1
GATE EE 2025
Numerical
+2
-0
Consider the state-space model $$ \begin{aligned} \dot{x}(t) & =A x(t)+B u(t) \\ y(t) & =C x(t) \end{aligned} $$ where $x(t), r(t), y(t)$ are the state, input and output, respectively. The matrices $A, B, C$ are given below $$ A=\left[\begin{array}{cc} 0 & 1 \\ -2 & -3 \end{array}\right], B=\left[\begin{array}{l} 0 \\ 1 \end{array}\right], C=\left[\begin{array}{ll} 1 & 0 \end{array}\right] $$ The sum of the magnitudes of the poles is ___________. (Round off to nearest integer)
Your input ____
2
GATE EE 2025
Numerical
+2
-0
A controller $D(s)$ of the form $\left(1+K_D s\right)$ is to be designed for the plant $G(s)=\frac{1000 \sqrt{2}}{s(s+10)^2}$ as shown in the figure. The value of $K_D$ that yields a phase margin of $45^{\circ}$ at the gain cross-over frequency of $10 \mathrm{rad} / \mathrm{sec}$ is _________(round off to one decimal place). GATE EE 2025 Control Systems - Controller and Compensator Question 1 English
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3
GATE EE 2025
MCQ (Single Correct Answer)
+2
-0.67

A Boolean function is given as

$$ f=(\bar{u}+\bar{v}+\bar{w}+\bar{x}) \cdot(\bar{u}+\bar{v}+\bar{w}+x) \cdot(\bar{u}+v+\bar{w}+\bar{x}) \cdot(\bar{u}+v+\bar{w}+x) $$

The simplified form of this function is represented by

A
GATE EE 2025 Digital Electronics - Boolean Algebra Question 1 English Option 1
B
GATE EE 2025 Digital Electronics - Boolean Algebra Question 1 English Option 2
C
GATE EE 2025 Digital Electronics - Boolean Algebra Question 1 English Option 3
D
GATE EE 2025 Digital Electronics - Boolean Algebra Question 1 English Option 4
4
GATE EE 2025
MCQ (Single Correct Answer)
+1
-0.33

$$ \text { The I-V characteristics of the elements between the nodes } X \text { and } Y \text { is best depicted } $$

GATE EE 2025 Electric Circuits - Network Elements Question 1 English
A
GATE EE 2025 Electric Circuits - Network Elements Question 1 English Option 1
B
GATE EE 2025 Electric Circuits - Network Elements Question 1 English Option 2
C
GATE EE 2025 Electric Circuits - Network Elements Question 1 English Option 3
D
GATE EE 2025 Electric Circuits - Network Elements Question 1 English Option 4
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