Solution:
Here, 'orator' is a general class and therefore indefinite article will be used. Word after the blank starts with vowel sound. 'An' article will be used.

Solution:
Here 'writer' is a common noun and will be preceded by indefinite article. 'A' is used because the word 'foreign' begins with consonant sound.

Solution:
No article is required.

Solution:
Option B is the answer since "first" is not succeeded by an event like day or month, and thus doesn't need an article to support it. The dry place mentioned in the statement is not a specific dry place that is being talked about, and thus will be accompanied by an indefinite article, which is "a".

Solution:
Here, it is specifically mentioned where the person was taken i.e. 'hospital'. Hence, definite article 'the' will be used.

Solution:
Here, price of specific thing i.e. 'Share' has been mentioned. Hence, 'the' article will be used.

Solution:
No article is required.