Explanation

Important gives vowel sound.

We use an when there is a vowel sound.

We use a when there is consonant sound. 

We use the for particular things.

A, An & The are called Articles. 

This is an important historical event. 

Explanation

Universal gives vowel sound.

Explanation

Article “the” is used before a superlative degree of Adjective.

More useful is comparative degree while the most useful is the superlative degree.

Explanation

Usually the is used before a mountain.

The is an article here.

We spent our holidays in the mountains. 

Explanation

The directors may terminate the chairman's appointment at any time.

Explanation

No article required before uncountable noun.

Poetry is an uncountable noun. 

Explanation

A mile is a unit of measurement for distance.

A litre is a unit of measurement for liquid — this is a similar relationship.

Explanation

Here the dog means all the dogs in the world.

"The" is a definite article used when referring to a specific thing or group of things.

In this case, "the dog" refers to all dogs, not just a single dog. 

"A" and "an" are indefinite articles used when referring to any member of a group or class, not a specific one. 

Explanation

Universal Truth doesn't require article.

Fish can't live without water.

Explanation

We use of with worthy.

Worthy of means اہل

Your remarks are really worthy of note.