GATE ECE 2015 Set 2

## GATE ECE

If the circuit shown has to function as a clamping circuit, which one of the following
conditions should be satisfied fo

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The diode in the circuit given below has
VON = 0.7V
but is ideal otherwise. The current (in mA) in the 4kΩ resistor is _

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In the ac equivalent circuit shown, the two BJTs are biased in active region and have identical
parameters with β >&

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In the circuit shown, VO = VOA for switch SW in position A and V0= VOB for SW in position B. Assume that the opamp is id

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In the bistable circuit shown, the ideal opamp has saturation levels of $$ \pm 5V.$$ The value of R1 (in k$$\Omega $$ )

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For the voltage regulator circuit shown, the input voltage (Vin) is 20V $$ \pm $$ 20% and the regulated output voltage

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Assuming that the op-amp in the circuit shown below is ideal, the output voltage V0 (in volts)

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A zero mean white Gaussian noise having power spectral density $${{{N_0}} \over 2}$$ is passed through an $$ LTI $$
filt

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$$\mathop {\left\{ {{X_n}} \right\}}\nolimits_{n = - \infty }^{n = \infty } $$ is an independent and identically distri

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Let $$X \in \left\{ {0,1} \right\}$$ and $$Y \in \left\{ {0,1} \right\}$$ be two independent binary random variables.
If

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A sinusoidal signal of amplitude A is quantized by a uniform quantizer. Assume that the signal
utilizes all the represen

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Consider a binary, digital communication system which uses pulses g (t) and − g (t)for transmitting bits over an AWGN ch

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By performing cascading and/or summing/differencing operations using transfer function
blocks G1(s) and G2(s), one CANNO

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For the signal flow graph shown in the figure, the value of $$\frac{\mathrm C\left(\mathrm s\right)}{\mathrm R\left(\mat

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A unity negative feedback system has an open–loop transfer function $$G\left(s\right)=\frac K{s\left(s+1\right)}$$.The
g

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The output of a standard second–order system for a unit step input is given as $$$y\left(t\right)=1-\frac2{\sqrt3}e^{-t}

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The transfer function of a mass-spring damper system is given by
$${\rm{G(s) = }}{1 \over {M{s^2} + Bs + K}}$$
The freq

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The state variable representation of a system is given as
$$$\eqalign{
& \mathop x\limits^ \bullet = \left[ {\ma

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A function of Boolean variables X,Y and Z is expressed in terms of the min-terms as F(X, Y, Z)=$$\sum\limits_{}^{} {} $$

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In the figure shown, the output ܻ is required to be ܻ Y=AB+ $$\overline C $$$$\overline D $$. The gates G1 and G2 must b

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A 1-to-8 demultiplexer with data input D$$_{in}$$ , address inputs S$$_{0}$$, S$$_{1}$$, S$$_{2}$$ (with S$$_{0}$$ as th

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A mod-n counter using a synchronous binary up-counter with synchronous clear input is shown in the figure. The value of

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The figure shows a binary counter with synchronous clear input. With the decoding logic shown,
the counter works as a

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In a source free region in vacuum, if the electrostatic potential
$$\varphi\;=\;2x^2\;+y^2+cz^2$$ , the value of
constan

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The electric field of a uniform plane electromagnetic wave is
$$$\vec E = \left( {{{\overrightarrow a }_x} + j4{{\overr

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The electric field intensity of a plane wave propagating in a lossless non-magnetic medium is given by the following exp

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An air-filled rectangular waveguide of internal dimension $$a\,\,cm\,\, \times \,\,b\,\,cm$$ (a > b) has a cutoff fre

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Two half-wave dipole antennas placed as shown in the figure are excited with sinusoidally varying currents of frequency

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An n–type silicon sample is uniformly illuminated with light which generates 1020
electron hole pairs per cm3
per second

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A piece of silicon is doped uniformly with phosphorous with a doping concentration of
$$10^{16}/cm^2$$. The expected val

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A dc voltage of 10V is applied across an n–type silicon bar having a rectangular cross–section
and a length of 1cm as sh

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In a MOS capacitor with an oxide layer thickness of 10 nm, the maximum depletion layer thickness is 100 nm. The permitti

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The value of $$'x'$$ for which all the eigenvalues of the matrix given below are real is $$\left[ {\matrix{
{10} &am

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The value of the integral $$\int_{ - \infty }^\infty {12\,\,\cos \left( {2\pi t} \right){{\sin \left( {4\pi t} \right)}

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Let the random variable $$X$$ represent the number of times a fair coin needs to be tossed till two consecutive heads ap

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Let $$\,\,X \in \left\{ {0,1} \right\}\,\,$$ and $$\,\,Y \in \left\{ {0,1} \right\}\,\,$$ be two independent binary rand

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Ram and Ramesh appeared in an interview for two vacancies in the same department. The probability of Ram's selection is

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The general solution of the differential equation $$\,\,{{dy} \over {dx}} = {{1 + \cos 2y} \over {1 - \cos 2x}}\,\,$$ i

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Consider the differential equation $$\,\,{{dx} \over {dt}} = 10 - 0.2\,x$$ with initial condition $$x(0)=1.$$ The respo

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Let $$f\left( z \right) = {{az + b} \over {cz + d}}.$$ If $$f\left( {{z_1}} \right) = f\left( {{z_2}} \right)$$ for all

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If $$C$$ denotes the counter clockwise unit circle. The value of the contour integral $${1 \over {2\pi i}}\oint\limits_c

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The bilateral Laplace transform of a function
$$f\left( t \right) = \left\{ {\matrix{
1 & {if\,\,a \le t \le b}

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In an 8085 microprocessor, which one of the following instructions changes the content of the accumulator?

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In the circuit shown, the Norton equivalent resistance
(in Ω) across terminals a–b is ___________.

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In the circuit shown, the initial voltages across the capacitors
C1 and C2
are 1 V and 3 V,
respectively. The switch is

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The voltage (VC) across the capacitor (in Volts) In the network shown is ________.

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The 2-port admittance matrix of the circuit shown is given by

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The bilateral Laplace transform of a function $$f\left( t \right) = \left\{ {\matrix{
{1\,if\,a \le t \le b} \cr

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Let x(t) = a s(t) +s(-t) with s(t) = $$\beta {e^{ - 4t}}u\left( t \right)$$, where u(t) is unit step function. If the bi

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Two casual discrete-time signals $$x\left[ n \right]$$ and $$y\left[ n \right]$$ =$$\sum\limits_{m = 0}^n x \left[ m \ri

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Input x(t) and output y(t) of an LTI system are related by the differential equation y"(t) - y'(t) - 6y(t) = x(t). If t

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The output of a standrad second-order system for a unit step input is given as $$y(t) = 1 - {2 \over {\sqrt 3 }}{e^{ - t

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The value of the integral $$\int_{ - \infty }^\infty {12\,\cos (2\pi )\,{{\sin (4\pi t)} \over {4\pi t}}\,dt\,} $$ is

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The signal $$\cos \left( {10\pi t + {\pi \over 4}} \right)$$ is ideally sampled at a sampling frequency of 15 Hz. Th

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## General Aptitude

Ram and Ramesh appeared in an interview for two vacancies in the same department. The
probability of Ram’s selection is

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