1
GATE ECE 2025
Numerical
+2
-0

$X$ and $Y$ are Bernoulli random variables taking values in $\{0,1\}$. The joint probability mass function of the random variables is given by:

$$ \begin{aligned} & P(X=0, Y=0)=0.06 \\ & P(X=0, Y=1)=0.14 \\ & P(X=1, Y=0)=0.24 \\ & P(X=1, Y=1)=0.56 \end{aligned} $$

The mutual information $I(X ; Y)$ is ___________(rounded off to two decimal places).

Your input ____
2
GATE ECE 2025
MCQ (Single Correct Answer)
+1
-0.33

The Nyquist plot of a system is given in the figure below. Let $\omega_{\mathrm{P}}, \omega_Q, \omega_R$, and $\omega_{\mathrm{S}}$ be the positive frequencies at the points $P, Q, R$, and $S$, respectively. Which one of the following statements is TRUE?

GATE ECE 2025 Control Systems - Frequency Response Analysis Question 1 English
A
$\omega_s$ is the gain crossover frequency and $\omega_p$ is the phase crossover frequency
B
$\omega_Q$ is the gain crossover frequency and $\omega_R$ is the phase crossover frequency
C
$\omega_Q$ is the gain crossover frequency and $\omega_S$ is the phase crossover frequency
D
$\omega_S$ is the gain crossover frequency and $\omega_Q$ is the phase crossover frequency
3
GATE ECE 2025
MCQ (Single Correct Answer)
+1
-0.33

Consider the unity-negative-feedback system shown in Figure (i) below, where gain $K \geq 0$. The root locus of this system is shown in Figure (ii) below. For what value(s) of $K$ will the system in Figure (i) have a pole at $-1+j 1$ ?

GATE ECE 2025 Control Systems - Root Locus Diagram Question 1 English 1 GATE ECE 2025 Control Systems - Root Locus Diagram Question 1 English 2
A
$K=5$
B
$K=\frac{1}{5}$
C
For no positive value of $K$
D
For all positive values of $K$
4
GATE ECE 2025
MCQ (Single Correct Answer)
+2
-0.67

Let $G(s)=\frac{1}{10 s^2}$ be the transfer function of a second-order system. A controller $M(s)$ is connected to the system $G(s)$ in the configuration shown below. Consider the following statements.

(i) There exists no controller of the form $M(s)=\frac{K_I}{s}$, where $K_I$ is a positive real number, such that the closed loop system is stable.

(ii) There exists at least one controller of the form $M(s)=K_P+s K_D$, where $K_P$ and $K_D$ are positive real numbers, such that the closed loop system is stable.

Which one of the following options is correct?

GATE ECE 2025 Control Systems - Compensators Question 1 English
A
(i) is TRUE and (ii) is FALSE
B
(i) is FALSE and (ii) is TRUE
C
Both (i) and (ii) are FALSE
D
Both (i) and (ii) are TRUE
EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12