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The correct answer to the given question is Cairn Energy (Option 1). Cairn Energy, a British company, is associated with the exploration and commercial production of oil in the Barmer-Sanchore basin of Rajasthan. The company made a large oil discovery in Rajasthan in 2004.
Option 2, Unocal Corporation, is an American oil company which has been involved in oil and gas exploration and production worldwide, but not specifically in the Barmer-Sanchore basin of Rajasthan.
Option 3, Reliance Energy Ventures, is an Indian company involved in electricity generation and distribution and doesn`t play a direct role in oil exploration.
Finally, while Option 4, ONGC (Oil and Natural Gas Corporation), is a state-owned Indian company involved in exploration and production of oil and gas across India and overseas, the specific oil exploration and production in the Barmer-Sanchore basin of Rajasthan is led by Cairn Energy.