The hints do not determine everything uniquely as the other answer shows.
But quite a bit is uniquely determined.
For easier reference, let me number the hints:
- The one who likes Qutub Minar works in field of Management only with G.
- The one who likes Charminar works with the one who likes Sanchi Stupa.
- J works with the one who like India Gate.
- I neither works with G nor in the field of Pharmacy.
- J does not like Charminar.
- D likes Red Fort.
- D does not work with J.
- F work with only one person.
- F does not like Qutub Minar.
- H works with I.
- I does not like Charminar.
- Neither G nor F likes Taj Mahal.
From the first hint:
The field of G is Management.
Therefore the fourth and tenth hints give:
The field of I is Economics, and so is that of H.
We can then figure out what F does:
By hint 7 and the previous observation, F can't do Economics. By the first hint only two people work in Management: G and the one who likes Gutub Minar. By hint 9 F is neither. Thus F is in Pharmacy.
We then now the distribution of work:
By hint 1 only to people work in Management, and by hint 8 (and the previous observation) only two work in Pharmacy. That leaves three people to Economics. Therefore D, E, and J are in three different fields.
We can restrict the possible monuments of G:
Charminar and Sanchi Stupa need to have the same field, but the only one that works with G is in management and likes Qutub Minar (hint 1). Thus the monument of G cannot be any of these three. Red Fort is ruled out by hint 6, Taj Mahal by hint 12. Thus the monument of G is either India Gate or Victoria Memorial.
We can further restrict the field of D:
It cannot be Management by hint 1.
And that of J:
Suppose J is in Engineering. Then D is in Pharmacy and E is in Management. Thus E is the one who likes Qutub Minar. The monument of F cannot be Charminar or Sanchi Stupa (per hint 2 and the observation that G likes India Gate or Victoria Memorial), Qutub Minar (taken), Red Fort (taken), or Taj Mahal (hint 12). Thus F and G like India Gate and Victoria Memorial in some order. But neither of them is in engineering, the field of J, which contradicts hint 3. Thus J is not in Engineering.
The solution is not unique as the other answer shows, but if it was (as it should!), it could be used:
People H and I are almost interchangeable. What we have figured out so far implies that hint 4 holds for H as well. The only asymmetry is hint 11. Therefore, if the solution is unique, one must not be able to swap I and H, and so H must like Charminar.