GATE EE 2023 Question Paper (05-Feb-2023) (Shift 1)

A 10-pole, 50 Hz, 240 V, single phase induction motor runs at 540 RPM while driving rated load. The frequency of induced rotor currents due to backward field is

A continuous-time system that is initially at rest is described by

$\frac{\mathrm{dy}(\mathrm{t})}{\mathrm{dt}}+3y(\mathrm{t})=2x(\mathrm{t})$,

where 𝑥(𝑡) is the input voltage and 𝑦(𝑡) is the output voltage. The impulse response of the system is

The Fourier transform 𝑋(𝜔) of the signal 𝑥(𝑡) is given by

𝑋(𝜔) = 1, for |𝜔| < 𝑊₀

= 0, for |𝜔| > 𝑊₀

The 𝑍-transform of a discrete signal 𝑥[𝑛] is

$\mathrm{X}(\mathrm{z})=\frac{4z}{\left(\mathrm{z}-\frac{1}{5}\right)\left(\mathrm{z}-\frac{2}{3}\right)(\mathrm{z}-3)}$ with ROC = R.

Which one of the following statements is true?

For the three-bus power system shown in the figure, the trip signals to the circuit breakers B₁ to B₉ are provided by overcurrent relays R₁ to R₉, respectively, some of which have directional properties also. The necessary condition for the system to be protected for short circuit fault at any part of the system between bus 1 and the R-L loads with isolation of minimum portion of the network using minimum number of directional relays is