"This is your banana."
Translation:यह तुम्हारा केला है।
You choose between the three forms depending on the noun that follows it.
It's तुम्हारा if the noun is masculine and singular. Eg: तुम्हारा कुत्ता (your dog)
It's तुम्हारे if the noun is masculine and plural. Eg: तुम्हारे कुत्ते (your dogs)
It's तुम्हारी if the noun is feminine. Eg: तुम्हारी बिल्ली (your cat), तुम्हारी बिल्लियाँ। (your cats)
You can, and it's grammatically correct. But it sounds odd to use the honorific plural in these cases, especially the one with the dog. And if the "you" you were talking to was so respect-worthy that you'd want to show respect to everything relating to that person, you'd probably go with "आपके कुत्ते" instead of "तुम्हारे कुत्ते". :-)
-- edit 21-september-2020 --
Ignore what I said here. Go with vinay92's reply to me. :-)
I think HarishAbbe3 was talking about the oblique case rather than the honorific plural. Though 'your dog' is 'तुम्हारा कुत्ता', in a sentence like तुम्हारे कुत्ते ने एक लड़की को काटा ('Your dog bit a girl'), we need to use the oblique-case form 'तुम्हारे कुत्ते' because it is the object of ने.
It's a matter of how much respect you want to show. Duolingo will take either, but should encourage more use of the latter. (BTW, it's tumhara).
You would only use 'tera' for talking to children, talking to your most intimate friends (probably only your mate), talking to pets, talking to your god, and talking to people you want to insult. It's also based on the only grammatically singular form of "you" and can only be used with a single addressee.
Tumharaa is appropriate for friends (one or many) or people of similar social status (one or many). Since it's based on "tum", a grammatically plural form of "you", you'd also use it for any group of more than one individual you'd otherwise use "tera" with.
And when you really want to show respect, use aapka. This is appropriate for elders and people of higher social status. And you should err on the side of using this when meeting people for the first time.
- intimate, just one addressee: तू / तेरा
- informal, one or more addressees: तुम / तुम्हारा
- formal, one or more addressees: आप / आपका