1
GATE ECE 2014 Set 4
MCQ (Single Correct Answer)
+2
-0.6
Consider a communication scheme where the binary valued signal X satisfies P{X = + 1} = 0.75 and P {X = - 1} = 0.25. The received signal Y = X + Z, where Z is a Gaussian random variable with zero mean and variance $${\sigma ^2}$$. The received signal Y is fed to the threshold detector. The output of the threshold detector $${\hat X}$$ is: $$$\hat X:\left\{ {\matrix{ { + \,1,} & {Y\, > \tau } \cr { - \,1,} & {Y\, \le \,\,\tau .} \cr } } \right.$$$ To achieve a minimum probability of error $$P\{ \hat X\, \ne \,X\} $$, the threshold $$\tau $$ should be
A
strictly positive
B
zero
C
strictly negative
D
strictly positive, zero, or strictly negative depending on the nonzero value of $${\sigma ^2}$$
2
GATE ECE 2014 Set 4
MCQ (Single Correct Answer)
+1
-0.3
For the second order closed-loop system shown in the figure, the natural frequency (in rad/s) is GATE ECE 2014 Set 4 Control Systems - Time Response Analysis Question 50 English
A
16
B
4
C
2
D
1
3
GATE ECE 2014 Set 4
Numerical
+2
-0
Consider a transfer function $$G_p\left(s\right)\;=\;\frac{ps^2+3ps\;-2}{s^2+\left(3+p\right)s\;+\left(2-p\right)}$$ with 'p' a positive real parameter. The maximum value of 'p' until which Gp remains stable is ________.
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4
GATE ECE 2014 Set 4
Numerical
+2
-0
The characteristic equation of a unity negative feedback system 1 + KG(s) = 0. The open loop transfer function G(s) has one pole at 0 and two poles at -1. The root locus of the system for varying K is shown in the figure. GATE ECE 2014 Set 4 Control Systems - Root Locus Diagram Question 13 English

The constant damping ratio line, for $$\xi$$ = 0.5 , intersects the root locus at point A. The distance from the origin to point A is given as 0.5. The value of K at point A is ________ .

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