The correct answer is option 2, gamma-rays. Gamma-rays are a form of electromagnetic radiation and have the highest frequency and energy among the options given. This high energy allows gamma-rays to penetrate deeper into living tissue and interact more strongly with cells and DNA. When gamma-rays interact with cells, they can cause damage to the DNA, leading to mutations and potential harm to the body.

Option 1, X-rays, also belong to the electromagnetic radiation spectrum, but they have lower energy than gamma-rays. Therefore, they are less damaging to biological tissues compared to gamma-rays.

Option 3, beta-rays, are high-energy electrons or positrons and can cause damage to DNA as well. However, gamma-rays have higher energy and thus typically cause more damage.

Option 4, alpha-rays, are the least penetrative form of radiation and tend to cause less damage to living tissue compared to the higher energy options like gamma-rays. Therefore, gamma-rays are the correct answer as they produce the maximum biological damage.