In the following question, out of the four alternatives, select the word opposite in meaning to the given word 'Waggish' (playfully humorous).

Introduction / Context:
This question tests your ability to find the correct antonym of an advanced adjective. The word 'Waggish' describes a person or remark that is playfully humorous or joking. In exams, such words often appear in synonym and antonym questions to check whether candidates can distinguish between subtle shades of humour and seriousness in English vocabulary.

Given Data / Assumptions:
- Target word: 'Waggish'.
- Options: 'Jocular', 'Whimsical', 'Flippant', 'Solemn'.
- Exactly one option should express the opposite quality of playfully humorous behaviour.
- Standard meanings from advanced English vocabulary are assumed.

Concept / Approach:
'Waggish' is used for someone who likes to make jokes, is mischievously humorous or clownish. Therefore, the antonym should describe a person or mood that is serious, grave or not given to joking. 'Solemn' directly means serious, formal and without any trace of joking. The other options—'jocular', 'whimsical' and 'flippant'—all describe different forms of humour or lightness, and are therefore closer to being synonyms of 'waggish' rather than opposites.

Step-by-Step Solution:
Step 1: Fix the meaning of 'Waggish': playful, joking, humorous in a slightly mischievous way. Step 2: Examine 'Jocular': this means fond of joking or playful, clearly similar to 'waggish'. Step 3: Examine 'Whimsical': this describes behaviour that is fanciful, unpredictable or playful, again close to humour and lightness. Step 4: Examine 'Flippant': this means not showing a serious or respectful attitude, teasing or lightly disrespectful, still on the humorous or casual side. Step 5: Examine 'Solemn': this means serious and dignified, without any sign of humour or playfulness, which is the true opposite of 'waggish'.

Verification / Alternative check:
Imagine two descriptions of the same person: 'He is a waggish speaker' suggests that he cracks jokes, tells funny stories and keeps the mood light. 'He is a solemn speaker' suggests that he is serious, grave and does not indulge in jokes. These two descriptions clearly stand in contrast. In contrast, calling someone 'jocular' or 'whimsical' reinforces the same playful, humorous nature as 'waggish', and 'flippant' also keeps the tone light and unserious, not opposite.

Why Other Options Are Wrong:
'Jocular' is wrong because it also means humorous and joking, so it is more a synonym than an antonym. 'Whimsical' is wrong because it suggests playful fancy or odd, lighthearted behaviour, related to humour instead of opposing it. 'Flippant' is wrong because it means casually disrespectful or joking when seriousness is expected; it opposes respect, not humour itself. All three still occupy the 'not serious' side of the spectrum, just like 'waggish'.

Common Pitfalls:
A typical mistake in such questions is to choose another unfamiliar or fancy looking word, assuming it must be the opposite. However, exam setters often place synonyms among the distractors. When dealing with tone words like 'waggish', always ask yourself whether the option describes humour or seriousness. The presence of 'solemn' among three humour related words is a strong clue that it is the correct antonym.

Final Answer:
The opposite in meaning to 'Waggish' is Solemn.