The correct answer is 3, which is alpha rays and beta rays. Alpha rays and beta rays are not considered electromagnetic in nature.

Option 1, X-rays and cathode rays: X-rays are high-energy electromagnetic waves, while cathode rays are streams of high-speed electrons. Both X-rays and cathode rays are electromagnetic in nature.

Option 2, Gamma rays and X-rays: Gamma rays and X-rays are both forms of high-energy electromagnetic radiation. They differ mainly in their sources and wavelengths. Gamma rays are emitted from the nucleus of unstable atoms, while X-rays are produced by energetic electron transitions.

Option 4, Beta rays and gamma rays: Beta rays are streams of fast-moving, high-energy electrons or positrons emitted during radioactive decay. Gamma rays, as mentioned earlier, are high-energy electromagnetic waves. Both beta rays and gamma rays are electromagnetic in nature.

Therefore, option 3, alpha rays and beta rays, is the correct answer, as they are not electromagnetic in nature.