Hi @Litty Kuriakose , welcmoe to Microsoft Q&A forum.
Using synthetic partition key seems like the right idea in this specific situation, however the queries mentioned above will not use the synthetic partition key because synthetic keys are created as concatenation of properties A and B (lets say "AB"), until we use "AB" in the queries it will not be used. As an example, below query will use the key:
Select from c where c.AB = sample
Please let us know if this helps or we can continue the discussion.