Who can jump higher than a Mountain?

In a certain country ½ of 5 = 3. If the same proportion holds, what is the value of 1/3 of 10?

A cricket has 6 legs, a squirrel has 4 legs and a spider has 8 legs.

In a local zoo, it was found that the total number of legs is 612. Also, there are equal number of each of the above animals/insects.

Can you find out how many animals are there in the zoo?

You are on a Boat in the mid of a river. You have two cigarettes with you. One of these two you have to light, how will you light the cigarette?

Can you convert the number zero(0) into a positive number using just one mathematical operator ?

Look at this sequence from top to bottom. What is the next number in the sequence?
1
11
21
1211
111221
312211

Two friends Smith and Andrew were talking about the bravery of their families. Smith told great stories about his courageous grandfather who fought for Britain in "World War I". Andrew told that his grandfather was so brave that in 1919 just after the war he was honoured with a bravery medal with the words "For our Courageous Soldiers In World War I" embedded into it. Smith knows that his friend is lying. How?

Below, you can see three complete equations and one incomplete. Based on the three complete ones, can you complete the incomplete one?

5 $ 4 $ 3 $ 9 = 4215
6 $ 9 $ 2 $ 6 = 3816
4 $ 7 $ 3 $ 3 = 1122
7 $ 2 $ 7 $ 4 = ____

How can you make the following equation true by drawing only one straight line: 5+5+5=550 ?

They are the five precious gems of an everyday sort and all can be found on a Tennis Court. Who are they?