What has hands, but can’t clap?

During a secret mission, an agent gave the following code to the higher authorities
AIM DUE OAT TIE MOD

However, the information is in one word only and the rest are fake. To assist the authorities in understanding better, he also sent them a clue, If I tell you any one character of the code, you can easily find out the number of vowels in the codeword.

Can you find out the code word?

You see a mathematical expression in the picture. Can you think of a movie that this expression refers to?

You may enter, but you may not come in. I have space, but no room. I have keys, but open no lock. What am I?

There are two candles. Both will only burn exactly for an hour. How will you use these two candles to measure forty-five minutes?

I am first found in caves, now prolific online; I am a depiction, a drawing, a symbol, or sign. I will convey whichever mood you could wish; or for that matter, a fist, flask, or fish. What am I?

Count the number of times the letter "F" appears in the following paragraph:

FAY FRIED FIFTY POUNDS OF
SALTED FISH AND THREE POUNDS
OF DRY FENNEL FOR DINNER FOR
FORTY MEMBERS OF HER FATHER'S FAMILY.

A mother bought three dress for her triplets daughters(one for each) and put the dresses in the dark. One by one the girls come and pick a dress.
What is the probability that no girl will choose her own dress?

John buys rice at Rs.60/kg from Britain and then sells them at Rs.5/kg in India. As a result of this, he becomes a millionaire. How come?

What seven-letter word has hundreds of letters in it?