Can you solve the below algebraic mathematical equation?

(J+O+I+N+T)3 = JOINT

What seven-letter word has hundreds of letters in it?

The great emperor Akbar once ruled India. He was well known for his intelligence. But along with that, he was known for the Nine Gems in his court. One of the nine gems was Birbal, a quick witted and extremely intelligent man. The stories of his wit were widely popular.

Once a king ruling in a distant land heard of Birbal. To check his wit, he sent an invitation and called him to visit his land. Akbar allowed Birbal to go and he took off on the journey.

Upon reaching that kings kingdom, he was welcomed with flowers. He was then escorted to the palace of the king. Upon entering the palace, Birbal found that there were six people sitting in front of him adorning the same robe. They were also lookalike and it was hard to judge who the real king was.

After a couple of minutes, Birbal approached one of them and bowed in front of him greeting him.

That was the real king. How did Birbal know who was the real king ?

I welcome the day with a show of light, I stealthily came here in the night. I bathe the earthy stuff at dawn, But by noon, alas! I'm gone.

Decode the below four famous ciphers:

8P of the SS
1M of the E
1S of the SS
60M in 1H

There is a box in which distinct numbered balls have been kept. You have to pick two balls randomly from the lot.

If someone is offering you a 2 to 1 odds that the numbers will be relatively prime, for example
If the balls you picked had the numbers 6 and 13, you lose $1.
If the balls you picked had the numbers 5 and 25, you win $2.

Will you accept that bet?

I don't get anymore wetter, no matter how much rain falls on me.

A finger goes in me. You fiddle with me when you're bored. The best man always has me first. What am I?

Can you find out which options fits best with the missing column?

If one and a half boys, eat one and a half burgers in one and a half hours.

How many burgers can 9 boys eat in 3 hours?