Photosynthetic pigments
A. Absorb specific wavelengths of light in their absorption spectra
B. Include chlorophyll a, b, and the carotenoids
C. Have their absorption spectra analyzed using a spectrophotometer
D. All of the above

Hint: Pigments that are present in chloroplasts of photosynthetic bacteria which helps in capturing energy from sunlight that is necessary for photosynthesis are termed as photosynthetic pigments. The different photosynthetic pigments are: Carotene, Xanthophyll, Phaeophytin A, Phaeophytin B, Chlorophyll A and Chlorophyll B. The most common photosynthetic pigment is Chlorophyll A which is present in all plants that perform the photosynthesis process.

Complete answer:
Option A - Absorb specific wavelengths of light in their absorption spectra: photosynthetic pigments interact with light to absorb only certain wavelengths which are useful to plants and other autotrophs. Each of the photosynthetic pigments reacts with only a narrow range of spectrum.
Hence option A is correct.
Option B - Include chlorophyll a, b, and the carotenoids: There are different types of photosynthetic pigments which includes chlorophyll a, b and carotenoids along with Xanthophyll, Phaeophytin A and Phaeophytin B.
Hence option B is also correct.
Option C - Have their absorption spectra analyzed using a spectrophotometer: The percentage of each wavelength of light absorbed by a pigment or the absorption spectrum can be measured using a spectrophotometer. The increase in light transmittance over time is measured using a spectrophotometer and thus can be used to indicate the rate of photosynthesis.
Hence option C is also correct.
Option D - All of the above: Since all of the above given options are correct, option D is the correct answer for the whole question.

Option D. All of the above

Note:
Each pigment absorbs light more efficiently in a different part of the electromagnetic spectrum, which is the reason that there are so many photosynthetic pigments. Chlorophyll absorbs light mostly at a wavelength of about \[400\] to \[450\]\[nm\] and between \[650\] to \[700\]. Chlorophyll b absorbs well between \[450\] to \[500\] \[nm\] and between \[600\] to \[650\]\[nm\]. A t\[400\] to \[530\]\[nm\], Xanthophyll absorbs well.