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

The operating region of the developed torque ($T_{em}$) and speed ($\omega$) of an induction motor drive is given by the shaded region OQRE in the figure. The load torque ($T_L$) characteristic is also shown. The motor drive moves from the initial operating point O to the final operating point S. Which one of the following trajectories will take the shortes time?

The input voltage $v(t)$ and current $i(t)$ of a converter are given by,
$v(t)=300\sin (\omega t)$ V
$i(t)=10\sin \left(\omega t-\frac{\pi }{6}\right)+2\sin \left(3\omega t+\frac{\pi }{6}\right)+\sin \left(5\omega t+\frac{\pi }{2}\right)$ A
where, $\omega =2\pi \times 50$ rad/s. The input power factor of the converter is closest to

Instruments required to synchronize an alternator to the grid is/are

The open-loop transfer function of the system shown in the figure, is
$G(s)=\frac{Ks(s+2)}{(s+5)(s+7)}$
For $K\ge 0$, which of the following real axis point(s) is/are on the root locus?

A continuous time periodic signal $x(t)$ is
$x(t)=1+2\cos 2\pi t+2\cos 4\pi t+2\cos 6\pi t$
If $T$ is the period of $x(t)$, then $\frac{1}{T}{\int }_0^T|x(t){|}^{2}dt=$ ___________ (round off to the nearest integer).