So here is a method resolve the problem....
Start Remix OS 2.0
1. Download GMSInstaller.apk from Mod edit: links removed (pay-per-click links are not allowed).
2. Install APK file and run it.
3.Click on "One-click to install Google Services" (this will automatically download google play services).
4.Go to Settings->Applications->Manage Applications->All
5.Select "Clear Data" for Google Play Services and Google Service Framework
6. Reboot OS.
7.Goto browser and search Google Play Services. click the link to the store. and click update
Download Remix os: www.jide.com
Disclaimer: I will not be responsible if you screw up with your device.