Formal:
* क्या आपने खाना खाया? (Kya aapne khana khaya?)
* क्या आपने भोजन किया? (Kya aapne bhojan kiya?)
Informal:
* क्या खाना खाया? (Kya khana khaya?)
* खाना खाया? (Khana khaya?)
* कुछ खाया? (Kuchh khaya?)
* खा लिया? (Kha liya?)
Note:
* खाना (khana) means food in general.
* भोजन (bhojan) is a more formal term for food.
* The question "Have you eaten?" is often used as a polite way of asking if someone is hungry and wants to eat.