C is studying in

• From condition (ii), the Arts college is in city S, which is in Rajasthan.

• From condition (v), the Science college is in Kerala.

• From condition (i), D is studying in Assam. Since D is in Assam, D cannot be in Rajasthan (Arts/S) or Kerala (Science).

• The remaining states for the colleges are Gujarat and Assam. The remaining cities are P, Q, and R (since S is Rajasthan).

• B is in city Q (condition iv). B cannot be in Rajasthan (S) or Kerala (Science) if we assume distinct mappings, but let's map colleges to states first: Arts=Rajasthan, Science=Kerala. Remaining colleges: Commerce, Engineering. Remaining states: Gujarat, Assam.

• D is in Assam. D is not in Arts (Rajasthan) or Science (Kerala). So D is in either Commerce or Engineering.

• A is in Commerce (condition iii). A is not D. So A is in Commerce.

• If A is in Commerce, and D is in Assam, we need to place A and D.

• Let's determine the state of each college. Arts=Rajasthan, Science=Kerala. Commerce and Engineering are in Gujarat and Assam.

• D is in Assam. D is not in Arts or Science. So D is in Commerce or Engineering.

• A is in Commerce. A is not D.

• If Commerce were in Assam, A would be in Assam. But D is in Assam. Two people cannot be in the same city/state if the problem implies one student per city/state? The prompt says 'studying in four different cities' and 'four different States'. It implies a 1-to-1 mapping between Student, City, College, State.

• Therefore, D (Assam) corresponds to one college. A (Commerce) corresponds to one state.

• Since D is in Assam, the college in Assam is either Commerce or Engineering.

• If the college in Assam is Commerce, then A is in Assam. But D is in Assam. Contradiction (A != D). Thus, the college in Assam is NOT Commerce.

• Therefore, the college in Assam is Engineering. So D is in Engineering college in Assam.

• This leaves Commerce college in Gujarat.

• So, A is in Commerce college in Gujarat.

• We have: D=Engineering/Assam, A=Commerce/Gujarat.

• Remaining students: B, C. Remaining colleges: Arts, Science. Remaining states: Rajasthan, Kerala. Remaining cities: P, Q, R (S is Rajasthan).

• Arts college is in Rajasthan (City S). Science college is in Kerala.

• B is in city Q. B cannot be in City S (Rajasthan/Arts) because B is in Q. So B is not in Arts college.

• Therefore, B is in Science college (Kerala).

• This leaves C to be in Arts college (Rajasthan, City S).

• So, C is studying in Arts college in Rajasthan.

• The question asks where C is studying. C is in Rajasthan.