During which month do people sleep the least?

Intelligence Agency need to break the vault but the problem is that they are not able to break the vault.

On the vault, a text is written as:

31 11 33 33 43 45
21 25
31 24 11 31 51 41

To Break the code Intelligence Agency brings a mathematician named Joseph.
Minutes later he deciphers the code.

Whats the code?

Detective Rockford was jogging near the beach at 4:30 am.
He hears a sound near the shack "No Michael, Please Do not shoot me".
Next instance he heard the sound of gunfire. Rockford rushes to the shack where he finds women lying dead and a gun in close proximity of three "Doctore Lawyer and a Teacher".

Rockford immediately knew that the Lawyer has committed the crime. How?

A large container is kept in open under the rain. Every passing hour, the water collected inside the container becomes double what it was.

In ten hours, the container is filled completely. Can you calculate how long would it have taken to be filled in half?

If you had a pizza with crust thickness 'a' and radius 'z', what's the volume of the pizza?

Count The number of F's in the paragraph below:

"FINISHED FILES ARE THE RESULT OF YEARS OF SCIENTIFIC STUDY COMBINED WITH THE EXPERIENCE OF YEARS"

A man has a barrel filled with oil that weighs 100 pounds, and then he puts something into it. Now the barrel weighs less than 100 pounds. What did he put in the barrel?

Two in a corner, one in a room, zero in a house, but one in a shelter. What is it?

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?

You can see it everyday, But cannot touch it at will. What is it?