GATE ECE 2007

## GATE ECE

In a transconductance amplifier , it is desirable to have

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

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

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

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

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

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A Hilbert transformer is a

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

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

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

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

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

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

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

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

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

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

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

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

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

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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

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

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

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

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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

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

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

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

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

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

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

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In the following circuit, X is given by

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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

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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

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

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

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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

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The RC circuit shown in the figure is

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

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

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

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

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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

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

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

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A Hilbert transformer is a

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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:

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