In British India, the first official and synchronous nationwide census operation was undertaken in which year?

Introduction / Context:
Census operations provide systematic information about the population of a country. In India, various partial counts were conducted in the nineteenth century, but one particular year marks the first official and synchronous all India census under British rule. This factual question checks whether you know that benchmark year.

Given Data / Assumptions:
- The question is about British India and a nationwide census operation.
- It seeks the year of the first official synchronous census conducted for the whole country under a common plan.
- The options list several years from the nineteenth and twentieth centuries.

Concept / Approach:
Although some earlier attempts at population counts were made, 1881 is usually identified as the year of the first regular all India census carried out simultaneously across British territories. Later censuses followed at ten year intervals. The correct approach is to recall this standard date from Indian demographic history.

Step-by-Step Solution:
Step 1: Remember that India has conducted census operations at intervals of ten years for more than a century.
Step 2: Note that 1881 is widely accepted as the first synchronous official census of British India.
Step 3: Earlier years like 1871 and 1841 saw partial or experimental counts, but not the fully standardised operation later recognised as the starting point.
Step 4: Later years such as 1921 and 1961 obviously cannot be the first census, since they are part of a sequence already in progress.
Step 5: Hence the correct year to mark is 1881.

Verification / Alternative check:
An alternative check is to recall that many textbooks explicitly state that the Indian census has been conducted regularly every ten years since 1881. This direct statement quickly confirms that 1881 is the key date, while also explaining why earlier scattered counts do not receive the same official status in exam questions.

Why Other Options Are Wrong:
Option a is wrong because 1841 refers to an early population enumeration attempt and not to a standardised all India synchronous census.
Option c is wrong as 1921 is important for demographic reasons, but it is not the first census year.
Option d is wrong because 1961 belongs to the post independence period and is far too late to be considered the first comprehensive census.
Option e is wrong since 1871 corresponded to earlier counts that were not yet part of the regular ten year census series starting in 1881.

Common Pitfalls:
Students sometimes confuse the first census of independent India with the first British census or they treat any early enumeration as the first official census. Keeping in mind the phrase regular systematic census at ten year intervals starting from 1881 helps avoid such confusion.

Final Answer:
The first official synchronous census of British India was undertaken in 1881.