In the following question on word relationships, four word pairs are given. Some pairs show a relation of antonyms (opposites), while another pair shows a relation of synonyms (similar meanings). Select the odd word pair from the given alternatives.

Introduction / Context:
This question belongs to the verbal reasoning and vocabulary section. You are given four word pairs: Error : Accurate, Careless : Casual, Strength : Lethargy and Gloomy : Cheerful. In three of these pairs, the two words express opposite or contrasting meanings (antonyms), while in one pair the words express similar meanings (synonyms). Your task is to identify the pair that shows similarity of meaning and therefore does not fit the antonym pattern of the others.

Given Data / Assumptions:

• Word pairs: Error : Accurate, Careless : Casual, Strength : Lethargy, Gloomy : Cheerful.
• We assume standard modern English meanings of these words.
• Three pairs are intended to represent contrast or opposition in meaning.
• One pair represents similarity in meaning and is the odd one out.
• We do not focus on part of speech differences, only semantic relationships.

Concept / Approach:
First, recognise that antonyms are pairs of words with opposite meanings, such as hot and cold, or happy and sad. Synonyms are pairs of words with similar meanings, such as big and large. In this question, the examiner has grouped three pairs which are antonyms and one pair which is a synonym pair. By identifying which pair expresses similarity rather than opposition, you can easily pick the odd pair from the list.

Step-by-Step Solution:
Step 1: Analyse Error : Accurate.Error refers to a mistake, while Accurate means correct or free from error. These words represent opposite ideas: one signifies a wrong outcome and the other signifies a correct outcome.Step 2: Analyse Strength : Lethargy.Strength suggests power, energy or vigour. Lethargy suggests drowsiness, lack of energy or sluggishness. These are contrasting ideas: one expresses high energy, the other low energy.Step 3: Analyse Gloomy : Cheerful.Gloomy means sad, dark or depressing in mood. Cheerful means bright, happy and full of positive emotion. Again, they are clear antonyms.Step 4: Analyse Careless : Casual.Careless describes someone who does not pay enough attention or is negligent. Casual often describes something relaxed or informal, and in many contexts it is close in meaning to Careless when we speak of a casual attitude. The two words are not opposites; they often overlap in sense.Step 5: Identify the odd pair.The first, third and fourth pairs express opposite meanings, while Careless : Casual shows similar or related meanings. Therefore Careless : Casual is the odd one out.

Verification / Alternative check:
A quick check is to ask: can you easily think of a clear opposite for each first word? Error naturally contrasts with correctness or accuracy. Strength naturally contrasts with weakness, tiredness or lethargy. Gloomy contrasts cleanly with cheerful or bright. However, the opposite of Careless would be Careful or Attentive, not Casual. Casual can sometimes be used positively to mean relaxed, or neutrally to mean informal. This test confirms that Careless : Casual does not form an antonym pair and so stands apart from the others.

Why Other Options Are Wrong:
Error : Accurate: These words describe opposite ideas of mistake versus correctness and so form an antonym pair.
Strength : Lethargy: One expresses energy while the other expresses lack of energy, another antonym pair.
Gloomy : Cheerful: Opposite moods, sadness versus happiness, forming a clear antonym pair.

Common Pitfalls:
Some learners may focus too much on subtle nuances, arguing that words like Casual can be neutral and not always negative. While that is true in a detailed vocabulary discussion, the exam pattern is simpler: it expects you to notice that Careless and Casual often describe similar attitudes in general conversation. In exam questions, always aim for the broad and obvious relationship that the majority of test takers would see, instead of overcomplicating the interpretation.

Final Answer:
The odd word pair is Careless : Casual, because it expresses a similarity in meaning, while the other three pairs represent opposite meanings (antonyms).