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

The three-bus power system shown in the figure has one alternator connected to bus 2 which supplies 200 MW and 40 MVAr power. Bus 3 is infinite bus having a voltage of magnitude |V₃| = 1.0 p.u. and angle of -15°. A variable current source, |I|∠ϕ is connected at bus 1 and controlled such that the magnitude of the bus 1 voltage is maintained at 1.05 p.u. and the phase angle of the source current, ϕ = θ₁ ± $\frac{\pi }{2}$, where θ₁ is the phase angle of the bus 1 voltage. The three buses can be categorized for load flow analysis as

Consider the following equation in a 2-D real-space.

|𝑥₁|${}^p$ + |𝑥₂|${}^{\text{p}}$ = 1 for 𝑝 > 0

Which of the following statement(s) is/are true.

In the figure, the electric field E and the magnetic field B point to x and z directions, respectively, and have constant magnitudes. A positive charge ‘q’ is released from rest at the origin. Which of the following statement(s) is/are true.

All the elements in the circuit shown in the following figure are ideal. Which of the following statements is/are true?

The expected number of trials for first occurrence of a “head” in a biased coin is known to be 4. The probability of first occurrence of a “head” in the second trial is _____________ (Round off to 3 decimal places).