Select the one word substitute for the phrase based on random choice or personal whim.

Introduction / Context:
This vocabulary question asks the learner to choose a single English word that can replace an entire descriptive phrase. One word substitution items are common in competitive exams because they test both vocabulary depth and precision. Here the phrase given is based on random choice or personal whim, which points to a specific adjective used frequently in legal writing, philosophy, and everyday speech to criticise decisions that lack rational basis.

Given Data / Assumptions:

• The phrase to be replaced is based on random choice or personal whim.
• Four candidate words are offered as possible substitutes.
• Only one option matches the phrase in meaning and common usage.
• The learner is expected to know standard dictionary meanings of the given words.

Concept / Approach:
One word substitution questions are solved by matching the sense and connotation of the phrase with each option. The phrase refers to something done without logic, system, or fairness, purely according to mood or personal liking. The standard English word for such behaviour or decisions is arbitrary. The other options describe completely different ideas. Auxiliary is related to help or support, allegory refers to a story with a hidden symbolic meaning, and ambulatory relates to walking. Understanding these meanings helps to eliminate incorrect choices and choose the best match.

Step-by-Step Solution:
Step 1: Read the phrase carefully and identify its key idea, which is random or whimsical choice. Step 2: Consider option a, auxiliary. This word describes a person or thing that provides help or support. It does not imply randomness or whim. Step 3: Consider option b, arbitrary. This adjective describes actions, rules, or decisions that are based on personal will or random choice rather than reason or a system. Step 4: Consider option c, allegory. This is a literary term for a story in which characters and events symbolise deeper moral or political meanings. Step 5: Consider option d, ambulatory. This usually means able to walk or relating to walking. Step 6: Compare all options with the phrase. Only arbitrary aligns directly with the idea of random choice or personal whim.

Verification / Alternative check:
A quick mental check is to think of sample sentences. One might say an arbitrary decision by the manager upset the team, meaning the decision seemed unfair and without proper reason. This fits perfectly with the phrase given in the question. On the other hand, auxiliary staff means supporting staff, an allegorical tale means a symbolic story, and ambulatory patients means patients who can walk. None of these sample uses match the sense of random behaviour. This confirms that arbitrary is the correct one word substitute.

Why Other Options Are Wrong:
auxiliary: Describes something that acts as a helper or supplement, not something based on whim.
allegory: Refers to a symbolic story or narrative technique, unrelated to random choice.
ambulatory: Connected with walking or mobility, not with decision making or personal whims.

Common Pitfalls:
Learners sometimes pick options that merely look sophisticated without checking meaning. Another pitfall is confusing allegory with arbitrary because both appear in academic contexts. To avoid such errors, aspirants should regularly revise one word substitution lists and learn words in context through reading. Creating personal example sentences also strengthens memory and makes it easier to recall the appropriate word during an exam.

Final Answer:
The correct one word substitute is arbitrary, so option b is correct.