are connected as show
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The saturation voltage of the ideal op-amp shown below is $$ \pm 10\,V.$$ The output voltage $${V_O}$$ of the following
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The unit step response of a system with the transfer function $$G\left( s \right) = {{1 - 2s} \over {1 + s}}$$ is given
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An open loop control system results in a response of $${e^{ - 2t}}\left( {\sin 5t + \cos 5t} \right)$$ for a unit impuls
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The following discrete-time equations result from the numerical integration of the differential equations of an un-dampe
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An open loop transfer function $$G(s)$$ of system is $$G\left( s \right) = {k \over {s\left( {s + 1} \right)\left( {s +
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Nyquist plots of two functions $${G_1}\left( s \right)$$ and $${G_2}\left( s \right)$$ are shown in figure. Nyquist p
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For the system governed by the set of equations: $$$\eqalign{ & d{x_1}/dt = 2{x_1} + {x_2} + u \cr & d{x_
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Consider the following Sum of products expression, $$F.$$ $$F = ABC + \overline A \overline B C + A\overline B C + \ove
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A Boolean function $$f\left( {A,B,C,D} \right) = \Pi \left( {1,5,12,15} \right)$$ is to be implemented using an $$8 \tim
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In the following sequential circuit, the initial state (before the first clock pulse) of the circuit is $${Q_1}{Q_0}$$ $
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A series RL circuit is excited at t = 0 by closing a switch as shown in the figure. Assuming zero initial conditions, th
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Find the transformer ratios a and b that the impedance (Zin) is resistive and equal 2.5 Ω when the network is excited wi
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In the given network $$V_1=100\angle0^\circ V$$, $$V_2=100\angle-120^\circ V$$, $$V_3=100\angle+120^\circ V$$. The phaso
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Two identical coils each having inductance L are placed together on the same core. If an overall inductance of $$\alpha$
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A symmetrical square wave of 50% duty cycle has amplitude of ±15V and time period of 0.4$$\mathrm\pi$$ ms. This square w
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The current i (in Ampere) in the 2 Ω resistor of the given network is _________.
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A capacitive voltage divider is used to measure the bus voltage Vbus in a high-voltage 50Hz AC system as shown in the fi
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Match the following.
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A 3-phase balanced load which has a power factor of 0.707 is connected to a balanced supply. The power consumed by the l
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The coils of a wattmeter have resistances $$0.01$$ $$\Omega $$ and $$1000$$ $$\Omega $$; their inductances may be neglec
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A three-phase, $$11$$ $$kV,$$ $$50$$ $$Hz,$$ $$2$$ pole, star connected, cylindrical rotor synchronous motor is connecte
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A 4-pole, separately excited, wave wound DC machine with negligible armature resistance is rated for 230 V and 5 kW at a
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A shunt-connected DC motor operates at its rated terminal voltage. Its no-load speed is 200 radian/second. At its rated
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With an armature voltage of 100 V and rated field winding voltage, the speed of a separately excited DC motor driving a
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Two three-phase transformers are realized using single-phase transformers as shown in the figure. The phase difference
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A balanced (positive sequence) three-phase AC voltage source is connected to a balanced, star connected load through a s
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A three-winding transformer is connected to an AC voltage source as shown in the figure. The number of turns are as foll
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The figure shows the per-phase equivalent circuit of a two-pole three-phase induction motor operating at 50 Hz. The 'air
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A 220 V, 3-phase, 4-pole, 50 Hz inductor motor of wound rotor type is supplied at rated voltage and frequency. The stato
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Match the following.
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Two semi-infinite conducting sheets are placed at right angles to each other as shown in the figure. A point charge of +
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Two semi-infinite dielectric regions are separated by a plane boundary at y = 0. The dielectric constants of region 1 (y
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A circular turn of radius 1 m revolves at 60 rpm about its diameter aligned with the x-axis as shown in the figure. The
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Given $$f\left( z \right) = g\left( z \right) + h\left( z \right),$$ where $$f,g,h$$ are complex valued functions of a c
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The Laplace transform of $$f\left( t \right) = 2\sqrt {t/\pi } $$$$\,\,\,\,\,$$ is$$\,\,\,\,\,$$ $${s^{ - 3/2}}.$$ The L
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We have a set of $$3$$ linear equations in $$3$$ unknown. $$'X \equiv Y'$$ means $$X$$ and $$Y$$ are equivalent statemen
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The volume enclosed by the surface $$f\left( {x,y} \right) = {e^x}$$ over the triangle bounded by the lines $$x=y;$$ $$x
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Match the following. List-$${\rm I}$$ $$P.$$ Stoke's Theorem $$Q.$$ Gauss's Theorem $$R.$$ Divergence Theorem $$S.$$ Ca
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Two coins $$R$$ and $$S$$ are tossed. The $$4$$ joint events $$\,\,\,\,\,\,{H_R}{H_S},\,\,\,\,{T_R}{T_S},\,\,\,\,{H_R}{T
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A differential equation $$\,\,{{di} \over {dt}} - 0.21 = 0\,\,$$ is applicable over $$\,\, - 10 < t < 10.\,\,$$ If
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In the given rectifier, the delay angle of the thyristor $${T_1}$$ measured from the positive going zero crossing of $${
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For the switching converter shown in the following figure, assume steady-state operation. Also assume that the component
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The incremental costs (in rupees/$$MWh$$) of operating two generating units are functions of their respective powers $${
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A $$3$$-phase transformer rated for $$33 kV/11kV$$ is connected in delta/star as shown in figure. The current transforme
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A $$3$$-bus power system network consists of $$3$$ transmission lines. The bus admittance matrix of the uncompensated sy
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The synchronous generator shown in the figure is supplying active power to an infinite bus via two short, lossless trans
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A composite conductor consists of three conductors of radius $$R$$ each. The conductors are arranged as shown below. The
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For linear time invariant systems, that are Bounded Input Bounded stable, which one of the following statement is TRUE?
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Consider a signal defined by $$$x\left(t\right)=\left\{\begin{array}{l}e^{j10t}\;\;\;for\;\left|t\right|\leq1\\0\;\;\;\;
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The Laplace transform of f(t)=$$2\sqrt{t/\mathrm\pi}$$ is $$s^{-3/2}$$. The Laplace transform of g(t)=$$\sqrt{1/\mathrm
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The z-Transform of a sequence x[n] is given as X(z) = 2z+4−4/z+3/z2. If y[n] is the first difference of x[n], then Y(Z)
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