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The measure or determination of uncertainty of a system is known as entropy. After the rich idea of entropy, it gains attraction and interest in graph theory, due to its applications in applied mathematical chemistry. First time the idea graph entropy was used in 1955, to know the structural information of chemical networks or graphs. In mathematical chemistry, structures are the build-up of atoms/vertices and bonds/edges. Carbon nanotubes are also very famous since they have been used for memory devices and tissue engineering. This productive chemical structure is studied in this paper by inserting a cap on one and both ends. We measure the entropy of these three topologies of carbon nanotube. Some comparative work is also given, along with the analytical study of entropy measures of armchair carbon nanotubes.