Hi,
It takes nearly 1 year to prepare for upsc exam  and you will be benefitted more when you will join coaching as they will provide you precise notes , daily current affairs and information regarding the exam and yes you can prepare for the exam along with your btech course but you have to make a proper time table so that you can give equal amount of  time to every subject  and then after completing your degree you have more chances to clear the exam in 1 attempt .