If 5 cats catch 5 mice in 5 minutes, how long will it take one cat to catch a mouse?

One is to three as three is to five and five is to four and four is the magic number.
What is the pattern?

Akbar summoned Birbal out of anger.
He told him that he will have to face death.
He asked him to make a statement and if the statement is true he will be buried alive and if the statement is false, he will be thrown at lions.
After hearing Birbal’s statement, Akbar could do nothing but smile.
He gave him 5 gold bars and let him go.

What did Birbal say?

There is a shop where written:
Buy 1 for $1
10 for $2
100 for $3
I needed 999 and still only paid $3. How could this be financially viable for the shop-keeper?

What does below chemistry rebus means?

Prove that twice of ten is the same as twice of eleven.

What has a ring but no finger?

You have a thousand Re. 1 coins with you. You have ten bags with you and you can put any number of coins in each of the bags. The condition is that if someone asks you for any amount between 1 and 1000, you must be able to give that amount by just giving the bag (you are not allowed to open the bag and give coins).

How will you do it?

A thief is convicted in Mexico. He gets the death penalty. The judge allows him to say the last sentence to determine how the penalty will be carried out. If the thief lies, he will be hanged, if he speaks the truth he will be beheaded. The thief tells the last sentence and to everybody's surprise some minutes later he is set free because the judge cannot determine his penalty. What did the thief say?

Living above a star, I do not burn
Eleven friends and they do not turn
I can just be visited in a sequence, not once or repeatedly
PQRS are my initials
Can you tell my name accurately?