What does below rebus means ?

One day, I thought of ways that can be used for creating a palindrome. So I decided that I will turn into a larger number by adding the reversed digits to the original number and keep doing it till I finally obtained a palindrome.

I am not sure if this process will always result in a palindrome eventually but I was able to produce a four-digit palindrome. Can you guess my starting number?

As you can see in the picture, you have a hole with dimensions 9 ft x 2 ft Also available is a wooden board with dimensions 6 ft x 3 ft Now you have to cover the hole with this board and you are allowed to cut the board into two pieces. Please see that the hole is completely covered and the boards should not overlap or extend beyond the edge. How will you cut the board?

I shave every day, but my beard stays the same. What am I?

I am written with two letters.
I said with the one.
I usually am seen with the two.

Who am I?

Make eight squares by moving only two matchsticks.
Note- Square can be of different sizes.

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?

See the given image carefully. What you have to do is move the blue checkers in the position of the black checkers and vice versa. You are only allowed to move the checker to an adjacent empty space. Do it in the least possible moves.

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?

In a university, a professor gave a set of three problems to the three brilliant students of his class. See the image for the questions.