In the first blank, article “the” will be used because “the” is used to refer to a particular/specific group of people.
In the second blank, article “a” will be used because the speaker is making a general statement.
In the third blank, article “the” will be used because article “the” is used to refer to a DEFINITE group of people like ‘BRITISH PEOPLE’.

The definitive article, ‘the’ is used before some proper nouns which are names of places. Example: The Black Sea, The Pacific Ocean, etc. However, the use of an article is omitted before most proper nouns which are names of people/countries/continents/cities.
In the given sentence, Europe is the name of a continent. Hence, no article is to be used before it. ‘Cape of Good Hope’ is the name of a place. Hence, the definitive article, ‘the’ is to be used before it. Hence, option A is correct.

Option C is correct as ‘The’ is used with words with superlatives. ‘Longest’ is superlative.

Here, a specific group ‘thief’ is being talked about. ‘The’ article will be used.

‘A’ article is used with general things. ‘Toothache’ is general and hence ‘a’ will be used.

Here, a specific newspaper ‘Times of India’ is being talked about. ‘The’ article will be used.

In the first blank, article “the” will be used because article ‘the’ is used with superlatives.
Similarly, In the second blank, article “the” will be used because article “the” is used with superlatives.
In the third blank, “no article” will be used because the term ‘college’ doesn’t need specification. It just refers to a place where the eldest boy is studying.

The most appropriate option is ‘the’ as ‘the’ is used before specific things. In this sentence, the specific abstract noun is ‘truth’.