GATE EE 2025 Question Paper (02-Feb-2025) (Shift-2)

Consider a continuous-time signal
$x(t)=\text{–}{t}^2\{u(t+4)\text{–}u(t\text{–}4)\}$
where $u(t)$ is the continuous-time unit step function. Let $\delta (t)$ be the continuous-time unit impulse function. The value of
${\int }_{-\infty }^{\infty }x(t)\delta (t+3)dt$ is

Selected data points of the step response of a stable first-order linear time-invariant (LTI) system are given below. The closest value of the time-constant, in sec, of the system is

The Nyquist plot of a strictly stable $G(s)$ having the numerator polynomial as $(s\text{–}3)$ encircles the critical point –1 once in the anti-clockwise direction. Which one of the following statements on the closed-loop system shown in figure, is correct?

During a power failure, a domestic household uninterruptible power supply (UPS) supplies AC power to a limited number of lights and fans in various rooms. As per a Newton-Raphson load-flow formulation, the UPS would be represented as a

Which one of the following figures represents the radial electric field distribution $E_R$ caused by a spherical cloud of electrons with a volume charge density. $\rho =-3{\rho }_o$ for $0\le R\le a$ (both ${\rho }_o$, $a$ are positive and $R$ is the radial distance) and $\rho =0$ for $R>a$?