The British might have increased their military presence near Sikkim’s borders during the Revolt as a:

Precaution
Show of force
Preparation for a possible invasion
Logistical necessity

The correct answer is: a) Precaution.

The British might have increased their military presence near Sikkim’s borders during the Revolt as a precaution against possible attacks from the rebels. Sikkim was a small kingdom located in the Himalayas, and it was not directly involved in the Revolt. However, the British were concerned that the rebels might try to use Sikkim as a base for launching attacks on British territory. By increasing their military presence near Sikkim’s borders, the British hoped to deter the rebels from attacking and to protect their own interests in the region.

The other options are not as likely. Option b, “Show of force,” is possible, but it is less likely than option a. The British were already showing their force by suppressing the Revolt in other parts of India. It is unlikely that they would have needed to show their force in Sikkim, which was not directly involved in the Revolt. Option c, “Preparation for a possible invasion,” is also possible, but it is less likely than option a. The British were not expecting an invasion from Sikkim, and they did not have any evidence that the rebels were planning to invade. Option d, “Logistical necessity,” is not a likely explanation. The British did not need to increase their military presence near Sikkim’s borders for logistical reasons. They already had a strong military presence in the region, and they were able to supply their troops without difficulty.