One can opt for a polytechnic course just after 10thor it can also be done after 12th. But one cannot opt for B.Tech only after 12thwith physics, chemistry and maths as compulsory subjects. The duration of a polytechnic course is of minimum 3 years but you can take a lateral entry in polytechnic if you have done ITI for which the duration of the course will then be 2 years. The admissions are based on Polytechnic Entrance Exam which happens in the month of May or June, in some states polytechnics also take direct admission in 3 years diploma course.
For B.Tech the duration of the course is 4 years, but a lateral entry can be taken directly to the second year if a person has done a polytechnic course. The admissions are based on JEE ranking and some other institutes and colleges conduct their own entrance exams.