The correct answer is option 4, X-rays.

To understand why X-rays have the smallest wavelength among the given types of radiations, let`s take a closer look at each option:

1. Microwaves: Microwaves have longer wavelengths compared to X-rays. They are a type of electromagnetic radiation that is commonly used in cooking appliances.

2. Infra-red: Infra-red waves have longer wavelengths than visible light but shorter wavelengths than microwaves. They are often used for heat sensing and remote controls.

3. Visible light: Visible light falls within a specific range of wavelengths that are visible to the human eye. While visible light can have different wavelengths within this range, it is generally longer than X-rays.

4. X-rays: X-rays have the smallest wavelengths among the given options. They are a form of high-energy electromagnetic radiation that can pass through soft tissues but are absorbed by denser materials, making them useful in medical imaging and security screening.

In summary, X-rays have the smallest wavelength among the given options, making them a powerful tool in various applications.