Consider the following sentences:

(i) The number of candidates who appear for the GATE examination is staggering.

(ii) A number of candidates from my class are appearing for the GATE examination.

(iii) The number of candidates who appear for the GATE examination are staggering.

(iv) A number of candidates from my class is appearing for the GATE examination.

Which of the above sentences are grammatically CORRECT?

The correct option is (i) and (ii).

To determine which sentences are grammatically correct, we must analyze the rules of subject-verb agreement associated with the phrases "The number of" and "A number of":

1. The phrase "The number of":
This phrase refers to a single, specific quantity or a collective total. Since it represents a single value, the subject is treated as singular and requires a singular verb (such as "is", "was", or "has").
• Sentence (i): "The number of candidates who appear for the GATE examination is staggering." — This is correct because the singular verb "is" agrees with the singular subject "The number".
• Sentence (iii): "The number of candidates who appear for the GATE examination are staggering." — This is incorrect because the plural verb "are" is incorrectly paired with "The number".

2. The phrase "A number of":
This phrase acts as a determiner meaning "several", "some", or "many". It focuses on the individual units of the plural noun that follows it. Therefore, it is treated as a plural subject and requires a plural verb (such as "are", "were", or "have").
• Sentence (ii): "A number of candidates from my class are appearing for the GATE examination." — This is correct because the plural verb "are" agrees with the plural subject "A number of candidates".
• Sentence (iv): "A number of candidates from my class is appearing for the GATE examination." — This is incorrect because the singular verb "is" cannot be paired with the plural phrase "A number of candidates".

Therefore, sentences (i) and (ii) are grammatically correct, making the first option the correct choice.