I am happy that you are looking out for options to further your studies. Here are few things you need to know about scholarship system in India.
1.National Talent Search Examination - First level exam for class X
SAT: The syllabus for Mathematics, Science and Social Science is broadly based on the prescribed respective State Board Syllabus from Std 9th to 10th class (100 questions in SAT) . Few states like Kerala refer both state board and NCERT books while few states like Maharashtra, Gujarat and Andhra Pradesh ask questions primarily from their state board books.
MAT: It has 50 questions of general nature.
Language Test: State Board books cover a lot. More focus is on vocabulary, grammar and basic understanding. Language in first stage is of qualifying purpose(40% of maximum score) only. It is the most prestigious exam of India.
The students who qualify second stage are eligible for scholarship. The amount of scholarship has been enhanced to Rs.1250 per month for class XI and XII and Rs.2000 per month for students studying under graduate and above.
2.Young India challenge for school students - This is a scholarship for students in their 8th-12th standard. The cash prize is of the amount Rs. 20,000. The selection process involves weekly writing challenges that one must enroll in. The winners of all the weekly challenges compete in the finals, whose final performance will be judged by top industry mentors. Official website (http://www.jwfiles.net/2015/03/young-india-challenge-for-school.html)
3.Foundation For Academic Excellence and Access (FAEA) - FAEA provides scholarships for students belonging to socially and economically disadvantaged sections of the society. It enables students to study in the institutions, which provide academic excellence and economic opportunity. Students are selected on the basis of their academic excellence and social and economic background. Scholarship Program will provide support to the students selected for up to three years in the first instance. This can be extended for another two years for postgraduate study. All the permanent resident Indian students who have passed 12th grade are eligible for this scholarship. Official Website (http://www.faeaindia.org/)