Here's a sample DNS setup for a test system using internal IP addresses
only
DNS server is running on 192.168.1.1

I am able to ping (-a) and resolve 192.168.1.1, abc.com, and
ns1.abc.com.
But, I cannot ping -a 192.168.1.2 (which should resolve to mail.abc.com)

Here's the export of the abc.com zone and the IN-ARPA

$ORIGIN abc.com.
@ IN SOA abc.com. ns1.abc.com. (
2006051151 ; Serial
10800 ; Refresh
3600 ; Retry
604800 ; Expire
86400 ) ; Minimum


$ORIGIN com.
abc IN A 192.168.1.1
IN NS ns1.abc.com.
IN MX 0 192.168.1.2.

$ORIGIN abc.com.
ns1 IN A 192.168.1.1
mail IN A 192.168.1.2



$ORIGIN 1.1.168.192.IN-ADDR.ARPA.
@ IN SOA abc.com. root.1.1.168.192.IN-ADDR.ARPA. (
2006051131 ; Serial
10800 ; Refresh
3600 ; Retry
604800 ; Expire
86400 ) ; Minimum


$ORIGIN 1.168.192.IN-ADDR.ARPA.
1 IN NS ns1.abc.com.
IN PTR ns1.abc.com.
IN PTR abc.com.
2 IN NS ns1.abc.com.
IN PTR mail.abc.com.