GATE EE 2021 Question Paper (07-Feb-2021) (Shift 1)

Two discrete-time linear time-invariant systems with impulse responses

h ₁[n] = δ[n - 1] + δ[n + 1] and h ₂[n] = δ[n] + δ[n - 1] are connected in cascade, where δ[n] is the Kronecker delta. The impulse response of the cascaded system is

An 8-pole, 50 Hz, three-phase, slip-ring induction motor has an effective rotor resistance of 0.08 Ω per phase. Its speed at maximum torque is 650 RPM. The additional resistance per phase that must be inserted in the rotor to achieve maximum torque at start is ____________ Ω. (Round off to 2 decimal places.)

Neglect magnetizing current and stator leakage impedance. Consider equivalent circuit parameters referred to stator.

In the circuit, switch 'S' is in the closed position for a very long time. If the switch is opened at time t = 0, then i ${}_L$ (t) in amperes, for t ≥ 0 is

In the open interval (0, 1), the polynomial p(x) = x⁴ - 4x³ + 2 has

A belt-driven DC shunt generator running at 300 RPM delivers 100 kW to a 200 V DC grid. It continues to run as a motor when the belt breaks, taking 10 kW from the DC grid. The armature resistance is 0.025 Ω, field resistance is 50 Ω, and brush drop is 2 V. Ignoring armature reaction, the speed of the motor is ____________ RPM. (Round off to 2 decimal places.)