Correctly Spelt Word: Rigorous

Rigorous is the correctly spelled word out of the options provided. Let's understand why.

Explanation:

1. Understanding the word "rigorous":
- The word "rigorous" is an adjective.
- It means extremely thorough, precise, or demanding.
- It is often used to describe a process, examination, or study that requires great attention to detail and strict adherence to rules or standards.

2. Analyzing the options:
a) Rigerous: This option misspells the word and is incorrect.
b) Rigourous: This option misspells the word and is incorrect.
c) Regerous: This option misspells the word and is incorrect.
d) Rigorous: This option correctly spells the word and is the correct answer.

3. Why is "rigorous" the correct spelling?
- The correct spelling of the word is "rigorous" as it follows the standard English spelling conventions.
- The word "rigorous" is derived from the Latin word "rigor," which means stiffness or rigor. The spelling "rigorous" reflects the pronunciation of the word and maintains consistency with its Latin origin.

In conclusion, the correct spelling of the word is "rigorous" (option D), which means extremely thorough or demanding.