In the following set of spellings of the word meaning "helping, providing support, or supplementary", which one is correctly spelt?

Introduction / Context:
This question asks you to identify the correct spelling of the word auxiliary, which is often used in grammar (auxiliary verb) and in general English to mean helping, supporting, or additional. Many exam questions test spelling of commonly confused words by presenting several incorrect variants along with one correct form.

Given Data / Assumptions:

• The intended word is auxiliary.
• Option A: Auixiliary.
• Option B: Auxiliary.
• Option C: Auxiliarry.
• Option D: Auixliary.
• We assume the standard English spelling is required.

Concept / Approach:
The correct spelling is auxiliary, with the sequence a u x i l i a r y and a single r near the end. The options include common types of spelling errors: misplaced letters, extra letters, and missing letters. By carefully comparing each option with the known correct form, you can identify the accurate spelling.

Step-by-Step Solution:
Step 1: Recall the correct dictionary form: auxiliary.Step 2: Compare Option B: Auxiliary. This matches exactly: a u x i l i a r y.Step 3: Check Option A: Auixiliary, where the sequence u i x is incorrect; it should be a u x, not a u i x.Step 4: Check Option C: Auxiliarry, which contains a double r (r r) that does not appear in the standard spelling.Step 5: Check Option D: Auixliary, which again jumbles the order of letters and is not a recognised form. Therefore, only Auxiliary is correctly spelt.

Verification / Alternative check:
Think of common phrases: auxiliary verb, auxiliary nurse, auxiliary engine. In all of these, the spelling never changes: a u x i l i a r y. If you try to write auxiliarry or auixliary in a text editor with spell check, it will be marked wrong. This strongly confirms that Auxiliary is the correct standard spelling.

Why Other Options Are Wrong:
Auixiliary and Auixliary both have the letters u and i in the wrong order and insert x in an incorrect position, making them non standard forms. Auxiliarry adds an extra r, which is not present in the word. Spelling questions often introduce such minor but damaging changes to test careful attention.

Common Pitfalls:
Because auxiliary has several vowels and consonants close together, students sometimes misplace the i or add extra r. A good way to remember the spelling is to break it into parts: aux (like auxiliary power) + i + l + iary (same ending as in unitary, fiduciary, etc.). Visualising it in these chunks can reduce errors.

Final Answer:
The correctly spelt form of the word is Auxiliary, so option B is correct.