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

The Nyquist plot of a system is given in the figure below. Let ${\omega }_P$, ${\omega }_Q$, ${\omega }_R$, and ${\omega }_S$ be the positive frequencies at the points P, Q, R, and S, respectively. Which one of the following statements is TRUE?

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 $h_2[n]\ne \delta [n]$, the overall system (denoted by the dashed box) is ____________.

Consider a continuous-time, real-valued signal $f(t)$ whose Fourier transform $F(\omega )={\int }_{-\infty }^{\infty }f(t)exp(-j\omega t)dt$ exists.
Which one of the following statements is always TRUE?

Consider a part of an electrical network as shown below. Some node voltages, and the current flowing through the $3\Omega$ resistor are as indicated. The voltage (in Volts) at node X is ________.

Let $i_C$, $i_L$, and $i_R$ be the currents flowing through the capacitor, inductor, and resistor, respectively, in the circuit given below. The AC admittances are given in Siemens(S). Which one of the following is true?