"It is your last evening."
Translation:Es ist dein letzter Abend.
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Possessive determiners such as dein-, mein-, sein-, ihr-, unser- and euer/eur- are declined in the same way as indefinite articles (ein-).
In this case, dein refers to a masculine noun in the nominative case, so no ending is required.
In German there is Strong, Weak and Mixed inflection (http://en.wikipedia.org/wiki/German_declension#Possessive_pronouns).
In this case, we use Mixed inflection because of the preceding possessive adjective "dein".
Strong would be used in the absence of a preceding article, and Weak would be used with a preceding definite article.
Because dein works like ein (which is used for both masculine and neuter nouns) it does not uniquely indicate the gender of the following noun, so the adjective has to be inflected to show that, so it is letzter with the ending er the same as der for masculine nouns. That's as ungrammatical as I can make it. I hope it helps a bit.
This is one of those questions that come with options to choose. I chose 1. Es ist dein letzter Abend 2. Es ist euer letzter Abend
Duo marked option 2 as incorrect answer. I was under the impression that "euer" can be used for plural informal "you". Am I wrong?
P.S: I'm reporting this.
No. Nacht is feminine, and here in the nominative case (when the main verb of the sentence is "to be", both sides are in the nominative case).
So you would need feminine nominative deine letzte Nacht -- but that would be "your last night" rather than "your last evening".