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

In the circuit below, $M_1$ is an ideal AC voltmeter and $M_2$ is an ideal AC ammeter. The source voltage (in Volts) is $v_s(t)=100 \cos (200 t)$.

What should be the value of the variable capacitor $C$ such that the RMS readings on $M_1$ and $M_2$ are 25 V and 5 A , respectively?

GATE ECE 2025 Network Theory - Sinusoidal Steady State Response Question 2 English
A
$25 \mu \mathrm{~F}$
B
$4 \mu \mathrm{~F}$
C
$0.25 \mu \mathrm{~F}$
D
Insufficient information to find $C$
2
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
$\left[\begin{array}{cc}\frac{10}{3} & \frac{1}{3} \\ \frac{1}{3} & \frac{10}{3}\end{array}\right]$
3
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
4
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
$|F(\omega)| \geq \mathop f\limits_{ - \infty }^\infty f(t) d t$
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