Skip and Limit on nested array element
You can try like this -
db.collection.find({}, {ObjectArray:{$slice:[0, 3]}})
This will provide you records from 0..3
$slice:[SKIP_VALUE, LIMIT_VALUE]}
For your example:-
db.collection.find({"_id":""}, {ObjectArray:{$slice:[0, 3]}})
Here is the reference for MongoDB Slice feature.http://docs.mongodb.org/manual/reference/operator/projection/slice/