[{"questions":[{"topics":["b","c","a"],},{"topics":["c"],},{"topics":["b"],}]}]

db.collection.aggregate([{$match:{"questions.topics":{$in:["b"]}}},{$project:{questions:{$filter:{input:"$questions",cond:{$ne:[{$filter:{input:"$$this.topics",cond:{$in:["$$this",["b"]]}}},[]]}}}}}])