In this English spelling question, four alternatives are given. Select the correctly spelt word from the options provided.

Introduction / Context:
This question checks spelling skills, which are important for writing error free English in exams, applications, and professional communication. The word being tested here is a common abstract noun related to pride. Correct spelling is essential because even minor mistakes can change the appearance and acceptability of formal writing.

Given Data / Assumptions:

• Four options are given which are similar in sound: arogance, arroganse, aroganse, and arrogance.
• Only one of them is the correct spelling accepted in standard English dictionaries.
• The pronunciation suggests three syllables: ar ro gance.

Concept / Approach:
To identify correct spellings, we rely on familiarity with frequent English words, knowledge of common suffixes, and sometimes patterns of double consonants. The word intended here is “arrogance”, which means excessive pride or a sense of superiority. This word is derived from “arrogant”. When forming the noun, the suffix “ance” is used, not “anse”, and the root “arrogant” already has a double “r”. So we expect “arrogance” with double “r” and the ending “ance”.

Step-by-Step Solution:
Step 1: Recall the base adjective “arrogant”. It clearly has double “r”. Step 2: Form the noun by replacing “ant” with “ance”. This produces “arrogance”. Step 3: Compare this standard form with each option. Option D matches exactly: arrogance. Step 4: Check Option A: arogance – it has only one “r”, which is incorrect. Step 5: Check Options B and C: both end with “anse”, which is not the usual English ending for this word.

Verification / Alternative check:
If you consult any recognised English dictionary or reliable digital dictionary, the word will appear as “arrogance”. It will be defined as an exaggerated sense of one's own importance or abilities, and the spelling will always show “rr” and “ance”. No standard dictionary records forms like “arogance” or “arroganse”. This independent check confirms that only one option is correct.

Why Other Options Are Wrong:
Option A: “arogance” has only one “r”, which does not match the correct form derived from “arrogant”. Option B: “arroganse” uses the ending “anse” which is not the standard suffix for this noun. Option C: “aroganse” is doubly wrong because it has one “r” and the wrong suffix “anse”.

Common Pitfalls:
Many learners confuse suffixes like “ance”, “ence”, “anse”, and “ense”. For nouns that come from adjectives ending in “ant”, the usual pattern is to change “ant” to “ance”, such as “important” to “importance” and “arrogant” to “arrogance”. Remembering the parent adjective often helps in fixing the spelling. Also, pay attention to doubled consonants; English sometimes doubles a consonant to preserve the short sound of a preceding vowel or due to the history of the word.

Final Answer:
The correctly spelt word among the options is arrogance.