I am a seven-letter word but if you remove four of my letters I will have one left. What word am I?

I am something people love or hate. I change peoples appearances and thoughts. If a person takes care of them self I will go up even higher. To some people I will fool them. To others I am a mystery. Some people might want to try and hide me but I will show. No matter how hard people try I will Never go down. What am I?

Alpha is Beta's sister.

Gamma is a Beta mother.

Delta is Gamma's father.

Tango is Delta's mother.

Then,

How is Alpha related to Delta?

If,

20 % 5 = 24

21 % 7 = 33

42 % 6 = 67

Then;

66 % 6 = ?

You are trapped in a room with two doors. One leads to certain death and the other leads to freedom. You don't know which is which.
There are two robots guarding the doors. They will let you choose one door but upon doing so you must go through it.
You can, however, ask one robot one question. The problem is one robot always tells the truth, the other always lies and you don't know which is which.
What is the question you ask?

There are a number of books on a shelf. If one book is the 4th from the left and 6th from the right, how many books are on the shelf?

I have feet, but no legs. Which animal Am I?

What word is pronounced the same if you take away four of its five letters?

You are an expert on paranormal activity and have been hired to locate a spirit haunting an old resort hotel. Strong signs indicate that the spirit lies behind one of four doors. The inscriptions on each door read as follows:

Door A: It's behind B or C
Door B: Its behind A or D
Door C: It's in here
Door D: It's not in here

Your psychic powers have told you three of the inscriptions are false, and one is true. Behind which door will you find the spirit?

A car is crossing a 20 km-long bridge. The bridge can support at most 1500kg of weight over it. If somehow, the weight on the bridge becomes more than that, it will break.

Now, the weight of the car is exactly 1500kg. At the midway, a bird comes and sits on the roof of the car. This bird weighs exactly 200 grams.
Can you tell if the bridge breaks at this point or not?