B.Tech

Hello Dumadiya! As you said that you completed your 12th standard in PCB, ( I. e; without mathematics) and preferring IT in Btech. The chances are less you get a admission.
But few institutes provide this opportunity by clearing their institute test which includes mathematics also. For example, LPU is providing LPU NEST entrance test, based on your marks and eligible criteria you will provided seat in respective branches.
On the other hand you are eligible for only few btech branches in some particular colleges. You are not allowed to join in NITs and IITs with PCB background because you are not allowed to give the JEE Mains and Advanced tests.
You will be eligible to do biotechnology in btech with PCB background in almost all the government institutions except NITs and IITs.
VIT Vellore, LPU Phagwara, SRM Chennai ,MIT Manipal, etc. are some of the best engineering colleges which are allowing PCB students in India.
Do proper research about the college and the courses it is providing and prepare for their tests and try to score best to join the branch you are preferring.

Yes, I'd like to let you know that, yes, you can apply to ordinary college after passing NIOS. It is a recognised board that holds the same weight as other boards. After completing your 12th grade at NIOS, you can apply to any of the colleges.
There are numerous colleges to which you can apply.you can get admission in any college for B.Tech being a NIOS board student. But you have to meet the expectations of the college requirements based on the score.
To pursue B.Tech from a reputable institute, candidates must meet all of the qualifying criteria listed below.
Students must have earned their 12th grade coursework in Science from a recognised Board.
Students must have completed qualifying courses in physics, chemistry, and mathematics.
At the qualifying level, students must have received a minimum of 50% in the abovementioned subjects and passing scores in the rest of the courses (varies from college to college)

Hello,
What happened that you are seeking a change of college in the sixth semester? The situation can arise when we feel suffocated in an institution and desire change. See theoretically it is possible. Just understand the different dynamics working. Your present college will not like to lose you since they may end up losing fees that you pay. The syllabus of your new college may not be compatible with your current syllabus. In view of all this, it's advisable not to break one's head over this issue. My advice is for you to continue in the same college if the situation is not alarming. But then if it's a must seek clarity on the procedure from the admin staff of your college. Best wishes to you.

Since you have not mentioned your caste, I am considering you as a general category student. Looking at the previous year WBJEE cut off, with 25 marks out of 200 in WBJEE you can accept a rank between 10,900 and 11,300. And considering this to be your general rank you have chance for government semi government or private colleges which include following college at the top: University of Kalyani. Haldia institute of technology. Feather please not that the above prediction is best on the previous year WBJEE cut off which match change this year as the WBJEE cut off bound to change every year and it depend on the various factors like: difficulty level of the, previous year cutoff trends, number of aspirants appearing, etc.