Hello dear student,
As you said you have not done anything in the past one year that is not a problem dear student. As your background is from science stream so you can take admission in BTech or in BE which is bachelors of engineering. There are many streams which you can opt for in both BTech or BE. Here I am mentioning few of the good streams in which you can take admission for BTech and don't worry 1 year gap will not be a problem for you career. Although jee mains was an option but I don't think you have applied to given the exam.
I hope this will be helpful for you dear student. There are many private institutes who provide admission in BTech to the students.
Best wishes
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