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 number comes next in this sequence:
7 8 5 5 3 4 4 _

2, 3, 5, 9, 17, _ What is the next number in the sequence?

A King wants to send the diamond ring to his girlfriend securely. He got multiple locks and their corresponding keys. His girlfriend does not have any keys to these locks and if he sends the key without a lock, the key can be copied in the way. How can King send the ring to his girlfriend securely?

Here is a mathematical expression that also secretly tells a movie name. What movie is that?

The King of a distant land had heard that Birbal was one of the wisest men in the East and so desired to meet Birbal. He sent Birbal an invitation to visit his country.

In due course, Birbal arrived in the distant kingdom. When he entered the palace he was flabbergasted to find not one but six kings seated there. All looked alike. All were dressed in kingly robes. Who was the real king?

The very next moment he got his answer. Confidently, he approached the king and bowed to him.

How did Birbal know who was the real king?

The first two letters signify a male, the first three letters signify a female, the first four letters signify a great, while the entire world signifies a great woman. What is the word?

Can you divide the below-given shape into four equal and identical pieces?

Only one color, 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?

A man was found murdered on Sunday morning. His wife immediately called the police. The police questioned the wife and staff and got these alibis: The Wife said she was sleeping. The Cook was cooking breakfast. The Gardener was picking vegetables. The Maid was getting the mail. The Butler was cleaning the closet. The police instantly arrested the murderer. Who did it and how did they know?