What has to be broken before you can use it?

If you say my name, I will no longer exist. What am I?

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?

There was once a college that offered a class on probability applied to the real world. The class was relatively easy, but there was a catch. There were no homework assignments or tests, but there was a final exam that would have only one question on it. When everyone received the test paper it was a blank sheet of paper with a solitary question on it: 'What is the risk?'.Most students were able to pass, but only one student received 100% for the class! Even stranger was that he only wrote down one word!
What did he write?

Remove two matchsticks to make the below equation correct.

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

I came first on earth but second on the heaven.
I also came twice in a week but found just once in a year.
I stay away from months but you can find me in February.

What am I?

Find the next number in the series

12, 20, 40, 72, 116, 172 ?

Alpha is Beta's sister.

Gamma is a Beta mother.

Delta is Gamma's father.

Tango is Delta's mother.

Then,

How is Alpha related to Delta?

Can you name four days which start with the letter 'T'?