A $746$ KW$,3$ Phase, $50$Hz$,16$ Pole induction motor has a rotor impedance of $(0\mathrm{.}02+$j$0\mathrm{.}15)$ ohm at standstill. Full load torque is obtained at $360$ r$.$p$.$m$.$ Calculate a$)$ the speed at which maximum torque occurs ; b$)$ the ratio of maximum to full load torque; c$)$ the external resistance per phase to be inserted in the rotor circuit to get maximum torque at starting