1
GATE ECE 2016 Set 1
MCQ (Single Correct Answer)
+1
-0.3
Match the inferences X, Y, and Z, about a system, to the corresponding properties of the elements of first column in Routh's Table of the system characteristic equation.

X: The system is stable …
Y: The system is unstable …
Z: The test breaks down …

P: … when all elements are positive
Q: … when any one element is zero
R: … when there is a change in sign of coefficients

A
X→P, Y→Q, Z→R
B
X→Q, Y→P, Z→R
C
X→R, Y→Q, Z→P
D
X→P, Y→R, Z→Q
2
GATE ECE 2015 Set 1
Numerical
+1
-0
A unity negative feedback system has the open-loop transfer function $$$G\left(s\right)\;=\;\frac K{s\left(s\;+\;1\right)\left(s\;+\;3\right)}$$$ The value of the gain K (>0) at which the root locus crosses the imaginary axis is _________.
Your input ____
3
GATE ECE 2014 Set 1
Numerical
+1
-0
The forward path transfer function of a unity negative feedback system is given by $$$G\left(s\right)\;=\;\frac k{\left(s\;+\;2\right)\left(s\;-\;1\right)}$$$ The value of K which will place both the poles of the closed-loop system at the same location, is ______.
Your input ____
4
GATE ECE 2013
MCQ (Single Correct Answer)
+1
-0.3
A polynomial $$f\left(x\right)\;=\;a_4x^4\;+\;a_3x^3\;+\;a_2x^2\;+\;a_1x\;-\;a_0$$ with all coefficients positive has
A
no real roots
B
no negative real root
C
odd number of real roots
D
at least one positive and one negative real root
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