I by mistake deleted the members group under people and groups in SharePoint 2010 site.
How to restore this?
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I do not think you can restore it but you can certainly create a new one and add the members back in. Members usually have the Contribute permission level.
I agree, deleted members don't go into a "recycle bin" so re-adding them would be the only option as far as I know.
In your Situation Only solution is restore the whole site collections from backup.
If you have SQL backup of your content db, restore just before the groups got deleted. Then mount it to test farm /web app. then you need to move the group from the that site to production site...either manually or pragmatically.
check this for move groups.