The correct answer is Option 3: Mahendragiri.

ISRO (Indian Space Research Organisation) successfully conducted a rocket test using cryogenic engines in the year 2007. The test-stand used for this purpose is located in Mahendragiri, which is situated in the southern Indian state of Tamil Nadu.

Mahendragiri is home to the ISRO Propulsion Complex (IPRC), which is responsible for the development and testing of various propulsion systems used in ISRO`s space missions. The IPRC is situated at Mahendragiri in the Tirunelveli district of Tamil Nadu.

The IPRC is a key facility for ISRO`s launch vehicle programs and houses advanced test facilities for solid propellant motors, liquid engines, and cryogenic engines. It has been instrumental in the development and testing of various stages and engines used in ISRO`s launch vehicles, including the PSLV (Polar Satellite Launch Vehicle) and the GSLV (Geosynchronous Satellite Launch Vehicle) series.

The successful cryogenic engine test conducted by ISRO in 2007 was a significant milestone for the organization. Cryogenic engines use liquid propellants, typically liquid oxygen and liquid hydrogen, which are stored at extremely low temperatures. These engines provide a higher thrust and efficiency compared to other types of rocket engines, making them crucial for launching heavy payloads into space.

To summarize, the rocket test using cryogenic engines conducted by ISRO in 2007 took place at the ISRO Propulsion Complex in Mahendragiri, Tamil Nadu. This facility has played a vital role in the development and testing of propulsion systems for ISRO`s launch vehicles.