What brings you down but never up?

Vin Diesel is pulling a theft and has planned to run away with all the cash kept in the safe. But the only way to open the safe is the 13 character password. He has a set of five clues given to him by a trustworthy source.

Exactly two of the below statements are false.
The password is contained within this sentence.
The password is not in this hint.
The password is within only one of these statements.
At least one of the above statements is a lie.

Transform the word THINK into BRAIN while changing only one letter at a time in a manner that each of the word in the process is a real word!!!

What can run but never walk, have a mouth that never speaks, have a head that never weeps, and have a bed but never sleeps?

Today, I celebrated my 32nd birthday but I was born in 1972.
How is this possible?

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 ?

A very interesting trivia question for all.

Why do men's shirts have their buttons on the right side and women's have buttons on the left-hand side?

Can you solve the tricky chess rebus puzzle below by ciphering the hidden meaning?

The current time can be represented by below textual rebus.

0
=========
B.Sc
LLB

Can you tell us the current time?

Which English verb becomes past tense just by rearranging the letters?