In the following question, select the option that best expresses the meaning of the idiom "tongue-in-cheek".

Introduction / Context:
The idiom "tongue in cheek" is commonly used in English to describe remarks that are not meant to be taken literally or seriously. Such remarks are often humorous, ironic or mildly mocking. Understanding this idiom is important when reading articles, interviews or stories where the writer or speaker may be joking or being sarcastic. The question asks you to select the option that best captures this nuance.

Given Data / Assumptions:

• Idiom: "tongue-in-cheek" (often written with hyphens).
• Options include: speaking insincerely, praising wholeheartedly, sensational news, saying something hurtful and speaking rapidly.
• We assume modern conversational and written English usage.
• The idiom typically describes the manner or tone of a remark rather than its speed or loudness.

Concept / Approach:
"Tongue in cheek" originates from the physical gesture of pressing one's tongue into the cheek while trying not to laugh, suggesting that the speaker is not entirely serious. In meaning, it refers to something said in an ironic, humorous or playful way, often pretending to be serious on the surface. It is not about genuine praise, literal insults or news reporting. Among the choices, "In an insincere or joking way, not meant to be taken seriously" best describes this tone.

Step-by-Step Solution:
Step 1: Recall that tongue-in-cheek comments are often lightly sarcastic or humorous. The speaker might sound serious, but the intention is playful or ironic.Step 2: Examine option A: "In an insincere or joking way, not meant to be taken seriously." This clearly reflects the idea of playful insincerity or irony.Step 3: Examine option B: "To praise wholeheartedly." This is the opposite of the usual tongue-in-cheek tone, which is not fully sincere.Step 4: Examine option C: "A sensational news." This is unrelated to the manner of speaking; tongue-in-cheek describes style, not the news itself.Step 5: Examine option D: "To say something hurtful." Although irony can sometimes be sharp, tongue-in-cheek usually implies light, humorous intent, not outright cruelty.Step 6: Examine option E: "To speak very rapidly." This concerns speed, not the sincerity or humorous intent of the comment. Therefore, option A is correct.

Verification / Alternative check:
Look at example sentences: "His speech was full of tongue-in-cheek comments about politics" or "The article was written in a tongue-in-cheek style." In both cases, we understand that the speaker or writer is joking or being ironic rather than making literal, serious claims. If we substitute option A into the sentence ("spoken in an insincere or joking way"), the meaning remains the same. Substituting any of the other options would distort or destroy the intended sense. Idiom dictionaries also gloss "tongue-in-cheek" as humorous, ironic or not meant to be taken seriously, confirming this interpretation.

Why Other Options Are Wrong:

• Praise wholeheartedly: This implies deep sincerity and approval, which conflicts with the ironic nature of tongue-in-cheek remarks.
• A sensational news: Focuses on content rather than tone and has nothing to do with playful irony.
• To say something hurtful: While sarcasm can be biting, the idiom usually suggests gentle humour rather than deliberate injury.
• To speak very rapidly: Concerns speed, not style or sincerity.

Common Pitfalls:
Students sometimes confuse "tongue-in-cheek" with ordinary sarcasm or even blunt insult. However, the phrase typically suggests light-hearted irony rather than harsh criticism. Another pitfall is focusing on the literal words (tongue and cheek) and guessing meanings related to speech mechanics, like speaking quickly or unclearly. To avoid such errors, always remember that many idioms describe attitudes and tones, not physical actions. Visualising someone trying not to laugh while making a joke can help you remember the playful, not-so-serious sense of this idiom.

Final Answer:
The idiom "tongue-in-cheek" means in an insincere or joking way, not meant to be taken seriously.