Replace the question mark with the number below given a simple math problem.

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 ?

What goes up but never comes down?

The following sentence is false. The preceding sentence is true.
Are these two sentences true or false?

A professor thinks of two consecutive numbers between 1 and 10.
'A' knows the 1st number and 'B' knows the second number

A: I do not know your number.
B: Nor do I know your number.
A: Now I know.

What are the four solutions for this?

A couple went to a hill station to enjoy their vacation. They have 12 sons, and each has a wife who has 3 sons further.

How many people went to the hill station?

Can you find the odd number in the following five choices?

1) 482636
2) 259807
3) 865195
4) 104739
5) 391744

An infinite number of mathematicians are standing behind a bar. The first asks the barman for half a pint of beer, the second for a quarter pint, the third an eighth, and so on. How many pints of beer will the barman need to fulfill all mathematicians' wishes?

There is a number which when you multiply by 3 and subtract 2 from the result, then the resulting number is the reverse of the actual number.

What is the smallest number that stands true on the statement?

Which is Odd One Out and why?

4377

3954

9862

8454

9831