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In order to find out which documents are required, you can run a Timatic search. Using your child's information:
Document Validity:
Passports and other documents accepted for entry issued to residents of Singapore must be valid on arrival.
Since your child is a resident of Singapore, they do not require 6 months validity on their passport. Timatic is the system which airlines use to check document validity, so you are unlikely to face problems with Air India.