The correct answer is option C) Less than 10 days.

Explanation:
Granulocytic white blood cells (WBCs), also known as granulocytes, are a type of immune cells that play a crucial role in the body's defense against infections. They are called granulocytes because their cytoplasm contains granules that are visible under a microscope.

The life span of granulocytic WBCs can vary depending on the specific type of granulocyte. There are three main types of granulocytes: neutrophils, eosinophils, and basophils. Let's analyze the life span of each type separately:

1. Neutrophils: Neutrophils are the most abundant type of granulocytes and are responsible for fighting bacterial infections. They have a relatively short life span, typically ranging from a few hours to a few days. Neutrophils are highly mobile and are usually the first immune cells to arrive at the site of infection.

2. Eosinophils: Eosinophils are involved in combating parasitic infections and allergic reactions. Their life span is longer than that of neutrophils, ranging from a few days to a few weeks.

3. Basophils: Basophils are the least abundant type of granulocytes and are involved in allergic reactions and inflammation. Their life span is also relatively short, similar to neutrophils, ranging from a few hours to a few days.

Overall, the life span of granulocytic WBCs is relatively short, with neutrophils having the shortest life span of less than 10 days. This is due to the fact that these cells are constantly being produced in the bone marrow and are quickly recruited to sites of infection or inflammation. Once they have fulfilled their role in fighting infection, they undergo programmed cell death, called apoptosis, and are then cleared from the body.

In summary, the life span of human granulocytic WBCs is less than 10 days, making option C the correct answer.