GATE EE 2022 Question Paper (05-Feb-2022) (Shift 2)

Let, f(x, y, z) = 4x² + 7xy + 3xz². The direction in which the function f(x, y, z) increases most rapidly at point P = (1, 0, 2) is

A 4-pole induction motor with the inertia of 0.1 kg-m² drives a constant load torque of 2 Nm. The speed of the motor is increased linearly from 1000 rpm to 1500 rpm in 4 seconds as shown in the figure below. Neglect losses in the motor. The energy, in joules, consumed by the motor during the speed change is ____________. (round off to nearest integer)

In the circuit shown below, the magnitude of the voltage V₁ in volts, across the 8 kΩ resistor is __________. (round off to nearest integer)

Two generating units rated for 250 MW and 400 MW have governor speed regulations of 6% and 6.4%, respectively, from no load to full load. Both the generating units are operating in parallel to share a load of 500 MW. Assuming free governor action, the load shared in MW, by the 250 MW generating unit is _________. (round off to nearest integer)

In the circuit shown below, a three-phase star-connected unbalanced load is connected to a balanced three-phase supply of 100√3 V with phase sequence ABC. The star connected load has Z${}_A$ = 10 Ω and Z${}_B$ = 20∠60° Ω. The value of Z${}_C$ in Ω, for which the voltage difference across the nodes n and n′ is zero, is