What is harder to catch the faster you run?

Solve the following series:
AZ, GT, MN, __, YB

Five lovely ladies(Sophia, Isabella, Madison, Emma and Olivia) planned a picnic.

They each buy one thing each for the picnic.

Sophia, Emma and Olivia got a drink : orange-Juice, apple-juice, and mango-juice.
Olivia got the drink with the same letter as the one in her first name.
Emma loves mango-juice.
The other two bring some food : chocolates and pizza.
Also Madison is allergic to cheese.

So which ladies bought what ?

Three fair coins are tossed in the air and they land with heads up. Can you calculate the chances that when they are tossed again, two coins will again land with heads up?

Move four matchsticks to the below square to form three squares?

Can you start the fire using two pieces of wood?

Can you replace the question mark with the correct number in the below table sequence?

Remove two matchsticks to make the below equation correct.

A man is lying dead in a field where no one is around. His head is split open and his legs are disfigured. Near to him, there is an unopened package. No living organism can be found anywhere at the crime scene.

How did he die?

Can you decipher the following common phrase?

T M C
A U O
H S M
W T E