No, it’s not a trick question. Shredded paper IS recyclable but it does need to be contained before you put it in your recycling bin. The best way to do it is to place it in a paper bag, fold over and staple. If you don’t have a stapler, roll the bag tightly so it doesn’t open up.
A few things to keep in mind:
Paper that’s shredded into tiny pieces vs strips aren’t recyclable, the paper fibers are too small. You can use that in your backyard compost bin or use it as a weed barrier under your mulch.
You can also reuse shredded paper for moving/packing, as bedding for pets and the type in the photo would be good to reuse in an Easter basket.