A, B, C and D are students. They are studying in four different cities, viz. P, Q, R and S (not necessarily in that order). They are studying in Science college, Arts college, Commerce college and Engineering college (not necessarily in that order), which are situated in four different States, viz. Gujarat, Rajasthan, Assam and Kerala (not necessarily in that order). Further, it is given that—
(i) D is studying in Assam
(ii) Arts college is located in city S which is in Rajasthan
(iii) A is studying in Commerce college
(iv) B is studying in city Q
(v) Science college is located in Kerala

Question: Science college is located in

The correct option is city Q.

Let's solve this step-by-step to understand why Science college is located in city Q.

We are given four students (A, B, C, D), studying in four different cities (P, Q, R, S), in four different colleges (Science, Arts, Commerce, Engineering), situated in four different States (Gujarat, Rajasthan, Assam, Kerala).

Let's analyze the given clues systematically:
1. From clue (i), D is studying in Assam.
2. From clue (ii), Arts college is located in city S which is in Rajasthan.
3. From clue (iii), A is studying in Commerce college.
4. From clue (iv), B is studying in city Q.
5. From clue (v), Science college is located in Kerala.

Now, let's match the colleges with the States:
- Arts college is in Rajasthan (clue ii).
- Science college is in Kerala (clue v).
- Since D is studying in Assam (clue i), D's college cannot be Arts (Rajasthan) or Science (Kerala).
- Since A is studying in Commerce college (clue iii), A cannot be studying in Assam (where D studies). Thus, the Commerce college cannot be in Assam. By process of elimination, the only remaining State for Commerce college is Gujarat, and the only remaining State for Assam must be the Engineering college.
- Therefore, we have the State-College pairs:
• Rajasthan - Arts college
• Kerala - Science college
• Assam - Engineering college (where D studies)
• Gujarat - Commerce college (where A studies)

Now, let's map the cities:
- City S is in Rajasthan (clue ii), which hosts the Arts college.
- Student B is in city Q (clue iv).
- Student D studies in Assam (Engineering college). Since S is in Rajasthan and Q is occupied by B, D must study in either city P or city R.
- Student A studies in Gujarat (Commerce college). A must also study in either city P or city R.
- Since A and D occupy cities P and R (in some order), the remaining cities are S and Q.
- We know B is in city Q. Since the Arts college is in city S, B cannot be studying in the Arts college. Thus, B must be studying in the Science college (which is in Kerala).
- Since B is studying in city Q and B studies in the Science college, the Science college must be located in city Q.