Quickly Solve this riddle

7 - 4 + 3 * 0 + 1 = ?

You see me once in June, twice in November, and not at all in May. What am I?

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?

Can you find the missing letter in the sequence?
S - T - I - L - ? - T - F - Y - C

I want to fill my bucket using both cold and hot water.
I have two taps for both cold and hot water. The hot water tap fills the bucket in exact 6 hours and the cold water tap fills the bucket in exact 4 hours.
I turn both of them simultaneously but I forgot to turn off another tap which removes the water out of the bucket. This tap can empty the bucket in 12 hours.

How Long will it take to fill the bucket?

John bought a new car. He has a habit of eating ice cream from a particular ice cream shop while returning home from office. Whenever, he eats strawberry ice cream, he faces no problem. But whenever, he eats chocolate ice cream, the car starts giving problem. At first, he thinks, it is just a co-incidence but when this awkward incident happens for 3-4 times, he reports this problem to the company.

The mechanic of the company checks but finds no problem at all. The next day, when he stops by to eat chocolate ice cream, the car again starts giving problem.

Can you find the possible reason?

No one wants to have it, but if one got it, he does not want to lose it. What is It?

The teacher told the student that if he told a lie then he will be expelled from school and if he told the truth then he still is expelled from school.

What can a student say to prevent his being expelled from school?

There is a number which when you multiply by 3 and subtract 2 from the result, then the resulting number is the reverse of the actual number.

What is the smallest number that stands true on the statement?

How could a baby fall out of a twenty-story building onto the ground and live?