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 Which one of the following statements is correct?

Let's deduce the information step-by-step:

1. From (i) D is studying in Assam.

2. From (iii) A is studying in Commerce college. Since A and D are different students, D cannot be in Commerce college.

3. There are four colleges: Science, Arts, Commerce, Engineering. Since D is in Assam and not in Commerce college, D must be in either Science, Arts, or Engineering.

4. From (v) Science college is in Kerala. So D is not in Science college.

5. From (ii) Arts college is in City S, Rajasthan. So D is not in Arts college.

6. Therefore, D must be studying in Engineering college. So, D is studying in Engineering college in Assam. (Matches D, Engineering, Assam)

7. Now we know the states for three colleges: Arts college is in Rajasthan (from ii). Science college is in Kerala (from v). Engineering college is in Assam (from step 6).

8. The only remaining college is Commerce, and the only remaining state is Gujarat. Therefore, Commerce college is in Gujarat.

9. From (iii) A is studying in Commerce college. So, A is studying in Commerce college in Gujarat. (Matches A, Commerce, Gujarat)

10. Now consider B. From (iv) B is studying in city Q.

11. From (ii) Arts college is located in city S. Since B is in city Q, B is not in Arts college.

12. The remaining colleges for B are Science. So, B is studying in Science college.

13. From (v) Science college is located in Kerala. Therefore, B is studying in Science college in city Q in Kerala. (Matches B, Q, Science, Kerala)

14. The only remaining student is C.

15. The only remaining college is Arts.

16. The only remaining state is Rajasthan. From (ii) Arts college is located in city S in Rajasthan. Therefore, C is studying in Arts college in city S in Rajasthan. (Matches C, S, Arts, Rajasthan)

Summary of assignments:

• A: Commerce college, Gujarat
• B: Science college, City Q, Kerala
• C: Arts college, City S, Rajasthan
• D: Engineering college, Assam

Now let's evaluate the options:

A) Engineering college is located in Assam. This is correct, as deduced in step 6.

B) City Q is situated in Assam. This is incorrect. City Q is in Kerala (from step 13).

C) C is studying in Kerala. This is incorrect. C is studying in Rajasthan (from step 16).

D) B is studying in Gujarat. This is incorrect. B is studying in Kerala (from step 13).

The final answer is A.