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Age of fossils in the past was generally determined by radio-carbon method and other methods involving radioactive elements found in the rocks. More precise methods, which were used recently and led to the revision of the evolutionary periods for different groups of organisms, includes
A. Study of carbohydrates/proteins in fossils
B. Study of the conditions of fossilization
C. Electron spin resonance (ESR) of fossil DNA
D. Study of carbohydrates/proteins in rocks

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Hint:- Fossils are preserved remnants of pre-existed specimens from the earlier periods (at least 10,000 years ago). They are compelling critical pieces of evidence that demonstrate how life on earth evolved. Paleontology deals with the study of fossils, their method of formation, their age, and their association with evolution.

Complete Answer:-
Fossilization of the remnant specimens may have occurred due to carbonization, permineralization, authigenesis, bioimmuration, replacement, or recrystallization. The theory regarding the formation of fossil fuels from the remains of dead plants and plants by exposure to heat and pressure in the Earth's crust over millions of years was first coined by Andreas Libavius and later by Mikhail Lomonosov.
Establishing the age of the fossils by absolute dating helps deduce connections to other related species specimens and rock sediments from relevant epochs. Doing so helps to make a stratigraphic correlation of the layers of the land, documentation, and interpretation of environmental changes, correlation to adaptive evolutionary changes, and understanding reasons for extinction.
Radiocarbon dating has been used for dating fossil records like bones, wood, and shells for the longest time. It is based on the radioactive decay of elements like potassium and carbon. ESR (electron spin resonance) method is based on the abundance of unpaired electrons in materials like enamel, tooth, and carbonates upon exposure to radiation (uranium). ESR has been useful for studying parts that have been newly formed or found in previously heated rocks.
Thus, the right option is C.

Note:- ESR has for the first time enabled analysis of a hominin tooth and subsequent dating of the Homo antecessor (oldest hominin species) which suggests that the connections between early modern man and Neanderthals date back earlier than believed so far.