Can you solve below mathematical equation?

2^1234 - 2^1233

You can win me and lose me but never buy me
You can not eat me and never want to part with me
I can make you cry or bring you joy
I am not a machine and definitely not a toy
You keep me but i am not forever just yours
You might find me in a case or on a shelf next to a vase
I am hard and i am tall if you bump me i am sure to fall
I am made of different materials and am at many events
If your lucky and fight hard I might be yours
What am I ?

How many sides does a circle have?

Twenty frogs are sitting on a log floating on the surface of a river. Two of them decide to jump off into the water.

How many frogs are there on the log at this moment?

You may enter, but you may not come in. I have space, but no room. I have keys, but open no lock. What am I?

On a certain day, John celebrated his birthday. Two days later, his older twin brother Jacob celebrated his birthday.

Is this even possible? How can it be?

Find the next number in the sequence

1, 2, 6, 21, 88, __?

You need to climb ten stairs. At every stair, you can either take one step up or you can jump two steps up.

In how many different ways you can climb 10 stairs?

On 26-01-2022, Juli was murdered at her house in a city in India in the afternoon. There were three suspects in the murder and the following are the statements that were given by them:

John: I visited my village that day.
Jacob: I was out to deposit my house tax in the municipality office at that time.
Jonny: I was at a friend's place having lunch at that time.

Can you find out who is the murderer?

In 1990, a person is 15 years old. In 1995, that same person is 10 years old. How can this be?