What is the Surname of Barbie Doll?

The following four words might seem abrupt to you. But you can make them meaningful by just adding vowels.
RDSH
GGPLNT
TMT
NN

Hint: All of them are vegetables.

Can you find out the next digit in the following series ?

0, 0, 1, 3, 2, 6, 3, 9, 4, 12, 5, ?

When you stop to look, you can always see me. But if you try to touch me, you can never feel me. Although you walk towards me, I remain the same distance from you. What am I?

The day after tomorrow will be three days before Tuesday. Can you find out what is today?

Take one out and scratch my head, I am now black but once was red. What am I?

Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start traveling. The pigeon flies back and forth at 18 MPH between the 2 friends until the friends meet.

How many miles does the pigeon travel?

In order to complete the racing competition, the Mexico racetrack has to submit its top and the most famous three horses to win the competition. Due to an electrical storm, all the records are cleared and no one knows which horse holds the record. They all look identical and it becomes even more difficult to differentiate the horses. There are 25 horses in the Mexico racetrack. But there can be only five horses at a time on the track. What will the least number of races that can be conducted to find out the three fastest horses?

How is the moon similar to a dollar?

Two in a corner, one in a room, zero in a house, but one in a shelter. What am I?