A $400$ V$,4$ pole, $3$ phase, $50$ Hz star connected induction motor has a rotor resistance and reactance per phase equal to $0\mathrm{.}01$ and $0\mathrm{.}1$ respectively. Assume ratio of stator to rotor turns as $4.$ Determine the following:

$($a$)$ Starting torque $(3$M$)$

$($b$)$ slip at which maximum torque will occur $(3$M$)$

$($c$)$ speed at which maximum torque will occur $(3$M$)$

$($d$)$ maximum torque $(3$M$)$

$($e$)$ full load torque if full load slip is $4\%.(3$M$)$

$17$