What is the word or phrase?

What has hands, but can’t clap?

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 hypothetical state between the USA and Mexico border 'Tango'.
Here 70 percent of the population have defective eyesight, 75 percent are hard of hearing, 80 percent have Nose trouble and 85 percent suffer from allergies, what percentage (at a minimum) suffer from all four ailments?

Today, I celebrated my 32nd birthday but I was born in 1972.
How is this possible?

I am a five-letter word under you,
Remove the first letter and I am above you,
Remove the second as well and I am around you.

Who am I?

If you say my name, I will no longer exist. What am I?

My friends called me Iron59 because my parents are a chemist and a mathematician. What is my real name?

If,
9 * 8 * 7 = 65
8 * 7 * 6 = 50
7 * 6 * 5 = 37

Find
6 * 5 * 4 = ?

A spaceship was lost. The detective was given a piece of paper. This was the location of the spaceship! This is what the slip had scribbled on it:
Juice, Umbrella, Potato, Ice, Tomato, Elephant, Rice.

Where is the spaceship?