I have branches, but no fruit, trunk or leaves. What am I?

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?

Can you find a five letter word that is left with only two letters if one is removed?

There is a five-letter word which has 3 consonants(all are same) and 2 different vowels.
Also, something wrong is associated with the word.

Can you name it?

What is full of holes but still holds water?

Two in a corner, one in a room, zero in a house, but one in a shelter. What is it?

I am not a bull but I have horns.
I am not an ass but I have a pack saddle.
Wherever I go, I leave silver behind me.

Who am I?

A farmer went to a market and bought a wolf, a goat, and a cabbage. On his way home, the farmer came to the bank of a river and rented a boat. But crossing the river by boat, the farmer could carry only himself and a single one of his purchases: the wolf, the goat, or the cabbage. If left unattended together, the wolf would eat the goat, or the goat would eat the cabbage. The farmer’s challenge was to carry himself and his purchases to the far bank of the river, leaving each purchase intact. How did he do it?

Three playing cards in a row. Can you name them with these clues? There is a two to the right of a king. A diamond will be found to the left of a spade. An ace is to the left of a heart. A heart is to the left of a spade. Now, identify all three cards.

Replace the question mark with the correct number, given the pair of numbers exhibits a similar relationship?

? : 3839 :: 11 : 1209