What has many keys but can’t open a single lock?

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

You are on your way to visit your Friend, who lives at the end of the hill. It is his birthday, and you want to give him the cakes you have made. Between your house and his house, you have to cross 5 bridges, and as it goes in the land of make believe, there is a troll under every bridge! Each troll, quite rightly, insists that you pay a troll toll. Before you can cross their bridge, you have to give them half of the cakes you are carrying, but as they are kind trolls, they each give you back a single cake. How many cakes do you have to leave home to make sure that you arrive at a friend's house with exactly two

Peter wakes up daily to pick up his cycle and crosses the border between Spain and France daily with a bag on his shoulder. He is investigated daily by the officials but they don't find anything suspicious.

If we tell you that he is smuggling something what would it be?

I am a five-letter word and comprises two different vowels and three same consonants. I am so strong that I can spoil your entire work.

Can you find out who am I?

P is the father of Q and S is the son of R. T is the brother of P and has a daughter U. If R is the sister of P, then what is the relation between U, Q and S?

A Club organizes a Running Race, and John, Jacob, Minda, and Tony participated.

The results are as follows

John beats Jacob
Minda beats Toni
Toni beats John

Who came first in the race?

The world's largest Thanksgiving turkey was on display at a fair. Everyone was admiring it when suddenly a woman ran up and shot the turkey and left. Everyone knew her yet nobody made any attempts to stop or report her. Why?

Complete the given grid with valid words. You can only use the letters AAEEIIMMPPTT.

Hint: The grid reads the same across as down.

What is the probability of choosing the correct answer at random from the options below?

a) 1/4
b) 1/2
c) 1
d) 1/4