1
GATE ECE 2025
MCQ (Single Correct Answer)
+2
-0.67

Consider a system where $x_1(t), x_2(t)$, and $x_3(t)$ are three internal state signals and $u(t)$ is the input signal. The differential equations governing the system are given by

$$ \frac{d}{d t}\left[\begin{array}{l} x_1(t) \\ x_2(t) \\ x_3(t) \end{array}\right]=\left[\begin{array}{ccc} 2 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & 0 \end{array}\right]\left[\begin{array}{l} x_1(t) \\ x_2(t) \\ x_3(t) \end{array}\right]+\left[\begin{array}{l} 1 \\ 1 \\ 1 \end{array}\right] u(t) $$

Which of the following statements is/are TRUE?

A
The signals $x_1(t), x_2(t)$, and $x_3(t)$ are bounded for all bounded inputs.
B
There exists a bounded input such that at least one of the signals $x_1(t), x_2(t)$, and $x_3(t)$ is unbounded.
C
There exists a bounded input such that the signals $x_1(t), x_2(t)$ and $x_3(t)$ are unbounded.
D
The signals $x_1(t), x_2(t)$ and $x_3(t)$ are unbounded for all bounded inputs.
2
GATE ECE 2025
MCQ (Single Correct Answer)
+2
-0.67

Consider a system represented by the block diagram shown below. Which of the following signal flow graphs represent(s) this system? Choose the correct option(s).

GATE ECE 2025 Control Systems - Signal Flow Graph and Block Diagram Question 1 English
A
GATE ECE 2025 Control Systems - Signal Flow Graph and Block Diagram Question 1 English Option 1
B
GATE ECE 2025 Control Systems - Signal Flow Graph and Block Diagram Question 1 English Option 2
C
GATE ECE 2025 Control Systems - Signal Flow Graph and Block Diagram Question 1 English Option 3
D
GATE ECE 2025 Control Systems - Signal Flow Graph and Block Diagram Question 1 English Option 4
3
GATE ECE 2025
MCQ (Single Correct Answer)
+1
-0.33
A 3-input majority logic gate has inputs $X, Y$ and $Z$. The output $F$ of the gate is logic ' 1 ' if two or more of the inputs are logic ' 1 '. The output $F$ is logic ' 0 ' if two or more of the inputs are logic '0'. Which one of the following options is a Boolean expression of the output $F$ ?
A
$X Y+Y Z+Z X$
B
$X \oplus Y \oplus Z$
C
$X+Y+Z$
D
$X Y Z$
4
GATE ECE 2025
MCQ (Single Correct Answer)
+1
-0.33

A full adder and an XOR gate are used to design a digital circuit with inputs $X, Y$, and $Z$, and output $F$, as shown below. The input $Z$ is connected to the carry-in input of the full adder.

If the input $Z$ is set to logic ' 1 ', then the circuit functions as __________ with $X$ and $Y$ as inputs.

GATE ECE 2025 Digital Circuits - Combinational Circuits Question 1 English
A
an adder
B
a subtractor
C
a multiplier
D
a binary to Gray code converter
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