Change the default version of MSSqlLocalDB for Visual Studio 2015
It took me 2 days to find the solution to this problem.

Posting here for anybody who faces the issue in future.

I basically removed all instances of LocalDB from my system and reinstalled them.
Following are the steps that were required to finally solve the issue


Remove all the databases attached to the LocalDB 2016
Remove LocalDB 2016
Remove LocalDB 2014
Restart the system
Reinstall LocalDB 2014 


For installation of LocalDB 2014, either use the standalone file from "https://www.microsoft.com/en-in/download/details.aspx?id=42299" OR
Select Express from standard Sql Server Setup and then select LocalDB in the component list