A fluorescent microscope is used
A. For increasing resolving power
B. For obtaining an X-ray diffraction pattern of DNA
C. To study cell and their components in their living state
D. To localise cell structure stained with fluorochrome dyes

Hint: A fluorescent microscope is a device that uses fluorescence and phosphorescence instead of reflecting or absorbing to observe properties of organic and inorganic substances. This equipment illuminates within the light of a specialized wavelength, which is absorbed by fluorophores, causing them to emit light of longer wavelength.

Complete answer:
The "fluorescence microscope" refers to any microscope that uses visible light to come up with an image, whether it is a more simple set up like an epifluorescence microscope. So, a fluorescent microscope is used to localize cell structure stained with fluorochrome dyes and not for increasing resolving power, for obtaining X-ray diffraction patterns of DNA and to study cells and their components in a living state.
So, the right answer is Option D (to localize cell structure stained with fluorochrome dye).
Additional Information:-
Fluorescence microscopy has become an important tool in biology as well as in materials science as it has characters that are easily not available in other optical microscopic techniques. The utilization of an array of fluorochromes made it possible to recognize cells and sub-microscopic cellular components and entities with a high degree of specificity amid non-fluorescing substance. The fluorescence microscope reveals the presence of a single fluorescent molecule. The biggest problems arise when we need to suppress the optical background sufficiently. As most of the materials used in microscopic lenses and filters show some or more autofluorescence, efforts were earlier directed on the manufacture of very low fluorescence components. However, it soon became evident that fluorescence microscopic methods utilizing total internal reflection gave the desired combination of low background and high exciting light flux.

Note: The fluorescence microscope depends heavily on electronic imaging to quickly receive information at low light levels. These technical enhancements don't seem to mere window dressing but are important components of the light microscope as a system.