GATE EC 2025 Question Paper (15-Feb-2025) (Shift 2)

Consider the unity-negative-feedback system shown in Figure (i) below, where gain $K\ge 0$.

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 $-1+j1$?

Let $x[n]$ be a discrete-time signal whose z-transform is $X(z)$. Which of the following statements is/are TRUE?

Consider a message signal $m(t)$ which is bandlimited to $[-W,W]$, where $W$ is in Hz. Consider the following two modulation schemes for the message signal:
• Double sideband-suppressed carrier (DSB-SC):
$f_{DSB}(t)=A_{c}m(t)\cos (2\pi f_{c}t)$
• Amplitude modulation (AM):
$f_{AM}(t)=A_c(1+\mu m(t))\cos (2\pi f_{c}t)$
Here, $A_c$ and $f_c$ are the amplitude and frequency (in Hz) of the carrier, respectively. In the case of AM, $\mu$ denotes the modulation index.
Consider the following statements:
(i) An envelope detector can be used for demodulation in the DSB-SC scheme if $m(t)>0$ for all $t$.
(ii) An envelope detector can be used for demodulation in the AM scheme only if $m(t)>0$ for all $t$.
Which of the following options is/are correct?

Which of the following statements is/are TRUE with respect to an ideal opamp?

Which of the following statements is/are TRUE with respect to ideal MOSFET-based DC-coupled single-stage amplifiers having finite load resistors?