S1: There is a touching story of Professor Hardy visiting Ramanujan as he lay desperately ill in hospital at Putney. P : ‘No Hardy, that is not a dull number in the very least. Q : Hardy, who was a very shy man, could not find the words for his distress. R : It was 1729. S : The best he could do, as he got to the beside was “I say Ramanujan, I thought the number of taxi I came down in was a very dull number”. S6: It is the lowest number that can be expressed in two different ways as the sum of two cubes. The Proper sequence should be: A. RPQS B. RPSQ C. PRQS D. QPRS

The correct answer is: A. RPQS

The story is about Professor Hardy visiting Ramanujan as he lay desperately ill in hospital at Putney. Hardy, who was a very shy man, could not find the words for his distress. The best he could do, as he got to the bedside was “I say Ramanujan, I thought the number of taxi I came down in was a very dull number”. Ramanujan replied, “No Hardy, that is not a dull number in the very least. It is the lowest number that can be expressed in two different ways as the sum of two cubes.” The number is 1729.

The correct sequence of the sentences is:

1. There is a touching story of Professor Hardy visiting Ramanujan as he lay desperately ill in hospital at Putney.
2. Hardy, who was a very shy man, could not find the words for his distress.
3. The best he could do, as he got to the bedside was “I say Ramanujan, I thought the number of taxi I came down in was a very dull number”.
4. Ramanujan replied, “No Hardy, that is not a dull number in the very least. It is the lowest number that can be expressed in two different ways as the sum of two cubes.”
5. The number is 1729.

The other options are incorrect because they do not follow the correct sequence of events in the story.