The correct answer is option 2, Charter Act, 1833.

Option 1, Charter Act, 1813, is not the correct answer. While the Charter Act of 1813 did make certain reforms in the administration of British India, it did not specifically address the issue of Indians entering higher posts in the administration.

Option 3, Charles Wood`s Education Despatch, 1854, is also not the correct answer. The Charles Wood`s Education Despatch of 1854 introduced a comprehensive educational policy in British India, but it did not specifically focus on allowing Indians entry to higher posts in the administration.

Option 4, Indian Councils Act, 1861, is not the correct answer either. The Indian Councils Act of 1861 expanded the legislative councils in British India and introduced some reforms, but it did not specifically address the issue of Indians entering higher posts in the administration.

Therefore, the correct answer is option 2, Charter Act, 1833. This act was significant as it allowed Indians, at least in theory, to have entry to higher posts in the British Indian administration for the first time. It can be recognized as an important step towards the empowerment and inclusion of Indians in the administrative structure.