Introduction:
During the colonial rule in India, the British government did not make any sincere attempt to estimate the country's national output and per capita income. This was primarily due to several reasons that can be explored in detail.

Lack of interest:
The British colonial government did not have a genuine interest in accurately estimating India's national output and per capita income. Their main focus was on exploiting the resources and wealth of India for their own benefit. Estimating these economic indicators would have required resources, time, and effort, which the colonial government was not willing to invest in.

Control over resources:
The British government had complete control over the resources of India, including land, labor, and capital. This control allowed them to extract wealth from the country without accurately measuring its economic productivity. They were more concerned with maximizing their own profits and ensuring a steady flow of resources back to Britain.

Lack of data collection infrastructure:
During the colonial period, there was a lack of proper infrastructure for data collection and statistical analysis. The British government did not invest in establishing comprehensive systems for gathering economic data. This lack of data made it difficult to estimate national output and per capita income accurately.

Political motives:
The colonial government had political motives for not estimating India's national output and per capita income. By keeping the economic indicators vague or unknown, they could maintain a sense of control and superiority over the Indian population. This lack of transparency allowed them to perpetuate the exploitative nature of their rule.

Resistance to change:
The colonial government resisted any changes that could potentially challenge their authority or disrupt their economic exploitation of India. Accurately estimating national output and per capita income would have provided a clearer picture of India's economic potential and could have led to demands for greater self-governance or economic reforms.

Lack of accountability:
The colonial government operated with limited accountability to the Indian population. They were not answerable to the people, and therefore, did not feel the need to provide accurate estimates of national output and per capita income. This lack of accountability further allowed them to maintain their exploitative rule without being held responsible for the economic conditions of the country.

Overall, the colonial government's lack of interest, control over resources, absence of proper data collection infrastructure, political motives, resistance to change, and lack of accountability contributed to their failure in making sincere attempts to estimate India's national output and per capita income.