I was disappointed with this carrot soup.
I gifted some carrot liqueur to the King, who loves alcohol, but he didn't like it.
Please. I'll eat anything else, just not the carrot. Please.
This meaning is a little weird, but I'm going to try my best to help you remember.
Every person has to participate in eating carrots. I don't care if you don't like them, if you don't eat at least one carrot in your life you'll die. So if you're a person you better participate in the eating of at least a single carrot.
This is a jukugo word, which usually means on'yomi readings from the kanji. You haven't learned this reading for 参 yet, so here's a mnemonic to help you:
You're craving a carrot, but you can't seem to find any. You look in your fridge, in your garden, and even in the trash. Finally you give up your carrot search and sit down when... ouch! The carrot was in your jeans (じん) the whole time!