The correct answer is option 2, the Charter Act of 1833. This act was passed by the British Parliament and it brought about significant changes in the governance of British India. One of the important provisions of this act was the pledge to not discriminate against Indians based on their religion, place of birth, descent, color or any other factors when it came to holding office or employment under the British East India Company.

Option 1, the Charter Act of 1813, is incorrect as it did not include this pledge. The Act of 1813 primarily focused on the regulation of trade between Great Britain and India.

Option 3, the Queen`s Proclamation of 1858, is incorrect as well. While it marked the end of the rule of the British East India Company and the beginning of direct rule by the British Crown, it did not specifically address the issue of non-discrimination in holding office or employment.

Option 4, the Indian Civil Service Act of 1861, is also incorrect. While this act did introduce some reforms in the Indian Civil Service, it did not include the pledge of non-discrimination mentioned in the question.

Therefore, the correct answer is the Charter Act of 1833.