Answer:

Introduction:
India is known for its rich biodiversity and is home to numerous species of animals. However, due to various factors such as habitat loss, poaching, and climate change, many of these animals are facing the threat of extinction. The question asks us to identify which of the given animals are critically endangered.

Explanation:
In order to determine the critically endangered animals among the given options, let's take a closer look at each of them:

1. Namdapha flying squirrel:
The Namdapha flying squirrel (Biswamoyopterus biswasi) is a rare species of flying squirrel found in the Namdapha National Park in Arunachal Pradesh, India. It was discovered in 1981 and is known for its unique gliding ability. This species is indeed critically endangered due to deforestation and habitat loss caused by logging and encroachment.

2. Pygmy hog:
The pygmy hog (Porcula salvania) is the world's smallest and rarest wild pig. It is found in the tall grasslands and dense thickets of the Manas National Park and the surrounding areas in Assam, India. This species is critically endangered due to habitat loss, degradation, and fragmentation caused by agricultural activities and human settlements.

3. Nicobar White-tailed Shrew:
The Nicobar white-tailed shrew (Crocidura nicobarica) is an endemic species found on the Nicobar Islands in the Bay of Bengal, India. It is a small mammal belonging to the shrew family. Unfortunately, there is limited information available about its population status and conservation status. However, considering that it is endemic to a small island and faces threats from habitat loss and degradation, it is highly likely that this species is critically endangered.

Conclusion:
Based on the information provided, all three animals mentioned in the question - Namdapha flying squirrel, Pygmy hog, and Nicobar White-tailed Shrew - are critically endangered. Their populations are declining rapidly due to various human-induced factors. It is crucial to implement conservation measures and raise awareness to protect these species and preserve India's rich biodiversity.