AI unfortunately is hit and miss when it comes to check baggage thru, most likely they will refuse at HYD. Also you will only get your domestic allowance, the TK ticket will not apply.

In BOM you just collect your intl baggage, pass customs and hand your baggage to AI or UK who have a checkin desk for transit pax there. Then you take your boarding pass and go upstairs to domestic security. On the way back you have to take your bags from domestic arrival to TK checkin and check in the bags there.