GATE ECE 2007

## GATE ECE

In a transconductance amplifier , it is desirable to have

View Question For the BJT circuit shown, assume that the $$\beta $$ of the transistor is very large and VBE = 0.7 V. The mode of oper

View Question For the Op-Amp circuit shown in the figure, V0 is

View Question In the Op-Amp circuit shown, assume that the diode current follows the equation I = Is exp (V/VT) . For Vi = 2V, Vo = V

View Question Consider the OP-Amp circuit shown in the figure.
The transfer function $${V_o}\left( s \right)/{V_i}\left( s \right)$$ i

View Question Consider the OP-Amp circuit shown in the figure.
If $${V_i} = {V_1}\,\,\sin \left( {\omega \tau + \phi } \right),$$ th

View Question A Hilbert transformer is a

View Question In delta modulation, the slope overload distortion can be reduced by

View Question In a GSM system, 8 channels can co-exist in 200 KHz bandwidth using TDMA. A GSM based cellular operator is allocated 5 M

View Question The raised cosine pulse p(t) is used for zero ISI in digital communications. The expression for p(t) with unity roll-off

View Question In a Direct sequence CDMA system the chip rate is $$1.2288\,\, \times \,\,{10^6}$$ chips per second. If the processing g

View Question During transmission over a certain binary communication channel, bit errors occurs independently with probability p. The

View Question An input to a 6-level quantizer has the probability density function f(X) as shown in the figure. Decision boundaries of

View Question An input to a 6-level quantizer has the probability density function f(X) as shown in the figure. Decision boundaries of

View Question If E denotes expectation, the variance of a random variable X is given by

View Question Two 4-ray signal constellations are shown. It is given that $${\phi _1}$$ and $${\phi _2}$$ constitute an orthonormal ba

View Question Two 4-ray signal constellations are shown. It is given that $${\phi _1}$$ and $${\phi _2}$$ constitute an orthonormal ba

View Question If the Laplace transform of a signal y(t) is $$Y\left(s\right)\;=\;\frac1{s\left(s\;-\;1\right)}$$ , then its final v

View Question The frequency response of a linear, time-invariant system is given by $$H\left(f\right)\;=\;\frac5{1\;+\;j10\mathrm{πf}}

View Question A unity feedback control system has an open-loop transfer function
$$$G\left(s\right)=\frac K{s\left(s^2+7s+12\right)}$$

View Question The transfer function of a plant is $$$T\left(s\right)=\frac5{\left(s+5\right)\left(s^2+s+1\right)}$$$ The second-order

View Question If the closed-loop transfer function of a control system is given as
T(s)=$${{s - 5} \over {(s + 2)(s + 3)}},$$ then it

View Question The asymptotic Bode plot of a transfer function is shown in the figure. the transfer function G(s) corresponding to this

View Question A control system with a PD controller is shown in the figure. If the velocity error constant $${K_v} = 1000$$ and the d

View Question The open-loop transfer function of a plant is given as $$G(s) = {1 \over {{s^2} - 1}}.$$ If the plant is operated in a

View Question The state space representation of a separately excited DC servo motor dynamics is given as
$$$\left[ {\matrix{
{{{d\o

View Question Consider a linear system whose state space Representation is $$\mathop x\limits^ \bullet \left( t \right) = AX\left( t

View Question Consider a linear system whose state space Representation is $$\mathop x\limits^ \bullet \left( t \right) = AX\left( t

View Question X = 01110 and Y = 11001 are two 5-bit binary numbers represented in two’s
complement format. The sum of X and Y represen

View Question The Boolean function Y=AB+CD is to be realized using only 2-input NAND gates. The minimum number of gates required is

View Question The Boolean expression
Y= $$\overline A \,\overline B \,\overline C \,D + \overline A BC\overline D + A\overline {B\,}

View Question In the following circuit, X is given by

View Question For the circuit shown, the counter state (Q1 Q0) follows the sequence

View Question The circuit diagram of a standard TTL NOT gate is shown in the figure. When $${V_i}$$= 2.5V, the modes of operation of

View Question The following binary values were applied to the X and Y inputs of the NAND latch
shown in the figure in the sequence ind

View Question In the digital-to-Analog converter circuit shown in the figure below,
$${V_{R\,}}\, = \,10V$$ and $$R\, = \,10k\Omega $$

View Question In the digital-to-Analog converter circuit shown in the figure below,
$${V_{R\,}}\, = \,10V$$ and $$R\, = \,10k\Omega $$

View Question A plane wave of wavelength $$\lambda $$ is traveling in a direction making an angle $${{{30}^ \circ }}$$ with positive $

View Question A load of 50 $$\Omega $$ is connected in shunt in a 2-wire transmission line of $$Z_0$$ = 50 $$\Omega $$ as shown in the

View Question The parallel branches of a 2-wire transmission line are terminated in 100 $$\Omega $$ and 200 $$\Omega $$ resistors as s

View Question If C is a closed curve enclosing a surface S, then the magnetic field intensity $$\overrightarrow H $$, the current dens

View Question The $$\overrightarrow H $$ field (in A/m) of a plane wave propagating in free space is given by
$$$\overrightarrow H

View Question An air-filled rectangular waveguide has inner dimensions of $$3\,cm\,\, \times \,\,2\,\,cm\,$$. The wave impedance of th

View Question The $$\mathop E\limits^ \to $$ field in a rectangular waveguide of inner dimensions $$a\,\, \times \,\,b$$ is given by

View Question A $$\lambda /2$$ dipole is kept horizontally at a height of $${\lambda _0}/2$$ above a perfectly conducting infinite gro

View Question In a p+n junction diode under reverse bias, the magnitude of electric field is
maximum at

View Question A P+-N junction has a built-in potential of 0.8 V. The depletion layer width at a
reverse bias of 1.2V is 2 µm. For a re

View Question The DC current gain ($$\beta$$) of a BJT is 50. Assuming that the emitter injection
efficiency is 0.995, the base transp

View Question In the CMOS inverter circuit shown, if the transconductance parameters of the
NMOS and PMOS transistors are
Kn = Kp = μ

View Question $$\mathop {Lim}\limits_{\theta \to 0} {{\sin \left( {\theta /2} \right)} \over \theta }\,\,\,$$ is

View Question The following plot shows a function $$y$$ which varies linearly with $$x$$. The value of the integral $$\,\,{\rm I} = \i

View Question For the function $${e^{ - x}},$$ the linear approximation around $$x=2$$ is

View Question For $$\left| x \right| < < 1,\,\cot \,h\left( x \right)\,\,\,$$ can be approximated as

View Question Consider the function $$\,f\left( x \right) = {x^2} - x - 2.\,$$ The maximum value of $$f(x)$$ in the closed interval $$

View Question If $$E$$ denotes expectation, the variance of a random variable $$X$$ is given by

View Question An examination consists of two papers, paper $$1$$ and paper $$2.$$ The probability of failing in paper $$1$$ is $$0.3$$

View Question The solution of the differential equation $${k^2}{{{d^2}y} \over {d\,{x^2}}} = y - {y_2}\,\,$$ under the boundary condi

View Question The value of $$\oint\limits_C {{1 \over {\left( {1 + {z^2}} \right)}}} dz$$ where C is the contour $$\,\left| {z - {i \o

View Question The equation $${x^3} - {x^2} + 4x - 4 = 0\,\,$$ is to be solved using the Newton - Raphson method. If $$x=2$$ taken as t

View Question If the semi-circular contour D of radius 2 is as shown in the figure, then the value
of the integral $$\oint\limits_D {{

View Question An 8085 assembly language program is given below.
Line 1: MVI A, B5H
2: MVI B, 0EH
3: XRI 69H
4: ADD B
5: ANI 9BH

View Question An 8085 assembly language program is given below.
Line 1: MVI A, B5H
2: MVI B, 0EH
3: XRI 69H
4: ADD B
5: ANI 9BH

View Question An independent voltage source in series with an impedance Zs=Rs+jXs delivers a maximum average power to a load impedance

View Question For the circuit shown in the figure, the Thevenin voltage and resistance looking
into X-Y are:

View Question In the circuit shown, VC is 0 volts at t = 0 sec. For t > 0, the capacitor current iC(t), where t is in seconds, is g

View Question The RC circuit shown in the figure is

View Question In the AC network shown in the figure, the phasor voltage VAB (in Volts) is:

View Question Two series resonant filters are as shown in the figure. Let the $$3$$-dB bandwidth of Filter $$1$$ be $${B_1}$$ and that

View Question If the Laplace transform of a signal y(t) is $$Y\left( s \right) = {1 \over {s\left( {s - 1} \right)}},$$ then its final

View Question A 5-point sequence x [n] is given as x$$\left[ { - 3} \right]$$ =1, x$$\left[ { - 2} \right]$$ =1, x$$\left[ { - 1} \ri

View Question The z-transform X (z) f a sequence x$$\left[ n \right]$$ is given by = $${{0.5} \over {1 - 2{z^{ - 1}}}}$$ . It is give

View Question The frequency response of a linear, time-invariant system is given by H(f) = $${5 \over {1 + j10\pi f}}$$. The step resp

View Question The 3 - dB bandwidth of the low - pass signal $${e^{ - 1}}$$ u(t), where u(t) is the unit step function, is given by

View Question A Hilbert transformer is a

View Question In the following scheme, if the spectrum M(f) of m(t) is as shown, then the spectrum Y(f) of y(t) will be:

View Question