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

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

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

View Question 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

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

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

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

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

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

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

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

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

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

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

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

View Question 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}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

View Question 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

View Question 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

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

View Question 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

View Question 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

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

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

View Question ## General Aptitude

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

View Question