^^ Do you have parallel telephone lines in your home ? If yes then try disconnecting all of them except the one where your modem is connected and then connect and observe the results for an hour or so. That should solve the problem.
MTNL suggests that the main line that comes to your house should first go into their modem and later on can be distributed to other parallel lines in the house. I too was facing similar issue as i had 5 parallel lines and had to disconnect (remove from wall socket) all of them except the modem one to make it work. This I did as rewiring was not possible in my house.