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

Complete the given grid with valid words. You can only use the letters AAEEIIMMPPTT.

Hint: The grid reads the same across as down.

In a contest, four fruits (an apple, a banana, an orange, and a pear) have been placed in four closed boxes (one fruit per box). People may guess which fruit is in which box. 123 people participate in the contest. When the boxes are opened, it turns out that 43 people have guessed none of the fruits correctly, 39 people have guessed one fruit correctly, and 31 people have guessed two fruits correctly.
How many people have guessed three fruits correctly, and how many people have guessed four fruits correctly

Can you think of a smallest +ve number such that if we shuffle the digits of the number, the new number becomes double the original number?

All of you like to eat me. I am a five-lettered word. Remove the first two and I turn into an infamous animal. Remove just the first and I become a heinous crime. Remove the first and the last and you can groove on me.

Can you guess who am I?

You have $100 with you and you have to buy 100 balls with it. 100 is the exact figure and you can't go below or above the numbers and you have to use the entire $100. If there is no kind of tax applied how many of each of the following balls will you be able to buy:

Green Balls costing $6
Yellow Balls costing $3
Black Balls costing $0.10

Now, how many of each must you buy to fulfil the condition given?

Which statement is true out of the following?
One statement here is false.
Two statements here are false.
Three statements here are false.

I always drive my customer away.

Who am I?

What is a word made up of 4 letters, yet is also made up of 3. Sometimes is written with 9 letters, and then with 4. Rarely consists of 6, and never is written with 5.

John was drowned by he was not wet. How?