What time is it when an elephant sits on a fence?

I have a clock(12-hour format) and both the needles of the clock overlap at 12:00.
After how much time, they will overlap again?

The host of a game show, offers the guest a choice of three doors. Behind one is a expensive car, but behind the other two are goats.
After you have chosen one door, he reveals one of the other two doors behind which is a goat (he wouldn't reveal a car).

Now he gives you the chance to switch to the other unrevealed door or stay at your initial choice. You will then get what is behind that door.

You cannot hear the goats from behind the doors, or in any way know which door has the prize.

Should you stay, or switch, or doesn't it matter?

It's been the first day of the school when a young girl was found raped and murdered.
Police suspect four male teachers as on the killers and ask them what they were doing in the morning in time 8:00 am.
1. Wayne: I was reading the newspaper.
2. Terry: I was checking chemistry papers
3. Bridge: I had locked myself in my room as my wife left me.
4. Cole: I dropped my wife to her office.

Who is the killer?

John and Jenni are a married couple. They have two kids, one of them is a girl. Assume safely that the probability of each gender is 1/2.
What is the probability that the other kid is also a girl?

Hint: It is not 1/2 as you would first think.

Look at me. I can bring a smile to your face, A tear to your eye, Or even a thought to your mind. But, I can't be seen. What am I?

In the Chess Board picture below white army is arranged. You need to add a black army on the board such that no piece is under any threat.
Note: Army comprised of 1 king, 1 queen, 2 rooks, 2 bishops, 2 knights, and 8 pawns.

Solve the equation by replacing the alphabet with numbers.

MOM + MOM + NO = BOOK=

Only one color, but not one size,
Stuck at the bottom, yet easily flies.
Present in sun, but not in rain,
Doing no harm, and feeling no pain.
What is it?

Spelt forwards I’m what you do every day, spelled backwards I’m something you hate. What am I?