1
GATE ECE 2016 Set 2
Numerical
+2
-0
A binary communication system makes use of the symbols “zero” and “one”. There are channel errors. Consider the following events:
$${x_0}$$ : a " zero " is transmitted
$${x_1}$$ : a " one " is transmitted
$${y_0}$$ : a " zero " is received
$${y_1}$$ : a " one " is received

The following probabilities are given:
$$P({x_0}) = \,{3 \over 4},\,\left( {\,\left. {{y_0}} \right|{x_0}} \right) = \,{1 \over 2},\,\,and\,P\,\,\left( {\,\left. {{y_0}} \right|{x_1}} \right) = \,{1 \over 2}$$.
The information in bits that you obtain when you learn which symbol has been received (while you know that a " zero " has been transmitted) is _____________

Your input ____
2
GATE ECE 2016 Set 2
Numerical
+1
-0
The response of the system $$G\left(s\right)\;=\;\frac{s\;-\;2}{\left(s\;+\;1\right)\left(s\;+\;3\right)}$$ to the unit step input u(t) is y(t). The value of $$\frac{\mathrm{dy}}{\mathrm{dt}}\;\mathrm{at}\;\mathrm t\;=\;0^+\;\mathrm{is}$$ ___________.
Your input ____
3
GATE ECE 2016 Set 2
Numerical
+2
-0
In the feedback system shown below $$$G\left(S\right)\;=\frac1{(s^2\;+\;2s)}$$$ The step response of the closed-loop system should have minimum settling time and have no overshoot. GATE ECE 2016 Set 2 Control Systems - Time Response Analysis Question 29 English The required value of gain k to achieve this is __________.
Your input ____
4
GATE ECE 2016 Set 2
MCQ (Single Correct Answer)
+1
-0.3
The number and direction of encirclements around the point −1 + j0 in the complex plane by the Nyquist plot of G(s) =$${{1 - s} \over {4 + 2s}}$$ is
A
zero
B
one, anti-clockwise
C
one, clockwise
D
two, clockwise
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