Explanation:

This is a geographical question requiring knowledge about the location of a specific dam project in Uttar Pradesh. - **Option (A) Ramganga:** The Ramganga River is a significant tributary of the Ganges. While there are dams constructed on the Ramganga (e.g., the Ramganga Dam in Uttarakhand), the Rani Laxmibai Dam Project is not situated on this river. Therefore, this option is incorrect. - **Option (B) Ghaghara:** The Ghaghara River, also known as Karnali in Nepal, is a major trans-boundary tributary of the Ganges, flowing through Nepal and India. Various irrigation and power projects exist on the Ghaghara, but the Rani Laxmibai Dam is not one of them. Thus, this option is incorrect. - **Option (C) Betwa:** This is the correct answer. The Rani Laxmibai Dam, also widely known as the Rajghat Dam, is a crucial inter-state dam project. It is constructed on the Betwa River, which is a tributary of the Yamuna River. The dam is strategically located on the border between the states of Uttar Pradesh and Madhya Pradesh, serving both states for irrigation and power generation. - **Option (D) Bhagirathi:** The Bhagirathi River is one of the two main headstreams of the Ganges, originating from the Gangotri Glacier in Uttarakhand. The Tehri Dam, one of India's largest multi-purpose river valley projects, is built on the Bhagirathi. The Rani Laxmibai Dam is not located on this river. Hence, this option is incorrect.\nTherefore, the Rani Laxmibai Dam Project is definitively situated on the Betwa River.