[{"Name":"Jack","info":{"eyes":"brown","city":"paris","accomodation":"house"}},{"Name":"Mathew","info":{"eyes":"yellow","city":"rome","accomodation":"apartment"}},{"Name":"Peter","info":{"eyes":"brown","city":"barcelona","accomodation":"house","hair_color":"black"}}]

db.collection.aggregate([{$addFields:{rawInput:{"$objectToArray":{"eyes":"brown","city":"paris","accomodation":"house","hair_color":"black"}}}},{$match:{$expr:{$eq:[{$size:{$filter:{input:{"$objectToArray":"$info"},as:"elem",cond:{$not:{"$in":["$$elem","$rawInput"]}}}}},0]}}},{"$project":{Name:1,info:1}}])