First, let's understand the given information. We have hydrazine (N₂H₄) losing 10 moles of electrons to form a new compound (Y). In this context, the oxidation state of hydrogen remains unchanged, which is +1.

To solve this problem, we should follow these steps:

1. Determine the initial oxidation state of nitrogen in N₂H₄.

In N₂H₄, hydrogen is in the +1 oxidation state. Since the molecule is neutral, the sum of oxidation states must equal 0. We can express this relationship as:

2x + 4(+1) = 0

Where x is the oxidation state of one nitrogen atom. This can be rearranged to find x:

2x = -4

x = -2

So, the initial oxidation state of nitrogen in N₂H₄ is -2.

2. Determine the change in oxidation state of nitrogen.

When 1 mole of N₂H₄ loses 10 moles of electrons, the nitrogen atoms undergo oxidation, meaning their oxidation state increases. The loss of 10 electrons per mole of N₂H₄ means that there's an increase of 5 oxidation states per nitrogen atom, because there are 2 nitrogen atoms in each molecule of N₂H₄.

3. Calculate the final oxidation state of nitrogen.

The initial oxidation state of nitrogen is -2. With the loss of electrons, the oxidation state increases by 5 for each nitrogen atom:

Final oxidation state = Initial oxidation state + Increase in oxidation state

Final oxidation state of nitrogen = -2 + 5 = +3

Therefore, the oxidation state of nitrogen in the new compound Y is +3.

The correct answer is Option C: +3.