Are you in Mumbai? Is your IP address range starting with 182.xx ??
This is because MTNL's server hardware (New Alcatel) handling that IP range is misconfigured or downright shitty. It's burst speed for every connection is not configured correctly which results in aggressive throttling of every data stream. Websites think that connection was lost and hence they don't load properly or time out. First rule out any line problem. New modem or will not help you.
If you read VDSL user experience thread, there are few guys talking about the same issue. They all solved their problem by migrating to SOTL server. They had to go to exchange and force the exchange people to change port of their line to SOTL system. There is no other way out really. My neighbor had same problem and we went to exchange and sat with the server team and explained the problem. They said that an engineer from Alcatel (Bangalore) was called in to rectify the problem. But the problem is sporadic and they could not replicate it in front of him. Hence they cannot do anything about it.
But if you are on VDSL, you will have to downgrade back to 8 Mbps
ADSL as SOTL system does not handle VDSL traffic.