How can you make number one disappear by adding something to it?

I start and end with 500 and carry a 5 in my heart. But I require the first letter and the first number to be complete. I am the name of a King.

Who am I ?

An infinite number of mathematicians are standing behind a bar. The first asks the barman for half a pint of beer, the second for a quarter pint, the third an eighth, and so on. How many pints of beer will the barman need to fulfill all mathematicians' wishes?

What common phrase is represented by the below lines

Easy going:
Weak, 'I'm going.'
Tough, 'I'm staying.'

Medium going:
Weak, 'I'm going.'
Tough, 'I'm staying.'

Tough going:
Weak, 'I can't do it, I'm staying!'
Tough, 'Let's get going.'

Why is a river so rich ?

John speaks the truth only once a day in a week. Below are a few hints for you:

First: Days are Sunday, Monday and so on.
Second: One day he says, "I lie on Monday and Tuesday".
Third: On the next day, he says, "Today is either Thursday, Saturday or Sunday".
Fourth: On the next day, he says, "I lie on Wednesday and Friday".

Can you identify the day on which he speaks the truth?

The chance of Mr John winning the lottery is 10%. All participants lined up and Mr John is 4th in the row. The first three participants lose the lottery.

What is the chance of Mr John now?

I know a country, If you remove the last alphabet of its name, it will become a part of your body. Do you name it?

I am sure no one can have two things for dinner. what are they?

The following four words might seem abrupt to you. But you can make them meaningful by just adding vowels.
RDSH
GGPLNT
TMT
NN

Hint: All of them are vegetables.