Solution:
No article is used before most proper nouns. 'Liverpool University' is a proper noun.

Solution:
'An' is an indefinite article used before the vowel sound "u". Hence, it is correct.

Solution:
In the sentence it is not specified which boy, girl and car. Hence, indefinite article will be followed. Both 'girl' and 'car' are beginning with consonant sound and 'A' article will be used.

Solution:
Peru is the name of a single country in South America. The articles 'a' and 'an' are synonymous with 'one', hence the article 'a' is correct for the first sentence. If we use 'the' in place of 'a' it changes the meaning of the sentence, it would then mean that Peru is the only country in South America. In the second sentence, the capital mentioned is the specific capital of Peru. Being a specific definite noun, we use 'the' in the second sentence.

Solution:
Here, a specific group 'physically challenged' has been mentioned. Hence, definite article 'the' will be used.

Solution:
We use 'A' before singular, countable nouns that are used in a general sense. Here, both 'camera' and 'photograph' are not specific (both are used in its general sense) and both begin with consonant sounds.

Solution:
The writer is talking about a particular pond. So, we need to use the definite article 'the'.