Correct option is A
The phrase "breathed his last" means to die. In this context, it means that Satyajit Ray died in his Kolkata home after receiving the award from Audrey Hepburn.
Option (a) is the correct answer.
Nipped in the bud means to stop something before it develops or becomes a problem. It does not fit in the context of the sentence.
Kept the ball rolling means to continue a process or activity. It does not fit in the context of the sentence.
Dug the grave means to prepare for a failure or disaster. It does not fit in the context of the sentence.