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?

What is the next number in the series?

15 29 56 108 208 ?

10 people came into a hotel with 9 rooms and each guest wanted his own room. The bellboy solved this problem.
He asked the tenth guest to wait for a little with the first guest in room number 1. So in the first room, there were two people. The bellboy took the third guest to room number 2, the fourth to number 3, ..., and the ninth guest to room number 8. Then he returned to room number 1 and took the tenth guest to room number 9, still vacant.
How can everybody have his own room?

In a chess board, the queen piece can move horizontally, vertically and diagonally freely. The picture represents the same.Can you place 8 queens on the board in a manner that none of the queens can attack each other?

When Jack was six years old he hammered a nail into his favourite tree to mark his height. Ten years later at age sixteen, Jack returned to see how much higher the nail was. If the tree grew by five centimetres each year, how much higher would the nail be?

As shown in the picture below, we can see a boy hanging on the tree branch to save his life. There are various ways in which he can die like1. A snake hanging toward the right waiting to bite the boy.2. A roaring Lion near the tree.3. Two crocodiles are ready to attack if the boy reaches near water. The tree is chopped to some extent, so can fall as if he moves a lot. Can you give this boy an escape plan?

It is a six-letter word.
The first four letters are me.
The second and last letters are the same.
The fourth second and last letter is payment.

Who is it?

A man is found unconscious in front of a store at two in the morning. His head is bleeding and there’s a brick laying next to him. When the police arrive, they carry the man to jail. Why did they arrest him?

Transform the word THINK into BRAIN while changing only one letter at a time in a manner that each of the word in the process is a real word!!!

Only one colour, but not one size,
Stuck at the bottom, yet easily flies.
Present in sun, but not in rain,
Doing no harm, and feeling no pain.
What is it?