GATE EE 2012

## GATE EE

The $$i$$-v characteristics of the diode in the circuit given below are
$$$i = \left\{ {\matrix{
{{{v - 0.7} \over {5

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The voltage gain $${A_V}$$ of the circuit shown below is

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The circuit shown is a

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The feedback system shown below oscillates at $$2$$ rad/s when

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A system with transfer function $$\,G\left( s \right) = {{\left( {{s^2} + 9} \right)\left( {s + 2} \right)} \over {\left

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The transfer function of a compensator is given as $${G_c}\left( s \right) = {{s + a} \over {s + b}}$$
$${G_c}\left( s

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The transfer function of a compensator is given as $${G_c}\left( s \right) = {{s + a} \over {s + b}}$$
The phase of the

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The state variable description of an $$LTI$$ system is given by
$$$\left( {\matrix{
{\mathop {{x_1}}\limits^ \bullet

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In the sum of products function $$f\,\left( {X,\,Y,\,Z} \right) = \sum \left( {2,\,\,3,\,\,4,\,\,5} \right),$$ the prime

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The output $$Y$$ of a $$2$$ $$-$$ bit comparator is logic $$1$$ whenever the $$2$$-bit input $$A$$ is greater than the $

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Consider the given circuit. In this circuit, the race around

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The state transition diagram for the logic circuit shown is

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The impedance looking into nodes 1 and 2 in the given circuit is

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In the circuit shown below, the current through the inductor is

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If $$V_A-V_B=\;6\;V$$, then $$V_C-V_D$$ is

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Assuming both the voltage sources are in phase, the value of R for which maximum power is
transferred from circuit A to

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In the following figure, C1 and C2 are ideal capacitors. C1 has been charged to 12 V before the ideal
switch S is closed

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The average power delivered to an impedance $$\left(4-j3\right)$$ Ω by a current $$5\cos\left(100\mathrm{πt}+100\right)\

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A two phase load draws the following phase currents:
$$i_1\left(t\right)=I_m\sin\left(\omega t-\phi_1\right)$$,

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In the circuit shown, the three voltmeter readings are V1 = 220V, V2 = 122V , V3 = 136V.
If RL=5 Ω , the approximate po

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In the circuit shown, the three voltmeter readings are V1 = 220V, V2 = 122V , V3 = 136V.
The power factor of the load i

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With 10 V dc connected at port A in the linear nonreciprocal two-port network shown below, the following
were observed:

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With 10 V dc connected at port A in the linear nonreciprocal two-port network shown below, the following
were observed:

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A periodic voltage waveform observed on an oscilloscope across a load is shown. A permanent magnet moving coil $$(PMMC)$

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An analog voltmeter uses external multiplier settings. With a multiplier setting of $$20\,\,k\Omega ,$$ it reads $$440$$

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The bridge method commonly used for finding mutual inductance is

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For the circuit shown in the figure, the voltage and current expressions are
$$v\left( t \right) = {E_1}\sin \left( {\o

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A 220 V, 15 kW, 1000 rpm shunt motor with armature resistance of 0.25 Ω , has a rated line
current of 68 A and a rated

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A single phase 10 kVA, 50 Hz transformer with 1 kV primary winding draws 0.5 A and 55 W, at
rated voltage and frequency,

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The slip of an induction motor normally does not depend on

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The locked rotor current in a 3-phase, star connected 15 kW, 4-pole, 230 V, 50 Hz induction motor
at rated conditions is

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Given that $$A = \left[ {\matrix{
{ - 5} & { - 3} \cr
2 & 0 \cr
} } \right]$$ and $${\rm I} = \left[

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The maximum value of $$f\left( x \right) = {x^3} - 9{x^2} + 24x + 5$$ in the interval $$\left[ {1,6} \right]$$ is

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The direction of vector $$A$$ is radially outward from the origin, with $$\left| A \right| = K\,{r^n}$$ where $${r^2} =

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Two independent random variables $$X$$ and $$Y$$ are uniformly distributed in the interval $$\left[ { - 1,1} \right].$$

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A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd

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With initial condition $$x\left( 1 \right)\,\,\, = \,\,\,\,0.5,\,\,\,$$ the solution of the differential equation, $$\,\

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If $$x\left[ N \right] = {\left( {1/3} \right)^{\left| n \right|}} - {\left( {1/2} \right)^n}\,u\left[ n \right],$$ then

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The unilateral Laplace transform of $$f(t)$$ is
$$\,{1 \over {{s^2} + s + 1}}.$$ The unilateral Laplace transform of $$

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Consider the differential equation
$${{{d^2}y\left( t \right)} \over {d{t^2}}} + 2{{dy\left( t \right)} \over {dt}} + y

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If $$x = \sqrt { - 1} ,\,\,$$ then the value of $${X^x}$$ is

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Given $$f\left( z \right) = {1 \over {z + 1}} - {2 \over {z + 3}}.$$ If $$C$$ is a counterclockwise path in the $$z$$-pl

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The typical ratio of latching current to holding current in a $$20$$ $$A$$ thyristor is

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A half-controlled single-phase bridge rectifier is supplying an $$R$$-$$L$$ load. It is operated at a firing angle $$α$$

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In the circuit shown, an ideal switch $$S$$ is operated at $$100$$ $$kHz$$ with a duty ratio of $$50%$$. Given that $$\D

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In the $$3$$-phase inverter circuit shown, the load is balanced and the gating scheme is $${180^ \circ }$$ -conduction m

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In the $$3$$-phase inverter circuit shown, the load is balanced and the gating scheme is $${180^ \circ }$$ -conduction m

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For the system shown below, SD1 and SD2 are complex power demands at bus $$1$$ and bus $$2$$ respectively. If $$\left| {

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The figure shows a two-generator system supplying a load of $${P_D} = 40\,MW,$$ connected at bus $$2.$$
The fuel cost

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A cylindrical rotor generator delivers $$0.5$$ pu power in the steady-state to an infinite bus through a transmission li

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The sequence components of the fault current are as follows:
$${{\rm I}_{positive}} = j1.5\,pu,\,\,{{\rm I}_{negative}}

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The bus admittance matrix of a three-bus three-line system is
$$y = j\left[ {\matrix{
{ - 13} & {10} & 5 \cr

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L et y[n] denote the convolution of h[n] and g[n], where $$h\left[n\right]=\left(1/2\right)^nu\left[n\right]$$ and g[n]

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The input x(t) and output y(t) of a system are related as $$\int_{-\infty}^tx\left(\tau\right)\cos\left(3\tau\right)d\ta

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The Fourier transform of a signal h(t) is $$H\left(j\omega\right)=\left(2\cos\omega\right)\left(\sin2\omega\right)/\omeg

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The unilateral Laplace transform of f(t) is
$$\frac1{s^2\;+\;s\;+\;1}$$. The unilateral Laplace transform of tf(t) is

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