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Here if check_txn contains its own attributes then during converting into a relational model where does its attributes will be placed either in account side ( strong entity set) or check side (weak entity set)? and why?

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In learndb he had not given about weak entity set. Also in the case study he mentioned that there are errors

And also what about in one-one and one-many?
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What I have written is not a rule.But how many example I have seen it will not merge with weak or strong entity table. So, either it  needs separate table, otherwise, there will be no attribute in relationship
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check_txn will be included in check side.
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From the ER diagram it is clear that the given relationship is many to one from check to the account.So if there is no attribute then it can be combined with the check side but if it has its own attributes then there should be a separate table for it.

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Because it's a many-to-one relationship, I can add the attributes of check_txn in the check table itself. I don't need a separate table for the relationship. 

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