Select the correctly spelt English word from the following options.

Introduction / Context:
Spelling questions test a candidate's familiarity with standard English vocabulary and the correct arrangement of letters in common words. In many competitive exams, a single correctly spelt word is hidden among distractors that contain typical spelling errors. This question requires careful observation and some prior exposure to written English, especially to words related to mathematics and social science.

Given Data / Assumptions:
The options given are femenism, acesses, permuted, vacuols, and one more slightly altered spelling. The candidate must identify the word that follows standard dictionary spelling. The options imitate real words such as feminism, accesses, permuted, and vacuoles. We assume that the test taker may have seen at least some of these words in textbooks or articles, which can help in spotting incorrect letter patterns.

Concept / Approach:
To answer correctly, it helps to separate each option and mentally match it with known words. Femenism looks like a misspelt form of feminism, where the vowel e has been used incorrectly. Acesses seems to be a wrong attempt at accesses, where the double c is missing. Vacuols is close to vacuoles, a biological term, but with letters omitted. The word permuted, however, is a valid English word from mathematics and combinatorics, meaning rearranged or changed in order. It matches standard spelling rules and is found in dictionaries.

Step-by-Step Solution:
Step 1: Compare femenism with the known term feminism and notice the wrong vowel arrangement.
Step 2: Compare acesses with accesses and see that the double c is missing, so it is incorrect.
Step 3: Look at permuted and recall that it is the correct past form of the verb permute, used in mathematics and statistics.
Step 4: Observe vacuols and remember that the correct biological term is vacuoles, with an extra e and correct plural ending.
Step 5: Conclude that permuted is the only option that matches standard English spelling.

Verification / Alternative check:
If we consult a standard dictionary or recall usage from textbooks, we easily find permute and permuted as correct words. The other forms either do not appear at all or appear only in error lists. This double check through memory or dictionary logic confirms that permuted is correctly spelt. Therefore it is safe to select option C in an exam situation.

Why Other Options Are Wrong:
Option A, femenism, incorrectly uses e in place of i and fails to represent the widely used term feminism. Option B, acesses, leaves out one c and breaks the pattern ac plus cess that is seen in access, accessable, and accessible. Option D, vacuols, omits e and changes the plural ending of vacuole, which normally becomes vacuoles. Any extra variant that slightly changes vowels or consonant doubling is also unacceptable because spelling questions require the exact standard form.

Common Pitfalls:
Candidates sometimes overthink such questions and suspect correct looking options simply because they seem easy. Another error is to be misled by pronunciation and forget that English spelling often preserves silent letters or doubled consonants. A useful strategy is to read widely and notice the written form of common academic words so that in an exam, your visual memory of the word helps you immediately reject incorrectly spelt distractors.

Final Answer:
The correctly spelt word is permuted.