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: C is studying in

The correct option is Rajasthan.

Let us analyze the given information step-by-step to determine where C is studying.
We have 4 students: A, B, C, D.
4 cities: P, Q, R, S.
4 colleges: Science, Arts, Commerce, Engineering.
4 States: Gujarat, Rajasthan, Assam, Kerala.

From the clues, we can build a matching table:
1. Clue (i) tells us: D is studying in the State of Assam.
2. Clue (ii) tells us: Arts college is located in city S, which is in the State of Rajasthan.
3. Clue (iii) tells us: A is studying in Commerce college.
4. Clue (iv) tells us: B is studying in city Q.
5. Clue (v) tells us: Science college is located in the State of Kerala.

Let us determine the State for each student:
- Since D is in Assam (Clue i), and Science college is in Kerala (Clue v), and Arts college is in Rajasthan (Clue ii), the remaining college/State combinations must be matched carefully.
- A is studying in Commerce college (Clue iii). Since the Arts college is in Rajasthan and Science college is in Kerala, A's State cannot be Rajasthan or Kerala. Also, A's State cannot be Assam because D is studying in Assam. Therefore, A must be studying in the remaining State, which is Gujarat.
- Now, let us look at B. B is studying in city Q (Clue iv). Since Arts college is in city S (Clue ii), B cannot be studying in the Arts college. Thus, B's State cannot be Rajasthan. Since D is in Assam and A is in Gujarat, B must be studying in either Kerala or Rajasthan. But since B cannot be in Rajasthan, B must be studying in Kerala (at the Science college).
- This leaves the State of Rajasthan (and consequently city S and the Arts college) for the remaining student, who is C.

Thus, C is studying in the Arts college, in city S, located in the State of Rajasthan.