The correct answer is option 4.

Let`s dissect each statement to understand why:

1. both the eyepiece and the objective of a microscope are convex lenses. This statement is correct. In a microscope, the objective lens collects light rays from the sample and forms a magnified real image, which is then further magnified by the eyepiece lens to produce a virtual image for the viewer.

2. the focal length of the objective of a telescope is larger than the focal length of its eyepiece. This statement is correct. In a telescope, the objective lens or mirror collects light from distant objects and forms a real image at its focal point. The eyepiece lens then magnifies this image for the viewer. To achieve higher magnification, the focal length of the objective lens needs to be longer compared to the focal length of the eyepiece.

3. the magnification of a telescope increases with the increase in the focal length of its objective. This statement is correct. The magnification of a telescope is determined by the ratio of the focal lengths of the objective and eyepiece lenses. As the focal length of the objective increases, the magnification also increases.

Therefore, option 4, which states that statements 1, 2,