Please note play school is also a school (public place) and as such they need permission under zoning(residential/commercial) from municipality.
Generally renting to schools has its own challenges as once the school becomes famous in locality, the land lords are forced to suffer .
Also courts show reluctance to grant any injunction to land lord as public interest(school children) are involved. So technically you cannot vacate them during academic year.
Better go for registered lease agreement for a fixed period of 3/4/5 years.
11 month lease is generally considered month on month lease and not advisable in case of commercial leases.
Also if you are a non resident indian, registered lease deed is preferred option to handle GST and income tax related processes (monthly rental invoices, rent remittances in NRO account, filing of GST, income tax annual returns etc)
Hope this information is useful