Ques. I plan to purchase HTC ONE MAX 32 GB 4 LTE from US.Will it work fine in India?
Ans.The phone will work in India on 2G and 3G networks but it's working on 4g networks depends upon the 4g bands it supports.
Make sure when you buy the phone . do activate it in the US with local service provider Sim to avoid regional sim lock.
Now comes 4g connectivity .
4g bands that are supported in India are.
TDD- LTE Band NO 40 2300 MHz
But the 4G bands phone supports are as below.
LTE 800 / 900 / 1800 / 2600 - EMEA
LTE 900 / 1800 / 2100 / 2600 - Asia
LTE 700 / 1700 / 2100 - for Verison
So there is no 2300 MHz support so the phone will not work on 4G network in India.
So, you would be able to make calls (on 2G), use data ( on 3G), but won't be able to use 4G for hi speed Internet.