In the nitrous oxide molecule, the $\mathrm{N}-\mathrm{N}$ as well as the $\mathrm{N}-\mathrm{O}$ bond have

We can find double bond in alkenes and triple bond in alkyne. Both are called as unsaturated compound. To find is there is single bond , double bond or triple bond between atoms, we need to find the formal charge on each atom in the molecule. Double bonds are more reactive due to the presence of more number of electrons.

Explanation for the correct answer-

(b) some triple bond character

The structure of nitrous oxide is as follows-

As we can see from the resonance structure of nitrous oxide, that nitrous oxide has triple bond structure. A triple bond  is a bond between two atoms it involves six bonding electrons instead of having two bonding electrons in a single bond. Due to formal charge reasons oxygen forms triple bond.

Explanation for the incorrect answer-

(a) some double bond character

As we can see from the above resonance structure that nitrous oxide has triple bond character and not double bond character. Therefore, (a) is the incorrect option.

(c) a d orbital involved in bonding

In nitrous oxide a d orbital is involved in bonding. Therefore, (c) is the incorrect answer.

(d) none of these

Since, option (b) is correct. Therefore (d) is incorrect.

In the nitrous oxide molecule there is some triple bond character. Therefore the correct answer is (b)