The speed of a $$4$$-pole induction motor is controlled by varying the supply frequency while maintaining the ratio of supply voltage to supply frequency $$(V/f)$$ constant. At rated frequency of $$50$$ $$Hz$$ and rated voltage of $$400$$ $$V$$ its speed is $$1440$$ $$rpm$$. Find the speed at $$30$$ $$Hz,$$ if the load torque is constant

A $$3$$ phase, $$10$$ $$kW$$, $$400$$ $$V,$$ $$4$$ pole, $$50$$ $$Hz$$, star connected induction motor draws $$20$$ A on full load. Its no load and blocked rotor test data are given below.
No Load Test: $$400V$$ $$6A$$ $$1002W$$
Blocked Rotor Test: $$90V$$ $$15A$$ $$762W$$
Neglecting copper loss in No Load Test and core loss in Blocked Rotor Test, estimate motor's full load efficiency.

Under no load condition, if the applied voltage to an induction motor is reduced from the rated voltage to half the rated value,

A three-phase cage induction motor is started by direct-on-line (DOL) switching at the rated voltage. If the starting current drawn is 6 times the full load current, and the full load slip is 4%, the ratio of the starting developed torque to the full load torque is approximately equal to