A $220 \mathrm{~V} / 12 \mathrm{~V}$ single-phase transformer is designed for use in India and rated 100 VA at 50 Hz . Later, this unit is shipped to the USA where it is used as a $110 \mathrm{~V} / 6 \mathrm{~V}$ transformer at 60 Hz . Which of the following statements is/are correct?

Three single-phase $11 \mathrm{kV} / 3.3 \mathrm{kV}$ transformers are connected to form a three-phase transformer bank with connections as shown.

Considering ABC phase sequence, the vector group of the transformer is:

A balanced three-phase supply is given to a $30 \mathrm{~kW}, 4$-pole, $400 \mathrm{~V}, 50 \mathrm{~Hz}$, wound rotor induction motor with Y-connected stator and rotor windings. The motor is driving a constant torque load. With shorted slip rings, the machine runs at 1476 rpm .

When an external non-inductive resistance of $0.27 \Omega$ per phase is connected in series in the rotor circuit, the steady-state speed drops to 1404 rpm .

Neglecting rotational losses, the actual per phase rotor winding resistance is $\_\_\_\_$ $\Omega$. (Round off to two decimal places)

A uniform ring charge of radius $R$ carries a total charge $Q$. Which one of the following options correctly quantifies the magnitude of the force on a point charge of strength kept at the center of the ring? ( $\in$ is the permittivity of the medium))