What begins with T, ends with T, and has T in it?

I never stop running even when I standstill. If I am formed by joining two identical bodies together, can you guess who I am?

What is both possible and impossible at the same time?

A number with an interesting property:

When I divide it by 2, the remainder is 1.
When I divide it by 3, the remainder is 2.
When I divide it by 4, the remainder is 3.
When I divide it by 5, the remainder is 4.
When I divide it by 6, the remainder is 5.
When I divide it by 7, the remainder is 6.
When I divide it by 8, the remainder is 7.
When I divide it by 9, the remainder is 8.
When I divide it by 10, the remainder is 9.

It's not a small number, but it's not really big, either.
When I looked for a smaller number with this property I couldn't find one.

Can you find it?

Spot the cat in the picture below

A donkey is behind another donkey
I'm behind that second donkey
But there is a whole nation behind me

It is a murder you can describe in a word.

Find the missing letter in the last circle logically in the given below picture.

Look at this sequence from top to bottom. What is the next number in the sequence?
1
11
21
1211
111221
312211

If eleven plus two equals one, what does nine plus five equal?

What is at the end of a rainbow?