Can you fill the blank with the correct number?

6 30 870 756030 _____

Below the four parts have been reorganised. The four partitions are exactly the same in both arrangements. Why is there a hole?

I am looking for a word that change both gender and number when i add the letter 'S'.

What Word am I Looking For ?

In the image below, can you find the value of an angle(y)

Why is the Hole below a Lock?

Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not rounded numerals equals 24.

Birbal was jester, counsellor, and fool to the great Moghul emperor, Akbar.
The villagers loved to talk of Birbal's wisdom and cleverness,
and the emperor loved to try to outsmart him.
One day Akbar (emperor) drew a line across the floor.
"Birbal," he ordered, "you must make this line shorter, but you cannot erase any bit of it."
Everyone present thought the emperor had finally outsmarted Birbal.
It was clearly an impossible task.
Yet within moments the emperor and everyone else present had to agree that Birbal had made the line shorter without erasing any of it.
How could this be?

Manish and Manoj play 5 games of chess.
Both Manish and Manoj win the exact same number of games. There is no tie at all.

How?

John has eleven friends. He has a bowl containing eleven apples. Now He wants to divide the eleven apples among his friends, in such a way that an apple should remain in his bowl.
How can He do it?

Take away my first letter, then take away my second letter. Then take away the rest of my letters, yet I remain the same. What am I?