I think that a major conflict in the exposition of Desai's short story is the fact that Rakesh does everything expected of him. He appears to be on automatic pilot, to a great extent. He does everything that is required of being a traditional and "devoted son." The opening exchange between father and son reveals this:
“A first division, son?” his father asked, beaming, reaching for the papers.
“At the top of the list, papa,” Rakesh murmured, as if awed. “First in the country.”
It is almost expected that Rakesh would be a "topper." As we don't really see much of Rakesh's voice, this could be one potential arena of conflict. Rakesh has lost his own particular voice to that of social expectation and understanding. The parents do not berate or abuse him, but there is a lack of voice present. His own desires are secondary to following what is expected of him. Going to America, marrying what his parents wished for him, doing their bidding are all a part of this. Rakesh is "the wunderkind" and nothing else.
Another source of conflict resides between father and son. As the father becomes older, the conflicts between he and the world, including his son, become more intense:
He developed so many complaints and fell ill so frequently and with such mysterious diseases that even his son could no longer make out when it was something of significance and when it was merely a peevish whim.
The role of Rakesh as devoted son and doctor was one where the base conflict between old and young, father and son, the life of sweets and the life devoid of them becomes the crux of the story:
“No more halwa for you, papa. We must be sensible, at your age. If you must have something sweet, Veena will cook you a little kheer, that’s light, just a little rice and milk. But nothing fried, nothing rich. We can’t have this happening again.”
In this, the greatest conflict is seen. It is also here in which one can see Rakesh develop a voice that is contrary to his father. The question emerges whether this conflict is rooted in the son doing his duty as prescribed to him or whether the complete adherence to an external reality is coming home to roost in the form of subjugating his father. The bitterness present is the root of this conflict.