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 Science college is located in

Here's a step-by-step deduction: 1. **Map knowns from the statements:** * (i) D is studying in Assam. * (ii) Arts college is in City S, in Rajasthan. * (iii) A is studying in Commerce college. * (iv) B is studying in City Q. * (v) Science college is in Kerala. 2. **Assign States to Colleges:** * From (ii), Arts college = Rajasthan. * From (v), Science college = Kerala. * We have 4 colleges (Science, Arts, Commerce, Engineering) and 4 states (Gujarat, Rajasthan, Assam, Kerala). * Since D is in Assam (i), and Arts is in Rajasthan, Science is in Kerala, D must be in either Commerce or Engineering college, and that college is in Assam. * Since A is in Commerce college (iii), D cannot be in Commerce. Therefore, D must be in Engineering college. * So, Engineering college = Assam (where D studies). * This leaves Commerce college and Gujarat. Therefore, Commerce college = Gujarat (where A studies). Current College-State mapping: * Arts college = Rajasthan * Science college = Kerala * Engineering college = Assam * Commerce college = Gujarat 3. **Assign Students to Colleges/States:** * A is in Commerce college, which is in Gujarat. * D is in Engineering college, which is in Assam. 4. **Determine B's College and State:** * B is studying in City Q (iv). * The remaining colleges for B and C are Science and Arts. * The remaining states for B and C are Kerala and Rajasthan. * From (ii), Arts college is in City S. * Since B is in City Q, B cannot be in Arts college (which is in City S). * Therefore, B must be in Science college. * If B is in Science college, then from (v), B is studying in Kerala. 5. **Final Deduction for Science College:** * We know B is studying in City Q (iv). * We deduced B is studying in Science college. * We deduced B is studying in Kerala (from Science college = Kerala). * Therefore, Science college is located in City Q. The final answer is A) city Q.