Boards-12th

No, anyhow you can't take admission in class 12. Everywhere you need to show your TC of class 11 to take admission so without completing 11 you can't study 12.

Generally most schools not easily give admission in 12 class until you have very good academics or give higher money,  

In this case no school give admission. So I'll suggest you to complete Your 11 class first.

Yes, Class 12 Math Relation and Function chapter is important for rither CBSE Board Exams or State Boards. The Relation and Function chapter have weightage of 6-8 marks in the CBSE board exam. Moreover Relation and function chapter forms the foundation for many other advanced topicssuch as  types of relations, functions, domain, range, composition of functions, and invertibility.  Relation and function is also important to understand complex JEE Mains topics such as calculus and inverse trigonometry.  For more information check below;

Class 12 Math Relation and Function NCERT Solutions

This is based on in which domain you are puruing your carrer .If you are wanna pursuing your carrer in the field of doctorate,engineering,and all you have to pass their entrance exams.But if wnat to purse bba,bca,general graduation (even for this also you have to appear in cuet exam from back some years) you can may take your admission.You have to understand without entrace exam for colleges ,in any field might be tough.Direct admission is possible or from distance course like ignoo,nios and all but less prefrabble.

The best source to download previous year HSC board papers is the official website of Maharashtra State Board of Secondary and Higher Secondary Education (MSBSHSE). You can visit this website and download the PDFs of the previous year papers. Although, there are many other third party sources, but the official one is recommended.

Hey,

Maths is crucial subject when it came to pursuing B.Tech. Pursuing B.Tech without knowing fundamentals (taught in 11-12th standard) will be challenging.

And you may not eligible for entrance exam for BTech as it has criteria of minimum 40% in pcm in some state (like maharashtra). 

But you can take admission through management quota. It may possible that some college provide you admission. You should contact or visit there.

Here is a list of colleges in Kolkata offering BCA programs with fees under INR 2 lakh:

1. Aliah University - Total fees: INR 1,19,700
2. Institute of Management Study (IMS) - Total fees: INR 1,95,000
3. George Group of Colleges - Total fees: INR 1,79,000
4. Gurukul Management Studies (GMS) - Total fees: INR 1,95,000
5. Syamaprasad Institute of Technology and Management (SITM) - Total fees: INR 2,10,000 (slightly above 2 lakh).

For further details, you can directly contact the colleges or visit their official websites.

No, you have to sit for every subjects next year. Because if you failed the annual exam and missed the compartment exam as well, then that means you failed in that course for that year. But you can reappear for the course again and give the exam very next year and complete your course. Check the notifications on the Bihar Secondary Education Board (BSEB) website for the latest informations.