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

The $Z$-parameter matrix of a two port network relates the port voltages and port currents as follows:

$$ \left[\begin{array}{l} V_1 \\ V_2 \end{array}\right]=Z\left[\begin{array}{l} I_1 \\ I_2 \end{array}\right] $$

The Z-parameter matrix (with each entry in Ohms) of the network shown below is

___________.

GATE ECE 2025 Network Theory - Two Port Networks Question 1 English
A
$\left[\begin{array}{cc}\frac{10}{3} & \frac{2}{3} \\ \frac{2}{3} & \frac{10}{3}\end{array}\right]$
B
$\left[\begin{array}{cc}\frac{2}{3} & \frac{10}{3} \\ \frac{10}{3} & \frac{2}{3}\end{array}\right]$
C
$\left[\begin{array}{cc}10 & 2 \\ 2 & 10\end{array}\right]$
D
$\left[\begin{array}{cc}\frac{10}{3} & \frac{1}{3} \\ \frac{1}{3} & \frac{10}{3}\end{array}\right]$
2
GATE ECE 2025
MCQ (Single Correct Answer)
+1
-0.33

Consider the discrete-time system below with input $x[n]$ and output $y[n]$. In the figure, $h_1[n]$ and $h_2[n]$ denote the impulse responses of LTI Subsystems 1 and 2, respectively. Also, $\delta[n]$ is the unit impulse, and $b>0$.

Assuming $h_2[n] \neq \delta[n]$, the overall system (denoted by the dashed box) is_________.

GATE ECE 2025 Signals and Systems - Discrete Time Linear Time Invariant Systems Question 1 English
A
linear and time invariant
B
linear and time variant
C
nonlinear and time invariant
D
nonlinear and time variant
3
GATE ECE 2025
MCQ (Single Correct Answer)
+1
-0.33

Consider a continuous-time, real-valued signal $f(t)$ whose Fourier transform $F(\omega)=$$\mathop f\limits_{ - \infty }^\infty $$ f(t) \exp (-j \omega t) d t$ exists.

Which one of the following statements is always TRUE?

A
$|F(\omega)| \leq \mathop f\limits_{ - \infty }^\infty|f(t)| d t$
B
$|F(\omega)|>\mathop f\limits_{ - \infty }^\infty|f(t)| d t$
C
$|F(\omega)| \leq \mathop f\limits_{ - \infty }^\infty f(t) d t$
D
$|F(\omega)| \geq \mathop f\limits_{ - \infty }^\infty f(t) d t$
4
GATE ECE 2025
MCQ (More than One Correct Answer)
+1
-0
Let $x[n]$ be a discrete-time signal whose $z$-transform is $X(z)$. Which of the following statements is/are TRUE?
A
The discrete-time Fourier transform (DTFT) of $x[n]$ always exists
B
The region of convergence (RoC) of $X(z)$ contains neither poles nor zeros
C
The discrete-time Fourier transform (DTFT) exists if the region of convergence (RoC) contains the unit circle
D
If $x[n]=\alpha \delta[n]$, where $\delta[n]$ is the unit impulse and $\alpha$ is a scalar, then the region of convergence (RoC) is the entire $z$-plane
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