Does BSNL broadband speed depend on the distance between exchange and my home?
Short answer: Yes.
distance between my house and bsnl exchange is around 3 kms
Even though the distance is only 3kms, the wires go through in a zig-zag manner between streets and roads, resulting in more distance.
Hard to say. If you are going to use it for
business and if you just need a bare minimum speed, request the exchange to lower the speed, only if you notice instability or frequent disconnections.
will it fluctuate a lot as distance is too much
Speed should never fluctuate, except on a busy hour. If it fluctuates, something is wrong with the wiring or with the exchange routing protocols. So, if you get 2mbps, it would stay at the same speed for most of the day. The fluctuation may come due to other reasons, but never due to the distance.
Also, will it disconnect frequently??
This question is hard to answer. If your line's SNR ratio goes below 10, yes, you'd see frequent disconnections. In this case, ask the exchange to lower the line rate. Lowering the line rate increases SNR ratio, thus bringing stability in your line.