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The correct answer is Option 3: II and III only.
Statement I is incorrect. INSAT-4A was not launched from New Mexico. Instead, it was launched by Arianespace from French Guiana.
Statement II is correct. Arianespace, a European commercial launch service provider, was indeed associated with the launch of INSAT-4A. This collaboration represented an international collaboration in the field of space exploration.
Statement III is also correct. Tata-Sky, a digital cable service provider, uses the resources of INSAT-4A for DTH television broadcasting services in India. Thus, it is closely associated with the satellite`s functioning and utilization. Therefore, options 1, 2, and 4, which include the incorrect statement I, are ruled out. The only possibility is option 3, which is the correct answer.