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?

Here's a step-by-step analysis: 1. **Understand the Setup:** There are four students (A, B, C, D), four cities (P, Q, R, S), four colleges (Science, Arts, Commerce, Engineering), and four states (Gujarat, Rajasthan, Assam, Kerala). The problem implies a one-to-one mapping for student-city-college-state. Each student is in a unique city, college, and state. 2. **List Given Information:** * (i) D is studying in Assam (Student D is associated with State Assam). * (ii) Arts college is in City S, which is in Rajasthan (College Arts -> City S -> State Rajasthan). * (iii) A is studying in Commerce college (Student A -> College Commerce). * (iv) B is studying in City Q (Student B -> City Q). * (v) Science college is in Kerala (College Science -> State Kerala). 3. **Deduce the Full Student-College-State Mapping:** * From (i), D's state is Assam. * From (iii), A's college is Commerce. * Since each student must be in a unique state (implied by "four different States" for four students), A's state cannot be Assam. * From (ii), Arts college is in Rajasthan. * From (v), Science college is in Kerala. * Therefore, Commerce college (A's college) cannot be in Assam, Rajasthan, or Kerala. The only remaining state is Gujarat. * So, **A is in Commerce college in Gujarat.** * Now, D is in Assam. D cannot be in Arts (Rajasthan), Science (Kerala), or Commerce (Gujarat). The only remaining college is Engineering. * So, **D is in Engineering college in Assam.** * B is in City Q. B's college cannot be Arts, Commerce, or Engineering. So B's college is Science. * So, **B is in Science college in Kerala.** * By elimination, C is the remaining student. C's college must be Arts. * So, **C is in Arts college in Rajasthan (City S).** This gives the definitive mapping: * A: Commerce college, Gujarat * B: Science college, Kerala (in City Q) * C: Arts college, Rajasthan (in City S) * D: Engineering college, Assam 4. **Evaluate the Options:** * **A) D is not studying in city S** * From our mapping, D is in Assam. * From (ii), City S is in Rajasthan. * Since Assam and Rajasthan are different states, D cannot be in City S. This statement is **correct**. * **B) A is studying in Science college** * From our mapping, A is studying in Commerce college. This statement is incorrect. * **C) A is studying in Kerala** * From our mapping, A is studying in Gujarat. This statement is incorrect. * **D) Engineering college is located in Gujarat.** * From our mapping, Engineering college is located in Assam (where D is studying). This statement is incorrect. The final answer is A.