Can you find out the remainder when 3^300 is divided by 5?

Something Extraordinary happened on May 6th 19778 at 12:34am what was that?

I can be cracked, made, told, and played. What am I?

There is a unique number which when multiplied by any number from 1 to 6, we will get the new number that contains the same digits only.

Can you find that number?

Using Only Five 5's and any mathematical operator make sum as 37

The following four words might seem abrupt to you. But you can make them meaningful by just adding vowels.
RDSH
GGPLNT
TMT
NN

Hint: All of them are vegetables.

A charming young lady was approached by a kind looking old woman in a restaurant. The old woman said to her, 'You look exactly like my younger daughter. Sadly she passed away a couple of months back. Could you do me a favor and say 'Goodbye, mother' with a kind smile on your face when I leave?

The young lady agreed for the same and said, 'Goodbye, mother' when the old woman left. Soon after, she got the most disengaging shock of her life.

Can you guess what the shock was?

I possess a head

I flaunt a tail

But I don't have mouth or legs

Can you find out who I am?

In the addition below, all digits have been replaced by letters. Equal letters represent equal digits and different letters represent different digits.
ABCABA
BBDCAA
ABEABB
ABDBAA
------- +
AAFGBDH
What does the complete addition look like in digits?

One absent-minded ancient philosopher forgot to wind up his only clock in the house. He had no radio, TV, telephone, internet, or any other means for telling time. So he travelled on foot to his friend's place a few miles down the straight desert road. He stayed at his friend's house for the night and when he came back home, he knew how to set his clock. How did he know?