机に猫と本があります is wrong. You must separate the English sentence " There is a cat and book on the desk." We(Japanese) use いる for animate and ある for inanimate. So you can not say it at once, of course. There is a cat and book on the desk. 1. 机の上に猫がいて、本があります。GRAMMATICALLY CORRECT BUT NOT SO NATURAL 2. 机の上に本があって猫がいます。（Ryoko-san wrote.）／机の上に本があり、猫がいます。GRAMMATICALLY CORRECT BUT NOT SO NATURAL 3. 机の上に本があって／あり、その横<よこ>に／傍<かたわ>らに猫が乗<の>っています。There is a book on the desk and next to it a cat has climbed on the desk. GRAMMATICALLY CORRECT AND NATURAL ※It is unusual that there is a cat on the desk, so 乗っています(has climbed on) is better. You can see my answer on: http://www.italki.com/entry/521340 .

Interesting question! I would say these things separately: 机の上に本があって猫がいます。However, I'd like to know the answer which is correct grammatically.

Hi Saraさん. 難しい質問ですね！ I also wonder which to use!?