GATE ECE 2014 Set 4

## GATE ECE

For a given sample-and-hold circuit, if the value of the hold capacitor is increased, then

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If the emitter resistance in a common-emitter voltage amplifier is not bypassed, it will

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Consider the common-collector amplifier in the figure (bias circuitry ensures that the transistor
operates in forward ac

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A BJT in common-base configuration is used to amplify a signal received by a $$50\,\Omega $$ antena. Assume kT/q = 25 m

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For the common collector amplifier shown in the figure, the BJT has high $${V_{CE\left( {sat} \right)}},$$ and $${V_{BE

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The circuit shown represents

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An M - level PSK modulation scheme is used to transmit independent binary digits over a band-pass channel with bandwidth

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Consider the Z- channel given in the figure. The input is 0 or 1 with equal probability.
If the output is 0, the probab

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If calls arrive at a telephone exchange such that the time of arrival of any call is independent of the time of arrival

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Consider a discrete-time channel Y = X + Z, where the additive noise Z is signal- dependent. In particular, given the tr

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Consider a communication scheme where the binary valued signal X satisfies P{X = + 1} = 0.75 and P {X = - 1} = 0.25. The

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For the second order closed-loop system shown in the figure, the natural frequency (in rad/s)
is

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Consider a transfer function $$G_p\left(s\right)\;=\;\frac{ps^2+3ps\;-2}{s^2+\left(3+p\right)s\;+\left(2-p\right)}$$ wit

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The characteristic equation of a unity negative feedback system 1 + KG(s) = 0. The open loop
transfer function G(s) has

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In a Bode magnitude plot, which one of the following slopes would be exhibited at high
frequencies by a 4th order all-po

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The state transition matrix $$\phi \left( t \right)$$ of a system $$$\left[ {\matrix{
{\mathop {{x_1}}\limits^ \bull

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In the circuit shown in the figure, if C = 0, the expression for Y is

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A 16-bit ripple carry adder is realized using 16 identical full adders (FA) as shown in the figure.
The carry-propagatio

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An 8-to-1 multiplexer is used to implement a logical function Y as shown in the figure. The output Y is given by

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The output (Y) of the circuit shown in the figure is

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If $$\overrightarrow{\mathrm E}=-\left(2\mathrm y^2\;-3\mathrm{yz}^2\right)\widehat{\mathrm x}\;-\left(6\mathrm{xy}^2-3\

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The electric field (assumed to be one-dimensional) between two points A and B is shown. Let
$$\psi_A$$ and $$\psi_B$$ be

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For an antenna radiating in free space, the electric field at a distance of 1 km is found to be 12 m V/m. Given that int

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Match column A with column B.
Column
1. Point electromagnetic source
2. Dish antenna
3. Yagi-Uda antenna
Colum

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In the figure ln(ρi) is plotted as a function of 1/T, where ρi
the intrinsic resistivity of silicon,
T is is the tempera

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The cut-off wavelength (in µm) of light that can be used for intrinsic excitation of a
semiconductor material of bandgap

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Consider a silicon sample doped with ND = 1×1015/cm3 donor atoms. Assume that the
intrinsic carrier concentration ni = 1

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An N-type semiconductor having uniform doping is biased as shown in the figure.
If EC is the lowest energy level of th

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Consider two BJT's biased at the same collector current with area A1 = 0.2 μm × 0.2 μm and
A2 = 300 μm × 300 μm. Assumin

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The series $$\sum\limits_{n = 0}^\infty {{1 \over {n!}}\,} $$ converges to

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For a right angled triangle, if the sum of the lengths of the hypotenuse and a side is kept constant, in order to have m

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The magnitude of the gradient for the function $$f\left( {x,y,z} \right) = {x^2} + 3{y^2} + {z^3}\,\,$$ at the point $$(

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The directional derivative of $$f\left( {x,y} \right) = {{xy} \over {\sqrt 2 }}\left( {x + y} \right)$$ at $$(1, 1)$$

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Given $$\,\,\overrightarrow F = z\widehat a{}_x + x\widehat a{}_y + y\widehat a{}_z.\,\,$$ If $$S$$ represents the po

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If calls arrive at a telephone exchange such that the time of arrival of any call is independent of the time of arrival

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Parcels from sender $$S$$ to receiver $$R$$ pass sequentially through two post - offices. Each post - office has a proba

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Let $$X$$ be a zero mean unit variance Gaussian random variable. $$E\left[ {\left| X \right|} \right]$$ is equal to ____

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With initial values $$\,\,\,y\left( 0 \right) = y'\left( 0 \right) = 1,\,\,\,$$ the solution of the differential equati

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If $$a$$ and $$b$$ are constants, the most general solution of the differential equation $$\,{{{d^2}x} \over {d{t^2}}}

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The unilateral Laplace transform of $$f(t)$$ is $${1 \over {{s^2} + s + 1}}$$. Which one of the following is the unilate

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An 8085 microprocessor executes “STA 1234H” with starting address location 1FFEH (STA copies the contents of the
Accumu

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The circuit shown in the figure represents a

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The magnitude of current (in mA) through the resistor R2 in the figure shown is _____.

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In the circuit shown in the figure, the value of V0(t) (in Volts) for $$t\rightarrow\infty$$ is ______.

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For the two-port network shown in the figure, the impedance (Z) matrix (in Ω) is

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The steady state output of the circuit shown in the figure is given by
$$$y\left( t \right) = {\rm A}\left( \omega \ri

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The equivalent resistance in the infinite ladder network shown in the figure, is$${R_e}$$
The value of $${R_e}/R$$ is

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A Fourier transform pair is given by $${\left( {{2 \over 3}} \right)^n}$$ u $$\left[ {n + 3} \right]\,\mathop \Leftrigh

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The unilateral Laplace transform of F(t) is $${1 \over {{s^2} + s + 1}}$$. Which one of the following is the unilateral

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A stable linear time invariant (LTI) system has a transfer function H(s) = $${1 \over {{s^2} + s - 6}}$$. To make this s

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A casual LTI system has zero initial conditions and impulse response h(t). Its input x(t) and output y(t) are related th

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The N-point DFT X of a sequence x[n] 0 ≤ n ≤ N − 1 is given by
$$X\left[ k \right] = {1 \over {\sqrt N }}\,\,\sum\lim

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The sequence x $$\left[ n \right]$$ = $${0.5^n}$$ u[n], where u$$\left[ n \right]$$ is the unit step sequence, is conv

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A real - values signal x(t) limited to the frequency band $$\left| f \right| \le {W \over 2}$$ is passed through a linea

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