1
GATE ECE 2022
MCQ (Single Correct Answer)
+1
-0.33

Consider an even polynomial p(s) given by

$$p(s) = {s^4} + 5{s^2} + 4 + K$$

where K is an unknown real parameter. The complete range of K for which p(s) has all its roots on the imaginary axis is __________.

A
$$ - 4 \le K \le {9 \over 4}$$
B
$$ - 3 \le K \le {9 \over 2}$$
C
$$ - 6 \le K \le {5 \over 4}$$
D
$$ - 5 \le K \le 0$$
2
GATE ECE 2018
MCQ (Single Correct Answer)
+1
-0.33
The Nyquist stability criterion and the Routh criterion both are powerful analysis tools for determining the stability of feedback controllers. Identify which of the following statements is FALSE.
A
The closed-loop frequency response for a unity feedback system cannot be obtained from the Nyquist plot.
B
The Routh criterion is not applicable in the condition of transport lag, which can be readily handled by the Nyquist criterion.
C
The general shape of the Nyquist plot is readily obtained from the Bode magnitude plot for all minimum-phase systems.
D
Both the criteria provide information relative to the stable gain range of the system.
3
GATE ECE 2018
MCQ (Single Correct Answer)
+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
4
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
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