what does the below rebus means?

What's the only room from which no one can enter or leave

You can take four of the five letters out of this word, but the pronunciation never changes. What is the word?

You are playing as white and given four rooks to checkmate the black king in four moves with the following rules 1. You can place one rook every move and ensure the black king should be in check position.2. After four moves the black king should be in the checkmate position.

A couple went to a hill station to enjoy their vacation. They have 12 sons, and each has a wife who has 3 sons further.

How many people went to the hill station?

Which digit occurred maximum times between the number 1 and 1000?

An inspection by the superintendent of St. Joseph School was scheduled on the next day. The class teacher Jenifer knew that he would be asking questions from her class and she would have to choose a pupil to answer. To offer a perfect impression over him, the teacher explained certain instructions to the students to maximise the chances of getting correct answer every time.

What did she say to the students?

What number does the below three word/phrase identify and why?
1. Deck
2. Year
3. Singing in the Rain

A convention is held where all the big logicians are summoned. The master places a band on everyone's forehead. Now all of them can see others bands but can't see his own. Then they are told that there are different colours of bands. All the logicians sit in circle and they are further explained that a bell will ring at regular intervals. The moment when a logician knew the colour of band on his forehead, he will leave at the next bell. If anyone leaves at the wrong bell, he will be disqualified.

The master assures the logicians that the puzzle will not be impossible for anyone of them. How will the logicians manage ?

Identify Me

Hint1: I am a god
Hint 2: I am a planet
Hint 3: measurer of heat