GATE ECE 2012

## GATE ECE

The diodes and capacitors in the circuit shown are ideal. The voltage v(t)
across the diode D1 is

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The current ib through the base of a silicon npn transistor is
$$1\;+\;0.1\;\cos\left(10000\;\mathrm\pi\;\mathrm t\right

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The voltage gain Av of the circuit shown below is

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The circuit shown is a

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The signal m(t) as shown is applied both to a phase modulator (with
kp
as the phase constant) and
a frequency modulator

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A source alphabet consists of N symbols with the probability of the first two symbols being the same. A source encoder i

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In a base band communications link, frequencies up to 3500 Hz are used for signaling. Using a raised cosine pulse with 7

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Two independent random variable X and Y are uniformly distributed in the interval [ - 1, 1]. The probability that max [X

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The power spectral density of a real process X(t) for positive frequencies is shown below. The value of $$E\,\left[ {{X^

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A BPSK scheme operating over an AWGN channel with noise power spectral density of N02, uses equi-probable signals
$$$

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A binary symmetric channel (BSC) has a transition probability of 1/8. If the binary transmit symbol X is such that P(X

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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(s) = $${{\left( {{s^2} + 9} \right)\left( {s + 2} \right)} \over {\left( {s + 1} \rig

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The transfer function of a compensator is given as $${G_C}(s) = {{s + a} \over {s + b}}.$$
$${G_C}(s)$$ is a lead compe

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The transfer function of a compensator is given as $${G_C}(s) = {{s + a} \over {s + b}}.$$
The phase of the above lead

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The state variable description of an LTI system is given by
where y is the output and u is input. The system is contro

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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 2-bit input B.
The number

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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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An infinitely long uniform solid wire of radius a carries a uniform dc current of density $$\widehat{\mathrm j}$$
The ma

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An infinitely long uniform solid wire of radius a carries a uniform dc current of density $$\widehat{\mathrm j}$$.
A hol

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The electric field of a uniform plane electromagnetic wave in free spce, along the positive x direction, is given by $

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A coaxial cable with an inner diameter of 1 mm and outer diameter of 2.4 mm is filled with a dielectric of relative perm

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A plane wave propagating in air with $$\vec E = \left( {8{{\widehat a}_x} + 6{{\widehat a}_y} + 5{{\widehat a}_z}} \righ

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A transmission line with a characteristic impedance of 100 $$\Omega $$ is used to match a 50 $$\Omega $$ section to a 20

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The magnetic field along the propagation direction inside a rectangular waveguide with the cross section shown in the fi

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The radiation pattern of an antenna in spherical co-ordinates is given by
$$$F\,(\theta )\, = {\cos ^4}\,\theta \,\,\,;\

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In the circuit shown

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The source of a silicon (ni = 1010 per cm3) n - channel MOS transistor has an aewa of 1 sq $$\mu m$$ and a depth of 1 $$

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In the three dimensional view of a silicon n-channel MOS transistor shown below, $$\delta = 20$$ nm. The transistor is

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In the three dimensional view of a silicon n-channel MOS transistor shown below, $$\delta = 20$$ nm. The transistor is

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In the CMOS circuit shown, electron and hole mobilities are equal, and M1 and M2 are equally sized. The device M1 is in

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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 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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In the circuit shown below, current through the inductor is

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

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If VA - VB = 6 V then VC - VD 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 c

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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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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 $(4-j 3) \Omega$ by a current $5 \cos (100 \pi t+100) A$ is

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

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The input x(t) and output y(t) of a system are related as y(t) = $$\int\limits_{ - \infty }^t x (\tau )\cos (3\tau )d\ta

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The Fourier transform of a signal h(t) is $$H(j\omega )$$ =(2 cos $$\omega $$) (sin 2$$\omega $$) / $$\omega $$. The val

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Let $$y\left[ n \right]$$ denote the convolution of $$h\left[ n \right]$$ and $$g\left[ n \right]$$, where $$h\left[ n \

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## General Aptitude

If (1.001)1259 = 3.52 and (1.001)2062 = 7.85, then (1.001)3321 =

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Raju has 14 currency notes in his pocket consisting of only Rs. 20 notes and Rs. 10 notes. The total money value of the

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A and B are friends. They decide to meet between 1 PM and 2 PM on a given day. There is a
condition that whoever arrives

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The data given in the following table summarizes the monthly budget of an average household.
The approximate percentage

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There are eight bags of rice looking alike, seven of which have equal weight and one is slightly
heavier. The weighing b

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One of the legacies of the Roman legions was discipline. In the legions, military law prevailed
and discipline was bruta

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Choose the most appropriate alternative from the options given below to complete the following
sentence:
If the tired so

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Choose the most appropriate word from the options given below to complete the following
sentence:
Given the seriousness

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Which one of the following options is the closest in meaning to the word given below?
Latitude

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One of the parts (A, B, C, D) in the sentence given below contains an ERROR. Which one of the
following is INCORRECT?
I

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