Quickly Solve this riddle

7 - 4 + 3 * 0 + 1 = ?

Take away my first letter, then take away my second letter. Then take away the rest of my letters, yet I remain the same. What am I?

A professor thinks of two consecutive numbers between 1 and 10.
'A' knows the 1st number and 'B' knows the second number

A: I do not know your number.
B: Nor do I know your number.
A: Now I know.

What are the four solutions for this?

Two-person want to cross a river. Only one boat is present on the riverside that can carry only one person at a time.

However, they still manage to cross the river. How is it possible?

What is the next shape from answers A, B, C, and D figure?

Can you place six X (crosses) in below board without making three in a row in any way ?

The answer I give is yes, but what I mean is no. What was the question?

A man was just doing his job when his suit was torn. Why did he die three minutes later?

A word I know has six letters it contains, remove one letter and 12 remain. What is it?

I am eight letters long - "12345678"
My 1234 is an atmospheric condition.
My 34567 supports a plant.
My 4567 is too appropriate.
My 45 is a friendly thank-you.
My 678 is a man's name.

What word am I?