✅ The statement "Nobody seems to understand the new rules" has a negative meaning because of the word "Nobody".

Therefore, the question tag must be positive.

When an indefinite pronoun like "Nobody," "No one," "Everybody," or "Someone" is the subject of the main clause, the pronoun "they" is used in the question tag.

The main verb "seems" is in the present simple tense, so the auxiliary verb for the tag is "do" (for "they").

Combining these rules, the correct positive tag with "they" is "do they?".

❌ Options A, C, and D are incorrect because "Nobody" makes the statement negative, requiring a positive tag, and "Nobody" requires the plural pronoun "they" in the tag, not "he".

✅ The correct question tag for sentences beginning with "Let's" (which is a contraction of "Let us" and indicates a suggestion or proposal) is always "shall we?".

❌ Option A ("don't we?") is incorrect because "do" auxiliaries are not used to form tags for "Let's" suggestions.

❌ Option C ("will we?") is incorrect; "will" is not the appropriate auxiliary for forming the tag with "Let's".

❌ Option D ("shouldn't we?") is incorrect as "should" does not form the standard question tag for "Let's" statements.

✅ The correct question tag for sentences beginning with "Let's" (which is a contraction of "let us") is always "shall we?". This is a fixed construction used to propose an action and ask for agreement or confirmation.

❌ Option B, "don't we?", is incorrect because "don't we?" is typically used for general present tense statements and does not follow the specific rule for suggestions initiated with "Let's."

❌ Option C, "will we?", is incorrect as "will" is not the auxiliary verb used in the fixed tag for "Let's" suggestions.

❌ Option D, "won't we?", is also incorrect; similar to "will we?", the auxiliary "will" (or its negative form "won't") does not form the standard question tag for "Let's" constructions.

✅ The correct question tag is "did they".

The main clause "Nobody came to the party" contains the word "Nobody", which makes the statement negative; therefore, the question tag must be positive.

When the subject of the main clause is an indefinite pronoun like "nobody," "somebody," "everyone," etc., the pronoun in the tag is "they."

The main verb "came" is in the simple past tense, so the auxiliary verb for the tag is "did."

❌ Option A ("didn't they") is incorrect because the main clause is already negative ("Nobody"), so the tag must be positive, not negative.

❌ Option C ("didn't he") is incorrect for two reasons: the tag should be positive, and the pronoun for "Nobody" in a question tag is "they," not "he."

❌ Option D ("did he") is incorrect because while the tag is positive, the pronoun for "Nobody" in a question tag is "they," not "he," as "nobody" implies an unspecified group or individual where "they" is the most appropriate general pronoun.

✅ The main statement "Nobody remembered to lock the door" has a negative meaning because of "Nobody" .

Therefore, the question tag must be positive.

The verb "remembered" is in the past simple tense, so the auxiliary verb for the tag is "did."

For indefinite pronouns like "nobody," "somebody," "everyone," etc., the pronoun in the question tag is typically "they."

Combining these rules, the correct tag is "did they?"

❌ Option A is incorrect because the statement is negative, so the tag cannot be negative ("didn't they?").

❌ Options C and D are incorrect because the pronoun for "nobody" in a question tag should be "they," not "he."