People put me on the table and cut me but do not eat me. What am I?

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

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

It's a 7-letter word.
If we remove 1 letter from it, it remains the same.
If we remove 2 letters from it, it remains the same.
If we remove 3 letters from it, it remains the same.
If we remove all the letters from it, still it remains the same.
What is it?

What kind of band never plays music?

Can you divide the below-given shape into four equal and identical pieces?

What is more useful when it is broken?

James ordered a fishing rod, priced at $3.56. Unfortunately, James is an Eskimo who lives in a very remote part of Greenland and the import rules forbid any package longer than 4 feet to be imported. The fishing rod was 4 feet and 1 inch, just a little too long, so how can the fishing rod be mailed to James without breaking the rules? Ideally James would like the fishing rod to arrive in one piece!

A man was driving a black truck. His lights were not on. The moon was not out. A lady was crossing the street. How did the man see her?

What is the four-digit number in which the first digit is one-third the second, the third is the sum of the first two, and the last is three times the second?