All three nations you mentioned have substantial islamic terror problems, especially India. But Russia has a big terrorist problem too, they just don't like to talk about it much while they try to crush Chechnya and keep their own muslim population appeased. Even China finds itself trying to keep the peace with its jihadi citizens. So what do you want to do, wait until it's too late and then face the problem?
If India, Russia and China were as worried as we are about world Jidad they would have troops in Iraq before it’s ‘too late’.