Well, I have news for you. Here is a
linky. This provides the categories under which the driving licenses are issued. Although this is the AP Transport Dept's site the rules are CMV rules and hence valid across India. Obviously, you do not need to reapply for license if you shift state.
So you see there? Nothing called LTV license exists. You can drive even cabs on LMV license. To confirm this fact I just now walked down to our car pool and talked to a couple of Indicabbies. They all hold LMV licences just like us.
Go and tell your instructor to shove it... The bugger is taking you for a ride. He has invented a category as well. LTV!