Can I put Virtual Server in different subnet from Self-IP?

A self-IP isn't required on the client-side (where the virtual server is located), but you'll need one on the server-side. At the very least you'll need the self-IP to conduct health monitoring of your backend servers.

-George

Yes, you can have a virtual server IP that doesn't belong to any subnets on the box at all.

If you do this, your routing should be airtight in your whole environment. Your clients and servers need to be configured to route the packets correctly back to the LTM.

Of course you can. You need to ensure 2 things: 1. The upstream routing device must have a route to your Virtual server subnet (using big-ip's client-side subnet self ip address as a next hop, floating self ip if you have a redundant pair of big-ips) 2. The Virtual server must be enabled on the big-ip vlan, where the client requests will come in - the default setting for a VS is 'enabled on all vlans', but you can limi it to specific vlan(s)