In this idiom based question, you must choose the alternative that best expresses the meaning of the expression Under a cloud as used in standard English.

Introduction / Context:
The idiom under a cloud is a commonly tested phrase in competitive exams. It does not refer to actual weather or a literal cloud in the sky. Instead, it describes a situation where a person is not trusted, is suspected of wrongdoing, or is in disgrace in the eyes of others. Correctly interpreting idioms like this is essential for understanding newspapers, novels, and formal English passages.

Given Data / Assumptions:

• The idiom is under a cloud.
• The context is general English usage, especially in exam and media language.
• The task is to select the meaning of the idiom, not a literal description.
• Options describe different emotional and social states, such as happiness, protection, or suspicion.

Concept / Approach:
In idiomatic English, clouds are often associated with doubt, trouble, or sadness, as in under a cloud, a cloud of suspicion, or dark clouds gathering. The phrase under a cloud specifically means that a person is suspected of something wrong or is in disgrace. It often appears when someone faces allegations, investigations, or loss of reputation. Therefore, the correct choice must include the idea of suspicion or disfavor, not joy or safety.

Step-by-Step Solution:
Step 1: Recall the phrase a cloud of suspicion, which directly connects clouds with doubt and mistrust. Step 2: Relate this idea to under a cloud, which suggests living or functioning under a shadow of suspicion or blame. Step 3: Examine option a, under suspicion or in disgrace, and notice that it matches this meaning exactly. Step 4: Examine option b, extremely happy and carefree, which is the opposite of the negative image created by a cloud. Step 5: Examine option c, protected from any difficulty, which would correspond more to under a protective shield, not under a cloud. Step 6: Examine option d, surrounded by close friends, which also has a positive feel and does not connect with suspicion or disgrace. Step 7: Conclude that option a is the only one that preserves the negative emotional and social sense implied by the idiom.

Verification / Alternative check:
Consider example sentences. For instance, After the corruption scandal, the minister was under a cloud for several years clearly means he was suspected and not trusted. If the idiom meant happy or protected, such sentences would not make sense. Dictionaries and exam guides also define under a cloud as being suspected or in disgrace, which confirms that under suspicion or in disgrace is accurate.

Why Other Options Are Wrong:
Extremely happy and carefree conflicts with the negative symbolism of a cloud. Protected from any difficulty suggests safety and comfort, while the idiom actually indicates social or moral trouble. Surrounded by close friends describes a positive supportive environment, which again does not match being in disgrace or mistrusted by others.

Common Pitfalls:
Learners sometimes associate cloud only with sadness and pick options related to feeling sad, ignoring the aspect of suspicion and blame. Others guess from partial memory and confuse this idiom with under the weather, which means feeling unwell. It is important to learn idioms in full and notice the typical contexts where they appear, such as legal troubles, scandals, or disciplinary action for under a cloud.

Final Answer:
The idiom Under a cloud means being under suspicion or in disgrace.