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

For the signals 𝑥(𝑡)and 𝑦(𝑡) shown in the figure, 𝑧(𝑡) = 𝑥(𝑡) ∗ 𝑦(𝑡) is maximum at 𝑡 = 𝑇₁. Then 𝑇₁ in seconds is ___________ (Round off to the nearest integer).

For the circuit shown in the figure, V1 = 8 V, DC and I1 = 8 A, DC. The voltage Vab in Volts is _________ (Round off to 1 decimal place).

A 50 Hz, 275 kV line of length 400 km has the following parameters:

Resistance, R = 0.035 Ω/km;

Inductance, L = 1 mH /km;

Capacitance, C = 0.01 μF/km;

The line is represented by the nominal-π model. With the magnitudes of the sending end and the receiving end voltages of the line (denoted by V${}_S$ and V${}_R$, respectively) maintained at 275 kV, the phase angle difference (θ) between V${}_S$ and V${}_R$ required for maximum possible active power to be delivered to the receiving end, in degree is _____________ (Round off to 2 decimal places).

In the following differential equation, the numerically obtained value of y(t), at t = 1, is _______________ (Round off to 2 decimal places).

$\frac{\mathrm{dy}}{\mathrm{dt}}=\frac{{\mathrm{e}}^{-\mathrm{at}}}{2+\mathrm{at}}$, 𝛼 = 0.01 and 𝑦(0) = 0

Three points in the x-y plane are (-1, 0.8), (0, 2.2) and (1, 2.8). The value of the slope of the best fit straight line in the least square sense is ____________ (Round off to 2 decimal places).