What breaks yet never falls, and what falls yet never breaks?

I am a word that begins with the letter “i.” If you add the letter “a” to me, I become a new word with a different meaning, but that sounds exactly the same. What word am I?

How many bananas can you eat if your stomach is empty?

In the Thar desert, 3 men found a big 24L Jar is full of water. Since there is a shortage of water so they decided to distribute the water among themselves such that they all have equal amounts of it. But they only have a 13L, a 5L and an 11-litre Jar.

How do they do it?

Considering the below equation:

V + II - VI = 10
IV - X + VIII = 20
IV - VII + VI = 30

Then, I + II + III = ?

There is a box full of marbles,
all but two are blue,
all but two are green,
and all but two are red.

How many marbles are in the box?

I’m tall when I’m young, and I’m short when I’m old. What am I?

A Shopkeeper collects 71 rupees in the form of 20 paisa and 25 paisa.
He collects a total of 324 coins.

Can you tell me how many number of 20-paisa and 25-paisa he got?

A convention is held where all the big logicians are summoned. The master places a band on everyone's forehead. Now all of them can see others bands but can't see his own. Then they are told that there are different colours of bands. All the logicians sit in circle and they are further explained that a bell will ring at regular intervals. The moment when a logician knew the colour of band on his forehead, he will leave at the next bell. If anyone leaves at the wrong bell, he will be disqualified.

The master assures the logicians that the puzzle will not be impossible for anyone of them. How will the logicians manage ?

I am a word of 12 alphabets.

* Alphabets 12, 4, 7, 2, 5 : Eastern beast of burden
* Alphabets 1, 8, 10, 9 are street made famous by Sinclair Lewis.
* Alphabets 11, 3, 6 are past.

On whole it means a person suffering from delusions of greatness.

What Is it ?