The National Highway connecting Siliguri (West Bengal) to Gangtok (Sikkim) is:

NH 31A
NH 58
NH 10
NH 20

The correct answer is: a) NH 31A.

NH 31A is a national highway in India that connects Siliguri in West Bengal to Gangtok in Sikkim. It is a two-lane highway that is 120 kilometers long. The highway was built in the 1970s and is a major artery for transportation between the two states.

NH 31A is a scenic highway that winds through the Himalayas. The highway passes through several towns and villages, including Mirik, Kalimpong, and Darjeeling. The highway is also a popular tourist destination, and many people travel along it to see the snow-capped mountains and the beautiful scenery.

The highway is well-maintained and is a safe and reliable way to travel between Siliguri and Gangtok. The highway is open all year round, but it is important to check the weather conditions before traveling, as the highway can be closed due to snow in the winter.

The other options are incorrect because they are not national highways that connect Siliguri to Gangtok. NH 58 is a national highway that connects Varanasi in Uttar Pradesh to Kolkata in West Bengal. NH 10 is a national highway that connects Chennai in Tamil Nadu to Srinagar in Jammu and Kashmir. NH 20 is a national highway that connects Agra in Uttar Pradesh to Kanyakumari in Tamil Nadu.