Step 1: Recall how the census is carried out.
The Census of India is a decadal exercise, meaning it is held once every ten years, and the actual head count of the huge population takes weeks to months to finish across the country.
Step 2: Recall the reference date.
Even though the count itself stretches over time, the final population figure is fixed as the population that existed at one single reference point, called the reckoning date. For the Indian census this reckoning date is 00:00 hours of 1st March of the census year.
Step 3: Rule out the other options.
January 1st is not used as the Indian census reference point.
April 1st is the date used for mid year population estimates in vital statistics, such as birth rate and death rate calculations, not for the census head count itself.
March 31st is close to the real date but is not the actual reckoning point, students often confuse it with the correct date, which is the first of March.
Step 4: Final answer.
The population count from the census is taken as the population existing on
\[ \boxed{\text{March 1st}} \]