The operating region of the developed torque ( $T_{\mathrm{em}}$ ) and speed ( $\omega$ ) of an induction motor drive is given by the shaded region OQRE in the figure. The load torque $\left(T_L\right)$ characteristic is also shown. The motor drive moves from the initial operating point O to the final operating point S . Which one of the following trajectories will take the shortes time?

A three phase, 50 Hz, 6 pole induction motor runs at 960 rpm. The stator copper loss, core loss, and the rotational loss of the motor can be neglected. The percentage efficiency of the motor is

A 10-pole, 50 Hz, 240 V, single phase induction motor runs at 540 RPM while driving rated load. The frequency of induced rotor currents due to backward field is

The frequencies of the stator and rotor currents flowing in the three-phase 8-pole induction motor are 40 Hz and 1 Hz, respectively. The motor speed, in rpm, is ________. (round off to nearest integer).