Step-up Chopper with R Load

The values of duty cycle (α) lies between ?
Find the expression for output voltage for a step-up chopper, assume linear variation of load current and α as the duty cycle?
Find the output voltage for a step-up chopper when it is operated at a duty cycle of 50 % and Vs = 240 V?
If a step up chopper’s switch is always kept open then (ideally) then?
For a step-up chopper, when the duty cycle is increased the average value of the output voltage?