1
GATE ECE 2018
+1
-0.33
Consider p(s) = s3 + $${a_2}$$s2 + $${a_1}$$s + $${a_0}$$ with all real coefficients. It is known that its derivative p'(s) has no real roots. The number of real roots of p(s) is
A
0
B
1
C
2
D
3
2
GATE ECE 2016 Set 1
+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
3
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 ____ 4 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 ______.