GATE EE 2025 Question Paper (02-Feb-2025) (Shift-2)

Let $G(s)=\frac{1}{(s+1)(s+2)}$. Then the closed-loop system shown in the figure below, is

The continuous-time unit impulse signal is applied as an input to a continuous-time linear time-invariant system $S$. The output is observed to be the continuous-time unit step signal $u(t)$. Which one of the following statements is true?

The transformer connection given in the figure is part of a balanced 3-phase circuit where the phase sequence is “abc”. The primary to secondary turns ratio is $2:1$. If $(I_a+I_b+I_c=0)$, then the relationship between $I_A$ and $I_{ad}$ will be

A DC series motor with negligible series resistance is running at a certain speed driving a load, where the load torque varies as cube of the speed. The motor is fed from a $400\text{ V}$ DC source and draws $40\text{ A}$ armature current. Assume linear magnetic circuit. The external resistance, in $\Omega$, that must be connected in series with the armature to reduce the speed of the motor by half, is closest to

A 3-phase, $400\text{ V}$, 4 pole, $50\text{ Hz}$ star connected induction motor has the following parameters referred to the stator :
$R_r^{\prime }=1\Omega$, $X_s=X_r^{\prime }=2\Omega$
Stator resistance, magnetizing reactance and core loss of the motor are neglected. The motor is run with constant $V/f$ control from a drive. For maximum starting torque, the voltage and frequency output, respectively, from the drive, is closest to,