Jsri,
How is aparna preparing yaar.
Getting admission into the 11th is a bit tricky. most schools are fussy about giving admission in the 11th to the extent there was this school which denied admission to its own 10th student for want of better marks??(that most of them had above 80 is a different story..)
Hey buddy this is not to scare you, this is to tell you be prepared to put in a fight

.
the safest bet would be try getting into Kendriya vidyalaya's which will definitely not say no for 11th. but it is cbse.
you have lot of state board schools.
After maharashtra board state board, state board should be more helpful. most of the schools will start placing ads in the papers. just ask your appa to check the local mylapore talk/adayar times and all. and you can pick the application from the schools.