We want to achieve this by automatically switching between the internet links if it fails (i.e for eg. if the BSNL link goes off, it has to take the AIRTEL link and once the BSNL link is ready, it has to switch automatically to it.)
BSNL and Airtel will give you two separate DSL lines with two distinct DSL modems to dial in, and hence, you'll end up with two distinct IP addresses. The only plausible solution that I can think of is to have a gateway box with two distinct ethernet interfaces. Unless you do something really clever, I'm not really sure how you'd really "switch" between them*. You'd effectively be using both simultaneously and you'd have 100% uptime unless both of them go down at the same time.
* Switching requires that you run a daemon that keeps pinging the ISP's gateway to check if the link is up. When the link goes down, it should automatically take the current ethernet interface down and bring up the other interface. I'm not sure it's worth the trouble.