1
GATE ECE 2025
MCQ (Single Correct Answer)
+2
-0.67
Consider the polynomial $p(s)=s^5+7 s^4+3 s^3-33 s^2+2 s-40$. Let $(L, I, R)$ be defined as follows. $L$ is the number of roots of $p(s)$ with negative real parts. $I$ is the number of roots of $p(s)$ that are purely imaginary. $R$ is the number of roots of $p(s)$ with positive real parts. Which one of the following options is correct?
A
$L=2, I=2$ and $R=1$
B
$L=3, I=2$ and $R=0$
C
$L=1, I=2$ and $R=2$
D
$L=0, I=4$ and $R=1$
2
GATE ECE 2022
MCQ (Single Correct Answer)
+2
-0.67

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
$$ - 5 \le K \le 0$$
3
GATE ECE 2017 Set 2
Numerical
+2
-0
A unity feedback control system is characterized by the open-loop transfer function $$$G\left(s\right)\;=\;\frac{2\left(s+1\right)}{s^3+ks^2+2s+1}$$$ The value of k for which the system oscillates at 2 rad/s is ________.
Your input ____
4
GATE ECE 2017 Set 1
MCQ (Single Correct Answer)
+2
-0.6
Which one of the following options correctly describes the locations of the roots of the equation s4 + s2 + 1 = 0 on the complex plane?
A
Four left half plane (LHP) roots
B
One right half plane (RHP) root, one LHP root and two roots on the imaginary axis
C
Two RHP roots and two LHP roots
D
All four roots are on the imaginary axis
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