Who among the following has the right to speak and take part in the proceedings of both the houses of a 'State Legislature'?

Correct option is A

The correct answer is (a) Advocate General of the State 

Explanation:
• According to Article 177 of the Indian Constitution, the Advocate General of a State has the right to speak and take part in the proceedings of both houses of the State Legislature (Legislative Assembly and Legislative Council).
• They can also be named a member of any committee of the State Legislature.
• However, despite these privileges, the Advocate General does not have the right to vote in the legislature.
• The Advocate General is the highest law officer in the state, appointed by the Governor under Article 165.
• They hold office during the pleasure of the Governor. 

Information Booster:
• The qualifications for the Advocate General are the same as those required for a High Court Judge.
• A similar provision exists at the Union level for the Attorney General of India under Article 88. 

Additional Knowledge:
(b) Governor of the State (Option b)
• While the Governor addresses the legislature, they are not a member and do not "take part in proceedings" in the same functional sense as a member or the Advocate General. 

(c) Chairman of the State Finance Commission (Option c)
• This is a statutory/constitutional post related to fiscal recommendations and carries no right to participate in legislative debates. 

(d) Chief Justice of High Court (Option d)
• The judiciary is separate from the legislature; the Chief Justice has no role in the proceedings of the State Legislature.