Engineering Entrance Exam

There is no other way as the application date is already over. Now, you cannot apply for paper 1. You can start preparing for paper 2.
All the best.

JEE Mains will allow you to take admission in state government colleges and NITs. For IITs, you need to crack JEE advance. You need to score above 180 marks in JEE Advance for IIT – Kharagpur, if you belong to SC category.
All the best.

280+ in JEE Mains for general category.

The last date of the application form for engineering colleges in India varies from institution to institution. In India, we have engineering colleges (Both government and private). You can get admission in a government college after appearing for an entrance exam. There are many private colleges also takes admission under management quota, if you are not qualified through entrance exam.
We also have many private/ deemed universities, which conducts their own entrance exams. In general, August month should be the deadline for admission to pursue B.Tech.
I hope it helps.

50 in Advanced of JEE Mains.

Yes, what Sohan Kumar said is right. I want to add some extra information.
JEE Mains has total of 90 questions each carrying 4 marks.
Total-360 marks
And there's negative marking also 1/4 negative for 1 wrong answer.

You basic concepts related to PCM subject needs to be cleared. You can refer to RD Sharma for mathematics.

Yes, you surely can. But you should practise a lot and maintain a proper schedule all throughout the year. Get your basics clear and move ahead and also don't forget to practise previous year's questions, you will learn a lot from that.

Make sure that you are really very interested in preparing for JEE Mains. If you are then you must have a strong reason for its preparation. Whenever you get demotivated think about the reason and then you will automatically get boosted up.