The correct answer is the Sutlej River, which meets all the given criteria. It is an antecedent river, meaning it has retained its course despite changes in the landscape, indicative of its long geological history. Originating from the Tibetan Plateau, the Sutlej flows through India, Pakistan, and China, serving as a crucial source for irrigation in the arid regions of Punjab and Haryana. Furthermore, it maintains a linear flow without forming extensive distributaries, distinguishing it from other major rivers of the Indian subcontinent, thus making it a key river in both geographical and agricultural contexts as outlined in standard UPSC-level sources.