Step 1: Understanding census in India.
The census is an official survey of the population conducted at regular intervals. It provides demographic, economic, and social data necessary for governance and planning.
Step 2: First census attempts.
The first attempt at a census in India was in 1872, but it was not conducted uniformly across the country. Different regions carried it out in different years.
Step 3: Beginning of regular decennial census.
From 1881 onwards, the census began to be conducted regularly every 10 years (decennial census). This marked the beginning of a continuous and systematic process of data collection.
Step 4: Conclusion.
Thus, the regular decennial census in India started in 1881.
\[
\boxed{\text{Correct Answer: 1881}}
\]