To test our DNS from internet we can use NSLOOKUP or use Online Tools.
  http://www.checkdns.net/quickcheckdomainf.aspx
  Use the CheckDNS.net analyzer to:
  Check if your domain has appropriate DNS servers delegated   See if your DNS servers are alive   Test if your hosting service is functioning   Verify if your DNS servers server the zone corresponding to your domain   Make out if all DNS servers have the same zone version   Check if your WWW-Web server is running   Verify if your hosting service is alive   Test if your mail server is receiving emails   Check if how many backup MX servers are configured within your zone   Test if these backup servers are functioning in case your primary MX is down   Validate if your backup mail server rejects your email in case of a failure because of an not optimal configured open relay restriction   Check your SOA record   Test if all your WWW-Server clustered nodes are up and running with DNS round robin   Web-Tool to get a full report to check if all relevant elements are in "the green range"   Get a step by DNS analysis and find out where the fault can be located, in a case when your Site is down or not reachable   Test if your Web Server is reachable from outside (from the internet)   Online Check if your mail servers are reachable from outside (from the internet)   Test if your Firewall allows the appropriate incoming communication for your DNS, mail, and web servers   Proof your ISP, if the a hosted DNS zone is properly and functioning   Hosting- and web server health check   
 
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