- Statement I is correct: Asteroids are indeed rocky, metallic, or icy bodies of varying sizes that orbit the Sun, primarily remnants from the early solar system. - Statement II is correct: While most asteroids are small, the largest ones like Ceres, Pallas, Vesta, and Hygiea have diameters ranging from over 400 km to nearly 940 km (for Ceres), which makes "as large as 1000 km" a reasonable statement for the largest known ones at the time this question might have been framed. Ceres is sometimes classified as a dwarf planet. - Statement III is incorrect: The main asteroid belt, where most asteroids are found, is located between the orbits of Mars and Jupiter, not Jupiter and Saturn.