GATE ECE 2012

## GATE ECE

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

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

View Question The voltage gain Av of the circuit shown below is

View Question The circuit shown is a

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

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

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

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

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

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

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

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

View Question A system with transfer function
g(s) = $${{\left( {{s^2} + 9} \right)\left( {s + 2} \right)} \over {\left( {s + 1} \rig

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

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

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

View Question 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

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

View Question The state transition diagram for the logic circuit shown is

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

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

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

View Question 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

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

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

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

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

View Question In the circuit shown

View Question 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 $$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

View Question If VA - VB = 6 V then VC - VD is

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

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

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

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

View Question The average power delivered to an impedance $(4-j 3) \Omega$ by a current $5 \cos (100 \pi t+100) A$ is

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

View Question 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

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

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

View Question ## General Aptitude

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

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

View Question 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

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

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

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

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

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

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

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

View Question