Hi,
Based on your info, the Application Server (AppSvr) in your DMZ (Delhi) need to access GIS server at Mumbai:
GIS svr (Mumbai) ->outside:PIX515E:DMZ-> AppSvr
ICMP & TCP/UDP is 2 different protocols, where you can always allow icmp/ping to pass through from internal (initiate icmp) to external network/host. But allowing ICMP doesn't mean that outbound TCP/UDP access is also permitted. You need to have proper ACL permitting your internal/dmz host to access outside host/resources. I assumed nat/global or static nat (if any) is already configured properly.
Quick check - do you have ACL that permits your AppSvr to access your GIS server (considered on the external network) via specific TCP/UDP protocols & ports?
Maybe for a start, use ACL to allow IP any any from your AppSvr to the GIS address.
Rgds,
AK