Correct about the four Indian metros. India made the decision to have the entire country on a single time zone (no summer time either), and the only one that was not too bizarre for either westernmost or easternmost India was the half hour. I think that if you look at a time zone map (oh so helpdfully provided in the reference section of mist 'business' diaries), you'll see that thanks to China also adopting a rather extreme policy on time zones, you can travel north from India into China and suddenly find 2 and a half hours added to your time. Also, if you travel from Assam through Bangladesh into West Bengal, your time (even though you're headed westwards) can go from, say, 0630 to 0700 (and then back to 0630 again).
A quick scan also seems to show that Nepal may be 5 and three quarter hours ahead of GMT.
