Correct Option (C):
Statement I is correct. Article 94 of the Constitution of India specifies that the Speaker of the House of the People does not vacate office immediately upon its dissolution. The Speaker continues in office until immediately before the first meeting of the House of the People after the dissolution. This provision ensures continuity of the office.
Statement III is correct. Article 94(c) of the Constitution outlines the procedure for the removal of the Speaker. The Speaker may be removed from office by a resolution of the House of the People passed by a majority of all the then Members of the House. Furthermore, no such resolution can be moved unless at least fourteen days' notice has been given of the intention to move the resolution.
Incorrect Options:
Statement II is incorrect. The Constitution of India does not mandate that a Member of the House of the People, upon being elected as Speaker, must resign from their political party. While the Speaker is expected to maintain impartiality, this is a matter of convention, not a constitutional requirement. The Tenth Schedule (Anti-defection Law) provides for special provisions regarding the Speaker's party membership, allowing them to voluntarily give up party membership without disqualification. Therefore, options that include Statement II (Options 1, 2, and 4) are incorrect.