The correct answer is: b) High construction costs due to mountainous terrain.
Sikkim is a mountainous state in the eastern Himalayas. The terrain is very rugged and mountainous, which makes it very difficult and expensive to build railways. The cost of building a railway in Sikkim would be much higher than the cost of building a railway in a flatter area.
The other options are not as significant challenges. Lack of demand is not a major issue, as there is a growing population in Sikkim and a need for better transportation. Limited government investment is also not a major issue, as the Indian government has been investing in infrastructure in Sikkim in recent years. Environmental concerns are a potential issue, but they can be mitigated through careful planning and construction.
In conclusion, the primary challenge for developing extensive railway networks in Sikkim is the high cost of construction due to the mountainous terrain.