A $$3$$ phase, $$4$$ pole, $$400$$ $$V,$$ $$50$$ $$Hz,$$ star connected induction motor has following circuit parameters $${r_1} = 1.0\Omega ,\,{r_2} = 0.5\Omega ,$$ $${\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {x_1} = x{'_2} = 1.2\Omega ,{\mkern 1mu} {x_m} = 35\Omega $$
The starting torque when the motor is started direct-on-line is (use approximate equivalent circuit model)

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.

In a single phase induction motor driving a fan load, the reason for having a high resistance rotor is to achieve

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