Find the Next Number in the Sequence

2 9 3 1 8 4 3 6 5 7 ?

Can you complete the sequence puzzle?

AR TA GE CA LE VI LI _

There is something which is always coming but never arrives?

Client Dempsey living in one of the East Coast states of the U.S. was talking to Landon Donovan, who was living in the West Coast state of the U.S.

Dempsey: What time is it?
Donovan: Wow, It is the same time here.

How is this possible?

An artist while painting a scenic beauty, decides to paint three layers of blue colour on the sky.

Which layer will go on the first?

One day, I thought of ways that can be used for creating a palindrome. So I decided that I will turn into a larger number by adding the reversed digits to the original number and keep doing it till I finally obtained a palindrome.

I am not sure if this process will always result in a palindrome eventually but I was able to produce a four-digit palindrome. Can you guess my starting number?

What is so fragile that saying its name breaks 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?

John was writing his first book. After saving the document, he locked his laptop with a password and mentioned some phrases for the hint box.

A friend of his tried opening his laptop but found out that it was password protected. Following is the hint that appeared.
1 mobile 3 books 2 roars 1 night 4 balls 2 lighters 1 ghost 1 hat 3 watches.

Can you help him in cracking the password?

There is a box. The area of its top is 240 square units, the area of the front is 300 square units and the area of the end is 180 square units.

Can you calculate the dimensions of this box with the given data?