**Explanation:**

Rajasthan is the largest state in India and is known for its arid and desert landscapes. There are several districts in Rajasthan that have predominantly desert areas. Among these districts, the two districts that are completely covered by desert are Jaisalmer and Barmer. Let's explore these districts in detail:

**1. Jaisalmer:**
Jaisalmer is a district located in the western part of Rajasthan. It is known as the "Golden City" due to its yellow sandstone architecture and the golden hues of the desert. Jaisalmer is entirely surrounded by the Thar Desert, which is one of the largest deserts in the world. The district is characterized by vast stretches of sand dunes, barren landscapes, and a harsh desert climate. It is a popular tourist destination, attracting visitors with its magnificent forts, havelis, and desert experiences like camel safaris.

**2. Barmer:**
Barmer is another district in Rajasthan that is predominantly covered by desert. It is located in the western part of the state, bordering Pakistan. The district is part of the Thar Desert and is known for its arid and barren landscapes. Barmer is sparsely populated and primarily inhabited by communities that have adapted to the desert environment. The district is rich in mineral resources and is known for its oil and gas fields.

**Conclusion:**
Therefore, the correct answer is option 'A' - Jaisalmer and Barmer. These two districts in Rajasthan are completely covered by desert and are known for their arid landscapes and desert experiences.