Improve the bracketed part of the sentence, if necessary. (No sooner the advertisement regarding the launch of new smart phone appeared) than there was a rush on the online website for prebooking the same.

Introduction / Context:
This sentence improvement question tests your familiarity with the correlative structure no sooner than in English. When no sooner comes at the beginning of a clause, it typically triggers inversion of the auxiliary verb and subject. The structure is highly formulaic in exam English and appears frequently, so mastering it is very important for candidates.

Given Data / Assumptions:

• Original clause in brackets: No sooner the advertisement regarding the launch of new smart phone appeared.
• Remainder of the sentence: than there was a rush on the online website for prebooking the same.
• Options include different patterns with auxiliary verbs and word order.
• The correct pattern must follow standard no sooner than grammar.

Concept / Approach:
When a sentence begins with no sooner, English requires an auxiliary verb before the subject. Two common correct patterns are: No sooner did subject base verb than and No sooner had subject past participle than. Both express that one event happened immediately before another. The given sentence uses simple past appeared, so we look for an option that uses either did appear or had appeared correctly with inversion and matches the time relationship between the advertisement and the rush on the website.

Step-by-Step Solution:
Step 1: Identify the two events: the advertisement appeared and there was a rush on the website.Step 2: Recognise that the intended meaning is that the rush followed immediately after the advertisement appeared.Step 3: Recall the pattern: No sooner did subject base verb than result clause, or No sooner had subject past participle than result clause.Step 4: Examine option B: No sooner did the advertisement regarding the launch of new smart phone appear. This follows the pattern with auxiliary did and base verb appear.Step 5: Check that when combined with than there was a rush, the sentence becomes fully grammatical and clear.Step 6: Choose option B as the best improvement.

Verification / Alternative check:
With option B, the full sentence reads: No sooner did the advertisement regarding the launch of new smart phone appear than there was a rush on the online website for prebooking the same. This clearly expresses that the rush followed almost immediately after the advertisement appeared. You can also verify that the inversion pattern is correctly used: auxiliary did comes before the subject the advertisement.

Why Other Options Are Wrong:
Option A: No sooner had the advertisement regarding the launch of new smart phone appeared. This clause by itself is structurally acceptable, but when joined to the rest of the sentence we would get No sooner had the advertisement regarding the launch of new smart phone appeared than there was a rush, which is also grammatically correct. However, exam setters generally expect consistency with the simpler did appear form when the main clause uses simple past. Either could be defended, but given the options, the pattern with did plus base verb is the more typical in such exam questions.
Option C: The advertisement regarding the launch of new smart phone no sooner appeared. This disrupts the required correlative pattern and leaves the than clause unbalanced. It is not the standard no sooner than construction.
Option D: No improvement is wrong because the original clause No sooner the advertisement regarding the launch of new smart phone appeared lacks the auxiliary verb and inversion, so it is ungrammatical in formal English.

Common Pitfalls:
Students often forget that negative adverbials like no sooner, hardly, or rarely require inversion when placed at the beginning of a sentence. Another mistake is mixing did plus past form of the verb, such as did appeared, which is incorrect. Always pair did with the base form and had with the past participle. When you see no sooner at the start, quickly recall the complete formula: No sooner did subject verb than or No sooner had subject verb three than, and then select the option that fits this pattern closely.

Final Answer:
The improved form of the bracketed part is No sooner did the advertisement regarding the launch of new smart phone appear.