What will be the best approach to finding all the prime numbers less than 75 that leave an odd reminder when we divide them with 5?

In one of the popular batman series movie "Batman Forever", there was a riddle that goes like "Tear me off and then scratch my head and I was red then and now I am back. Who am I?

A man calls his dog from the opposite side of a river. The dog crosses the river without a bridge or a boat and manages to not get wet. How is this possible?

There were two grandmothers and their two granddaughters.
There were two husbands and their two wives.
There were two fathers and their two daughters.
There were two mothers and their two sons.
There were two maidens and their two mothers.
There were two sisters and their two brothers.
Yet there are only six, who are buried here,
All are born legitimate and relationships clear.
How can this happen?

When you say goodbye, I am what you need to tie.
I come as a couple and go wherever you run.
Who am I?

As easy as you can get into me, it is as hard to get out of me.

Do you know what I am?

500 women soldiers are arranged in an array of ten rows and fifty columns in accordance with their respective heights. Now, the tallest woman from each row is asked to move out in the front. From them, the shortest one is labelled as Alpha. They are then asked to resume their original position.

Now, the shortest woman in each column is asked to come out in front. The tallest among them is labelled as Beta.

Can you find out if Alpha will be taller or Beta?

You are given four results as below:
1111 = F
2222 = E
3333 = T
Then, can you find out how to code 4444?

Can you find a seven digit number which describes itself. The first digit is the number of zeros in the number. The second digit is the number of ones in the number, etc. For example, in the number 21200, there are 2 zeros, 1 one, 2 twos, 0 threes and 0 fours.

If we tell you that there is a relation between the numbers and letters in the given figure, can you analyze it and find the missing letter in the last box?