The vast majority of the really good colleges and universities in India, specially for science, technology, law, hotel management and medicine related fields; primarily use their own entrance examinations such as the IIT JEE, JEE-Mains or the NEET. The upscale private universities, for liberal arts, largely use the board exam as a very coarse filter and depend on SAT scores and interviews. The same goes for those applying abroad for whom a board exam score of 85 or 90 is sufficient to get into the best of colleges as their primary filter is a combination of SAT, AP test, Olympiads, SOP letters - and money (sad but true).  Nearly 50,000 of the best seats for science, engineering and technology education are available through the JEE/IITJEE. The number of high quality seats in these areas, available via the board examinations is almost zero.

In the light of all this, the board exam average, often becomes an worthless metric, because many (not all) of the schools which see averages cross 90, are those which conduct several rounds of internal examinations and pre-boards and misguide students into preparing well for an examination which has largely been reduced to a formality and will not open the doors to respectable institutions. The cost for such a heavy emphasis on inconsequential board exam scores, is ultimately borne by the students who are left high and dry with 95+ in the boards, but no respectable place to go: because these scores come at the cost of their entrance examination performance. At the same time, students who get into the best of colleges in India (or abroad) by acing the SATs or the JEE, invariably end up scoring more than 85 or 90 in the boards, even if they bunk school for half the year. It simply does not make sense to call a school, one of the "top CBSE schools" for an average score in the nineties, when the school sees almost nobody qualify within the first 500 of JEE or NEET, or for an Ivy League scholarship.  

A school has to maintain the right balance in doing just enough so that its best students get ample time for the entrance examinations which really matter while the rest score respectably in board examinations. 

Among the colleges which do rely on board scores for general BA, BCom, BSc programs: unfortunately there is not much difference between those available to a 95 percenter versus those available to an 80 percenter. 

For better or for worse, beyond providing a general and sound academic base, the expectation of a good school nowadays, is good grooming, good extra-curriculars and exposure to sports and a variety of areas. 

For the really intense academic accomplishment of the kind which really matters, it is the coaching industry (or admission consultants for foreign universities) who are expected to help students deliver excellent results, specially in classes 11 and 12. 

So, this list, contains schools which definintely have respectable academic standards (class average of 80+) but at the same time, offer a large number of subjects, which is indicative of how well they cater to the needs of a diverse student body.