I was wondering if there is a way to execute mongo like query directly through Java i.e. we give mongoDB like query as a String to a function in Java driver for mongoDB as a
What you showed here is not JSON, it's Javascript code for embedded MongoDB Shell. If you need for some reason to execute the code inside Java environment you will have to embed Javascript engine (like Rhino) and implement compatible API.
Otherwise you just need to convert JSON to DBObject and you can do this with JSON.parse() method or any other JSON-mapping library like Jackson. Note that MongoDB uses extended set of data types that are not present in JSON: http://www.mongodb.org/display/DOCS/Data+Types+and+Conventions
UPD: Scott Hernandez pointed out about JSON.parse.