GATE ECE 2014 Set 2

## GATE ECE

A cascade connection of two voltage amplifiers A1 and A2 is shown in the figure. The open-loop
gain Av0, input resistanc

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In the differential amplifier shown in the figure, the magnitudes of the common-mode and
differential-mode gains are ðīc

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The feedback topology in the amplifier circuit (the base bias circuit is not shown for simplicity) in the figure is

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The power spectral density of a real stationary random process X(t) is given by
$$${S_x}\left( f \right) = \left\{ {\ma

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The input to a 1-bit quantizer is a random variable X with pdf $${f_x}(x) = 2{e^{ - 2x}}\,\,for\,\,x \ge 0$$ and $${f_x}

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The capacity of band-limited additive white Gaussian noise (AWGN) channel is given by $$C = \,W\,\,{\log _2}\left( {1 +

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Coherent orthogonal binary FSK modulation is used to transmit two equiprobable symbol waveforms $${s_1}\,(t)\, = \,\alp

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The natural frequency of an undamped second-order system is 40 rad/s. If the system is
damped with a damping ratio 0.3,

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For the following system,
When X1(s) = 0 , the transfer function $$\frac{\mathrm Y\left(\mathrm s\right)}{{\mathrm X}_2

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The Bode asymptotic magnitude plot of a minimum phase system is shown in the figure.
If the system is connected in a

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An unforced linear time invariant (LTI) system is represented by
$$$\left[ {\matrix{
{\mathop {{x_1}}\limits^ \bullet

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Consider the state space system expressed by the signal flow diagram shown in the figure.
The corresponding system is

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The number of bytes required to represent the decimal number 1856357 in packed BCD
(Binary Coded Decimal) form is ______

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For an n - variable Boolean function maximum number of prime implicants is

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In a half-subtractor circuit with X and Y as inputs, the Borrow (M) and Difference (N = X - Y) are given by

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The outputs of the two flip-flops Q1, Q2 in the figure shown are initialized to 0, 0. The sequence
generated at Q1 upon

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In the circuit shown, choose the correct timing diagram of the output (y) from the given waveforms
W1, W2, W3 and W4.

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To maximize power transfer, a lossless transmission line is to be matched to a resistive load impedance via a $$\lambda

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Which one of the following field patterns represents a TEM wave traveling in the positive $$x$$ direction?

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In the transmission line shown, the impedance $${Z_{in}}$$ (in ohms) between node A and the ground is

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If the electric field of a plane wave is
$$$\overrightarrow E \left( {z,t} \right) = \widehat x3\cos \left( {\omega t -

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For a rectangular waveguide of internal dimensions $$a\,\, \times \,\,b$$ (a > b), the cut-off frequency for the $$T{

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Assume electronic charge q = 1.6Ã10-19 C, kT/q = 25 mV and electron mobility Îžn = 1000
cm2/V-s. If the concentration gra

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Consider an abrupt PN junction (at T = 300 K) shown in the figure. The depletion region width Xn
on the N-side of the ju

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An increase in the base recombination of a BJT will increase

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In CMOS technology, shallow P-well or N-well regions can be formed using

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For the n-channel MOS transistor shown in the figure, the threshold voltage VTh is 0.8V. Neglect channel length modulati

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For the MOSFETs shown in the figure, the threshold voltage |Vt| = 2V and K=$${1 \over 2}\mu {C_{OX}}\left( {{W \over L}}

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The system of linear equations $$\left( {\matrix{
2 & 1 & 3 \cr
3 & 0 & 1 \cr
1 & 2 &am

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The determinant of matrix $$A$$ is $$5$$ and the determinant of matrix $$B$$ is $$40.$$ The determinant of matrix $$AB$

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The maximum value of the determinant among all $$2 \times 2$$ real symmetric matrices with trace $$14$$ is ______.

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For $$0 \le t < \infty ,$$ the maximum value of the function $$f\left( t \right) = {e^{ - t}} - 2{e^{ - 2t}}\,$$ occ

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The value of $$\mathop {\lim }\limits_{x \to \infty } {\left( {1 + {1 \over x}} \right)^x}\,\,$$ is

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If $$\,\overrightarrow r = x\widehat a{}_x + y\widehat a{}_y + z\widehat a{}_z\,\,\,\,$$ and $$\,\left| {\overrightarr

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Let $$X$$ be a random variable which is uniformly chosen from the set of positive odd numbers less than $$100.$$ The exp

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If the characteristic equation of the differential equation $$\,{{{d^2}y} \over {d{x^2}}} + 2\alpha {{dy} \over {dx}} +

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The real part of an analytic function $$f(z)$$ where $$z=x+jy$$ is given by $${e^{ - y}}\cos \left( x \right).$$ The ima

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For the 8085 microprocessor, the interfacing circuit to input 8-bit digital data (DI0 â DI7)
from an external device is

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In the magnetically coupled circuit shown in the figure, 56 % of the total flux emanating from
one coil links the other

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Norton's theorem states that a complex network connected to a load can be replaced with an equivalent impedance

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In the figure shown, the ideal switch has been open for a long time. If it is closed at t=0, then
the magnitude of the c

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A series LCR circuit is operated at a frequency different from its resonant frequency. The
operating frequency is such t

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In the h-parameter model of the 2-port network given in the figure shown, the value of h22 (in
S) is _____ .

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In the figure shown, the capacitor is initially uncharged. Which one of the following
expressions describes the current

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Consider the periodic square wave in the figure shown.
The ratio of the power in the 7th harmonic to the power in the 5

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Let x$$\left[ n \right]$$ = x$$\left[- n \right]$$ . Let X(z) be the z-transform of x$$\left[ n \right]$$. if 0.5 +j 0.2

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An FIR system is described by the system function
$$$H(z) = 1 + {7 \over 2}{z^{ - 1}} + {3 \over 2}{z^{ - 2}}$$$

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The input-output relationship of a causal stable LTI system is given as
ðĶ[ð] = ðž ðĶ[ð â 1] + $$\beta $$ x[n].
If

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The value of the integral $$\int\limits_{ - \infty }^\infty {\sin \,{c^2}} $$ (5t) dt is

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Consider a discrete-time signal
$$x\left[ n \right] = \left\{ {\matrix{
{n\,\,for\,\,0 \le n \le 10} \cr
{0\,\

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