The topology is as below, the right one is added to  ADC whose effective state shows "up" , the left one is the default DNS server, which is unable to check from show dns nameServer in CLI or Traffic Management--DNS--nameServer in GUI.

 when try to resolve the local domain hostname, will returns a failure and the DNS server shows the 172.1.x.x.rather than 172.16.7.1
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dig ad.test.local
……
;; Query time: 1 msec
;; SERVER: 172.1.0.2#53(172.1.x.x)
;; WHEN: Sat Mar 25 03:05:44 2017
;; MSG SIZE  rcvd: 48;; Query time: 1 msec
​-------------------------------------------------------
but if we assign the 172.16.7.1 or the 127.0.0.2(local default DNS,pointing to the added DNS server) to resolve it, it returns a normal result.
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dig ad.test.local @172.16.7.1
……
;; Query time: 1 msec
;; SERVER: 127.0.0.2#53(127.0.0.2)
;; WHEN: Sat Mar 25 03:05:44 2017
;; MSG SIZE  rcvd: 48;; Query time: 1 msec
​-------------------------------------------------------

when we check the /etc/resolv.conf , we found that there are 2 DNS server, 172.1.x.x  prior to 127.0.0.2,
this is a by design for ADC VPX running on AWS.

Note:- /etc/resolv.conf is on the shell prompt , you can reach shell prompt by typing in shell at ADC prompt(>)