Let's analyze each statement separately to determine the correct answer:

Statement I: Parenchyma is living but collenchyma is dead tissue.

This statement is incorrect. Parenchyma and collenchyma are both types of simple tissues found in plants. Parenchyma is indeed a living tissue comprised of cells that are often involved in metabolic processes, storage, and photosynthesis. Collenchyma, similarly, is also a living tissue. It is known for providing support and mechanical strength to growing parts of a plant such as leaves and stems, particularly in areas where growth is active. The cells of collenchyma are elongated and have thicker primary walls compared to parenchyma, but they are definitely living.

Statement II: Gymnosperms lack xylem vessels but the presence of xylem vessels is the characteristic of angiosperms.

This statement is true. Gymnosperms are a group of seed-producing plants that include conifers, cycads, Ginkgo, and Gnetales. One of the distinguishing features of gymnosperms is that their xylem consists of tracheids but lacks vessels. Tracheids are elongated cells in the xylem of vascular plants that facilitate the transport of water and mineral salts. On the other hand, angiosperms, or flowering plants, have a more advanced xylem that contains both tracheids and vessels. Vessels are more efficient at transporting water than tracheids, which is one of the evolutionary advantages of angiosperms over gymnosperms.

Therefore, considering the above explanations:

• Statement I is false as both parenchyma and collenchyma are living tissues.
• Statement II is true regarding the absence of xylem vessels in gymnosperms and their presence in angiosperms.

Based on the analysis, the correct answer is:

Option D: Statement I is false but Statement II is true