What has many keys but can’t open a single lock?

There are three boxes of different sizes with three cupcakes inside each of the boxes in Christina's kitchen. At night her daughter wakes up and goes to the kitchen. She opens a box and eats all three cakes.

But in the morning Christina finds out that each box still had three cupcakes. How?

They are three errirs in this question. Can you find them?

I have nine bottles of wine and one of the nine bottles is poisoned.
I need to find the poisoned bottle with two facts
(1) Poison is deadly, only a sip will cost death
(2) I have two mice to do so.

How should I do it?

You are an expert on paranormal activity and have been hired to locate a spirit haunting an old resort hotel. Strong signs indicate that the spirit lies behind one of four doors. The inscriptions on each door read as follows:

Door A: It's behind B or C
Door B: Its behind A or D
Door C: It's in here
Door D: It's not in here

Your psychic powers have told you three of the inscriptions are false, and one is true. Behind which door will you find the spirit?

Name a key which is hardest to turn.

There is a brick of gold and a brick of iron in a boat (both 10-inch blocks), if they are both dropped into the water which will make the water level higher?

There was a blind man. He had four socks in his drawer either black or white. He opened it and took out two socks. Now the probability that it was a pair of white socks is 1/2.

Can you find out the probability that he had taken out a pair of black socks ?

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?

Here is a mathematical expression that also secretly tells a movie name. What movie is that?