Statement (a) claims Karnataka has the world's largest population of LTMs based on a study. While Karnataka forests are a major habitat and host significant LTM populations, claiming the absolute "world's largest" population based on this specific study (which focused on parts of Karnataka) might be an overstatement without a comparative global census. Statement (b) is correct; LTMs are indeed indicators of healthy evergreen forests, are arboreal (prefer canopy), and are rarely seen on the ground. Statement (c) is correct; the study conducted by Karnataka Forest Department and SACON focused on the Sharavathi Valley Sanctuary in Shivamogga circle and was highlighted as the first specific assessment for LTMs in this area. Statement (d) is incorrect; the Lion-Tailed Macaque is classified as Endangered by the IUCN, not extinct, and is endemic to the Western Ghats of South India. Given the options, and that (b) and (c) are demonstrably correct characteristics and study facts, while (a) might be debated as a definitive claim about the world population, (b) and (c) are the intended pair of correct statements.