The question asks to identify the criterion that is NOT a mandatory eligibility requirement for the appointment of a State Governor according to the Constitution of India.

Governor Eligibility Criteria Analysis

Article 157 of the Constitution of India outlines the basic qualifications for a person to be appointed as the Governor of a state. Let's examine each option:

• Citizen of India: This is a fundamental requirement. Article 157 clearly states that the Governor must be a citizen of India.
• Completed 35 years of age: This is also explicitly mentioned in Article 157 as a mandatory age qualification for the Governor.
• Qualified for Rajya Sabha membership: This is NOT a constitutional requirement for appointing a Governor. While a Governor should possess qualities suitable for high office, there is no specific clause mandating that they must be qualified to be elected to the Rajya Sabha.
• Must not hold any other office of profit: While Article 157 does not explicitly mention this, the role of Governor is a constitutional office. Holding an 'office of profit' can lead to disqualification for many public offices to prevent conflicts of interest. It is generally understood that a person appointed as Governor should not hold any other gainful employment or office that might compromise their position. However, compared to the Rajya Sabha qualification, this is a more nuanced point related to holding public office, but the Rajya Sabha specific qualification is definitively not required.

Conclusion on Governor Appointment

Based on the constitutional provisions, specifically Article 157, the requirement to be qualified for election as a member of the Rajya Sabha is not an eligibility criterion for the appointment of a State Governor. The primary criteria are Indian citizenship and having completed the age of 35 years.

Therefore, the condition that is NOT an eligibility criteria is having qualified for elections as a member of the Rajya Sabha.