GATE ECE 2009

## GATE ECE

A small signal source Vi(t) = A cos 20t + B sin 106 t, is applied to a transistor Amplifier as shown in fig. The transis

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A communication channel with AWGN operating at a signal to noise ratio SNR > > 1 and band width B has capacity $${

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The amplitude of random signal is uniformly distributed between $$-$$5V and 5V
If the signal to quantization noise rati

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The amplitude of random signal is uniformly distributed between $$-$$5V and 5V
If the positive values of the signal are

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The unit step response of an under-damped second order system has steady state value of -2.
Which one of the following t

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The Nyquist plot of a stable transfer function G(s) is shown in the figure. We are interested in the stability of the cl

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The Nyquist plot of a stable transfer function G(s) is shown in the figure. We are interested in the stability of the cl

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The magnitude plot of a rational transfer function G(s), with real coefficient is shown in figure.
Which of the followin

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Consider the system $${{dx} \over {dt}} = Ax + Bu$$ with $${\rm A} = \left[ {\matrix{
1 & 0 \cr
0 & 1

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If X=1 in the logic equation
$$\left[ {X + Z\left\{ {\overline Y + (\overline Z + X\overline {Y)} } \right\}} \right]$

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What are the minimum number of 2-to 1 multiplexers required to generate a 2-input AND gate and a 2-input EX-OR gate?

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What are the counting states (Q1, Q2) for the counter shown in the figure below?

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The full forms of the abbreviations TTL and COMS in reference to logic families are

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Two infinitely long wires carrying current are as shown in the figure below. One wire is in the
y-z plane and parallel t

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A transmission line terminates in two branches, each of length $$\lambda /4$$, as shown.The branches are terminated by 5

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Which of the following statements is true regarding the fundamental mode of the metallic waveguides shown?

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In the circuit below, the diode is ideal. The voltage V is given by

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Consider the CMOS circuit shown, where the gate voltage of the n-MOSFET is increased
from zero, while the gate voltage o

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Consider the CMOS circuit shown, where the gate voltage of the n-MOSFET is increased
from zero, while the gate voltage o

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The eigen values of the following matrix $$\left[ {\matrix{
{ - 1} & 3 & 5 \cr
{ - 3} & { - 1} &

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The Taylor series expansion of $$\,\,{{\sin x} \over {x - \pi }}\,\,$$ at $$x = \pi $$ is given by

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If a vector field$$\overrightarrow V $$ is related to another field $$\overrightarrow A $$ through $$\,\overrightarrow

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A fair coin is tossed $$10$$ times. What is the probability that only the first two tosses will yield heads?

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A discrete random variable $$X$$ takes value from $$1$$ to $$5$$ with probabilities as shown in the table. A student cal

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Consider two independent random variables $$X$$ and $$Y$$ with identical distributions. The variables $$X$$ and $$Y$$ ta

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Match each differential equation in Group $$I$$ to its family of solution curves from Group $$II.$$
Group $$I$$
$$P:$

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The order of differential equation $$\,\,{{{d^2}y} \over {d{t^2}}} + {\left( {{{dy} \over {dx}}} \right)^3} + {y^4} = {e

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Given that $$F(s)$$ is the one-sided Laplace transform of $$f(t),$$ the Laplace transform of $$\int\limits_0^t {f\left(

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If $$f\left( z \right) = {C_0} + {C_1}{z^{ - 1}}\,\,$$ then $$\oint\limits_{|z| = 1} {{{1 + f\left( z \right)} \over z}}

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In the interconnection of ideal sources shown in the figure, it is known that the 60V source is absorbing power.
Which

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In the circuit shown, what value of RL maximizes the power delivered to RL?

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The time domain behavior of an RL circuit is represented by
$$$\mathrm L\frac{\mathrm{di}\left(\mathrm t\right)}{\mathrm

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The switch in the circuit shown was on position ‘a’ for a long time and is moved to position ‘b’
at time t = 0. The curr

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A fully charged mobile phone with a 12 V battery is good for a 10 minute talk-time. Assume that, during the talk-time, t

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An AC source of RMS voltage $$20$$ $$V$$ with internal impedance $${Z_s} = \left( {1 + 2j} \right)\Omega $$ feeds a loa

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If the transfer function of the following network is $$\,{{{V_0}(s)} \over {{V_i}(s)}} = {1 \over {2\, + \,sCR}}$$
The

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The Fourier series of a real periodic function has only
P. Cosine terms if it is even
Q. Sine terms if it is even
R. Cos

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A function is given by f(t) = sin2t +cos2t . Which of the following is true?

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Given that F(s) is the one-sided Laplace transform of f(t), the Laplace transform of $$\int\limits_0^t {f\left( \tau \r

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The 4-point Discrete Fourier Transform (DFT) of a discrete time sequence $$\left\{ {1,\,0,\,2,\,3} \right\}$$ is

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The ROC of Z-transform of the discrete time sequence
x(n)= $${\left( {{1 \over 3}} \right)^{n}}u(n) - {\left( {{1 \over

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Consider a system whose input x and output y are related by the equation
$$$y(t) = \int\limits_{ - \infty }^\infty {x(

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A system with transfer function H(z) has impulse response h(.) defined as h(2) = 1, h(3) = - 1 and h (k) = 0 otherwise.

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An LTI system having transfer function $${{{s^2} + 1} \over {{s^2} + 2s + 1}}$$ and input x(t) = sin (t + 1) is in stead

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