How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?

I have one of the three numbers: 1, 2, or 3 in my mind. I speak only truth. You can ask me just one question for which I will only reply in yes or no or don't know. What question will you ask from me so that you are able to know the number?

Astrology starts with the alphabet A, Biology starts with B, Psychology with P and Limnology with L.

Can you find an "ology" that begins with a P?

Below rebus represent famous DiCaprio movie. Can you name it?

Can you find the key in the picture below?

What has many teeth, but cannot bite?

What makes this number unique: 8,549,176,320?

Given below is simple addition with a defined pattern pattern:
7 + 7 = 2
8 + 8 = 4
8 + 5 = 1
6 + 9 = 3
10 + 11 = 9

Can you analyze the pattern and find out the answer for:

4 + 9 = ?

Its something that each of us devours,
Not just us but birds, beats, trees, and flowers,
Frets iron and nibbles steel,
Toil hard stones to meal,
Exterminates king, collapse town,
And blows the mountains down.

On a bright sunny day, two fathers took their son fishing in the lake. Each man and son were able to catch one fish. When they returned to their camp, there were only three fishes in the basket. What happened?

PS: None of the fish were eaten, lost, or thrown back.