1
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 _________.
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2
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 ______.
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3
GATE ECE 2013
MCQ (Single Correct Answer)
+1
-0.3
Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system?
A
All the poles of the system must lie on the left side of the jω axis
B
Zeros of the system can lie anywhere in the s-plane
C
All the poles must lie within $$\left|s\right|\;=\;1$$
D
All the roots of the characteristic equation must be located on the left side of the jω axis
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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